{"header":{"message":"BaikalX: add NRPy+ version 9832d44\n","description":null,"timestamp":"2019-12-17T04:50:22Z","authors":[{"email":"rhaas@tapir.caltech.edu","name":"Roland Haas"}]},"hash":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC","authors":[],"deps":{"hashes":[["5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC","BaikalX: add NRPy+ version 9832d44\n"],["AA",null],["J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC","BaikalX: add skeleton thorn\n"],["DNSXJFJKNEMA4ZFID4NDMIYFZ2M5NOKNYUO4V642BHI4DJKOSH7AC","BaikalX: add Zach Etienne's BaikalETK notebook\n\ngit hash 36ebd00 in https://github.com/zachetienne/nrpytutorial\n"]],"deps":["J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC"],"known":["DNSXJFJKNEMA4ZFID4NDMIYFZ2M5NOKNYUO4V642BHI4DJKOSH7AC"]},"hunks":[{"FileDel":{"deleted_names":[{"basename":"configuration.ccl","metadata":420}],"path":"BaikalX/configuration.ccl","del":{"EdgeMap":{"edges":[{"previous":"BLOCK | FOLDER","flag":"BLOCK | FOLDER | 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More","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:980"}},{"Del":{"text":"% information is available in the Cactus UsersGuide.","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1034"}},{"Del":{"text":"%","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1036"}},{"Del":{"text":"% Guidelines:","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1051"}},{"Del":{"text":"% - Do not change anything before the line","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1096"}},{"Del":{"text":"% % START CACTUS THORNGUIDE\",","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1132"}},{"Del":{"text":"% except for filling in the title, author, date, etc. fields.","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1198"}},{"Del":{"text":"% - Each of these fields should only be on ONE line.","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1258"}},{"Del":{"text":"% - Author names should be separated with a \\\\ or a comma.","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1324"}},{"Del":{"text":"% - You can define your own macros, but they must appear after","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1389"}},{"Del":{"text":"% the START CACTUS THORNGUIDE line, and must not redefine standard","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1460"}},{"Del":{"text":"% latex commands.","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1482"}},{"Del":{"text":"% - To avoid name clashes with other thorns, 'labels', 'citations',","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1552"}},{"Del":{"text":"% 'references', and 'image' names should conform to the following","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1622"}},{"Del":{"text":"% convention:","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1640"}},{"Del":{"text":"% ARRANGEMENT_THORN_LABEL","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1672"}},{"Del":{"text":"% For example, an image wave.eps in the arrangement CactusWave and","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1743"}},{"Del":{"text":"% thorn WaveToyC should be renamed to CactusWave_WaveToyC_wave.eps","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1814"}},{"Del":{"text":"% - Graphics should only be included using the graphicx package.","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:1881"}},{"Del":{"text":"% More specifically, with the \"\\includegraphics\" command. 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$Header$","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3284"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3285"}},{"Del":{"text":"\\documentclass{article}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3309"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3310"}},{"Del":{"text":"% Use the Cactus ThornGuide style file","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3349"}},{"Del":{"text":"% (Automatically used from Cactus distribution, if you have a","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3411"}},{"Del":{"text":"% thorn without the Cactus Flesh download this from the Cactus","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3475"}},{"Del":{"text":"% homepage at www.cactuscode.org)","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3510"}},{"Del":{"text":"\\usepackage{../../../../doc/latex/cactus}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3552"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3553"}},{"Del":{"text":"\\begin{document}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3570"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3571"}},{"Del":{"text":"% The author of the documentation","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3605"}},{"Del":{"text":"\\author{Roland Haas \\textless rhaas@illinois.edu\\textgreater}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3667"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3668"}},{"Del":{"text":"% The title of the document (not necessarily the name of the Thorn)","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3736"}},{"Del":{"text":"\\title{BaikalX}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3752"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3753"}},{"Del":{"text":"% the date your document was last changed, if your document is in CVS,","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3824"}},{"Del":{"text":"% please use:","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3838"}},{"Del":{"text":"% \\date{$ $Date$ $}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3861"}},{"Del":{"text":"\\date{December 16 2019}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3885"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3886"}},{"Del":{"text":"\\maketitle","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3897"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3898"}},{"Del":{"text":"% Do not delete next line","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3924"}},{"Del":{"text":"% START CACTUS THORNGUIDE","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3950"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:3951"}},{"Del":{"text":"% Add all definitions used in this documentation here","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4005"}},{"Del":{"text":"% \\def\\mydef etc","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4024"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4025"}},{"Del":{"text":"% Add an abstract for this thorn's documentation","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4074"}},{"Del":{"text":"\\begin{abstract}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4091"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4092"}},{"Del":{"text":"\\end{abstract}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4107"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4108"}},{"Del":{"text":"% The following sections are suggestive only.","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4154"}},{"Del":{"text":"% Remove them or add your own.","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4185"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4186"}},{"Del":{"text":"\\section{Introduction}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4209"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4210"}},{"Del":{"text":"\\section{Physical System}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4236"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4237"}},{"Del":{"text":"\\section{Numerical Implementation}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4272"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4273"}},{"Del":{"text":"\\section{Using This Thorn}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4300"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4301"}},{"Del":{"text":"\\subsection{Obtaining This Thorn}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4335"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4336"}},{"Del":{"text":"\\subsection{Basic Usage}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4361"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4362"}},{"Del":{"text":"\\subsection{Special Behaviour}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4393"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4394"}},{"Del":{"text":"\\subsection{Interaction With Other Thorns}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4437"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4438"}},{"Del":{"text":"\\subsection{Examples}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4460"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4461"}},{"Del":{"text":"\\subsection{Support and Feedback}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4495"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4496"}},{"Del":{"text":"\\section{History}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4514"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4515"}},{"Del":{"text":"\\subsection{Thorn Source Code}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4546"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4547"}},{"Del":{"text":"\\subsection{Thorn Documentation}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4580"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4581"}},{"Del":{"text":"\\subsection{Acknowledgements}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4611"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4612"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4613"}},{"Del":{"text":"\\begin{thebibliography}{9}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4640"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4641"}},{"Del":{"text":"\\end{thebibliography}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4663"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4664"}},{"Del":{"text":"% Do not delete next line","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4690"}},{"Del":{"text":"% END CACTUS THORNGUIDE","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4714"}},{"Del":{"text":"","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4715"}},{"Del":{"text":"\\end{document}","pos":"J2KCRSBTR7GESH52YMDW6SDMYQE6NLL5EZKX2TKG2O7UX4RATNLQC:4730"}}]}},{"FileAdd":{"meta":{"basename":"nrpytutorial","metadata":1005},"path":"BaikalX/doc/nrpytutorial","context":[{"change":2,"pos":341}],"contents":[]}},{"FileAdd":{"meta":{"basename":"BSSN","metadata":1005},"path":"BaikalX/doc/nrpytutorial/BSSN","context":[{"change":0,"pos":15}],"contents":[]}},{"FileAdd":{"meta":{"basename":"ADMBSSN_tofrom_4metric.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/ADMBSSN_tofrom_4metric.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97"}},{"Add":{"text":"# Tutorial-ADMBSSN_tofrom_4metric.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140"}},{"Add":{"text":"# this module will construct expressions for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187"}},{"Add":{"text":"# ADM or BSSN quantities in terms of the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230"}},{"Add":{"text":"# 4-metric g4DD, and g4DD/g4UU in terms of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:275"}},{"Add":{"text":"# ADM/BSSN quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:300"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:301"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:590"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:687"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:688"}},{"Add":{"text":"def setup_ADM_quantities(inputvars):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:725"}},{"Add":{"text":" if inputvars == \"ADM\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:752"}},{"Add":{"text":" gammaDD = ixp.declarerank2(\"gammaDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:807"}},{"Add":{"text":" betaU = ixp.declarerank1(\"betaU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:849"}},{"Add":{"text":" alpha = sp.symbols(\"alpha\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:896"}},{"Add":{"text":" elif inputvars == \"BSSN\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:926"}},{"Add":{"text":" import BSSN.ADM_in_terms_of_BSSN as AitoB","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:976"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:977"}},{"Add":{"text":" # Construct gamma_{ij} in terms of cf & gammabar_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1039"}},{"Add":{"text":" AitoB.ADM_in_terms_of_BSSN()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1076"}},{"Add":{"text":" gammaDD = AitoB.gammaDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1108"}},{"Add":{"text":" # Next construct beta^i in terms of vet^i and reference metric quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1190"}},{"Add":{"text":" import BSSN.BSSN_quantities as Bq","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1232"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1233"}},{"Add":{"text":" Bq.BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1265"}},{"Add":{"text":" betaU = Bq.betaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1290"}},{"Add":{"text":" alpha = sp.symbols(\"alpha\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1337"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1347"}},{"Add":{"text":" print(\"inputvars = \" + str(inputvars) + \" not supported. Please choose ADM or BSSN.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1441"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1461"}},{"Add":{"text":" return gammaDD,betaU,alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1492"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1493"}},{"Add":{"text":"# g_{mu nu} in terms of BSSN (if inputvars==\"BSSN\") or ADM (if inputvars==\"ADM\") variables.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1585"}},{"Add":{"text":"def g4DD_ito_BSSN_or_ADM(inputvars,gammaDD=None,betaU=None,alpha=None):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1657"}},{"Add":{"text":" # Step 0: Declare g4DD as globals, to make interfacing with other modules/functions easier","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1752"}},{"Add":{"text":" global g4DD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1768"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1769"}},{"Add":{"text":" # Step 1: Set gammaDD, betaU, and alpha if not already input.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1835"}},{"Add":{"text":" if gammaDD==None and betaU==None and alpha==None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1889"}},{"Add":{"text":" gammaDD,betaU,alpha = setup_ADM_quantities(inputvars)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1951"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1952"}},{"Add":{"text":" # Step 2: Compute g4DD = g_{mu nu}:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:1992"}},{"Add":{"text":" # To get \\gamma_{\\mu \\nu} = gamma4DD[mu][nu], we'll need to construct the 4-metric, using Eq. 2.122 in B&S:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2104"}},{"Add":{"text":" g4DD = ixp.zerorank2(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2136"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2137"}},{"Add":{"text":" # Step 2.a: Compute beta_i via Eq. 2.121 in B&S","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2189"}},{"Add":{"text":" betaD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2217"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2240"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2267"}},{"Add":{"text":" betaD[i] += gammaDD[i][j] * betaU[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2316"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2317"}},{"Add":{"text":" # Step 2.b: Compute beta_i beta^i, the beta contraction.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2378"}},{"Add":{"text":" beta2 = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2404"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2427"}},{"Add":{"text":" beta2 += betaU[i] * betaD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2464"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2465"}},{"Add":{"text":" # Step 2.c: Construct g4DD via Eq. 2.122 in B&S","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2517"}},{"Add":{"text":" g4DD[0][0] = -alpha ** 2 + beta2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2554"}},{"Add":{"text":" for mu in range(1, 4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2581"}},{"Add":{"text":" g4DD[mu][0] = g4DD[0][mu] = betaD[mu - 1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2631"}},{"Add":{"text":" for mu in range(1, 4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2658"}},{"Add":{"text":" for nu in range(1, 4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2689"}},{"Add":{"text":" g4DD[mu][nu] = gammaDD[mu - 1][nu - 1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2740"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2741"}},{"Add":{"text":"# g^{mu nu} in terms of BSSN (if inputvars==\"BSSN\") or ADM (if inputvars==\"ADM\") variables.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2833"}},{"Add":{"text":"def g4UU_ito_BSSN_or_ADM(inputvars,gammaDD=None,betaU=None,alpha=None, gammaUU=None):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:2919"}},{"Add":{"text":" # Step 0: Declare g4UU as globals, to make interfacing with other modules/functions easier","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3014"}},{"Add":{"text":" global g4UU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3030"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3031"}},{"Add":{"text":" # Step 1: Set gammaDD, betaU, and alpha if not already input.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3097"}},{"Add":{"text":" if gammaDD==None and betaU==None and alpha==None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3151"}},{"Add":{"text":" gammaDD,betaU,alpha = setup_ADM_quantities(inputvars)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3213"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3214"}},{"Add":{"text":" # Step 2: Compute g4UU = g_{mu nu}:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3254"}},{"Add":{"text":" # To get \\gamma^{\\mu \\nu} = gamma4UU[mu][nu], we'll need to use Eq. 2.119 in B&S.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3340"}},{"Add":{"text":" g4UU = ixp.zerorank2(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3372"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3373"}},{"Add":{"text":" # Step 3: Construct g4UU = g^{mu nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3414"}},{"Add":{"text":" # Step 3.a: Compute gammaUU based on provided gammaDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3473"}},{"Add":{"text":" if gammaUU==None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3495"}},{"Add":{"text":" gammaUU, gammaDET = ixp.symm_matrix_inverter3x3(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3560"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3561"}},{"Add":{"text":" # Then evaluate g4UU:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3587"}},{"Add":{"text":" g4UU = ixp.zerorank2(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3619"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3620"}},{"Add":{"text":" g4UU[0][0] = -1 / alpha ** 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3653"}},{"Add":{"text":" for mu in range(1, 4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3680"}},{"Add":{"text":" g4UU[0][mu] = g4UU[mu][0] = betaU[mu - 1] / alpha ** 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3743"}},{"Add":{"text":" for mu in range(1, 4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3770"}},{"Add":{"text":" for nu in range(1, 4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3801"}},{"Add":{"text":" g4UU[mu][nu] = gammaUU[mu - 1][nu - 1] - betaU[mu - 1] * betaU[nu - 1] / alpha ** 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3897"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3898"}},{"Add":{"text":"# BSSN (if inputvars==\"BSSN\") or ADM (if inputvars==\"ADM\") metric variables in terms of g_{mu nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:3996"}},{"Add":{"text":"def BSSN_or_ADM_ito_g4DD(inputvars,g4DD=None):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4043"}},{"Add":{"text":" # Step 0: Declare output variables as globals, to make interfacing with other modules/functions easier","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4150"}},{"Add":{"text":" if inputvars == \"ADM\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4177"}},{"Add":{"text":" global gammaDD, betaU, alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4214"}},{"Add":{"text":" elif inputvars == \"BSSN\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4244"}},{"Add":{"text":" global hDD, cf, vetU, alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4280"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4290"}},{"Add":{"text":" print(\"inputvars = \" + str(inputvars) + \" not supported. Please choose ADM or BSSN.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4384"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4404"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4405"}},{"Add":{"text":" # Step 1: declare g4DD as symmetric rank-4 tensor:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4460"}},{"Add":{"text":" g4DD_is_input_into_this_function = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4504"}},{"Add":{"text":" if g4DD == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4525"}},{"Add":{"text":" g4DD = ixp.declarerank2(\"g4DD\", \"sym01\", DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4581"}},{"Add":{"text":" g4DD_is_input_into_this_function = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4630"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4631"}},{"Add":{"text":" # Step 2: Compute gammaDD & betaD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4669"}},{"Add":{"text":" betaD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4697"}},{"Add":{"text":" gammaDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4727"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4750"}},{"Add":{"text":" betaD[i] = g4DD[0][i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4780"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4807"}},{"Add":{"text":" gammaDD[i][j] = g4DD[i + 1][j + 1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4854"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4855"}},{"Add":{"text":" # Step 3: Compute betaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4883"}},{"Add":{"text":" # Step 3.a: Compute gammaUU based on provided gammaDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:4941"}},{"Add":{"text":" gammaUU, gammaDET = ixp.symm_matrix_inverter3x3(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5002"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5003"}},{"Add":{"text":" # Step 3.b: Use gammaUU to raise betaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5046"}},{"Add":{"text":" betaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5074"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5097"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5124"}},{"Add":{"text":" betaU[i] += gammaUU[i][j] * betaD[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5173"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5174"}},{"Add":{"text":" # Step 4: Compute alpha = sqrt(beta^2 - g_{00}):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5229"}},{"Add":{"text":" # Step 4.a: Compute beta^2 = beta^k beta_k:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5277"}},{"Add":{"text":" beta_squared = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5310"}},{"Add":{"text":" for k in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5333"}},{"Add":{"text":" beta_squared += betaU[k] * betaD[k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5377"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5378"}},{"Add":{"text":" # Step 4.b: alpha = sqrt(beta^2 - g_{00}):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5425"}},{"Add":{"text":" if g4DD_is_input_into_this_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5475"}},{"Add":{"text":" alpha = sp.sqrt(sp.simplify(beta_squared) - g4DD[0][0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5539"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5549"}},{"Add":{"text":" alpha = sp.sqrt(beta_squared - g4DD[0][0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5600"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5601"}},{"Add":{"text":" # Step 5: If inputvars == \"ADM\", we are finished. Return.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5663"}},{"Add":{"text":" if inputvars == \"ADM\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5690"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5705"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5706"}},{"Add":{"text":" # Step 6: If inputvars == \"BSSN\", convert ADM to BSSN","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5764"}},{"Add":{"text":" import BSSN.BSSN_in_terms_of_ADM as BitoA","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5810"}},{"Add":{"text":" dummyBU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5840"}},{"Add":{"text":" BitoA.gammabarDD_hDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5874"}},{"Add":{"text":" BitoA.cf_from_gammaDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5909"}},{"Add":{"text":" BitoA.betU_vetU(betaU, dummyBU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5945"}},{"Add":{"text":" hDD = BitoA.hDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5966"}},{"Add":{"text":" cf = BitoA.cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:5986"}},{"Add":{"text":" vetU = BitoA.vetU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6008"}}]}},{"FileAdd":{"meta":{"basename":"ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module performs the conversion between ADM","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6116"}},{"Add":{"text":"# spacetime variables in Spherical or Cartesian coordinates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6176"}},{"Add":{"text":"# given as *exact* SymPy expressions (i.e., direct functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6237"}},{"Add":{"text":"# of r,th,ph or x,y,z), to rescaled BSSN-in-curvilinear","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6293"}},{"Add":{"text":"# coordinate quantities, as defined in BSSN_RHSs.py","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6345"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6346"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6377"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6420"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6421"}},{"Add":{"text":"# Step P0: Import needed Python/NRPy+ modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6467"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6571"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6681"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6749"}},{"Add":{"text":"import sys # Standard Python module for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6845"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6846"}},{"Add":{"text":"def Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear(CoordType_in, Sph_r_th_ph_or_Cart_xyz,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:6944"}},{"Add":{"text":" gammaDD_inSphorCart, KDD_inSphorCart, alpha_inSphorCart, betaU_inSphorCart, BU_inSphorCart):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7045"}},{"Add":{"text":" # This routine converts the ADM variables","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7091"}},{"Add":{"text":" # $$\\left\\{\\gamma_{ij}, K_{ij}, \\alpha, \\beta^i\\right\\}$$","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7156"}},{"Add":{"text":" # in Spherical or Cartesian basis+coordinates, first to the BSSN variables","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7238"}},{"Add":{"text":" # in the chosen reference_metric::CoordSystem coordinate system+basis:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7316"}},{"Add":{"text":" # $$\\left\\{\\bar{\\gamma}_{i j},\\bar{A}_{i j},\\phi, K, \\bar{\\Lambda}^{i}, \\alpha, \\beta^i, B^i\\right\\},$$","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7424"}},{"Add":{"text":" # and then to the rescaled variables:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7469"}},{"Add":{"text":" # $$\\left\\{h_{i j},a_{i j},\\phi, K, \\lambda^{i}, \\alpha, \\mathcal{V}^i, \\mathcal{B}^i\\right\\}.$$","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7570"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7571"}},{"Add":{"text":" # The ADM & BSSN formalisms only work in 3D; they are 3+1 decompositions of Einstein's equations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7673"}},{"Add":{"text":" # To implement axisymmetry or spherical symmetry, simply set all spatial derivatives in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7768"}},{"Add":{"text":" # the relevant angular directions to zero; DO NOT SET DIM TO ANYTHING BUT 3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7852"}},{"Add":{"text":" # Step P1: Set spatial dimension (must be 3 for BSSN)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7910"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7922"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:7927"}},{"Add":{"text":" # Step P2: Copy gammaSphDD_in to gammaSphDD, KSphDD_in to KSphDD, etc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8002"}},{"Add":{"text":" # This ensures that the input arrays are not modified below;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8070"}},{"Add":{"text":" # modifying them would result in unexpected effects outside","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8137"}},{"Add":{"text":" # this function.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8161"}},{"Add":{"text":" alphaSphorCart = alpha_inSphorCart","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8200"}},{"Add":{"text":" betaSphorCartU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8239"}},{"Add":{"text":" BSphorCartU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8278"}},{"Add":{"text":" gammaSphorCartDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8317"}},{"Add":{"text":" KSphorCartDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8356"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8381"}},{"Add":{"text":" betaSphorCartU[i] = betaU_inSphorCart[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8430"}},{"Add":{"text":" BSphorCartU[i] = BU_inSphorCart[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8476"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8505"}},{"Add":{"text":" gammaSphorCartDD[i][j] = gammaDD_inSphorCart[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8568"}},{"Add":{"text":" KSphorCartDD[i][j] = KDD_inSphorCart[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8627"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8628"}},{"Add":{"text":" # Make sure that rfm.reference_metric() has been called.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8689"}},{"Add":{"text":" # We'll need the variables it defines throughout this module.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8758"}},{"Add":{"text":" if rfm.have_already_called_reference_metric_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8825"}},{"Add":{"text":" print(\"Error. Called Convert_Spherical_ADM_to_BSSN_curvilinear() without\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:8908"}},{"Add":{"text":" print(\" first setting up reference metric, by calling rfm.reference_metric().\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9002"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9022"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9027"}},{"Add":{"text":" # Step 1: All input quantitiefs are in terms of r,th,ph or x,y,z. We want them in terms","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9119"}},{"Add":{"text":" # of xx0,xx1,xx2, so here we call sympify_integers__replace_rthph() to replace","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9210"}},{"Add":{"text":" # r,th,ph or x,y,z, respectively, with the appropriate functions of xx0,xx1,xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9302"}},{"Add":{"text":" # as defined for this particular reference metric in reference_metric.py's ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9390"}},{"Add":{"text":" # xxSph[] or xxCart[], respectively:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9439"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9440"}},{"Add":{"text":" # Note that substitution only works when the variable is not an integer. Hence the ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9528"}},{"Add":{"text":" # if isinstance(...,...) stuff:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9572"}},{"Add":{"text":" def sympify_integers__replace_rthph_or_Cartxyz(obj, rthph_or_xyz, rthph_or_xyz_of_xx):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9663"}},{"Add":{"text":" if isinstance(obj, int):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9696"}},{"Add":{"text":" return sp.sympify(obj)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9731"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9745"}},{"Add":{"text":" return obj.subs(rthph_or_xyz[0], rthph_or_xyz_of_xx[0]).\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9815"}},{"Add":{"text":" subs(rthph_or_xyz[1], rthph_or_xyz_of_xx[1]).\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9878"}},{"Add":{"text":" subs(rthph_or_xyz[2], rthph_or_xyz_of_xx[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9939"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9940"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_of_xx = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:9975"}},{"Add":{"text":" if CoordType_in == \"Spherical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10011"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_of_xx = rfm.xxSph","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10057"}},{"Add":{"text":" elif CoordType_in == \"Cartesian\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10095"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_of_xx = rfm.xxCart","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10142"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10152"}},{"Add":{"text":" print(\"Error: Can only convert ADM Cartesian or Spherical initial data to BSSN Curvilinear coords.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10261"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10281"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10282"}},{"Add":{"text":" alphaSphorCart = sympify_integers__replace_rthph_or_Cartxyz(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10347"}},{"Add":{"text":" alphaSphorCart, Sph_r_th_ph_or_Cart_xyz, r_th_ph_or_Cart_xyz_of_xx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10423"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10448"}},{"Add":{"text":" betaSphorCartU[i] = sympify_integers__replace_rthph_or_Cartxyz(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10520"}},{"Add":{"text":" betaSphorCartU[i], Sph_r_th_ph_or_Cart_xyz, r_th_ph_or_Cart_xyz_of_xx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10603"}},{"Add":{"text":" BSphorCartU[i] = sympify_integers__replace_rthph_or_Cartxyz(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10675"}},{"Add":{"text":" BSphorCartU[i], Sph_r_th_ph_or_Cart_xyz, r_th_ph_or_Cart_xyz_of_xx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10758"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10787"}},{"Add":{"text":" gammaSphorCartDD[i][j] = sympify_integers__replace_rthph_or_Cartxyz(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10868"}},{"Add":{"text":" gammaSphorCartDD[i][j], Sph_r_th_ph_or_Cart_xyz, r_th_ph_or_Cart_xyz_of_xx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:10960"}},{"Add":{"text":" KSphorCartDD[i][j] = sympify_integers__replace_rthph_or_Cartxyz(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11041"}},{"Add":{"text":" KSphorCartDD[i][j], Sph_r_th_ph_or_Cart_xyz, r_th_ph_or_Cart_xyz_of_xx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11133"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11134"}},{"Add":{"text":" # Step 2: All ADM initial data quantities are now functions of xx0,xx1,xx2, but","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11218"}},{"Add":{"text":" # they are still in the Spherical or Cartesian basis. We can now directly apply","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11310"}},{"Add":{"text":" # Jacobian transformations to get them in the correct xx0,xx1,xx2 basis:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11395"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11396"}},{"Add":{"text":" # alpha is a scalar, so no Jacobian transformation is necessary.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11465"}},{"Add":{"text":" alpha = alphaSphorCart","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11492"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11493"}},{"Add":{"text":" Jac_dUSphorCart_dDrfmUD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11539"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11564"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11593"}},{"Add":{"text":" Jac_dUSphorCart_dDrfmUD[i][j] = sp.diff(r_th_ph_or_Cart_xyz_of_xx[i],rfm.xx[j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11685"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11686"}},{"Add":{"text":" Jac_dUrfm_dDSphorCartUD, dummyDET = ixp.generic_matrix_inverter3x3(Jac_dUSphorCart_dDrfmUD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11782"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11783"}},{"Add":{"text":" betaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11813"}},{"Add":{"text":" BU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11843"}},{"Add":{"text":" gammaDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11873"}},{"Add":{"text":" KDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11903"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11928"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:11957"}},{"Add":{"text":" betaU[i] += Jac_dUrfm_dDSphorCartUD[i][j] * betaSphorCartU[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12031"}},{"Add":{"text":" BU[i] += Jac_dUrfm_dDSphorCartUD[i][j] * BSphorCartU[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12102"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12135"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12172"}},{"Add":{"text":" gammaDD[i][j] += Jac_dUSphorCart_dDrfmUD[k][i]*Jac_dUSphorCart_dDrfmUD[l][j] * gammaSphorCartDD[k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12294"}},{"Add":{"text":" KDD[i][j] += Jac_dUSphorCart_dDrfmUD[k][i]*Jac_dUSphorCart_dDrfmUD[l][j] * KSphorCartDD[k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12416"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12417"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12418"}},{"Add":{"text":" # Step 3: All ADM quantities were input into this function in the Spherical or Cartesian","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12511"}},{"Add":{"text":" # basis, as functions of r,th,ph or x,y,z, respectively. In Steps 1 and 2 above,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12604"}},{"Add":{"text":" # we converted them to the xx0,xx1,xx2 basis, and as functions of xx0,xx1,xx2.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12695"}},{"Add":{"text":" # Here we convert ADM quantities in the \"rfm\" basis to their BSSN Curvilinear","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12785"}},{"Add":{"text":" # counterparts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12813"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12814"}},{"Add":{"text":" import BSSN.BSSN_in_terms_of_ADM as BitoA","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12860"}},{"Add":{"text":" BitoA.gammabarDD_hDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12894"}},{"Add":{"text":" BitoA.trK_AbarDD_aDD(gammaDD, KDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12933"}},{"Add":{"text":" BitoA.LambdabarU_lambdaU__exact_gammaDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:12986"}},{"Add":{"text":" BitoA.cf_from_gammaDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13021"}},{"Add":{"text":" BitoA.betU_vetU(betaU, BU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13052"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13053"}},{"Add":{"text":" # Step 4: Return the BSSN Curvilinear variables in the desired xx0,xx1,xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13132"}},{"Add":{"text":" # basis, and as functions of the consistent xx0,xx1,xx2 coordinates.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13213"}},{"Add":{"text":" return BitoA.cf, BitoA.hDD, BitoA.lambdaU, BitoA.aDD, BitoA.trK, alpha, BitoA.vetU, BitoA.betU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13312"}}]}},{"FileAdd":{"meta":{"basename":"ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module performs the conversion between ADM","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13425"}},{"Add":{"text":"# spacetime variables in Spherical or Cartesian coordinates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13485"}},{"Add":{"text":"# given as *numerical* expressions (i.e., ADM quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13542"}},{"Add":{"text":"# are only given to floating-point precision; e.g., in the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13601"}},{"Add":{"text":"# case of an initial data solver), to rescaled BSSN-in-curvilinear","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13668"}},{"Add":{"text":"# coordinate quantities, as defined in BSSN_RHSs.py","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13720"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13721"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13752"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13795"}},{"Add":{"text":"# Step P1: Initialize core Python/NRPy+ modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13843"}},{"Add":{"text":"from outputC import * # NRPy+: Core C code output module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:13912"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14016"}},{"Add":{"text":"import finite_difference as fin # NRPy+: Finite difference C code generation module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14102"}},{"Add":{"text":"import grid as gri # NRPy+: Functions having to do with numerical grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14189"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14299"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14367"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq # NRPy+: Computes useful BSSN quantities; e.g., gammabarUU & GammabarUDD needed below","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14487"}},{"Add":{"text":"import os, sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14584"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14585"}},{"Add":{"text":"def Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear(CoordType_in, ADM_input_function_name, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14684"}},{"Add":{"text":" Ccodesdir = \"BSSN\", pointer_to_ID_inputs=False,loopopts=\",oldloops\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14812"}},{"Add":{"text":" # The ADM & BSSN formalisms only work in 3D; they are 3+1 decompositions of Einstein's equations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:14914"}},{"Add":{"text":" # To implement axisymmetry or spherical symmetry, simply set all spatial derivatives in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15009"}},{"Add":{"text":" # the relevant angular directions to zero; DO NOT SET DIM TO ANYTHING BUT 3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15093"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15094"}},{"Add":{"text":" # Step 0: Set spatial dimension (must be 3 for BSSN)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15151"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15163"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15164"}},{"Add":{"text":" # Step 1: All ADM initial data quantities are now functions of xx0,xx1,xx2, but","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15248"}},{"Add":{"text":" # they are still in the Spherical or Cartesian basis. We can now directly apply","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15340"}},{"Add":{"text":" # Jacobian transformations to get them in the correct xx0,xx1,xx2 basis:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15425"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15426"}},{"Add":{"text":" # All input quantities are in terms of r,th,ph or x,y,z. We want them in terms","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15517"}},{"Add":{"text":" # of xx0,xx1,xx2, so here we call sympify_integers__replace_rthph() to replace","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15608"}},{"Add":{"text":" # r,th,ph or x,y,z, respectively, with the appropriate functions of xx0,xx1,xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15700"}},{"Add":{"text":" # as defined for this particular reference metric in reference_metric.py's","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15787"}},{"Add":{"text":" # xxSph[] or xxCart[], respectively:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15836"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15837"}},{"Add":{"text":" # Define the input variables:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15871"}},{"Add":{"text":" gammaSphorCartDD = ixp.declarerank2(\"gammaSphorCartDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:15940"}},{"Add":{"text":" KSphorCartDD = ixp.declarerank2(\"KSphorCartDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16001"}},{"Add":{"text":" alphaSphorCart = sp.symbols(\"alphaSphorCart\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16051"}},{"Add":{"text":" betaSphorCartU = ixp.declarerank1(\"betaSphorCartU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16107"}},{"Add":{"text":" BSphorCartU = ixp.declarerank1(\"BSphorCartU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16157"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16158"}},{"Add":{"text":" # Make sure that rfm.reference_metric() has been called.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16219"}},{"Add":{"text":" # We'll need the variables it defines throughout this module.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16288"}},{"Add":{"text":" if rfm.have_already_called_reference_metric_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16355"}},{"Add":{"text":" print(\"Error. Called Convert_Spherical_ADM_to_BSSN_curvilinear() without\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16438"}},{"Add":{"text":" print(\" first setting up reference metric, by calling rfm.reference_metric().\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16532"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16552"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16553"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_oID_xx = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16589"}},{"Add":{"text":" if CoordType_in == \"Spherical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16625"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_oID_xx = rfm.xxSph","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16672"}},{"Add":{"text":" elif CoordType_in == \"Cartesian\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16710"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_oID_xx = rfm.xxCart","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16758"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16768"}},{"Add":{"text":" print(\"Error: Can only convert ADM Cartesian or Spherical initial data to BSSN Curvilinear coords.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16877"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16897"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16898"}},{"Add":{"text":" # Step 2: All ADM initial data quantities are now functions of xx0,xx1,xx2, but","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:16982"}},{"Add":{"text":" # they are still in the Spherical or Cartesian basis. We can now directly apply","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17074"}},{"Add":{"text":" # Jacobian transformations to get them in the correct xx0,xx1,xx2 basis:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17159"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17160"}},{"Add":{"text":" # alpha is a scalar, so no Jacobian transformation is necessary.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17229"}},{"Add":{"text":" alpha = alphaSphorCart","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17256"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17257"}},{"Add":{"text":" Jac_dUSphorCart_dDrfmUD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17303"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17328"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17357"}},{"Add":{"text":" Jac_dUSphorCart_dDrfmUD[i][j] = sp.diff(r_th_ph_or_Cart_xyz_oID_xx[i], rfm.xx[j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17451"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17452"}},{"Add":{"text":" Jac_dUrfm_dDSphorCartUD, dummyDET = ixp.generic_matrix_inverter3x3(Jac_dUSphorCart_dDrfmUD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17548"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17553"}},{"Add":{"text":" betaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17581"}},{"Add":{"text":" BU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17606"}},{"Add":{"text":" gammaDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17636"}},{"Add":{"text":" KDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17662"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17687"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17716"}},{"Add":{"text":" betaU[i] += Jac_dUrfm_dDSphorCartUD[i][j] * betaSphorCartU[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17790"}},{"Add":{"text":" BU[i] += Jac_dUrfm_dDSphorCartUD[i][j] * BSphorCartU[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17858"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17891"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:17928"}},{"Add":{"text":" gammaDD[i][j] += Jac_dUSphorCart_dDrfmUD[k][i] * Jac_dUSphorCart_dDrfmUD[l][j] * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18031"}},{"Add":{"text":" gammaSphorCartDD[k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18091"}},{"Add":{"text":" KDD[i][j] += Jac_dUSphorCart_dDrfmUD[k][i] * Jac_dUSphorCart_dDrfmUD[l][j] * KSphorCartDD[k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18207"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18208"}},{"Add":{"text":" # Step 3: All ADM quantities were input into this function in the Spherical or Cartesian","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18301"}},{"Add":{"text":" # basis, as functions of r,th,ph or x,y,z, respectively. In Steps 1 and 2 above,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18394"}},{"Add":{"text":" # we converted them to the xx0,xx1,xx2 basis, and as functions of xx0,xx1,xx2.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18485"}},{"Add":{"text":" # Here we convert ADM quantities in the \"rfm\" basis to their BSSN Curvilinear","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18575"}},{"Add":{"text":" # counterparts, for all BSSN quantities *except* lambda^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18646"}},{"Add":{"text":" import BSSN.BSSN_in_terms_of_ADM as BitoA","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18692"}},{"Add":{"text":" BitoA.gammabarDD_hDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18726"}},{"Add":{"text":" BitoA.trK_AbarDD_aDD(gammaDD, KDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18765"}},{"Add":{"text":" BitoA.cf_from_gammaDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18800"}},{"Add":{"text":" BitoA.betU_vetU(betaU, BU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18831"}},{"Add":{"text":" hDD = BitoA.hDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18851"}},{"Add":{"text":" trK = BitoA.trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18871"}},{"Add":{"text":" aDD = BitoA.aDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18891"}},{"Add":{"text":" cf = BitoA.cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18909"}},{"Add":{"text":" vetU = BitoA.vetU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18931"}},{"Add":{"text":" betU = BitoA.betU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18953"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:18954"}},{"Add":{"text":" # Step 4: Compute $\\bar{\\Lambda}^i$ (Eqs. 4 and 5 of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19011"}},{"Add":{"text":" # [Baumgarte *et al.*](https://arxiv.org/pdf/1211.6632.pdf)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19085"}},{"Add":{"text":" # from finite-difference derivatives of rescaled metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19153"}},{"Add":{"text":" # quantities $h_{ij}$:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19188"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19189"}},{"Add":{"text":" # \\bar{\\Lambda}^i = \\bar{\\gamma}^{jk}\\left(\\bar{\\Gamma}^i_{jk} - \\hat{\\Gamma}^i_{jk}\\right).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19286"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19287"}},{"Add":{"text":" # The reference_metric.py module provides us with analytic expressions for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19366"}},{"Add":{"text":" # $\\hat{\\Gamma}^i_{jk}$, so here we need only compute","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19432"}},{"Add":{"text":" # finite-difference expressions for $\\bar{\\Gamma}^i_{jk}$, based on","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19512"}},{"Add":{"text":" # the values for $h_{ij}$ provided in the initial data. Once","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19585"}},{"Add":{"text":" # $\\bar{\\Lambda}^i$ has been computed, we apply the usual rescaling","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19665"}},{"Add":{"text":" # procedure:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19690"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19691"}},{"Add":{"text":" # \\lambda^i = \\bar{\\Lambda}^i/\\text{ReU[i]},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19740"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19741"}},{"Add":{"text":" # and then output the result to a C file using the NRPy+","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19802"}},{"Add":{"text":" # finite-difference C output routine.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19852"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19853"}},{"Add":{"text":" # We will need all BSSN gridfunctions to be defined, as well as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19921"}},{"Add":{"text":" # expressions for gammabarDD_dD in terms of exact derivatives of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:19994"}},{"Add":{"text":" # the rescaling matrix and finite-difference derivatives of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20062"}},{"Add":{"text":" # hDD's. This functionality is provided by BSSN.BSSN_unrescaled_and_barred_vars,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20151"}},{"Add":{"text":" # which we call here to overwrite above definitions of gammabarDD,gammabarUU, etc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20242"}},{"Add":{"text":" Bq.gammabar__inverse_and_derivs() # Provides gammabarUU and GammabarUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20318"}},{"Add":{"text":" gammabarUU = Bq.gammabarUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20352"}},{"Add":{"text":" GammabarUDD = Bq.GammabarUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20387"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20388"}},{"Add":{"text":" # Next evaluate \\bar{\\Lambda}^i, based on GammabarUDD above and GammahatUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20468"}},{"Add":{"text":" # (from the reference metric):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20509"}},{"Add":{"text":" LambdabarU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20542"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20567"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20596"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20629"}},{"Add":{"text":" LambdabarU[i] += gammabarUU[j][k] * (GammabarUDD[i][j][k] - rfm.GammahatUDD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20731"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20732"}},{"Add":{"text":" # Finally apply rescaling:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20763"}},{"Add":{"text":" # lambda^i = Lambdabar^i/\\text{ReU[i]}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20806"}},{"Add":{"text":" lambdaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20836"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20861"}},{"Add":{"text":" lambdaU[i] = LambdabarU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20909"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20910"}},{"Add":{"text":" if ADM_input_function_name == \"DoNotOutputADMInputFunction\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:20975"}},{"Add":{"text":" return hDD,aDD,trK,vetU,betU,alpha,cf,lambdaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21029"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21030"}},{"Add":{"text":" # Step 5.A: Output files containing finite-differenced lambdas.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21098"}},{"Add":{"text":" outCparams = \"preindent=1,outCfileaccess=a,outCverbose=False,includebraces=False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21184"}},{"Add":{"text":" lambdaU_expressions = [lhrh(lhs=gri.gfaccess(\"in_gfs\", \"lambdaU0\"), rhs=lambdaU[0]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21273"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"lambdaU1\"), rhs=lambdaU[1]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21362"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"lambdaU2\"), rhs=lambdaU[2])]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21451"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21452"}},{"Add":{"text":" desc = \"Output lambdaU[i] for BSSN, built using finite-difference derivatives.\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21536"}},{"Add":{"text":" name = \"ID_BSSN_lambdas\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21565"}},{"Add":{"text":" params = \"const paramstruct *restrict params,REAL *restrict xx[3],REAL *restrict in_gfs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21658"}},{"Add":{"text":" preloop = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21675"}},{"Add":{"text":" opts = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21689"}},{"Add":{"text":" idx4replace = \"IDX4S\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21715"}},{"Add":{"text":" if \"oldloops\" in loopopts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21746"}},{"Add":{"text":" params = \"const int Nxx[3],const int Nxx_plus_2NGHOSTS[3],REAL *xx[3],const REAL dxx[3],REAL *in_gfs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21856"}},{"Add":{"text":" opts = \"DisableCparameters\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21892"}},{"Add":{"text":" idx4replace = \"IDX4\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21921"}},{"Add":{"text":" preloop = \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21943"}},{"Add":{"text":"const REAL invdx0 = 1.0/dxx[0];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:21975"}},{"Add":{"text":"const REAL invdx1 = 1.0/dxx[1];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22007"}},{"Add":{"text":"const REAL invdx2 = 1.0/dxx[2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22039"}},{"Add":{"text":"\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22043"}},{"Add":{"text":" outCfunction(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22061"}},{"Add":{"text":" outfile=os.path.join(Ccodesdir, name + \".h\"), desc=desc, name=name, params=params,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22152"}},{"Add":{"text":" preloop=preloop,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22177"}},{"Add":{"text":" body=fin.FD_outputC(\"returnstring\", lambdaU_expressions, outCparams).replace(\"IDX4\",idx4replace),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22283"}},{"Add":{"text":" loopopts=\"InteriorPoints,Read_xxs\"+loopopts, opts=opts)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22347"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22348"}},{"Add":{"text":" # Step 5: Output all ADM-to-BSSN expressions to a C function. This function","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22428"}},{"Add":{"text":" # must first call the ID_ADM_SphorCart() defined above. Using these","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22508"}},{"Add":{"text":" # Spherical or Cartesian data, it sets up all quantities needed for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22588"}},{"Add":{"text":" # BSSNCurvilinear initial data, *except* $\\lambda^i$, which must be","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22668"}},{"Add":{"text":" # computed from numerical data using finite-difference derivatives.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22748"}},{"Add":{"text":" ID_inputs_param = \"ID_inputs other_inputs,\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22796"}},{"Add":{"text":" if pointer_to_ID_inputs == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22833"}},{"Add":{"text":" ID_inputs_param = \"ID_inputs *other_inputs,\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22886"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22887"}},{"Add":{"text":" desc = \"Write BSSN variables in terms of ADM variables at a given point xx0,xx1,xx2\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:22976"}},{"Add":{"text":" name = \"ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23041"}},{"Add":{"text":" opts = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23055"}},{"Add":{"text":" params = \"const paramstruct *restrict params, \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23107"}},{"Add":{"text":" if \"oldloops\" in loopopts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23138"}},{"Add":{"text":" opts = \"DisableCparameters\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23174"}},{"Add":{"text":" params = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23194"}},{"Add":{"text":" params += \"const REAL xx0xx1xx2[3],\" + ID_inputs_param + \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23259"}},{"Add":{"text":" REAL *hDD00,REAL *hDD01,REAL *hDD02,REAL *hDD11,REAL *hDD12,REAL *hDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23352"}},{"Add":{"text":" REAL *aDD00,REAL *aDD01,REAL *aDD02,REAL *aDD11,REAL *aDD12,REAL *aDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23445"}},{"Add":{"text":" REAL *trK, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23477"}},{"Add":{"text":" REAL *vetU0,REAL *vetU1,REAL *vetU2,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23534"}},{"Add":{"text":" REAL *betU0,REAL *betU1,REAL *betU2,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23591"}},{"Add":{"text":" REAL *alpha, REAL *cf\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23637"}},{"Add":{"text":" outCparams = \"preindent=1,outCverbose=False,includebraces=False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23706"}},{"Add":{"text":" outCfunction(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23724"}},{"Add":{"text":" outfile=os.path.join(Ccodesdir, name + \".h\"), desc=desc, name=name, params=params,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23815"}},{"Add":{"text":" body=\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23832"}},{"Add":{"text":" REAL gammaSphorCartDD00,gammaSphorCartDD01,gammaSphorCartDD02,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23901"}},{"Add":{"text":" gammaSphorCartDD11,gammaSphorCartDD12,gammaSphorCartDD22;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:23970"}},{"Add":{"text":" REAL KSphorCartDD00,KSphorCartDD01,KSphorCartDD02,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24027"}},{"Add":{"text":" KSphorCartDD11,KSphorCartDD12,KSphorCartDD22;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24084"}},{"Add":{"text":" REAL alphaSphorCart,betaSphorCartU0,betaSphorCartU1,betaSphorCartU2;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24159"}},{"Add":{"text":" REAL BSphorCartU0,BSphorCartU1,BSphorCartU2;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24210"}},{"Add":{"text":" const REAL xx0 = xx0xx1xx2[0];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24247"}},{"Add":{"text":" const REAL xx1 = xx0xx1xx2[1];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24284"}},{"Add":{"text":" const REAL xx2 = xx0xx1xx2[2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24321"}},{"Add":{"text":" REAL xyz_or_rthph[3];\\n\"\"\" +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24356"}},{"Add":{"text":" outputC(r_th_ph_or_Cart_xyz_oID_xx[0:3], [\"xyz_or_rthph[0]\", \"xyz_or_rthph[1]\", \"xyz_or_rthph[2]\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24469"}},{"Add":{"text":" \"returnstring\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24506"}},{"Add":{"text":" outCparams + \",CSE_enable=False\") + \" \" + ADM_input_function_name + \"\"\"(xyz_or_rthph, other_inputs,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24632"}},{"Add":{"text":" &gammaSphorCartDD00,&gammaSphorCartDD01,&gammaSphorCartDD02,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24716"}},{"Add":{"text":" &gammaSphorCartDD11,&gammaSphorCartDD12,&gammaSphorCartDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24800"}},{"Add":{"text":" &KSphorCartDD00,&KSphorCartDD01,&KSphorCartDD02,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24872"}},{"Add":{"text":" &KSphorCartDD11,&KSphorCartDD12,&KSphorCartDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:24944"}},{"Add":{"text":" &alphaSphorCart,&betaSphorCartU0,&betaSphorCartU1,&betaSphorCartU2,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25035"}},{"Add":{"text":" &BSphorCartU0,&BSphorCartU1,&BSphorCartU2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25102"}},{"Add":{"text":" // Next compute all rescaled BSSN curvilinear quantities:\\n\"\"\" +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25173"}},{"Add":{"text":" outputC([hDD[0][0], hDD[0][1], hDD[0][2], hDD[1][1], hDD[1][2], hDD[2][2],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25261"}},{"Add":{"text":" aDD[0][0], aDD[0][1], aDD[0][2], aDD[1][1], aDD[1][2], aDD[2][2],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25349"}},{"Add":{"text":" trK, vetU[0], vetU[1], vetU[2], betU[0], betU[1], betU[2],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25430"}},{"Add":{"text":" alpha, cf],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25464"}},{"Add":{"text":" [\"*hDD00\", \"*hDD01\", \"*hDD02\", \"*hDD11\", \"*hDD12\", \"*hDD22\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25546"}},{"Add":{"text":" \"*aDD00\", \"*aDD01\", \"*aDD02\", \"*aDD11\", \"*aDD12\", \"*aDD22\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25628"}},{"Add":{"text":" \"*trK\", \"*vetU0\", \"*vetU1\", \"*vetU2\", \"*betU0\", \"*betU1\", \"*betU2\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25718"}},{"Add":{"text":" \"*alpha\", \"*cf\"], \"returnstring\", params=outCparams),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25794"}},{"Add":{"text":" opts = opts)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25815"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25816"}},{"Add":{"text":" # Step 5.a: Output the driver function for the above","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25873"}},{"Add":{"text":" # function ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:25952"}},{"Add":{"text":" # Next write the driver function for ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26048"}},{"Add":{"text":" desc = \"\"\"Driver function for ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs(), ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26138"}},{"Add":{"text":"which writes BSSN variables in terms of ADM variables at a given point xx0,xx1,xx2\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26224"}},{"Add":{"text":" name = \"ID_BSSN__ALL_BUT_LAMBDAs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26262"}},{"Add":{"text":" params = \"const paramstruct *restrict params,REAL *restrict xx[3],\" + ID_inputs_param + \"REAL *in_gfs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26369"}},{"Add":{"text":" opts = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26383"}},{"Add":{"text":" funccallparams = \"params, \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26415"}},{"Add":{"text":" idx3replace = \"IDX3S\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26443"}},{"Add":{"text":" idx4ptreplace = \"IDX4ptS\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26473"}},{"Add":{"text":" if \"oldloops\" in loopopts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26504"}},{"Add":{"text":" params = \"const int Nxx_plus_2NGHOSTS[3],REAL *xx[3],\" + ID_inputs_param + \"REAL *in_gfs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26602"}},{"Add":{"text":" opts = \"DisableCparameters\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26638"}},{"Add":{"text":" funccallparams = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26666"}},{"Add":{"text":" idx3replace = \"IDX3\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26697"}},{"Add":{"text":" idx4ptreplace = \"IDX4pt\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26730"}},{"Add":{"text":" outCfunction(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26748"}},{"Add":{"text":" outfile=os.path.join(Ccodesdir, name + \".h\"), desc=desc, name=name, params=params,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26839"}},{"Add":{"text":" body=\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26856"}},{"Add":{"text":"const int idx = IDX3(i0,i1,i2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26888"}},{"Add":{"text":"const REAL xx0xx1xx2[3] = {xx0,xx1,xx2};","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:26929"}},{"Add":{"text":"ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs(\"\"\".replace(\"IDX3\",idx3replace)+funccallparams+\"\"\"xx0xx1xx2,other_inputs,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27055"}},{"Add":{"text":" &in_gfs[IDX4pt(HDD00GF,idx)],&in_gfs[IDX4pt(HDD01GF,idx)],&in_gfs[IDX4pt(HDD02GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27163"}},{"Add":{"text":" &in_gfs[IDX4pt(HDD11GF,idx)],&in_gfs[IDX4pt(HDD12GF,idx)],&in_gfs[IDX4pt(HDD22GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27271"}},{"Add":{"text":" &in_gfs[IDX4pt(ADD00GF,idx)],&in_gfs[IDX4pt(ADD01GF,idx)],&in_gfs[IDX4pt(ADD02GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27379"}},{"Add":{"text":" &in_gfs[IDX4pt(ADD11GF,idx)],&in_gfs[IDX4pt(ADD12GF,idx)],&in_gfs[IDX4pt(ADD22GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27487"}},{"Add":{"text":" &in_gfs[IDX4pt(TRKGF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27535"}},{"Add":{"text":" &in_gfs[IDX4pt(VETU0GF,idx)],&in_gfs[IDX4pt(VETU1GF,idx)],&in_gfs[IDX4pt(VETU2GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27643"}},{"Add":{"text":" &in_gfs[IDX4pt(BETU0GF,idx)],&in_gfs[IDX4pt(BETU1GF,idx)],&in_gfs[IDX4pt(BETU2GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27751"}},{"Add":{"text":" &in_gfs[IDX4pt(ALPHAGF,idx)],&in_gfs[IDX4pt(CFGF,idx)]);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27828"}},{"Add":{"text":"\"\"\".replace(\"IDX4pt\",idx4ptreplace),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27865"}},{"Add":{"text":" loopopts=\"AllPoints,Read_xxs\"+loopopts, opts=opts)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27924"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27925"}}]}},{"FileAdd":{"meta":{"basename":"ADM_in_terms_of_BSSN.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/ADM_in_terms_of_BSSN.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:27998"}},{"Add":{"text":"# Tutorial-ADM_in_terms_of_BSSN.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28039"}},{"Add":{"text":"# this module will construct expressions for ADM","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28090"}},{"Add":{"text":"# quantities in terms of BSSN quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28134"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28135"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28166"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28209"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28210"}},{"Add":{"text":"# Step 1.a: import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28260"}},{"Add":{"text":"from outputC import * # NRPy+: Core C code output module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28329"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28433"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28543"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28611"}},{"Add":{"text":"import sys # Standard Python module for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28707"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28708"}},{"Add":{"text":"def ADM_in_terms_of_BSSN():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28736"}},{"Add":{"text":" global gammaDD, gammaDDdD, gammaDDdDD, gammaUU, detgamma, GammaUDD, KDD, KDDdD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28819"}},{"Add":{"text":" # Step 1.c: Given the chosen coordinate system, set up","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28878"}},{"Add":{"text":" # corresponding reference metric and needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28936"}},{"Add":{"text":" # reference metric quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:28980"}},{"Add":{"text":" # The following function call sets up the reference metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29043"}},{"Add":{"text":" # and related quantities, including rescaling matrices ReDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29111"}},{"Add":{"text":" # ReU, and hatted quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29148"}},{"Add":{"text":" rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29175"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29176"}},{"Add":{"text":" # Step 1.d: Set spatial dimension (must be 3 for BSSN, as BSSN is","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29246"}},{"Add":{"text":" # a 3+1-dimensional decomposition of the general","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29309"}},{"Add":{"text":" # relativistic field equations)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29355"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29367"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29368"}},{"Add":{"text":" # Step 1.e: Import all basic (unrescaled) BSSN scalars & tensors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29437"}},{"Add":{"text":" import BSSN.BSSN_quantities as Bq","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29475"}},{"Add":{"text":" Bq.BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29503"}},{"Add":{"text":" gammabarDD = Bq.gammabarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29534"}},{"Add":{"text":" cf = Bq.cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29557"}},{"Add":{"text":" AbarDD = Bq.AbarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29584"}},{"Add":{"text":" trK = Bq.trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29608"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29609"}},{"Add":{"text":" Bq.gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29647"}},{"Add":{"text":" gammabarDD_dD = Bq.gammabarDD_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29685"}},{"Add":{"text":" gammabarDD_dDD = Bq.gammabarDD_dDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29724"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29725"}},{"Add":{"text":" Bq.AbarUU_AbarUD_trAbar_AbarDD_dD()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29765"}},{"Add":{"text":" AbarDD_dD = Bq.AbarDD_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29794"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29795"}},{"Add":{"text":" # Step 2: The ADM three-metric gammaDD and its","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29846"}},{"Add":{"text":" # derivatives in terms of BSSN quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29901"}},{"Add":{"text":" gammaDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29931"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29932"}},{"Add":{"text":" exp4phi = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:29960"}},{"Add":{"text":" if par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"phi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30026"}},{"Add":{"text":" exp4phi = sp.exp(4 * cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30059"}},{"Add":{"text":" elif par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"chi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30127"}},{"Add":{"text":" exp4phi = (1 / cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30154"}},{"Add":{"text":" elif par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"W\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30220"}},{"Add":{"text":" exp4phi = (1 / cf ** 2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30252"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30262"}},{"Add":{"text":" print(\"Error EvolvedConformalFactor_cf type = \\\"\" + par.parval_from_str(\"EvolvedConformalFactor_cf\") + \"\\\" unknown.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30388"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30408"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30409"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30434"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30463"}},{"Add":{"text":" gammaDD[i][j] = exp4phi * gammabarDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30518"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30519"}},{"Add":{"text":" # Step 2.a: Derivatives of $e^{4\\phi}$","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30562"}},{"Add":{"text":" phidD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30590"}},{"Add":{"text":" phidDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30619"}},{"Add":{"text":" cf_dD = ixp.declarerank1(\"cf_dD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30658"}},{"Add":{"text":" cf_dDD = ixp.declarerank2(\"cf_dDD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30706"}},{"Add":{"text":" if par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"phi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30772"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30801"}},{"Add":{"text":" phidD[i] = cf_dD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30834"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30867"}},{"Add":{"text":" phidDD[i][j] = cf_dDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30911"}},{"Add":{"text":" elif par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"chi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:30979"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31008"}},{"Add":{"text":" phidD[i] = -sp.Rational(1,4)*exp4phi*cf_dD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31067"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31100"}},{"Add":{"text":" phidDD[i][j] = sp.Rational(1,4)*( exp4phi**2*cf_dD[i]*cf_dD[j] - exp4phi*cf_dDD[i][j] )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31204"}},{"Add":{"text":" elif par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"W\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31270"}},{"Add":{"text":" exp2phi = (1 / cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31297"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31326"}},{"Add":{"text":" phidD[i] = -sp.Rational(1,2)*exp2phi*cf_dD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31385"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31418"}},{"Add":{"text":" phidDD[i][j] = sp.Rational(1,2)*( exp4phi*cf_dD[i]*cf_dD[j] - exp2phi*cf_dDD[i][j] )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31519"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31529"}},{"Add":{"text":" print(\"Error EvolvedConformalFactor_cf type = \\\"\"+par.parval_from_str(\"EvolvedConformalFactor_cf\")+\"\\\" unknown.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31651"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31671"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31672"}},{"Add":{"text":" exp4phidD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31705"}},{"Add":{"text":" exp4phidDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31738"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31763"}},{"Add":{"text":" exp4phidD[i] = 4*exp4phi*phidD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31805"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31834"}},{"Add":{"text":" exp4phidDD[i][j] = 16*exp4phi*phidD[i]*phidD[j] + 4*exp4phi*phidDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31919"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31920"}},{"Add":{"text":" # Step 2.b: Derivatives of gammaDD, the ADM three-metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:31981"}},{"Add":{"text":" gammaDDdD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32013"}},{"Add":{"text":" gammaDDdDD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32046"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32047"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32072"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32101"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32134"}},{"Add":{"text":" gammaDDdD[i][j][k] = exp4phidD[k] * gammabarDD[i][j] + exp4phi * gammabarDD_dD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32238"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32275"}},{"Add":{"text":" gammaDDdDD[i][j][k][l] = exp4phidDD[k][l] * gammabarDD[i][j] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32360"}},{"Add":{"text":" exp4phidD[k] * gammabarDD_dD[i][j][l] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32447"}},{"Add":{"text":" exp4phidD[l] * gammabarDD_dD[i][j][k] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32534"}},{"Add":{"text":" exp4phi * gammabarDD_dDD[i][j][k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32616"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32617"}},{"Add":{"text":" # Step 2.c: 3-Christoffel symbols associated with ADM 3-metric gammaDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32692"}},{"Add":{"text":" # Step 2.c.i: First compute the inverse 3-metric gammaUU:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32754"}},{"Add":{"text":" gammaUU, detgamma = ixp.symm_matrix_inverter3x3(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32815"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32816"}},{"Add":{"text":" GammaUDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32847"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32848"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32873"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32902"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32935"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:32972"}},{"Add":{"text":" GammaUDD[i][j][k] += sp.Rational(1,2)*gammaUU[i][l]* \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33047"}},{"Add":{"text":" (gammaDDdD[l][j][k] + gammaDDdD[l][k][j] - gammaDDdD[j][k][l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33146"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33167"}},{"Add":{"text":" # Step 3: Define ADM extrinsic curvature KDD and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33220"}},{"Add":{"text":" # its first spatial derivatives KDDdD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33270"}},{"Add":{"text":" # in terms of BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33312"}},{"Add":{"text":" KDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33338"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33339"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33364"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33393"}},{"Add":{"text":" KDD[i][j] = exp4phi * AbarDD[i][j] + sp.Rational(1, 3) * gammaDD[i][j] * trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33482"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33483"}},{"Add":{"text":" KDDdD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33511"}},{"Add":{"text":" trK_dD = ixp.declarerank1(\"trK_dD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33551"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33576"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33605"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33638"}},{"Add":{"text":" KDDdD[i][j][k] = exp4phidD[k] * AbarDD[i][j] + exp4phi * AbarDD_dD[i][j][k] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33734"}},{"Add":{"text":" sp.Rational(1, 3) * (gammaDDdD[i][j][k] * trK + gammaDD[i][j] * trK_dD[k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33842"}}]}},{"FileAdd":{"meta":{"basename":"BSSN_ID_function_string.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BSSN_ID_function_string.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module sets up a standard initial data function used for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33936"}},{"Add":{"text":"# setting up SENR initial data at all gridpoints.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33988"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:33989"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34020"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34063"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34064"}},{"Add":{"text":"from outputC import *","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34086"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34087"}},{"Add":{"text":"def BSSN_ID_function_string(cf,hDD,lambdaU,aDD,trK,alpha,vetU,betU):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34156"}},{"Add":{"text":" rhss = [trK,alpha,cf]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34182"}},{"Add":{"text":" lhss = [\"in_gfs[IDX4S(TRKGF,i0,i1,i2)]\",\"in_gfs[IDX4S(ALPHAGF,i0,i1,i2)]\",\"in_gfs[IDX4S(CFGF,i0,i1,i2)]\"]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34292"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34315"}},{"Add":{"text":" rhss.append(lambdaU[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34347"}},{"Add":{"text":" lhss.append(\"in_gfs[IDX4S(LAMBDAU\"+str(i)+\"GF,i0,i1,i2)]\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34414"}},{"Add":{"text":" rhss.append(vetU[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34443"}},{"Add":{"text":" lhss.append(\"in_gfs[IDX4S(VETU\"+str(i)+\"GF,i0,i1,i2)]\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34507"}},{"Add":{"text":" rhss.append(betU[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34536"}},{"Add":{"text":" lhss.append(\"in_gfs[IDX4S(BETU\"+str(i)+\"GF,i0,i1,i2)]\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34600"}},{"Add":{"text":" for j in range(i,3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34629"}},{"Add":{"text":" rhss.append(hDD[i][j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34664"}},{"Add":{"text":" lhss.append(\"in_gfs[IDX4S(HDD\" + str(i) + str(j) + \"GF,i0,i1,i2)]\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34744"}},{"Add":{"text":" rhss.append(aDD[i][j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34779"}},{"Add":{"text":" lhss.append(\"in_gfs[IDX4S(ADD\" + str(i) + str(j) + \"GF,i0,i1,i2)]\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34859"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34860"}},{"Add":{"text":" # Sort the lhss list alphabetically, and rhss to match:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:34920"}},{"Add":{"text":" lhss,rhss = [list(x) for x in zip(*sorted(zip(lhss, rhss), key=lambda pair: pair[0]))]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35011"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35012"}},{"Add":{"text":" body = outputC(rhss, lhss, filename=\"returnstring\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35068"}},{"Add":{"text":" params=\"preindent=1,CSE_enable=True,outCverbose=False\", # outCverbose=False to prevent","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35175"}},{"Add":{"text":" # enormous output files.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35276"}},{"Add":{"text":" prestring=\"\", poststring=\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35324"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35325"}},{"Add":{"text":" desc = \"Set up the initial data at all points on the numerical grid.\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35399"}},{"Add":{"text":" add_to_Cfunction_dict(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35426"}},{"Add":{"text":" desc =desc,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35449"}},{"Add":{"text":" name =\"initial_data\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35482"}},{"Add":{"text":" params =\"const paramstruct *restrict params,REAL *restrict xx[3], REAL *restrict in_gfs\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35581"}},{"Add":{"text":" body =body,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35604"}},{"Add":{"text":" loopopts=\"AllPoints,Read_xxs\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35643"}}]}},{"FileAdd":{"meta":{"basename":"BSSN_RHSs.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BSSN_RHSs.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35704"}},{"Add":{"text":"# Tutorial-BSSN_time_evolution-BSSN_RHSs.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35754"}},{"Add":{"text":"# this module will construct the right-hand sides (RHSs)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35813"}},{"Add":{"text":"# expressions of the BSSN time evolution equations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35867"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35869"}},{"Add":{"text":"# Time-evolution equations for the BSSN gauge conditions are","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35930"}},{"Add":{"text":"# specified in the BSSN_gauge_RHSs module and documented in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:35992"}},{"Add":{"text":"# the Tutorial-BSSN_time_evolution-BSSN_gauge_RHSs.ipynb","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36051"}},{"Add":{"text":"# NRPy+ tutorial module.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36078"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36079"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36110"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36153"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36154"}},{"Add":{"text":"# Step 1.a: import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36204"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36308"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36371"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36481"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36549"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36646"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq # NRPy+: This module depends on the parameter EvolvedConformalFactor_cf,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36753"}},{"Add":{"text":" # which is defined in BSSN.BSSN_quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36837"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36838"}},{"Add":{"text":"have_already_called_BSSN_RHSs_function = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36885"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36886"}},{"Add":{"text":"# Step 1.b: Set the coordinate system for the numerical grid:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36948"}},{"Add":{"text":"# DO NOT SET IN STANDALONE PYTHON MODULE","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:36990"}},{"Add":{"text":"# par.set_parval_from_str(\"reference_metric::CoordSystem\",\"Spherical\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37061"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37062"}},{"Add":{"text":"def BSSN_RHSs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37079"}},{"Add":{"text":" # Step 1.c: Given the chosen coordinate system, set up","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37138"}},{"Add":{"text":" # corresponding reference metric and needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37196"}},{"Add":{"text":" # reference metric quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37240"}},{"Add":{"text":" # The following function call sets up the reference metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37303"}},{"Add":{"text":" # and related quantities, including rescaling matrices ReDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37371"}},{"Add":{"text":" # ReU, and hatted quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37408"}},{"Add":{"text":" rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37435"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37436"}},{"Add":{"text":" global have_already_called_BSSN_RHSs_function # setting to global enables other modules to see updated value.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37550"}},{"Add":{"text":" have_already_called_BSSN_RHSs_function = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37600"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37601"}},{"Add":{"text":" # Step 1.d: Set spatial dimension (must be 3 for BSSN, as BSSN is","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37671"}},{"Add":{"text":" # a 3+1-dimensional decomposition of the general","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37734"}},{"Add":{"text":" # relativistic field equations)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37780"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37792"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37793"}},{"Add":{"text":" # Step 1.e: Import all basic (unrescaled) BSSN scalars & tensors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37862"}},{"Add":{"text":" import BSSN.BSSN_quantities as Bq","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37900"}},{"Add":{"text":" Bq.BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37928"}},{"Add":{"text":" gammabarDD = Bq.gammabarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37959"}},{"Add":{"text":" AbarDD = Bq.AbarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:37986"}},{"Add":{"text":" LambdabarU = Bq.LambdabarU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38017"}},{"Add":{"text":" trK = Bq.trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38036"}},{"Add":{"text":" alpha = Bq.alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38057"}},{"Add":{"text":" betaU = Bq.betaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38078"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38079"}},{"Add":{"text":" # Step 1.f: Import all neeeded rescaled BSSN tensors:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38137"}},{"Add":{"text":" aDD = Bq.aDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38154"}},{"Add":{"text":" cf = Bq.cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38170"}},{"Add":{"text":" lambdaU = Bq.lambdaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38195"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38196"}},{"Add":{"text":" # Step 2.a.i: Import derivative expressions for betaU defined in the BSSN.BSSN_quantities module:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38298"}},{"Add":{"text":" Bq.betaU_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38320"}},{"Add":{"text":" betaU_dD = Bq.betaU_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38347"}},{"Add":{"text":" betaU_dDD = Bq.betaU_dDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38376"}},{"Add":{"text":" # Step 2.a.ii: Import derivative expression for gammabarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38439"}},{"Add":{"text":" Bq.gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38477"}},{"Add":{"text":" gammabarDD_dupD = Bq.gammabarDD_dupD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38518"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38519"}},{"Add":{"text":" # Step 2.a.iii: First term of \\partial_t \\bar{\\gamma}_{i j} right-hand side:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38600"}},{"Add":{"text":" # \\beta^k \\bar{\\gamma}_{ij,k} + \\beta^k_{,i} \\bar{\\gamma}_{kj} + \\beta^k_{,j} \\bar{\\gamma}_{ik}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38700"}},{"Add":{"text":" gammabar_rhsDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38737"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38762"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38791"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38824"}},{"Add":{"text":" gammabar_rhsDD[i][j] += betaU[k] * gammabarDD_dupD[i][j][k] + betaU_dD[k][i] * gammabarDD[k][j] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:38938"}},{"Add":{"text":" + betaU_dD[k][j] * gammabarDD[i][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39014"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39015"}},{"Add":{"text":" # Step 2.b.i: First import \\bar{A}_{ij} = AbarDD[i][j], and its contraction trAbar = \\bar{A}^k_k","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39116"}},{"Add":{"text":" # from BSSN.BSSN_quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39158"}},{"Add":{"text":" Bq.AbarUU_AbarUD_trAbar_AbarDD_dD()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39198"}},{"Add":{"text":" trAbar = Bq.trAbar","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39221"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39222"}},{"Add":{"text":" # Step 2.b.ii: Import detgammabar quantities from BSSN.BSSN_quantities:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39298"}},{"Add":{"text":" Bq.detgammabar_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39330"}},{"Add":{"text":" detgammabar = Bq.detgammabar","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39363"}},{"Add":{"text":" detgammabar_dD = Bq.detgammabar_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39402"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39403"}},{"Add":{"text":" # Step 2.b.ii: Compute the contraction \\bar{D}_k \\beta^k = \\beta^k_{,k} + \\frac{\\beta^k \\bar{\\gamma}_{,k}}{2 \\bar{\\gamma}}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39530"}},{"Add":{"text":" Dbarbetacontraction = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39570"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39595"}},{"Add":{"text":" Dbarbetacontraction += betaU_dD[k][k] + betaU[k] * detgammabar_dD[k] / (2 * detgammabar)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39692"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39693"}},{"Add":{"text":" # Step 2.b.iii: Second term of \\partial_t \\bar{\\gamma}_{i j} right-hand side:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39775"}},{"Add":{"text":" # \\frac{2}{3} \\bar{\\gamma}_{i j} \\left (\\alpha \\bar{A}_{k}^{k} - \\bar{D}_{k} \\beta^{k}\\right )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39874"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39899"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:39928"}},{"Add":{"text":" gammabar_rhsDD[i][j] += sp.Rational(2, 3) * gammabarDD[i][j] * (alpha * trAbar - Dbarbetacontraction)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40042"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40043"}},{"Add":{"text":" # Step 2.c: Third term of \\partial_t \\bar{\\gamma}_{i j} right-hand side:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40120"}},{"Add":{"text":" # -2 \\alpha \\bar{A}_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40149"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40174"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40203"}},{"Add":{"text":" gammabar_rhsDD[i][j] += -2 * alpha * AbarDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40265"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40266"}},{"Add":{"text":" # Step 3.a: First term of \\partial_t \\bar{A}_{i j}:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40322"}},{"Add":{"text":" # \\beta^k \\partial_k \\bar{A}_{ij} + \\partial_i \\beta^k \\bar{A}_{kj} + \\partial_j \\beta^k \\bar{A}_{ik}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40428"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40429"}},{"Add":{"text":" # First define AbarDD_dupD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40461"}},{"Add":{"text":" AbarDD_dupD = Bq.AbarDD_dupD # From Bq.AbarUU_AbarUD_trAbar_AbarDD_dD()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40537"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40538"}},{"Add":{"text":" Abar_rhsDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40571"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40596"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40625"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40658"}},{"Add":{"text":" Abar_rhsDD[i][j] += betaU[k] * AbarDD_dupD[i][j][k] + betaU_dD[k][i] * AbarDD[k][j] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40760"}},{"Add":{"text":" + betaU_dD[k][j] * AbarDD[i][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40828"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40829"}},{"Add":{"text":" # Step 3.b: Second term of \\partial_t \\bar{A}_{i j}:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:40886"}},{"Add":{"text":" # - (2/3) \\bar{A}_{i j} \\bar{D}_{k} \\beta^{k} - 2 \\alpha \\bar{A}_{i k} {\\bar{A}^{k}}_{j} + \\alpha \\bar{A}_{i j} K","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41004"}},{"Add":{"text":" gammabarUU = Bq.gammabarUU # From Bq.gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41077"}},{"Add":{"text":" AbarUD = Bq.AbarUD # From Bq.AbarUU_AbarUD_trAbar()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41134"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41159"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41188"}},{"Add":{"text":" Abar_rhsDD[i][j] += -sp.Rational(2, 3) * AbarDD[i][j] * Dbarbetacontraction + alpha * AbarDD[i][j] * trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41305"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41338"}},{"Add":{"text":" Abar_rhsDD[i][j] += -2 * alpha * AbarDD[i][k] * AbarUD[k][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41415"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41416"}},{"Add":{"text":" # Step 3.c.i: Define partial derivatives of \\phi in terms of evolved quantity \"cf\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41504"}},{"Add":{"text":" Bq.phi_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41528"}},{"Add":{"text":" phi_dD = Bq.phi_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41551"}},{"Add":{"text":" phi_dupD = Bq.phi_dupD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41578"}},{"Add":{"text":" phi_dDD = Bq.phi_dDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41603"}},{"Add":{"text":" exp_m4phi = Bq.exp_m4phi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41632"}},{"Add":{"text":" phi_dBarD = Bq.phi_dBarD # phi_dBarD = Dbar_i phi = phi_dD (since phi is a scalar)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41720"}},{"Add":{"text":" phi_dBarDD = Bq.phi_dBarDD # phi_dBarDD = Dbar_i Dbar_j phi (covariant derivative)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41808"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41809"}},{"Add":{"text":" # Step 3.c.ii: Define RbarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41842"}},{"Add":{"text":" Bq.RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41898"}},{"Add":{"text":" RbarDD = Bq.RbarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41921"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:41922"}},{"Add":{"text":" # Step 3.c.iii: Define first and second derivatives of \\alpha, as well as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42000"}},{"Add":{"text":" # \\bar{D}_i \\bar{D}_j \\alpha, which is defined just like phi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42073"}},{"Add":{"text":" alpha_dD = ixp.declarerank1(\"alpha_dD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42117"}},{"Add":{"text":" alpha_dDD = ixp.declarerank2(\"alpha_dDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42172"}},{"Add":{"text":" alpha_dBarD = alpha_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42199"}},{"Add":{"text":" alpha_dBarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42234"}},{"Add":{"text":" GammabarUDD = Bq.GammabarUDD # Defined in Bq.gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42315"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42340"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42369"}},{"Add":{"text":" alpha_dBarDD[i][j] = alpha_dDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42418"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42451"}},{"Add":{"text":" alpha_dBarDD[i][j] += - GammabarUDD[k][i][j] * alpha_dD[k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42526"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42527"}},{"Add":{"text":" # Step 3.c.iv: Define the terms in curly braces:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42580"}},{"Add":{"text":" curlybrackettermsDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42622"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42647"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42676"}},{"Add":{"text":" curlybrackettermsDD[i][j] = -2 * alpha * phi_dBarDD[i][j] + 4 * alpha * phi_dBarD[i] * phi_dBarD[j] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42790"}},{"Add":{"text":" + 2 * alpha_dBarD[i] * phi_dBarD[j] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42868"}},{"Add":{"text":" + 2 * alpha_dBarD[j] * phi_dBarD[i] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:42946"}},{"Add":{"text":" - alpha_dBarDD[i][j] + alpha * RbarDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43030"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43031"}},{"Add":{"text":" # Step 3.c.v: Compute the trace:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43068"}},{"Add":{"text":" curlybracketterms_trace = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43112"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43137"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43166"}},{"Add":{"text":" curlybracketterms_trace += gammabarUU[i][j] * curlybrackettermsDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43250"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43251"}},{"Add":{"text":" # Step 3.c.vi: Third and final term of Abar_rhsDD[i][j]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43312"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43337"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43366"}},{"Add":{"text":" Abar_rhsDD[i][j] += exp_m4phi * (curlybrackettermsDD[i][j] -","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43439"}},{"Add":{"text":" sp.Rational(1, 3) * gammabarDD[i][j] * curlybracketterms_trace)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43548"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43549"}},{"Add":{"text":" # Step 4: Right-hand side of conformal factor variable \"cf\". Supported","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43624"}},{"Add":{"text":" # options include: cf=phi, cf=W=e^(-2*phi) (default), and cf=chi=e^(-4*phi)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43713"}},{"Add":{"text":" # \\partial_t phi = \\left[\\beta^k \\partial_k \\phi \\right] <- TERM 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43784"}},{"Add":{"text":" # + \\frac{1}{6} \\left (\\bar{D}_{k} \\beta^{k} - \\alpha K \\right ) <- TERM 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43880"}},{"Add":{"text":" global cf_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43898"}},{"Add":{"text":" cf_rhs = sp.Rational(1, 6) * (Dbarbetacontraction - alpha * trK) # Term 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:43977"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44002"}},{"Add":{"text":" cf_rhs += betaU[k] * phi_dupD[k] # Term 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44053"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44054"}},{"Add":{"text":" # Next multiply to convert phi_rhs to cf_rhs.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44104"}},{"Add":{"text":" if par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") == \"phi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44192"}},{"Add":{"text":" pass # do nothing; cf_rhs = phi_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44237"}},{"Add":{"text":" elif par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") == \"W\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44325"}},{"Add":{"text":" cf_rhs *= -2 * cf # cf_rhs = -2*cf*phi_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44377"}},{"Add":{"text":" elif par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") == \"chi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44467"}},{"Add":{"text":" cf_rhs *= -4 * cf # cf_rhs = -4*cf*phi_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44519"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44529"}},{"Add":{"text":" print(\"Error: EvolvedConformalFactor_cf == \" +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44584"}},{"Add":{"text":" par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") + \" unsupported!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44688"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44708"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44709"}},{"Add":{"text":" # Step 5: right-hand side of trK (trace of extrinsic curvature):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44778"}},{"Add":{"text":" # \\partial_t K = \\beta^k \\partial_k K <- TERM 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44830"}},{"Add":{"text":" # + \\frac{1}{3} \\alpha K^{2} <- TERM 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44883"}},{"Add":{"text":" # + \\alpha \\bar{A}_{i j} \\bar{A}^{i j} <- TERM 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:44946"}},{"Add":{"text":" # - - e^{-4 \\phi} (\\bar{D}_{i} \\bar{D}^{i} \\alpha + 2 \\bar{D}^{i} \\alpha \\bar{D}_{i} \\phi ) <- TERM 4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45062"}},{"Add":{"text":" global trK_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45081"}},{"Add":{"text":" # TERM 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45095"}},{"Add":{"text":" trK_rhs = sp.Rational(1, 3) * alpha * trK * trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45147"}},{"Add":{"text":" trK_dupD = ixp.declarerank1(\"trK_dupD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45191"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45216"}},{"Add":{"text":" # TERM 1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45234"}},{"Add":{"text":" trK_rhs += betaU[i] * trK_dupD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45276"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45301"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45330"}},{"Add":{"text":" # TERM 4:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45352"}},{"Add":{"text":" trK_rhs += -exp_m4phi * gammabarUU[i][j] * (alpha_dBarDD[i][j] + 2 * alpha_dBarD[j] * phi_dBarD[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45464"}},{"Add":{"text":" AbarUU = Bq.AbarUU # From Bq.AbarUU_AbarUD_trAbar()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45521"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45546"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45575"}},{"Add":{"text":" # TERM 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45597"}},{"Add":{"text":" trK_rhs += alpha * AbarDD[i][j] * AbarUU[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45656"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45657"}},{"Add":{"text":" # Step 6: right-hand side of \\partial_t \\bar{\\Lambda}^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45718"}},{"Add":{"text":" # \\partial_t \\bar{\\Lambda}^i = \\beta^k \\partial_k \\bar{\\Lambda}^i - \\partial_k \\beta^i \\bar{\\Lambda}^k <- TERM 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45835"}},{"Add":{"text":" # + \\bar{\\gamma}^{j k} \\hat{D}_{j} \\hat{D}_{k} \\beta^{i} <- TERM 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:45933"}},{"Add":{"text":" # + \\frac{2}{3} \\Delta^{i} \\bar{D}_{j} \\beta^{j} <- TERM 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46023"}},{"Add":{"text":" # + \\frac{1}{3} \\bar{D}^{i} \\bar{D}_{j} \\beta^{j} <- TERM 4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46114"}},{"Add":{"text":" # - 2 \\bar{A}^{i j} (\\partial_{j} \\alpha - 6 \\partial_{j} \\phi) <- TERM 5","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46219"}},{"Add":{"text":" # + 2 \\alpha \\bar{A}^{j k} \\Delta_{j k}^{i} <- TERM 6","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46304"}},{"Add":{"text":" # - \\frac{4}{3} \\alpha \\bar{\\gamma}^{i j} \\partial_{j} K <- TERM 7","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46402"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46403"}},{"Add":{"text":" # Step 6.a: Term 1 of \\partial_t \\bar{\\Lambda}^i: \\beta^k \\partial_k \\bar{\\Lambda}^i - \\partial_k \\beta^i \\bar{\\Lambda}^k","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46529"}},{"Add":{"text":" # First we declare \\bar{\\Lambda}^i and \\bar{\\Lambda}^i_{,j} in terms of \\lambda^i and \\lambda^i_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46634"}},{"Add":{"text":" global LambdabarU_dupD # Used on the RHS of the Gamma-driving shift conditions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46717"}},{"Add":{"text":" LambdabarU_dupD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46755"}},{"Add":{"text":" lambdaU_dupD = ixp.declarerank2(\"lambdaU_dupD\", \"nosym\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46816"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46841"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46870"}},{"Add":{"text":" LambdabarU_dupD[i][j] = lambdaU_dupD[i][j] * rfm.ReU[i] + lambdaU[i] * rfm.ReUdD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46969"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:46970"}},{"Add":{"text":" global Lambdabar_rhsU # Used on the RHS of the Gamma-driving shift conditions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47052"}},{"Add":{"text":" Lambdabar_rhsU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47089"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47114"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47143"}},{"Add":{"text":" Lambdabar_rhsU[i] += betaU[k] * LambdabarU_dupD[i][k] - betaU_dD[i][k] * LambdabarU[k] # Term 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47252"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47253"}},{"Add":{"text":" # Step 6.b: Term 2 of \\partial_t \\bar{\\Lambda}^i = \\bar{\\gamma}^{jk} (Term 2a + Term 2b + Term 2c)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47356"}},{"Add":{"text":" # Term 2a: \\bar{\\gamma}^{jk} \\beta^i_{,kj}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47403"}},{"Add":{"text":" Term2aUDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47435"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47460"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47489"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47522"}},{"Add":{"text":" Term2aUDD[i][j][k] += betaU_dDD[i][k][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47579"}},{"Add":{"text":" # Term 2b: \\hat{\\Gamma}^i_{mk,j} \\beta^m + \\hat{\\Gamma}^i_{mk} \\beta^m_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47659"}},{"Add":{"text":" # + \\hat{\\Gamma}^i_{dj}\\beta^d_{,k} - \\hat{\\Gamma}^d_{kj} \\beta^i_{,d}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47743"}},{"Add":{"text":" Term2bUDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47775"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47800"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47829"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47862"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47899"}},{"Add":{"text":" Term2bUDD[i][j][k] += rfm.GammahatUDDdD[i][m][k][j] * betaU[m] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:47984"}},{"Add":{"text":" + rfm.GammahatUDD[i][m][k] * betaU_dD[m][j] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48072"}},{"Add":{"text":" + rfm.GammahatUDD[i][m][j] * betaU_dD[m][k] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48160"}},{"Add":{"text":" - rfm.GammahatUDD[m][k][j] * betaU_dD[i][m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48246"}},{"Add":{"text":" # Term 2c: \\hat{\\Gamma}^i_{dj}\\hat{\\Gamma}^d_{mk} \\beta^m - \\hat{\\Gamma}^d_{kj} \\hat{\\Gamma}^i_{md} \\beta^m","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48358"}},{"Add":{"text":" Term2cUDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48390"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48415"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48444"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48477"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48514"}},{"Add":{"text":" for d in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48555"}},{"Add":{"text":" Term2cUDD[i][j][k] += (rfm.GammahatUDD[i][d][j] * rfm.GammahatUDD[d][m][k] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48656"}},{"Add":{"text":" - rfm.GammahatUDD[d][k][j] * rfm.GammahatUDD[i][m][d]) * betaU[m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48769"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48770"}},{"Add":{"text":" Lambdabar_rhsUpieceU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48813"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48814"}},{"Add":{"text":" # Put it all together to get Term 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48855"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48880"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48909"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:48942"}},{"Add":{"text":" Lambdabar_rhsU[i] += gammabarUU[j][k] * (Term2aUDD[i][j][k] + Term2bUDD[i][j][k] + Term2cUDD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49061"}},{"Add":{"text":" Lambdabar_rhsUpieceU[i] += gammabarUU[j][k] * (","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49125"}},{"Add":{"text":" Term2aUDD[i][j][k] + Term2bUDD[i][j][k] + Term2cUDD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49215"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49216"}},{"Add":{"text":" # Step 6.c: Term 3 of \\partial_t \\bar{\\Lambda}^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49270"}},{"Add":{"text":" # \\frac{2}{3} \\Delta^{i} \\bar{D}_{j} \\beta^{j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49324"}},{"Add":{"text":" DGammaU = Bq.DGammaU # From Bq.RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49409"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49434"}},{"Add":{"text":" Lambdabar_rhsU[i] += sp.Rational(2, 3) * DGammaU[i] * Dbarbetacontraction # Term 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49526"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49527"}},{"Add":{"text":" # Step 6.d: Term 4 of \\partial_t \\bar{\\Lambda}^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49581"}},{"Add":{"text":" # \\frac{1}{3} \\bar{D}^{i} \\bar{D}_{j} \\beta^{j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49643"}},{"Add":{"text":" detgammabar_dDD = Bq.detgammabar_dDD # From Bq.detgammabar_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49720"}},{"Add":{"text":" Dbarbetacontraction_dBarD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49768"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49793"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49822"}},{"Add":{"text":" Dbarbetacontraction_dBarD[m] += betaU_dDD[k][k][m] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49889"}},{"Add":{"text":" (betaU_dD[k][m] * detgammabar_dD[k] +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:49971"}},{"Add":{"text":" betaU[k] * detgammabar_dDD[k][m]) / (2 * detgammabar) \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50072"}},{"Add":{"text":" - betaU[k] * detgammabar_dD[k] * detgammabar_dD[m] / (","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50171"}},{"Add":{"text":" 2 * detgammabar * detgammabar)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50258"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50283"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50312"}},{"Add":{"text":" Lambdabar_rhsU[i] += sp.Rational(1, 3) * gammabarUU[i][m] * Dbarbetacontraction_dBarD[m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50413"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50414"}},{"Add":{"text":" # Step 6.e: Term 5 of \\partial_t \\bar{\\Lambda}^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50468"}},{"Add":{"text":" # - 2 \\bar{A}^{i j} (\\partial_{j} \\alpha - 6 \\alpha \\partial_{j} \\phi)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50553"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50578"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50607"}},{"Add":{"text":" Lambdabar_rhsU[i] += -2 * AbarUU[i][j] * (alpha_dD[j] - 6 * alpha * phi_dD[j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50698"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50699"}},{"Add":{"text":" # Step 6.f: Term 6 of \\partial_t \\bar{\\Lambda}^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50753"}},{"Add":{"text":" # 2 \\alpha \\bar{A}^{j k} \\Delta^{i}_{j k}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50809"}},{"Add":{"text":" DGammaUDD = Bq.DGammaUDD # From RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50895"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50920"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50949"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:50982"}},{"Add":{"text":" Lambdabar_rhsU[i] += 2 * alpha * AbarUU[j][k] * DGammaUDD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51065"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51066"}},{"Add":{"text":" # Step 6.g: Term 7 of \\partial_t \\bar{\\Lambda}^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51120"}},{"Add":{"text":" # -\\frac{4}{3} \\alpha \\bar{\\gamma}^{i j} \\partial_{j} K","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51190"}},{"Add":{"text":" trK_dD = ixp.declarerank1(\"trK_dD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51230"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51255"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51284"}},{"Add":{"text":" Lambdabar_rhsU[i] += -sp.Rational(4, 3) * alpha * gammabarUU[i][j] * trK_dD[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51375"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51376"}},{"Add":{"text":" # Step 7: Rescale the RHS quantities so that the evolved","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51437"}},{"Add":{"text":" # variables are smooth across coord singularities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51499"}},{"Add":{"text":" global h_rhsDD,a_rhsDD,lambda_rhsU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51538"}},{"Add":{"text":" h_rhsDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51568"}},{"Add":{"text":" a_rhsDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51598"}},{"Add":{"text":" lambda_rhsU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51632"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51657"}},{"Add":{"text":" lambda_rhsU[i] = Lambdabar_rhsU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51713"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51742"}},{"Add":{"text":" h_rhsDD[i][j] = gammabar_rhsDD[i][j] / rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51808"}},{"Add":{"text":" a_rhsDD[i][j] = Abar_rhsDD[i][j] / rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:51870"}},{"Add":{"text":" # print(str(Abar_rhsDD[2][2]).replace(\"**\",\"^\").replace(\"_\",\"\").replace(\"xx\",\"x\").replace(\"sin(x2)\",\"Sin[x2]\").replace(\"sin(2*x2)\",\"Sin[2*x2]\").replace(\"cos(x2)\",\"Cos[x2]\").replace(\"detgbaroverdetghat\",\"detg\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52085"}},{"Add":{"text":" # print(str(Dbarbetacontraction).replace(\"**\",\"^\").replace(\"_\",\"\").replace(\"xx\",\"x\").replace(\"sin(x2)\",\"Sin[x2]\").replace(\"detgbaroverdetghat\",\"detg\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52241"}},{"Add":{"text":" # print(betaU_dD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52263"}},{"Add":{"text":" # print(str(trK_rhs).replace(\"xx2\",\"xx3\").replace(\"xx1\",\"xx2\").replace(\"xx0\",\"xx1\").replace(\"**\",\"^\").replace(\"_\",\"\").replace(\"sin(xx2)\",\"Sinx2\").replace(\"xx\",\"x\").replace(\"sin(2*x2)\",\"Sin2x2\").replace(\"cos(x2)\",\"Cosx2\").replace(\"detgbaroverdetghat\",\"detg\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52526"}},{"Add":{"text":" # print(str(bet_rhsU[0]).replace(\"xx2\",\"xx3\").replace(\"xx1\",\"xx2\").replace(\"xx0\",\"xx1\").replace(\"**\",\"^\").replace(\"_\",\"\").replace(\"sin(xx2)\",\"Sinx2\").replace(\"xx\",\"x\").replace(\"sin(2*x2)\",\"Sin2x2\").replace(\"cos(x2)\",\"Cosx2\").replace(\"detgbaroverdetghat\",\"detg\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52793"}}]}},{"FileAdd":{"meta":{"basename":"BSSN_T4UUmunu_vars.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BSSN_T4UUmunu_vars.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module registers rescaled BSSN T^{mu nu} source term variables","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52889"}},{"Add":{"text":"# as AUX (i.e., not evolved) gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52935"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52936"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:52967"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53010"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53011"}},{"Add":{"text":"# Step P1: import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53060"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53170"}},{"Add":{"text":"import grid as gri # NRPy+: Functions having to do with numerical grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53257"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53258"}},{"Add":{"text":"def define_BSSN_T4UUmunu_rescaled_source_terms():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53308"}},{"Add":{"text":" # Step 0: First check to see if this function has already been called.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53383"}},{"Add":{"text":" # If so, do not register the gridfunctions again!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53439"}},{"Add":{"text":" for i in range(len(gri.glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53486"}},{"Add":{"text":" if \"sDD00\" in gri.glb_gridfcs_list[i].name:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53538"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53557"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53558"}},{"Add":{"text":" # Step 1: Declare as globals all quantities declared in this function.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53633"}},{"Add":{"text":" global rho,S,sD,sDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53657"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53658"}},{"Add":{"text":" # Step 2: Register all needed *evolved* gridfunctions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53717"}},{"Add":{"text":" # Step 2a: Register indexed quantities, using ixp.register_... functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53794"}},{"Add":{"text":" sDD = ixp.register_gridfunctions_for_single_rank2(\"AUX\", \"sDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53871"}},{"Add":{"text":" sD = ixp.register_gridfunctions_for_single_rank1(\"AUX\", \"sD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:53938"}},{"Add":{"text":" # Step 2b: Register scalar quantities, using gri.register_gridfunctions()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54016"}},{"Add":{"text":" rho, S = gri.register_gridfunctions(\"AUX\",[\"rho\",\"S\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54075"}}]}},{"FileAdd":{"meta":{"basename":"BSSN_constraints.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BSSN_constraints.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54144"}},{"Add":{"text":"# Tutorial-BSSN_constraints.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54181"}},{"Add":{"text":"# this module will construct expressions for the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54232"}},{"Add":{"text":"# BSSN Hamiltonian and momentum constraint equations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54288"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54289"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54320"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54363"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54364"}},{"Add":{"text":"# Step 1: Initialize needed Python/NRPy+ modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54413"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54517"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54580"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54690"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54758"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq # NRPy+: Computes useful BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54833"}},{"Add":{"text":"import BSSN.BSSN_T4UUmunu_vars as BTmunu","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54874"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54875"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54897"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54898"}},{"Add":{"text":"def BSSN_constraints(add_T4UUmunu_source_terms=False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:54953"}},{"Add":{"text":" # Step 1.a: Set spatial dimension (must be 3 for BSSN, as BSSN is","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55023"}},{"Add":{"text":" # a 3+1-dimensional decomposition of the general","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55086"}},{"Add":{"text":" # relativistic field equations)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55132"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55144"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55145"}},{"Add":{"text":" # Step 1.b: Given the chosen coordinate system, set up","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55204"}},{"Add":{"text":" # corresponding reference metric and needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55262"}},{"Add":{"text":" # reference metric quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55306"}},{"Add":{"text":" # The following function call sets up the reference metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55369"}},{"Add":{"text":" # and related quantities, including rescaling matrices ReDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55437"}},{"Add":{"text":" # ReU, and hatted quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55474"}},{"Add":{"text":" rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55501"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55502"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55503"}},{"Add":{"text":" # Step 2: Hamiltonian constraint.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55541"}},{"Add":{"text":" # First declare all needed variables","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55582"}},{"Add":{"text":" Bq.declare_BSSN_gridfunctions_if_not_declared_already() # Sets trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55654"}},{"Add":{"text":" Bq.BSSN_basic_tensors() # Sets AbarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55697"}},{"Add":{"text":" Bq.gammabar__inverse_and_derivs() # Sets gammabarUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55754"}},{"Add":{"text":" Bq.AbarUU_AbarUD_trAbar_AbarDD_dD() # Sets AbarUU and AbarDD_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55823"}},{"Add":{"text":" Bq.RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU() # Sets RbarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55894"}},{"Add":{"text":" Bq.phi_and_derivs() # Sets phi_dBarD & phi_dBarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55949"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55950"}},{"Add":{"text":" ###############################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:55986"}},{"Add":{"text":" ###############################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56022"}},{"Add":{"text":" # HAMILTONIAN CONSTRAINT","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56052"}},{"Add":{"text":" ###############################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56088"}},{"Add":{"text":" ###############################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56124"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56125"}},{"Add":{"text":" # Term 1: 2/3 K^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56147"}},{"Add":{"text":" global H","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56160"}},{"Add":{"text":" H = sp.Rational(2, 3) * Bq.trK ** 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56200"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56201"}},{"Add":{"text":" # Term 2: -A_{ij} A^{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56230"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56255"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56284"}},{"Add":{"text":" H += -Bq.AbarDD[i][j] * Bq.AbarUU[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56336"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56337"}},{"Add":{"text":" # Term 3a: trace(Rbar)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56364"}},{"Add":{"text":" Rbartrace = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56394"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56419"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56448"}},{"Add":{"text":" Rbartrace += Bq.gammabarUU[i][j] * Bq.RbarDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56511"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56512"}},{"Add":{"text":" # Term 3b: -8 \\bar{\\gamma}^{ij} \\bar{D}_i \\phi \\bar{D}_j \\phi = -8*phi_dBar_times_phi_dBar","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56607"}},{"Add":{"text":" # Term 3c: -8 \\bar{\\gamma}^{ij} \\bar{D}_i \\bar{D}_j \\phi = -8*phi_dBarDD_contraction","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56701"}},{"Add":{"text":" phi_dBar_times_phi_dBar = sp.sympify(0) # Term 3b","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56756"}},{"Add":{"text":" phi_dBarDD_contraction = sp.sympify(0) # Term 3c","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56810"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56835"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56864"}},{"Add":{"text":" phi_dBar_times_phi_dBar += Bq.gammabarUU[i][j] * Bq.phi_dBarD[i] * Bq.phi_dBarD[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:56959"}},{"Add":{"text":" phi_dBarDD_contraction += Bq.gammabarUU[i][j] * Bq.phi_dBarDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57039"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57040"}},{"Add":{"text":" # Add Term 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57058"}},{"Add":{"text":" H += Bq.exp_m4phi * (Rbartrace - 8 * (phi_dBar_times_phi_dBar + phi_dBarDD_contraction))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57151"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57152"}},{"Add":{"text":" if add_T4UUmunu_source_terms:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57186"}},{"Add":{"text":" M_PI = par.Cparameters(\"#define\", thismodule, \"M_PI\",\"\") # M_PI is pi as defined in C","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57281"}},{"Add":{"text":" BTmunu.define_BSSN_T4UUmunu_rescaled_source_terms()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57341"}},{"Add":{"text":" rho = BTmunu.rho","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57366"}},{"Add":{"text":" H += -16*M_PI*rho","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57392"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57393"}},{"Add":{"text":" # FIXME: ADD T4UUmunu SOURCE TERMS TO MOMENTUM CONSTRAINT!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57456"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57457"}},{"Add":{"text":" # Step 3: M^i, the momentum constraint","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57500"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57501"}},{"Add":{"text":" ###############################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57537"}},{"Add":{"text":" ###############################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57573"}},{"Add":{"text":" # MOMENTUM CONSTRAINT","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57600"}},{"Add":{"text":" ###############################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57636"}},{"Add":{"text":" ###############################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57672"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57673"}},{"Add":{"text":" # SEE Tutorial-BSSN_constraints.ipynb for full documentation.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57739"}},{"Add":{"text":" global MU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57753"}},{"Add":{"text":" MU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57778"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57779"}},{"Add":{"text":" # Term 2: 6 A^{ij} \\partial_j \\phi:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57819"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57844"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57873"}},{"Add":{"text":" MU[i] += 6*Bq.AbarUU[i][j]*Bq.phi_dD[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57925"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57926"}},{"Add":{"text":" # Term 3: -2/3 \\bar{\\gamma}^{ij} K_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:57970"}},{"Add":{"text":" trK_dD = ixp.declarerank1(\"trK_dD\") # Not defined in BSSN_RHSs; only trK_dupD is defined there.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58070"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58095"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58124"}},{"Add":{"text":" MU[i] += -sp.Rational(2,3)*Bq.gammabarUU[i][j]*trK_dD[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58193"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58194"}},{"Add":{"text":" # Next evaluate the conformal covariant derivative \\bar{D}_j \\bar{A}_{lm}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58272"}},{"Add":{"text":" AbarDD_dBarD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58307"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58332"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58361"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58394"}},{"Add":{"text":" AbarDD_dBarD[i][j][k] = Bq.AbarDD_dD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58456"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58493"}},{"Add":{"text":" AbarDD_dBarD[i][j][k] += -Bq.GammabarUDD[l][k][i] * Bq.AbarDD[l][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58581"}},{"Add":{"text":" AbarDD_dBarD[i][j][k] += -Bq.GammabarUDD[l][k][j] * Bq.AbarDD[i][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58669"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58670"}},{"Add":{"text":" # Term 1: Contract twice with the metric to make \\bar{D}_{j} \\bar{A}^{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58748"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58773"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58802"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58835"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58872"}},{"Add":{"text":" MU[i] += Bq.gammabarUU[i][k] * Bq.gammabarUU[j][l] * AbarDD_dBarD[k][l][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58967"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:58968"}},{"Add":{"text":" # Finally, we multiply by e^{-4 phi} and rescale the momentum constraint:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59046"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59071"}},{"Add":{"text":" MU[i] *= Bq.exp_m4phi / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59114"}}]}},{"FileAdd":{"meta":{"basename":"BSSN_gauge_RHSs.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BSSN_gauge_RHSs.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59181"}},{"Add":{"text":"# Tutorial-BSSN_time_evolution-BSSN_gauge_RHSs.ipynb","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59236"}},{"Add":{"text":"# this module will construct the right-hand sides (RHSs)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59295"}},{"Add":{"text":"# expressions for the time evolution equations of the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59351"}},{"Add":{"text":"# BSSN gauge quantities alpha and beta^i (i.e., the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59405"}},{"Add":{"text":"# lapse and shift)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59426"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59428"}},{"Add":{"text":"# Non-gauge BSSN time-evolution equations are documented in the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59492"}},{"Add":{"text":"# NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59518"}},{"Add":{"text":"# Tutorial-BSSN_time_evolution-BSSN_RHSs.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59568"}},{"Add":{"text":"# and separately constructed in the BSSN.BSSN_RHSs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59621"}},{"Add":{"text":"# Python module.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59640"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59641"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59672"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59715"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59716"}},{"Add":{"text":"# Step 1: Import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59764"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59868"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:59931"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60041"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60109"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq # NRPy+: Computes useful BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60184"}},{"Add":{"text":"import BSSN.BSSN_RHSs as Brhs # NRPy+: Constructs BSSN right-hand-side expressions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60271"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60368"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60369"}},{"Add":{"text":"# Step 1.a: Declare/initialize parameters for this module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60427"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60449"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"LapseEvolutionOption\", \"OnePlusLog\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60543"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"ShiftEvolutionOption\", \"GammaDriving2ndOrder_Covariant\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60657"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60658"}},{"Add":{"text":"def BSSN_gauge_RHSs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60681"}},{"Add":{"text":" # Step 1.d: Set spatial dimension (must be 3 for BSSN, as BSSN is","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60751"}},{"Add":{"text":" # a 3+1-dimensional decomposition of the general","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60814"}},{"Add":{"text":" # relativistic field equations)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60860"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60872"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60873"}},{"Add":{"text":" # Step 1.e: Given the chosen coordinate system, set up","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60932"}},{"Add":{"text":" # corresponding reference metric and needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:60990"}},{"Add":{"text":" # reference metric quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61034"}},{"Add":{"text":" # The following function call sets up the reference metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61097"}},{"Add":{"text":" # and related quantities, including rescaling matrices ReDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61165"}},{"Add":{"text":" # ReU, and hatted quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61202"}},{"Add":{"text":" rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61229"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61230"}},{"Add":{"text":" # Step 1.f: Define needed BSSN quantities:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61277"}},{"Add":{"text":" # Declare scalars & tensors (in terms of rescaled BSSN quantities)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61348"}},{"Add":{"text":" Bq.BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61376"}},{"Add":{"text":" Bq.betaU_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61398"}},{"Add":{"text":" # Declare BSSN_RHSs (excluding the time evolution equations for the gauge conditions),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61489"}},{"Add":{"text":" # if they haven't already been declared.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61537"}},{"Add":{"text":" if Brhs.have_already_called_BSSN_RHSs_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61598"}},{"Add":{"text":" print(\"BSSN_gauge_RHSs() Error: You must call BSSN_RHSs() before calling BSSN_gauge_RHSs().\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61700"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61720"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61721"}},{"Add":{"text":" # Step 2: Lapse conditions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61752"}},{"Add":{"text":" LapseEvolOption = par.parval_from_str(thismodule + \"::LapseEvolutionOption\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61833"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61834"}},{"Add":{"text":" # Step 2.a: The 1+log lapse condition:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61877"}},{"Add":{"text":" # \\partial_t \\alpha = \\beta^i \\alpha_{,i} - 2*\\alpha*K","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61938"}},{"Add":{"text":" # First import expressions from BSSN_quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:61990"}},{"Add":{"text":" cf = Bq.cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62005"}},{"Add":{"text":" trK = Bq.trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62022"}},{"Add":{"text":" alpha = Bq.alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62043"}},{"Add":{"text":" betaU = Bq.betaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62064"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62065"}},{"Add":{"text":" # Implement the 1+log lapse condition","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62107"}},{"Add":{"text":" global alpha_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62128"}},{"Add":{"text":" alpha_rhs = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62158"}},{"Add":{"text":" if LapseEvolOption == \"OnePlusLog\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62198"}},{"Add":{"text":" alpha_rhs = -2 * alpha * trK","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62235"}},{"Add":{"text":" alpha_dupD = ixp.declarerank1(\"alpha_dupD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62287"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62316"}},{"Add":{"text":" alpha_rhs += betaU[i] * alpha_dupD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62366"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62367"}},{"Add":{"text":" # Step 2.b: Implement the harmonic slicing lapse condition","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62430"}},{"Add":{"text":" elif LapseEvolOption == \"HarmonicSlicing\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62477"}},{"Add":{"text":" if par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") == \"W\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62567"}},{"Add":{"text":" alpha_rhs = -3 * cf ** (-4) * Brhs.cf_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62621"}},{"Add":{"text":" elif par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") == \"phi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62715"}},{"Add":{"text":" alpha_rhs = 6 * sp.exp(6 * cf) * Brhs.cf_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62772"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62786"}},{"Add":{"text":" print(\"Error LapseEvolutionOption==HarmonicSlicing unsupported for EvolvedConformalFactor_cf!=(W or phi)\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62905"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62929"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62930"}},{"Add":{"text":" # Step 2.c: Frozen lapse","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62959"}},{"Add":{"text":" # \\partial_t \\alpha = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:62990"}},{"Add":{"text":" elif LapseEvolOption == \"Frozen\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63028"}},{"Add":{"text":" alpha_rhs = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63062"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63071"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63081"}},{"Add":{"text":" print(\"Error: \"+thismodule + \"::LapseEvolutionOption == \"+LapseEvolOption+\" not supported!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63182"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63202"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63203"}},{"Add":{"text":" # Step 3.a: Set \\partial_t \\beta^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63242"}},{"Add":{"text":" # First check that ShiftEvolutionOption parameter choice is supported.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63317"}},{"Add":{"text":" ShiftEvolOption = par.parval_from_str(thismodule + \"::ShiftEvolutionOption\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63398"}},{"Add":{"text":" if ShiftEvolOption != \"Frozen\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63439"}},{"Add":{"text":" ShiftEvolOption != \"GammaDriving2ndOrder_NoCovariant\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63507"}},{"Add":{"text":" ShiftEvolOption != \"GammaDriving2ndOrder_Covariant\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63574"}},{"Add":{"text":" ShiftEvolOption != \"GammaDriving2ndOrder_Covariant__Hatted\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63648"}},{"Add":{"text":" ShiftEvolOption != \"GammaDriving1stOrder_Covariant\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63714"}},{"Add":{"text":" ShiftEvolOption != \"GammaDriving1stOrder_Covariant__Hatted\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63783"}},{"Add":{"text":" print(\"Error: ShiftEvolutionOption == \" + ShiftEvolOption + \" unsupported!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63868"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63888"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63889"}},{"Add":{"text":" # Next import expressions from BSSN_quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63940"}},{"Add":{"text":" BU = Bq.BU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63955"}},{"Add":{"text":" betU = Bq.betU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:63974"}},{"Add":{"text":" betaU_dupD = Bq.betaU_dupD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64005"}},{"Add":{"text":" # Define needed quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64036"}},{"Add":{"text":" beta_rhsU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64068"}},{"Add":{"text":" B_rhsU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64097"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64098"}},{"Add":{"text":" # In the case of Frozen shift condition, we","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64146"}},{"Add":{"text":" # explicitly set the betaU and BU RHS's to zero","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64201"}},{"Add":{"text":" # instead of relying on the ixp.zerorank1()'s above,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64261"}},{"Add":{"text":" # for safety.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64282"}},{"Add":{"text":" if ShiftEvolOption == \"Frozen\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64318"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64347"}},{"Add":{"text":" beta_rhsU[i] = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64388"}},{"Add":{"text":" BU[i] = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64429"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64430"}},{"Add":{"text":" if ShiftEvolOption == \"GammaDriving2ndOrder_NoCovariant\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64492"}},{"Add":{"text":" # Step 3.a.i: Compute right-hand side of beta^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64548"}},{"Add":{"text":" # * \\partial_t \\beta^i = \\beta^j \\beta^i_{,j} + B^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64609"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64638"}},{"Add":{"text":" beta_rhsU[i] += BU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64672"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64705"}},{"Add":{"text":" beta_rhsU[i] += betaU[j] * betaU_dupD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64765"}},{"Add":{"text":" # Compute right-hand side of B^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64807"}},{"Add":{"text":" eta = par.Cparameters(\"REAL\", thismodule, [\"eta\"],2.0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64870"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64871"}},{"Add":{"text":" # Step 3.a.ii: Compute right-hand side of B^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:64925"}},{"Add":{"text":" # * \\partial_t B^i = \\beta^j B^i_{,j} + 3/4 * \\partial_0 \\Lambda^i - eta B^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65015"}},{"Add":{"text":" # Step 3.a.iii: Define BU_dupD, in terms of derivative of rescaled variable \\bet^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65106"}},{"Add":{"text":" BU_dupD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65140"}},{"Add":{"text":" betU_dupD = ixp.declarerank2(\"betU_dupD\", \"nosym\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65199"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65228"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65261"}},{"Add":{"text":" BU_dupD[i][j] = betU_dupD[i][j] * rfm.ReU[i] + betU[i] * rfm.ReUdD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65350"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65351"}},{"Add":{"text":" # Step 3.a.iv: Compute \\partial_0 \\bar{\\Lambda}^i = (\\partial_t - \\beta^i \\partial_i) \\bar{\\Lambda}^j","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65461"}},{"Add":{"text":" Lambdabar_partial0 = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65506"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65535"}},{"Add":{"text":" Lambdabar_partial0[i] = Brhs.Lambdabar_rhsU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65594"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65623"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65656"}},{"Add":{"text":" Lambdabar_partial0[j] += -betaU[i] * Brhs.LambdabarU_dupD[j][i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65736"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65737"}},{"Add":{"text":" # Step 3.a.v: Evaluate RHS of B^i:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65780"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65809"}},{"Add":{"text":" B_rhsU[i] += sp.Rational(3, 4) * Lambdabar_partial0[i] - eta * BU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65890"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65923"}},{"Add":{"text":" B_rhsU[i] += betaU[j] * BU_dupD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65977"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:65978"}},{"Add":{"text":" # Step 3.b: The right-hand side of the \\partial_t \\beta^i equation","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66049"}},{"Add":{"text":" if \"GammaDriving2ndOrder_Covariant\" in ShiftEvolOption:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66109"}},{"Add":{"text":" # Step 3.b Option 2: \\partial_t \\beta^i = \\left[\\beta^j \\bar{D}_j \\beta^i\\right] + B^{i}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66206"}},{"Add":{"text":" # First we need GammabarUDD, defined in Bq.gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66288"}},{"Add":{"text":" Bq.gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66330"}},{"Add":{"text":" ConnectionUDD = Bq.GammabarUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66369"}},{"Add":{"text":" # If instead we wish to use the Hatted covariant derivative, we replace","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66449"}},{"Add":{"text":" # ConnectionUDD with GammahatUDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66494"}},{"Add":{"text":" if ShiftEvolOption == \"GammaDriving2ndOrder_Covariant__Hatted\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66566"}},{"Add":{"text":" ConnectionUDD = rfm.GammahatUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66610"}},{"Add":{"text":" # Then compute right-hand side:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66650"}},{"Add":{"text":" # Term 1: \\beta^j \\beta^i_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66689"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66718"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66751"}},{"Add":{"text":" beta_rhsU[i] += betaU[j] * betaU_dupD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66811"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66812"}},{"Add":{"text":" # Term 2: \\beta^j \\bar{\\Gamma}^i_{mj} \\beta^m","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66866"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66895"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66928"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:66965"}},{"Add":{"text":" beta_rhsU[i] += betaU[j] * ConnectionUDD[i][m][j] * betaU[m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67046"}},{"Add":{"text":" # Term 3: B^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67068"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67097"}},{"Add":{"text":" beta_rhsU[i] += BU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67131"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67132"}},{"Add":{"text":" if \"GammaDriving2ndOrder_Covariant\" in ShiftEvolOption:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67192"}},{"Add":{"text":" ConnectionUDD = Bq.GammabarUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67231"}},{"Add":{"text":" # If instead we wish to use the Hatted covariant derivative, we replace","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67311"}},{"Add":{"text":" # ConnectionUDD with GammahatUDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67356"}},{"Add":{"text":" if ShiftEvolOption == \"GammaDriving2ndOrder_Covariant__Hatted\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67428"}},{"Add":{"text":" ConnectionUDD = rfm.GammahatUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67472"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67473"}},{"Add":{"text":" # Step 3.c: Covariant option:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67511"}},{"Add":{"text":" # \\partial_t B^i = \\beta^j \\bar{D}_j B^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67561"}},{"Add":{"text":" # + \\frac{3}{4} ( \\partial_t \\bar{\\Lambda}^{i} - \\beta^j \\bar{D}_j \\bar{\\Lambda}^{i} )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67670"}},{"Add":{"text":" # - \\eta B^{i}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67707"}},{"Add":{"text":" # = \\beta^j B^i_{,j} + \\beta^j \\bar{\\Gamma}^i_{mj} B^m","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67786"}},{"Add":{"text":" # + \\frac{3}{4}[ \\partial_t \\bar{\\Lambda}^{i}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67854"}},{"Add":{"text":" # - \\beta^j (\\bar{\\Lambda}^i_{,j} + \\bar{\\Gamma}^i_{mj} \\bar{\\Lambda}^m)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:67963"}},{"Add":{"text":" # - \\eta B^{i}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68000"}},{"Add":{"text":" # Term 1, part a: First compute B^i_{,j} using upwinded derivative","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68075"}},{"Add":{"text":" BU_dupD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68109"}},{"Add":{"text":" betU_dupD = ixp.declarerank2(\"betU_dupD\", \"nosym\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68168"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68197"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68230"}},{"Add":{"text":" BU_dupD[i][j] = betU_dupD[i][j] * rfm.ReU[i] + betU[i] * rfm.ReUdD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68319"}},{"Add":{"text":" # Term 1: \\beta^j B^i_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68354"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68383"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68416"}},{"Add":{"text":" B_rhsU[i] += betaU[j] * BU_dupD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68470"}},{"Add":{"text":" # Term 2: \\beta^j \\bar{\\Gamma}^i_{mj} B^m","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68520"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68549"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68582"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68619"}},{"Add":{"text":" B_rhsU[i] += betaU[j] * ConnectionUDD[i][m][j] * BU[m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68694"}},{"Add":{"text":" # Term 3: \\frac{3}{4}\\partial_t \\bar{\\Lambda}^{i}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68752"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68781"}},{"Add":{"text":" B_rhsU[i] += sp.Rational(3, 4) * Brhs.Lambdabar_rhsU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68849"}},{"Add":{"text":" # Term 4: -\\frac{3}{4}\\beta^j \\bar{\\Lambda}^i_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68908"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68937"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:68970"}},{"Add":{"text":" B_rhsU[i] += -sp.Rational(3, 4) * betaU[j] * Brhs.LambdabarU_dupD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69058"}},{"Add":{"text":" # Term 5: -\\frac{3}{4}\\beta^j \\bar{\\Gamma}^i_{mj} \\bar{\\Lambda}^m","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69132"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69161"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69194"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69231"}},{"Add":{"text":" B_rhsU[i] += -sp.Rational(3, 4) * betaU[j] * ConnectionUDD[i][m][j] * Bq.LambdabarU[m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69338"}},{"Add":{"text":" # Term 6: - \\eta B^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69367"}},{"Add":{"text":" # eta is a free parameter; we declare it here:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69422"}},{"Add":{"text":" eta = par.Cparameters(\"REAL\", thismodule, [\"eta\"],2.0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69485"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69514"}},{"Add":{"text":" B_rhsU[i] += -eta * BU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69552"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69553"}},{"Add":{"text":" if \"GammaDriving1stOrder_Covariant\" in ShiftEvolOption:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69613"}},{"Add":{"text":" # Step 3.c: \\partial_t \\beta^i = \\left[\\beta^j \\bar{D}_j \\beta^i\\right] + 3/4 Lambdabar^i - eta*beta^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69724"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69725"}},{"Add":{"text":" # First set \\partial_t B^i = 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69765"}},{"Add":{"text":" B_rhsU = ixp.zerorank1() # \\partial_t B^i = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69820"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69821"}},{"Add":{"text":" # Second, set \\partial_t beta^i RHS:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69866"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69867"}},{"Add":{"text":" # Compute covariant advection term:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69911"}},{"Add":{"text":" # We need GammabarUDD, defined in Bq.gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:69988"}},{"Add":{"text":" Bq.gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70030"}},{"Add":{"text":" ConnectionUDD = Bq.GammabarUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70069"}},{"Add":{"text":" # If instead we wish to use the Hatted covariant derivative, we replace","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70149"}},{"Add":{"text":" # ConnectionUDD with GammahatUDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70194"}},{"Add":{"text":" if ShiftEvolOption == \"GammaDriving1stOrder_Covariant__Hatted\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70266"}},{"Add":{"text":" ConnectionUDD = rfm.GammahatUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70310"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70311"}},{"Add":{"text":" # Term 1: \\beta^j \\beta^i_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70350"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70379"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70412"}},{"Add":{"text":" beta_rhsU[i] += betaU[j] * betaU_dupD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70472"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70473"}},{"Add":{"text":" # Term 2: \\beta^j \\bar{\\Gamma}^i_{mj} \\beta^m","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70527"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70556"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70589"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70626"}},{"Add":{"text":" beta_rhsU[i] += betaU[j] * ConnectionUDD[i][m][j] * betaU[m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70707"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70708"}},{"Add":{"text":" # Term 3: 3/4 Lambdabar^i - eta*beta^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70755"}},{"Add":{"text":" eta = par.Cparameters(\"REAL\", thismodule, [\"eta\"], 2.0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70819"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70848"}},{"Add":{"text":" beta_rhsU[i] += sp.Rational(3, 4) * Bq.LambdabarU[i] - eta * betaU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70930"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:70931"}},{"Add":{"text":" # Step 4: Rescale the BSSN gauge RHS quantities so that the evolved","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71003"}},{"Add":{"text":" # variables may remain smooth across coord singularities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71072"}},{"Add":{"text":" global vet_rhsU,bet_rhsU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71101"}},{"Add":{"text":" vet_rhsU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71132"}},{"Add":{"text":" bet_rhsU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71163"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71188"}},{"Add":{"text":" vet_rhsU[i] = beta_rhsU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71236"}},{"Add":{"text":" bet_rhsU[i] = B_rhsU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71281"}},{"Add":{"text":" # print(str(Abar_rhsDD[2][2]).replace(\"**\",\"^\").replace(\"_\",\"\").replace(\"xx\",\"x\").replace(\"sin(x2)\",\"Sin[x2]\").replace(\"sin(2*x2)\",\"Sin[2*x2]\").replace(\"cos(x2)\",\"Cos[x2]\").replace(\"detgbaroverdetghat\",\"detg\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71496"}},{"Add":{"text":" # print(str(Dbarbetacontraction).replace(\"**\",\"^\").replace(\"_\",\"\").replace(\"xx\",\"x\").replace(\"sin(x2)\",\"Sin[x2]\").replace(\"detgbaroverdetghat\",\"detg\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71652"}},{"Add":{"text":" # print(betaU_dD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71674"}},{"Add":{"text":" # print(str(trK_rhs).replace(\"xx2\",\"xx3\").replace(\"xx1\",\"xx2\").replace(\"xx0\",\"xx1\").replace(\"**\",\"^\").replace(\"_\",\"\").replace(\"sin(xx2)\",\"Sinx2\").replace(\"xx\",\"x\").replace(\"sin(2*x2)\",\"Sin2x2\").replace(\"cos(x2)\",\"Cosx2\").replace(\"detgbaroverdetghat\",\"detg\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:71937"}},{"Add":{"text":" # print(str(bet_rhsU[0]).replace(\"xx2\",\"xx3\").replace(\"xx1\",\"xx2\").replace(\"xx0\",\"xx1\").replace(\"**\",\"^\").replace(\"_\",\"\").replace(\"sin(xx2)\",\"Sinx2\").replace(\"xx\",\"x\").replace(\"sin(2*x2)\",\"Sin2x2\").replace(\"cos(x2)\",\"Cosx2\").replace(\"detgbaroverdetghat\",\"detg\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72204"}}]}},{"FileAdd":{"meta":{"basename":"BSSN_in_terms_of_ADM.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BSSN_in_terms_of_ADM.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72277"}},{"Add":{"text":"# Tutorial-BSSN_in_terms_of_ADM.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72318"}},{"Add":{"text":"# this module will construct expressions for BSSN","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72370"}},{"Add":{"text":"# quantities in terms of ADM quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72413"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72414"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72445"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72488"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72489"}},{"Add":{"text":"# Step 1: Import needed core NRPy+ modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72532"}},{"Add":{"text":"from outputC import * # NRPy+: Core C code output module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72601"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72664"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72774"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72842"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:72939"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq # NRPy+: This module depends on the parameter EvolvedConformalFactor_cf,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73046"}},{"Add":{"text":" # which is defined in BSSN.BSSN_quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73130"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73131"}},{"Add":{"text":"# Step 1.a: Set DIM=3, as we're using a 3+1 decomposition of Einstein's equations","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73213"}},{"Add":{"text":"DIM=3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73219"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73220"}},{"Add":{"text":"# Step 2: All ADM quantities were input into this function in the Spherical or Cartesian","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73309"}},{"Add":{"text":"# basis, as functions of r,th,ph or x,y,z, respectively. In Steps 1 and 2 above,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73398"}},{"Add":{"text":"# we converted them to the xx0,xx1,xx2 basis, and as functions of xx0,xx1,xx2.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73485"}},{"Add":{"text":"# Here we convert ADM quantities to their BSSN Curvilinear counterparts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73566"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73567"}},{"Add":{"text":"# Step 2.a: Convert ADM $\\gamma_{ij}$ to BSSN $\\bar{gamma}_{ij}$:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73633"}},{"Add":{"text":"# We have (Eqs. 2 and 3 of [Ruchlin *et al.*](https://arxiv.org/pdf/1712.07658.pdf)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73729"}},{"Add":{"text":"def gammabarDD_hDD(gammaDD):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73758"}},{"Add":{"text":" global gammabarDD,hDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73784"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73785"}},{"Add":{"text":" if gammaDD == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73809"}},{"Add":{"text":" gammaDD = ixp.declarerank2(\"gammaDD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73863"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73864"}},{"Add":{"text":" if rfm.have_already_called_reference_metric_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:73931"}},{"Add":{"text":" print(\"BSSN.BSSN_in_terms_of_ADM.hDD_given_ADM(): Must call reference_metric() first!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74027"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74047"}},{"Add":{"text":" # \\bar{gamma}_{ij} = (\\frac{\\bar{gamma}}{gamma})^{1/3}*gamma_{ij}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74118"}},{"Add":{"text":" gammaUU, gammaDET = ixp.symm_matrix_inverter3x3(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74179"}},{"Add":{"text":" gammabarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74212"}},{"Add":{"text":" hDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74245"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74270"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74299"}},{"Add":{"text":" gammabarDD[i][j] = (rfm.detgammahat/gammaDET)**(sp.Rational(1,3))*gammaDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74391"}},{"Add":{"text":" hDD[i][j] = (gammabarDD[i][j] - rfm.ghatDD[i][j]) / rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74470"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74471"}},{"Add":{"text":"# Step 2.b: Convert the extrinsic curvature K_{ij} to the trace-free extrinsic","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74550"}},{"Add":{"text":"# curvature \\bar{A}_{ij}, plus the trace of the extrinsic curvature K,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74631"}},{"Add":{"text":"# where (Eq. 3 of [Baumgarte *et al.*](https://arxiv.org/pdf/1211.6632.pdf)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74719"}},{"Add":{"text":"def trK_AbarDD_aDD(gammaDD,KDD):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74752"}},{"Add":{"text":" global trK,AbarDD,aDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74778"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74779"}},{"Add":{"text":" if gammaDD == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74803"}},{"Add":{"text":" gammaDD = ixp.declarerank2(\"gammaDD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74857"}},{"Add":{"text":" if KDD == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74877"}},{"Add":{"text":" KDD = ixp.declarerank2(\"KDD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74923"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74924"}},{"Add":{"text":" if rfm.have_already_called_reference_metric_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:74991"}},{"Add":{"text":" print(\"BSSN.BSSN_in_terms_of_ADM.trK_AbarDD(): Must call reference_metric() first!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75084"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75104"}},{"Add":{"text":" # \\bar{gamma}_{ij} = (\\frac{\\bar{gamma}}{gamma})^{1/3}*gamma_{ij}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75175"}},{"Add":{"text":" gammaUU, gammaDET = ixp.symm_matrix_inverter3x3(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75236"}},{"Add":{"text":" # K = gamma^{ij} K_{ij}, and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75269"}},{"Add":{"text":" # \\bar{A}_{ij} &= (\\frac{\\bar{gamma}}{gamma})^{1/3}*(K_{ij} - \\frac{1}{3}*gamma_{ij}*K)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75361"}},{"Add":{"text":" trK = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75385"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75410"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75439"}},{"Add":{"text":" trK += gammaUU[i][j]*KDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75482"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75483"}},{"Add":{"text":" AbarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75512"}},{"Add":{"text":" aDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75541"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75566"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75595"}},{"Add":{"text":" AbarDD[i][j] = (rfm.detgammahat/gammaDET)**(sp.Rational(1,3))*(KDD[i][j] - sp.Rational(1,3)*gammaDD[i][j]*trK)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75718"}},{"Add":{"text":" aDD[i][j] = AbarDD[i][j] / rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75775"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75776"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75777"}},{"Add":{"text":"# Step 2.c: Define \\bar{Lambda}^i (Eqs. 4 and 5 of [Baumgarte *et al.*](https://arxiv.org/pdf/1211.6632.pdf)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75888"}},{"Add":{"text":"def LambdabarU_lambdaU__exact_gammaDD(gammaDD):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75936"}},{"Add":{"text":" global LambdabarU, lambdaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75967"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75968"}},{"Add":{"text":" if gammaDD == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:75992"}},{"Add":{"text":" gammaDD = ixp.declarerank2(\"gammaDD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76046"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76047"}},{"Add":{"text":" # \\bar{Lambda}^i = \\bar{gamma}^{jk}(\\bar{Gamma}^i_{jk} - \\hat{Gamma}^i_{jk}).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76129"}},{"Add":{"text":" gammabarDD_hDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76157"}},{"Add":{"text":" gammabarUU, gammabarDET = ixp.symm_matrix_inverter3x3(gammabarDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76227"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76228"}},{"Add":{"text":" # First compute Christoffel symbols \\bar{Gamma}^i_{jk}, with respect to barred metric:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76319"}},{"Add":{"text":" GammabarUDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76353"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76378"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76407"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76440"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76477"}},{"Add":{"text":" GammabarUDD[i][j][k] += sp.Rational(1, 2) * gammabarUU[i][l] * (","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76562"}},{"Add":{"text":" sp.diff(gammabarDD[l][j], rfm.xx[k]) +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76633"}},{"Add":{"text":" sp.diff(gammabarDD[l][k], rfm.xx[j]) -","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76704"}},{"Add":{"text":" sp.diff(gammabarDD[j][k], rfm.xx[l]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76774"}},{"Add":{"text":" # Next evaluate \\bar{Lambda}^i, based on GammabarUDD above and GammahatUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76853"}},{"Add":{"text":" # (from the reference metric):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76894"}},{"Add":{"text":" LambdabarU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76927"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76952"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:76981"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77014"}},{"Add":{"text":" LambdabarU[i] += gammabarUU[j][k] * (GammabarUDD[i][j][k] - rfm.GammahatUDD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77116"}},{"Add":{"text":" lambdaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77149"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77174"}},{"Add":{"text":" lambdaU[i] = LambdabarU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77222"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77223"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77224"}},{"Add":{"text":"# Step 2.d: Set the conformal factor variable cf, which is set","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77287"}},{"Add":{"text":"# by the \"BSSN_quantities::EvolvedConformalFactor_cf\" parameter. For example if","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77377"}},{"Add":{"text":"# \"EvolvedConformalFactor_cf\" is set to \"phi\", we can use Eq. 3 of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77454"}},{"Add":{"text":"# [Ruchlin *et al.*](https://arxiv.org/pdf/1712.07658.pdf),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77524"}},{"Add":{"text":"# which in arbitrary coordinates is written:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77579"}},{"Add":{"text":"def cf_from_gammaDD(gammaDD):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77609"}},{"Add":{"text":" global cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77623"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77624"}},{"Add":{"text":" if gammaDD == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77648"}},{"Add":{"text":" gammaDD = ixp.declarerank2(\"gammaDD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77702"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77703"}},{"Add":{"text":" # \\bar{Lambda}^i = \\bar{gamma}^{jk}(\\bar{Gamma}^i_{jk} - \\hat{Gamma}^i_{jk}).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77785"}},{"Add":{"text":" gammabarDD_hDD(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77813"}},{"Add":{"text":" gammabarUU, gammabarDET = ixp.symm_matrix_inverter3x3(gammabarDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77883"}},{"Add":{"text":" gammaUU, gammaDET = ixp.symm_matrix_inverter3x3(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77950"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77951"}},{"Add":{"text":" cf = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77974"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:77975"}},{"Add":{"text":" if par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"phi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78041"}},{"Add":{"text":" # phi = \\frac{1}{12} log(\\frac{gamma}{\\bar{gamma}}).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78102"}},{"Add":{"text":" cf = sp.Rational(1, 12) * sp.log(gammaDET / gammabarDET)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78167"}},{"Add":{"text":" elif par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"chi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78235"}},{"Add":{"text":" # chi = exp(-4*phi) = exp(-4*\\frac{1}{12}*(\\frac{gamma}{\\bar{gamma}}))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78314"}},{"Add":{"text":" # = exp(-\\frac{1}{3}*log(\\frac{gamma}{\\bar{gamma}})) = (\\frac{gamma}{\\bar{gamma}})^{-1/3}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78418"}},{"Add":{"text":" #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78428"}},{"Add":{"text":" cf = (gammaDET / gammabarDET) ** (-sp.Rational(1, 3))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78490"}},{"Add":{"text":" elif par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"W\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78556"}},{"Add":{"text":" # W = exp(-2*phi) = exp(-2*\\frac{1}{12}*log(\\frac{gamma}{\\bar{gamma}}))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78636"}},{"Add":{"text":" # = exp(-\\frac{1}{6}*log(\\frac{gamma}{\\bar{gamma}})) = (\\frac{gamma}{bar{gamma}})^{-1/6}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78736"}},{"Add":{"text":" cf = (gammaDET / gammabarDET) ** (-sp.Rational(1, 6))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78798"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78808"}},{"Add":{"text":" print(\"Error EvolvedConformalFactor_cf type = \\\"\" + par.parval_from_str(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78889"}},{"Add":{"text":" \"EvolvedConformalFactor_cf\") + \"\\\" unknown.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78947"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78967"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:78968"}},{"Add":{"text":"# Step 2.e: Rescale beta^i and B^i according to the prescription described in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79046"}},{"Add":{"text":"# the [BSSN in curvilinear coordinates tutorial module](Tutorial-BSSNCurvilinear.ipynb)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79142"}},{"Add":{"text":"# (also [Ruchlin *et al.*](https://arxiv.org/pdf/1712.07658.pdf)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79217"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79219"}},{"Add":{"text":"# \\mathcal{V}^i &= beta^i/(ReU[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79254"}},{"Add":{"text":"# \\mathcal{B}^i &= B^i/(ReU[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79286"}},{"Add":{"text":"def betU_vetU(betaU,BU):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79311"}},{"Add":{"text":" global vetU,betU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79332"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79333"}},{"Add":{"text":" if betaU == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79355"}},{"Add":{"text":" betaU = ixp.declarerank1(\"betaU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79397"}},{"Add":{"text":" if BU == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79416"}},{"Add":{"text":" BU = ixp.declarerank1(\"BU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79452"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79453"}},{"Add":{"text":" if rfm.have_already_called_reference_metric_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79520"}},{"Add":{"text":" print(\"BSSN.BSSN_in_terms_of_ADM.bet_vet(): Must call reference_metric() first!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79610"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79630"}},{"Add":{"text":" vetU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79660"}},{"Add":{"text":" betU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79690"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79715"}},{"Add":{"text":" vetU[i] = betaU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79763"}},{"Add":{"text":" betU[i] = BU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79811"}}]}},{"FileAdd":{"meta":{"basename":"BSSN_quantities.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BSSN_quantities.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module provides functions that declare and define useful BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79914"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79915"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79946"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79989"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:79990"}},{"Add":{"text":"# Step 1: Import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80038"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80101"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80205"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80315"}},{"Add":{"text":"import grid as gri # NRPy+: Functions having to do with numerical grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80402"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80470"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80567"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80568"}},{"Add":{"text":"# Step 1.a: Set the coordinate system for the numerical grid","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80629"}},{"Add":{"text":"# DO NOT SET IN STANDALONE PYTHON MODULE","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80671"}},{"Add":{"text":"# par.set_parval_from_str(\"reference_metric::CoordSystem\",\"Spherical\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80742"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80743"}},{"Add":{"text":"# Step 1.b: Given the chosen coordinate system, set up ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80799"}},{"Add":{"text":"# corresponding reference metric and needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80853"}},{"Add":{"text":"# reference metric quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80893"}},{"Add":{"text":"# The following function call sets up the reference metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:80952"}},{"Add":{"text":"# and related quantities, including rescaling matrices ReDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81016"}},{"Add":{"text":"# ReU, and hatted quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81049"}},{"Add":{"text":"# DO NOT CALL IN STANDALONE PYTHON MODULE","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81092"}},{"Add":{"text":"# rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81117"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81118"}},{"Add":{"text":"# Step 1.c: Set spatial dimension (must be 3 for BSSN, as BSSN is ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81185"}},{"Add":{"text":"# a 3+1-dimensional decomposition of the general ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81245"}},{"Add":{"text":"# relativistic field equations)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81287"}},{"Add":{"text":"# DO NOT CALL IN STANDALONE PYTHON MODULE","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81330"}},{"Add":{"text":"# DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81340"}},{"Add":{"text":"# par.set_parval_from_str(\"grid::DIM\",DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81383"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81384"}},{"Add":{"text":"# Step 1.d: Declare/initialize parameters for this module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81442"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81464"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"EvolvedConformalFactor_cf\", \"W\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81554"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"bool\", thismodule, \"detgbarOverdetghat_equals_one\", \"True\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81651"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"bool\", thismodule, \"LeaveRicciSymbolic\", \"False\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81738"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81739"}},{"Add":{"text":"def declare_BSSN_gridfunctions_if_not_declared_already():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81797"}},{"Add":{"text":" # Step 2: Register all needed BSSN gridfunctions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81851"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81852"}},{"Add":{"text":" # Declare as globals all variables that may be","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81903"}},{"Add":{"text":" # used outside this function","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81936"}},{"Add":{"text":" global hDD,aDD,lambdaU,vetU,betU,trK,cf,alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81986"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:81987"}},{"Add":{"text":" # Check to see if this function has already been called.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82050"}},{"Add":{"text":" # If so, do not register the gridfunctions again!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82106"}},{"Add":{"text":" for i in range(len(gri.glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82153"}},{"Add":{"text":" if \"hDD00\" in gri.glb_gridfcs_list[i].name:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82205"}},{"Add":{"text":" hDD = ixp.declarerank2(\"hDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82256"}},{"Add":{"text":" aDD = ixp.declarerank2(\"aDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82307"}},{"Add":{"text":" lambdaU = ixp.declarerank1(\"lambdaU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82357"}},{"Add":{"text":" vetU = ixp.declarerank1(\"vetU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82401"}},{"Add":{"text":" betU = ixp.declarerank1(\"betU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82445"}},{"Add":{"text":" trK, cf, alpha = sp.symbols('trK cf alpha', real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82512"}},{"Add":{"text":" return hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82577"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82578"}},{"Add":{"text":" # Step 2.a: Register indexed quantities, using ixp.register_... functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82656"}},{"Add":{"text":" hDD = ixp.register_gridfunctions_for_single_rank2(\"EVOL\", \"hDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82734"}},{"Add":{"text":" aDD = ixp.register_gridfunctions_for_single_rank2(\"EVOL\", \"aDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82812"}},{"Add":{"text":" lambdaU = ixp.register_gridfunctions_for_single_rank1(\"EVOL\", \"lambdaU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82889"}},{"Add":{"text":" vetU = ixp.register_gridfunctions_for_single_rank1(\"EVOL\", \"vetU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:82960"}},{"Add":{"text":" betU = ixp.register_gridfunctions_for_single_rank1(\"EVOL\", \"betU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83031"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83032"}},{"Add":{"text":" # Step 2.b: Register scalar quantities, using gri.register_gridfunctions()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83111"}},{"Add":{"text":" trK, cf, alpha = gri.register_gridfunctions(\"EVOL\", [\"trK\", \"cf\", \"alpha\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83191"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83192"}},{"Add":{"text":" return hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83249"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83250"}},{"Add":{"text":"# Step 3: Define all basic conformal BSSN tensors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83300"}},{"Add":{"text":"# gammabarDD,AbarDD,LambdabarU,betaU,BU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83347"}},{"Add":{"text":"# in terms of BSSN gridfunctions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83388"}},{"Add":{"text":"def BSSN_basic_tensors():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83414"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83415"}},{"Add":{"text":" # Step 3.a: Declare as globals all variables that may be used","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83481"}},{"Add":{"text":" # outside this function, declare BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83547"}},{"Add":{"text":" # if not defined already, and set DIM=3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83602"}},{"Add":{"text":" global gammabarDD,AbarDD,LambdabarU,betaU,BU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83651"}},{"Add":{"text":" hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha = declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83756"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83768"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83769"}},{"Add":{"text":" # Step 3.a.i: gammabarDD and AbarDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83810"}},{"Add":{"text":" gammabarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83843"}},{"Add":{"text":" AbarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83872"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83897"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83926"}},{"Add":{"text":" # gammabar_{ij} = h_{ij}*ReDD[i][j] + gammahat_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:83991"}},{"Add":{"text":" gammabarDD[i][j] = hDD[i][j] * rfm.ReDD[i][j] + rfm.ghatDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84068"}},{"Add":{"text":" # Abar_{ij} = a_{ij}*ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84117"}},{"Add":{"text":" AbarDD[i][j] = aDD[i][j] * rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84171"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84172"}},{"Add":{"text":" # Step 3.a.ii: LambdabarU, betaU, and BU:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84218"}},{"Add":{"text":" LambdabarU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84251"}},{"Add":{"text":" betaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84279"}},{"Add":{"text":" BU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84304"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84329"}},{"Add":{"text":" LambdabarU[i] = lambdaU[i] * rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84377"}},{"Add":{"text":" betaU[i] = vetU[i] * rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84417"}},{"Add":{"text":" BU[i] = betU[i] * rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84454"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84455"}},{"Add":{"text":"# Step 4: gammabarUU and spatial derivatives of gammabarDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84515"}},{"Add":{"text":"# including GammabarUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84547"}},{"Add":{"text":"def gammabar__inverse_and_derivs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84583"}},{"Add":{"text":" # Step 4.a: Declare as globals all expressions that may be used","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84651"}},{"Add":{"text":" # outside this function, declare BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84717"}},{"Add":{"text":" # if not defined already, and set DIM=3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84772"}},{"Add":{"text":" global gammabarUU, gammabarDD_dD, gammabarDD_dupD, gammabarDD_dDD, GammabarUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84855"}},{"Add":{"text":" hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha = declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84960"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:84972"}},{"Add":{"text":" # This function needs gammabarDD, defined in BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85042"}},{"Add":{"text":" BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85067"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85068"}},{"Add":{"text":" # Step 4.a.i: gammabarUU:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85098"}},{"Add":{"text":" gammabarUU, dummydet = ixp.symm_matrix_inverter3x3(gammabarDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85165"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85166"}},{"Add":{"text":" # Step 4.b.i: gammabarDDdD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85206"}},{"Add":{"text":" # = \\hat{\\gamma}_{ij,k} + h_{ij,k} \\text{ReDD[i][j]} + h_{ij} \\text{ReDDdD[i][j][k]}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85310"}},{"Add":{"text":" gammabarDD_dD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85346"}},{"Add":{"text":" gammabarDD_dupD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85384"}},{"Add":{"text":" hDD_dD = ixp.declarerank3(\"hDD_dD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85433"}},{"Add":{"text":" hDD_dupD = ixp.declarerank3(\"hDD_dupD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85486"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85511"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85540"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85573"}},{"Add":{"text":" gammabarDD_dD[i][j][k] = rfm.ghatDDdD[i][j][k] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85640"}},{"Add":{"text":" hDD_dD[i][j][k] * rfm.ReDD[i][j] + hDD[i][j] * rfm.ReDDdD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85748"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85749"}},{"Add":{"text":" # Compute associated upwinded derivative, needed for the \\bar{\\gamma}_{ij} RHS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85844"}},{"Add":{"text":" gammabarDD_dupD[i][j][k] = rfm.ghatDDdD[i][j][k] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:85913"}},{"Add":{"text":" hDD_dupD[i][j][k] * rfm.ReDD[i][j] + hDD[i][j] * rfm.ReDDdD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86025"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86026"}},{"Add":{"text":" # Step 4.b.ii: Compute gammabarDD_dDD in terms of the rescaled BSSN quantity hDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86111"}},{"Add":{"text":" # and its derivatives, as well as the reference metric and rescaling","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86189"}},{"Add":{"text":" # matrix, and its derivatives (expression given below):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86254"}},{"Add":{"text":" hDD_dDD = ixp.declarerank4(\"hDD_dDD\", \"sym01_sym23\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86311"}},{"Add":{"text":" gammabarDD_dDD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86348"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86373"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86402"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86435"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86472"}},{"Add":{"text":" # gammabar_{ij,kl} = gammahat_{ij,kl}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86530"}},{"Add":{"text":" # + h_{ij,kl} ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86592"}},{"Add":{"text":" # + h_{ij,k} ReDDdD[i][j][l] + h_{ij,l} ReDDdD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86685"}},{"Add":{"text":" # + h_{ij} ReDDdDD[i][j][k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86753"}},{"Add":{"text":" gammabarDD_dDD[i][j][k][l] = rfm.ghatDDdDD[i][j][k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86828"}},{"Add":{"text":" gammabarDD_dDD[i][j][k][l] += hDD_dDD[i][j][k][l] * rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:86915"}},{"Add":{"text":" gammabarDD_dDD[i][j][k][l] += hDD_dD[i][j][k] * rfm.ReDDdD[i][j][l] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87007"}},{"Add":{"text":" hDD_dD[i][j][l] * rfm.ReDDdD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87095"}},{"Add":{"text":" gammabarDD_dDD[i][j][k][l] += hDD[i][j] * rfm.ReDDdDD[i][j][k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87181"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87182"}},{"Add":{"text":" # Step 4.b.iii: Define barred Christoffel symbol \\bar{\\Gamma}^{i}_{kl} = GammabarUDD[i][k][l] (see expression below)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87303"}},{"Add":{"text":" GammabarUDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87337"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87362"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87391"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87424"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87461"}},{"Add":{"text":" # Gammabar^i_{kl} = 1/2 * gammabar^{im} ( gammabar_{mk,l} + gammabar_{ml,k} - gammabar_{kl,m}):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87577"}},{"Add":{"text":" GammabarUDD[i][k][l] += sp.Rational(1, 2) * gammabarUU[i][m] * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87662"}},{"Add":{"text":" (gammabarDD_dD[m][k][l] + gammabarDD_dD[m][l][k] - gammabarDD_dD[k][l][m])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87781"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87782"}},{"Add":{"text":"# Step 5: det(gammabarDD) and its derivatives","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87828"}},{"Add":{"text":"def detgammabar_and_derivs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87858"}},{"Add":{"text":" # Step 5.a: Declare as globals all expressions that may be used","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87926"}},{"Add":{"text":" # outside this function, declare BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:87992"}},{"Add":{"text":" # if not defined already, and set DIM=3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88047"}},{"Add":{"text":" global detgammabar,detgammabar_dD,detgammabar_dDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88101"}},{"Add":{"text":" hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha = declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88206"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88218"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88219"}},{"Add":{"text":" detgbarOverdetghat = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88258"}},{"Add":{"text":" detgbarOverdetghat_dD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88302"}},{"Add":{"text":" detgbarOverdetghat_dDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88347"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88348"}},{"Add":{"text":" if par.parval_from_str(thismodule + \"::detgbarOverdetghat_equals_one\") == \"False\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88435"}},{"Add":{"text":" print(\"Error: detgbarOverdetghat_equals_one=\\\"False\\\" is not fully implemented yet.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88529"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88549"}},{"Add":{"text":" ## Approach for implementing detgbarOverdetghat_equals_one=False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88619"}},{"Add":{"text":" # detgbarOverdetghat = gri.register_gridfunctions(\"AUX\", [\"detgbarOverdetghat\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88708"}},{"Add":{"text":" # detgbarOverdetghatInitial = gri.register_gridfunctions(\"AUX\", [\"detgbarOverdetghatInitial\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88811"}},{"Add":{"text":" # detgbarOverdetghat_dD = ixp.declarerank1(\"detgbarOverdetghat_dD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88887"}},{"Add":{"text":" # detgbarOverdetghat_dDD = ixp.declarerank2(\"detgbarOverdetghat_dDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88974"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:88975"}},{"Add":{"text":" # Step 5.b: Define detgammabar, detgammabar_dD, and detgammabar_dDD (needed for \\partial_t \\bar{\\Lambda}^i below)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89093"}},{"Add":{"text":" detgammabar = detgbarOverdetghat * rfm.detgammahat","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89148"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89149"}},{"Add":{"text":" detgammabar_dD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89186"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89211"}},{"Add":{"text":" detgammabar_dD[i] = detgbarOverdetghat_dD[i] * rfm.detgammahat + detgbarOverdetghat * rfm.detgammahatdD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89326"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89327"}},{"Add":{"text":" detgammabar_dDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89365"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89390"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89419"}},{"Add":{"text":" detgammabar_dDD[i][j] = detgbarOverdetghat_dDD[i][j] * rfm.detgammahat + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89506"}},{"Add":{"text":" detgbarOverdetghat_dD[i] * rfm.detgammahatdD[j] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89594"}},{"Add":{"text":" detgbarOverdetghat_dD[j] * rfm.detgammahatdD[i] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89682"}},{"Add":{"text":" detgbarOverdetghat * rfm.detgammahatdDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89764"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89765"}},{"Add":{"text":"# Step 6: Quantities related to conformal traceless","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89817"}},{"Add":{"text":"# extrinsic curvature AbarDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89855"}},{"Add":{"text":"# AbarUU, AbarUD, and trAbar","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89892"}},{"Add":{"text":"def AbarUU_AbarUD_trAbar_AbarDD_dD():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89930"}},{"Add":{"text":" # Step 6.a: Declare as globals all expressions that may be used","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:89998"}},{"Add":{"text":" # outside this function, declare BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90064"}},{"Add":{"text":" # if not defined already, and set DIM=3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90119"}},{"Add":{"text":" global AbarUU,AbarUD,trAbar,AbarDD_dD,AbarDD_dupD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90173"}},{"Add":{"text":" hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha = declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90278"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90290"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90291"}},{"Add":{"text":" # Define AbarDD and gammabarDD in terms of BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90357"}},{"Add":{"text":" BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90382"}},{"Add":{"text":" # Define gammabarUU in terms of BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90437"}},{"Add":{"text":" gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90472"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90473"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90474"}},{"Add":{"text":" # Step 6.a.i: Compute Abar^{ij} in terms of Abar_{ij} and gammabar^{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90550"}},{"Add":{"text":" AbarUU = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90579"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90604"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90633"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90666"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90703"}},{"Add":{"text":" # Abar^{ij} = gammabar^{ik} gammabar^{jl} Abar_{kl}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90775"}},{"Add":{"text":" AbarUU[i][j] += gammabarUU[i][k] * gammabarUU[j][l] * AbarDD[k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90862"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90863"}},{"Add":{"text":" # Step 6.a.ii: Compute Abar^i_j in terms of Abar_{ij} and gammabar^{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90939"}},{"Add":{"text":" AbarUD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90968"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:90993"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91022"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91055"}},{"Add":{"text":" # Abar^i_j = gammabar^{ik} Abar_{kj}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91108"}},{"Add":{"text":" AbarUD[i][j] += gammabarUU[i][k] * AbarDD[k][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91172"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91173"}},{"Add":{"text":" # Step 6.a.iii: Compute Abar^k_k = trace of Abar:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91227"}},{"Add":{"text":" trAbar = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91254"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91279"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91308"}},{"Add":{"text":" # Abar^k_k = gammabar^{kj} Abar_{jk}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91357"}},{"Add":{"text":" trAbar += gammabarUU[k][j] * AbarDD[j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91411"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91424"}},{"Add":{"text":" # Step 6.a.iv: Compute Abar_{ij,k}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91463"}},{"Add":{"text":" AbarDD_dD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91495"}},{"Add":{"text":" AbarDD_dupD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91529"}},{"Add":{"text":" aDD_dD = ixp.declarerank3(\"aDD_dD\" ,\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91581"}},{"Add":{"text":" aDD_dupD = ixp.declarerank3(\"aDD_dupD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91633"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91658"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91687"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91720"}},{"Add":{"text":" AbarDD_dupD[i][j][k] = rfm.ReDDdD[i][j][k]*aDD[i][j] + rfm.ReDD[i][j]*aDD_dupD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91824"}},{"Add":{"text":" AbarDD_dD[i][j][k] = rfm.ReDDdD[i][j][k]*aDD[i][j] + rfm.ReDD[i][j]*aDD_dD[ i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91928"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91929"}},{"Add":{"text":"# Step 7: The conformal (\"barred\") Ricci tensor RbarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:91984"}},{"Add":{"text":"# and associated quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92020"}},{"Add":{"text":"def RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92074"}},{"Add":{"text":" # Step 7.a: Declare as globals all expressions that may be used","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92142"}},{"Add":{"text":" # outside this function, declare BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92208"}},{"Add":{"text":" # if not defined already, and set DIM=3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92263"}},{"Add":{"text":" global RbarDD,DGammaUDD,gammabarDD_dHatD,DGammaU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92316"}},{"Add":{"text":" hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha = declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92421"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92433"}},{"Add":{"text":" # GammabarUDD is used below, defined in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92477"}},{"Add":{"text":" # gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92517"}},{"Add":{"text":" gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92552"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92553"}},{"Add":{"text":" # Step 7.a.i: Define \\varepsilon_{ij} = epsDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92609"}},{"Add":{"text":" epsDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92637"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92662"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92691"}},{"Add":{"text":" epsDD[i][j] = hDD[i][j] * rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92744"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92745"}},{"Add":{"text":" # Step 7.a.ii: Define epsDD_dD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92789"}},{"Add":{"text":" hDD_dD = ixp.declarerank3(\"hDD_dD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92838"}},{"Add":{"text":" epsDD_dD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92869"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92894"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92923"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:92956"}},{"Add":{"text":" epsDD_dD[i][j][k] = hDD_dD[i][j][k] * rfm.ReDD[i][j] + hDD[i][j] * rfm.ReDDdD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93059"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93060"}},{"Add":{"text":" # Step 7.a.iii: Define epsDD_dDD[i][j][k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93109"}},{"Add":{"text":" hDD_dDD = ixp.declarerank4(\"hDD_dDD\", \"sym01_sym23\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93166"}},{"Add":{"text":" epsDD_dDD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93198"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93223"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93252"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93285"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93322"}},{"Add":{"text":" epsDD_dDD[i][j][k][l] = hDD_dDD[i][j][k][l] * rfm.ReDD[i][j] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93407"}},{"Add":{"text":" hDD_dD[i][j][k] * rfm.ReDDdD[i][j][l] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93493"}},{"Add":{"text":" hDD_dD[i][j][l] * rfm.ReDDdD[i][j][k] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93579"}},{"Add":{"text":" hDD[i][j] * rfm.ReDDdDD[i][j][k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93659"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93660"}},{"Add":{"text":" # Step 7.a.iv: DhatgammabarDDdD[i][j][l] = \\bar{\\gamma}_{ij;\\hat{l}}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93733"}},{"Add":{"text":" # \\bar{\\gamma}_{ij;\\hat{l}} = \\varepsilon_{i j,l}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93787"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{i l} \\varepsilon_{m j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93860"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{j l} \\varepsilon_{i m}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93933"}},{"Add":{"text":" gammabarDD_dHatD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93972"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:93997"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94026"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94059"}},{"Add":{"text":" gammabarDD_dHatD[i][j][l] = epsDD_dD[i][j][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94121"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94158"}},{"Add":{"text":" gammabarDD_dHatD[i][j][l] += - rfm.GammahatUDD[m][i][l] * epsDD[m][j] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94250"}},{"Add":{"text":" - rfm.GammahatUDD[m][j][l] * epsDD[i][m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94340"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94341"}},{"Add":{"text":" # Step 7.a.v: \\bar{\\gamma}_{ij;\\hat{l},k} = DhatgammabarDD_dHatD_dD[i][j][l][k]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94426"}},{"Add":{"text":" # \\bar{\\gamma}_{ij;\\hat{l},k} = \\varepsilon_{ij,lk}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94489"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{i l,k} \\varepsilon_{m j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94575"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{i l} \\varepsilon_{m j,k}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94661"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{j l,k} \\varepsilon_{i m}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94747"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{j l} \\varepsilon_{i m,k}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94833"}},{"Add":{"text":" gammabarDD_dHatD_dD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94875"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94900"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94929"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94962"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:94999"}},{"Add":{"text":" gammabarDD_dHatD_dD[i][j][l][k] = epsDD_dDD[i][j][l][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95075"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95116"}},{"Add":{"text":" gammabarDD_dHatD_dD[i][j][l][k] += -rfm.GammahatUDDdD[m][i][l][k] * epsDD[m][j] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95222"}},{"Add":{"text":" - rfm.GammahatUDD[m][i][l] * epsDD_dD[m][j][k] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95330"}},{"Add":{"text":" - rfm.GammahatUDDdD[m][j][l][k] * epsDD[i][m] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95437"}},{"Add":{"text":" - rfm.GammahatUDD[m][j][l] * epsDD_dD[i][m][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95543"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95544"}},{"Add":{"text":" # Step 7.a.vi: \\bar{\\gamma}_{ij;\\hat{l}\\hat{k}} = DhatgammabarDD_dHatDD[i][j][l][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95632"}},{"Add":{"text":" # \\bar{\\gamma}_{ij;\\hat{l}\\hat{k}} = \\partial_k \\hat{D}_{l} \\varepsilon_{i j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95723"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{lk} \\left(\\hat{D}_{m} \\varepsilon_{i j}\\right)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95836"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{ik} \\left(\\hat{D}_{l} \\varepsilon_{m j}\\right)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:95949"}},{"Add":{"text":" # - \\hat{\\Gamma}^m_{jk} \\left(\\hat{D}_{l} \\varepsilon_{i m}\\right)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96062"}},{"Add":{"text":" gammabarDD_dHatDD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96102"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96127"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96156"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96189"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96226"}},{"Add":{"text":" gammabarDD_dHatDD[i][j][l][k] = gammabarDD_dHatD_dD[i][j][l][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96310"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96351"}},{"Add":{"text":" gammabarDD_dHatDD[i][j][l][k] += - rfm.GammahatUDD[m][l][k] * gammabarDD_dHatD[i][j][m] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96465"}},{"Add":{"text":" - rfm.GammahatUDD[m][i][k] * gammabarDD_dHatD[m][j][l] \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96579"}},{"Add":{"text":" - rfm.GammahatUDD[m][j][k] * gammabarDD_dHatD[i][m][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96691"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96692"}},{"Add":{"text":" # Step 7.b: Second term of RhatDD: compute \\hat{D}_{j} \\bar{\\Lambda}^{k} = LambarU_dHatD[k][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96791"}},{"Add":{"text":" lambdaU_dD = ixp.declarerank2(\"lambdaU_dD\", \"nosym\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96848"}},{"Add":{"text":" LambarU_dHatD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96884"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96909"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:96938"}},{"Add":{"text":" LambarU_dHatD[k][j] = lambdaU_dD[k][j] * rfm.ReU[k] + lambdaU[k] * rfm.ReUdD[k][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97033"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97066"}},{"Add":{"text":" LambarU_dHatD[k][j] += rfm.GammahatUDD[k][m][j] * lambdaU[m] * rfm.ReU[m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97156"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97173"}},{"Add":{"text":" # Step 7.c: Conformal Ricci tensor, part 3: The \\Delta^{k} \\Delta_{(i j) k} ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97255"}},{"Add":{"text":" # + \\bar{\\gamma}^{k l}*(2 \\Delta_{k(i}^{m} \\Delta_{j) m l} ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97329"}},{"Add":{"text":" # + \\Delta_{i k}^{m} \\Delta_{m j l}) terms","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97386"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97387"}},{"Add":{"text":" # Step 7.c.i: Define \\Delta^i_{jk} = \\bar{\\Gamma}^i_{jk} - \\hat{\\Gamma}^i_{jk} = DGammaUDD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97491"}},{"Add":{"text":" DGammaUDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97523"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97548"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97577"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97610"}},{"Add":{"text":" DGammaUDD[i][j][k] = GammabarUDD[i][j][k] - rfm.GammahatUDD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97695"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97696"}},{"Add":{"text":" # Step 7.c.ii: Define \\Delta^i = \\bar{\\gamma}^{jk} \\Delta^i_{jk}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97765"}},{"Add":{"text":" DGammaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97795"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97820"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97849"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97882"}},{"Add":{"text":" DGammaU[i] += gammabarUU[j][k] * DGammaUDD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97950"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:97951"}},{"Add":{"text":" # Step 7.c.iii: Define \\Delta_{ijk} = \\bar{\\gamma}_{im} \\Delta^m_{jk}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98025"}},{"Add":{"text":" DGammaDDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98057"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98082"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98111"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98144"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98181"}},{"Add":{"text":" DGammaDDD[i][j][k] += gammabarDD[i][m] * DGammaUDD[m][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98261"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98262"}},{"Add":{"text":" if par.parval_from_str(thismodule+\"::LeaveRicciSymbolic\") == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98335"}},{"Add":{"text":" for i in range(len(gri.glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98386"}},{"Add":{"text":" if \"RbarDD00\" in gri.glb_gridfcs_list[i].name:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98445"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98468"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98469"}},{"Add":{"text":" RbarDD = ixp.register_gridfunctions_for_single_rank2(\"AUXEVOL\",\"RbarDD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98558"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98573"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98574"}},{"Add":{"text":" # Step 7.d: Summing the terms and defining \\bar{R}_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98634"}},{"Add":{"text":" # Step 7.d.i: Add the first term to RbarDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98682"}},{"Add":{"text":" # Rbar_{ij} += - \\frac{1}{2} \\bar{\\gamma}^{k l} \\hat{D}_{k} \\hat{D}_{l} \\bar{\\gamma}_{i j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98785"}},{"Add":{"text":" RbarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98814"}},{"Add":{"text":" RbarDDpiece = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98848"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98873"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98902"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98935"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:98972"}},{"Add":{"text":" RbarDD[i][j] += -sp.Rational(1, 2) * gammabarUU[k][l] * gammabarDD_dHatDD[i][j][l][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99078"}},{"Add":{"text":" RbarDDpiece[i][j] += -sp.Rational(1, 2) * gammabarUU[k][l] * gammabarDD_dHatDD[i][j][l][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99189"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99190"}},{"Add":{"text":" # Step 7.d.ii: Add the second term to RbarDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99240"}},{"Add":{"text":" # Rbar_{ij} += (1/2) * (gammabar_{ki} Lambar^k_{;\\hat{j}} + gammabar_{kj} Lambar^k_{;\\hat{i}})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99347"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99372"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99401"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99434"}},{"Add":{"text":" RbarDD[i][j] += sp.Rational(1, 2) * ( gammabarDD[k][i] * LambarU_dHatD[k][j] +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99529"}},{"Add":{"text":" gammabarDD[k][j] * LambarU_dHatD[k][i] )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99625"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99626"}},{"Add":{"text":" # Step 7.d.iii: Add the remaining term to RbarDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99680"}},{"Add":{"text":" # Rbar_{ij} += \\Delta^{k} \\Delta_{(i j) k} = 1/2 \\Delta^{k} (\\Delta_{i j k} + \\Delta_{j i k})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99783"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99808"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99837"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99870"}},{"Add":{"text":" RbarDD[i][j] += sp.Rational(1, 2) * DGammaU[k] * (DGammaDDD[i][j][k] + DGammaDDD[j][i][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99977"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:99978"}},{"Add":{"text":" # Step 7.d.iv: Add the final term to RbarDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100027"}},{"Add":{"text":" # Rbar_{ij} += \\bar{\\gamma}^{k l} (\\Delta^{m}_{k i} \\Delta_{j m l}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100103"}},{"Add":{"text":" # + \\Delta^{m}_{k j} \\Delta_{i m l}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100161"}},{"Add":{"text":" # + \\Delta^{m}_{i k} \\Delta_{m j l})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100220"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100245"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100274"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100307"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100344"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100385"}},{"Add":{"text":" RbarDD[i][j] += gammabarUU[k][l] * (DGammaUDD[m][k][i] * DGammaDDD[j][m][l] +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100487"}},{"Add":{"text":" DGammaUDD[m][k][j] * DGammaDDD[i][m][l] +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100589"}},{"Add":{"text":" DGammaUDD[m][i][k] * DGammaDDD[m][j][l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100690"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100691"}},{"Add":{"text":"# Step 8: The unrescaled shift vector betaU spatial derivatives:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100756"}},{"Add":{"text":"# betaUdD & betaUdDD, written in terms of the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100810"}},{"Add":{"text":"# rescaled shift vector vetU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100847"}},{"Add":{"text":"def betaU_derivs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100867"}},{"Add":{"text":" # Step 8.i: Declare as globals all expressions that may be used","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:100935"}},{"Add":{"text":" # outside this function, declare BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101001"}},{"Add":{"text":" # if not defined already, and set DIM=3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101056"}},{"Add":{"text":" global betaU_dD,betaU_dupD,betaU_dDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101097"}},{"Add":{"text":" hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha = declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101202"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101214"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101215"}},{"Add":{"text":" # Step 8.ii: Compute the unrescaled shift vector beta^i = ReU[i]*vet^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101290"}},{"Add":{"text":" vetU_dD = ixp.declarerank2(\"vetU_dD\", \"nosym\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101341"}},{"Add":{"text":" vetU_dupD = ixp.declarerank2(\"vetU_dupD\", \"nosym\") # Needed for upwinded \\beta^i_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101432"}},{"Add":{"text":" vetU_dDD = ixp.declarerank3(\"vetU_dDD\", \"sym12\") # Needed for \\beta^i_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101512"}},{"Add":{"text":" betaU_dD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101543"}},{"Add":{"text":" betaU_dupD = ixp.zerorank2() # Needed for, e.g., \\beta^i RHS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101609"}},{"Add":{"text":" betaU_dDD = ixp.zerorank3() # Needed for, e.g., \\bar{\\Lambda}^i RHS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101682"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101707"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101736"}},{"Add":{"text":" betaU_dD[i][j] = vetU_dD[i][j] * rfm.ReU[i] + vetU[i] * rfm.ReUdD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101820"}},{"Add":{"text":" betaU_dupD[i][j] = vetU_dupD[i][j] * rfm.ReU[i] + vetU[i] * rfm.ReUdD[i][j] # Needed for \\beta^i RHS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101934"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:101967"}},{"Add":{"text":" # Needed for, e.g., \\bar{\\Lambda}^i RHS:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102024"}},{"Add":{"text":" betaU_dDD[i][j][k] = vetU_dDD[i][j][k] * rfm.ReU[i] + vetU_dD[i][j] * rfm.ReUdD[i][k] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102130"}},{"Add":{"text":" vetU_dD[i][k] * rfm.ReUdD[i][j] + vetU[i] * rfm.ReUdDD[i][j][k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102231"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102232"}},{"Add":{"text":"# Step 9: Standard BSSN conformal factor phi,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102278"}},{"Add":{"text":"# and its partial and covariant derivatives,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102331"}},{"Add":{"text":"# all in terms of BSSN gridfunctions like cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102384"}},{"Add":{"text":"def phi_and_derivs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102406"}},{"Add":{"text":" # Step 9.a: Declare as globals all expressions that may be used","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102474"}},{"Add":{"text":" # outside this function, declare BSSN gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102540"}},{"Add":{"text":" # if not defined already, and set DIM=3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102595"}},{"Add":{"text":" global phi_dD,phi_dupD,phi_dDD,exp_m4phi,phi_dBarD,phi_dBarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102661"}},{"Add":{"text":" hDD, aDD, lambdaU, vetU, betU, trK, cf, alpha = declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102766"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102778"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102779"}},{"Add":{"text":" # GammabarUDD is used below, defined in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102823"}},{"Add":{"text":" # gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102863"}},{"Add":{"text":" gammabar__inverse_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102898"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102899"}},{"Add":{"text":" # Step 9.a.i: Define partial derivatives of \\phi in terms of evolved quantity \"cf\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:102987"}},{"Add":{"text":" cf_dD = ixp.declarerank1(\"cf_dD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103025"}},{"Add":{"text":" cf_dupD = ixp.declarerank1(\"cf_dupD\") # Needed for \\partial_t \\phi next.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103103"}},{"Add":{"text":" cf_dDD = ixp.declarerank2(\"cf_dDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103152"}},{"Add":{"text":" phi_dD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103181"}},{"Add":{"text":" phi_dupD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103212"}},{"Add":{"text":" phi_dDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103242"}},{"Add":{"text":" exp_m4phi = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103272"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103273"}},{"Add":{"text":" # Step 9.a.ii: Assuming cf=phi, define exp_m4phi, phi_dD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103335"}},{"Add":{"text":" # phi_dupD (upwind finite-difference version of phi_dD), and phi_DD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103420"}},{"Add":{"text":" if par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") == \"phi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103508"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103537"}},{"Add":{"text":" phi_dD[i] = cf_dD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103570"}},{"Add":{"text":" phi_dupD[i] = cf_dupD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103607"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103640"}},{"Add":{"text":" phi_dDD[i][j] = cf_dDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103685"}},{"Add":{"text":" exp_m4phi = sp.exp(-4 * cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103721"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103722"}},{"Add":{"text":" # Step 9.a.iii: Assuming cf=W=e^{-2 phi}, define exp_m4phi, phi_dD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103794"}},{"Add":{"text":" # phi_dupD (upwind finite-difference version of phi_dD), and phi_DD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103880"}},{"Add":{"text":" if par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") == \"W\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:103966"}},{"Add":{"text":" # \\partial_i W = \\partial_i (e^{-2 phi}) = -2 e^{-2 phi} \\partial_i phi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104046"}},{"Add":{"text":" # -> \\partial_i phi = -\\partial_i cf / (2 cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104100"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104129"}},{"Add":{"text":" phi_dD[i] = - cf_dD[i] / (2 * cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104175"}},{"Add":{"text":" phi_dupD[i] = - cf_dupD[i] / (2 * cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104225"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104258"}},{"Add":{"text":" # \\partial_j \\partial_i phi = - \\partial_j [\\partial_i cf / (2 cf)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104342"}},{"Add":{"text":" # = - cf_{,ij} / (2 cf) + \\partial_i cf \\partial_j cf / (2 cf^2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104449"}},{"Add":{"text":" phi_dDD[i][j] = (- cf_dDD[i][j] + cf_dD[i] * cf_dD[j] / cf) / (2 * cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104536"}},{"Add":{"text":" exp_m4phi = cf * cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104564"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104565"}},{"Add":{"text":" # Step 9.a.iv: Assuming cf=chi=e^{-4 phi}, define exp_m4phi, phi_dD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104638"}},{"Add":{"text":" # phi_dupD (upwind finite-difference version of phi_dD), and phi_DD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104723"}},{"Add":{"text":" if par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") == \"chi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104811"}},{"Add":{"text":" # \\partial_i chi = \\partial_i (e^{-4 phi}) = -4 e^{-4 phi} \\partial_i phi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104893"}},{"Add":{"text":" # -> \\partial_i phi = -\\partial_i cf / (4 cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104947"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:104976"}},{"Add":{"text":" phi_dD[i] = - cf_dD[i] / (4 * cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105022"}},{"Add":{"text":" phi_dupD[i] = - cf_dupD[i] / (4 * cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105072"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105105"}},{"Add":{"text":" # \\partial_j \\partial_i phi = - \\partial_j [\\partial_i cf / (4 cf)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105189"}},{"Add":{"text":" # = - cf_{,ij} / (4 cf) + \\partial_i cf \\partial_j cf / (4 cf^2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105296"}},{"Add":{"text":" phi_dDD[i][j] = (- cf_dDD[i][j] + cf_dD[i] * cf_dD[j] / cf) / (4 * cf)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105383"}},{"Add":{"text":" exp_m4phi = cf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105406"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105407"}},{"Add":{"text":" # Step 9.a.v: Error out if unsupported EvolvedConformalFactor_cf choice is made:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105492"}},{"Add":{"text":" cf_choice = par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105579"}},{"Add":{"text":" if not (cf_choice == \"phi\" or cf_choice == \"W\" or cf_choice == \"chi\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105654"}},{"Add":{"text":" print(\"Error: EvolvedConformalFactor_cf == \" + par.parval_from_str(\"BSSN.BSSN_quantities::EvolvedConformalFactor_cf\") + \" unsupported!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105799"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105819"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105820"}},{"Add":{"text":" # Step 9.b: Define phi_dBarD = phi_dD (since phi is a scalar) and phi_dBarDD (covariant derivative)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:105924"}},{"Add":{"text":" # \\bar{D}_i \\bar{D}_j \\phi = \\phi_{;\\bar{i}\\bar{j}} = \\bar{D}_i \\phi_{,j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106011"}},{"Add":{"text":" # = \\phi_{,ij} - \\bar{\\Gamma}^k_{ij} \\phi_{,k}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106096"}},{"Add":{"text":" phi_dBarD = phi_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106119"}},{"Add":{"text":" phi_dBarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106152"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106177"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106206"}},{"Add":{"text":" phi_dBarDD[i][j] = phi_dDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106251"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106284"}},{"Add":{"text":" phi_dBarDD[i][j] += - GammabarUDD[k][i][j] * phi_dD[k]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106355"}}]}},{"FileAdd":{"meta":{"basename":"BSSN_stress_energy_source_terms.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BSSN_stress_energy_source_terms.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106439"}},{"Add":{"text":"# Tutorial-BSSN_stress_energy_source_terms.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106491"}},{"Add":{"text":"# this module will construct expressions for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106538"}},{"Add":{"text":"# BSSN stress-energy source terms, in terms of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106587"}},{"Add":{"text":"# elements of T^{mu nu}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106614"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106615"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106646"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106689"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106690"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106803"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106875"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:106994"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107071"}},{"Add":{"text":"import BSSN.ADMBSSN_tofrom_4metric as AB4m # NRPy+: ADM/BSSN <-> 4-metric conversions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107157"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107263"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107264"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107286"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107287"}},{"Add":{"text":"# Define BSSN source terms in terms of T^{mu nu} or T_{mu nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107349"}},{"Add":{"text":"def stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(inputvars,custom_T4UU=None):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107445"}},{"Add":{"text":" # Step 1: Check if rfm.reference_metric() already called. If not, BSSN","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107520"}},{"Add":{"text":" # quantities are not yet defined, so cannot proceed!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107585"}},{"Add":{"text":" if rfm.have_already_called_reference_metric_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107652"}},{"Add":{"text":" print(\"BSSN_source_terms_ito_T4UU(): Must call reference_metric() first!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107735"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107755"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107756"}},{"Add":{"text":" # Step 2.a: Define gamma4DD[mu][nu] = g_{mu nu} + n_{mu} n_{nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107824"}},{"Add":{"text":" alpha = sp.symbols(\"alpha\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107867"}},{"Add":{"text":" zero = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107892"}},{"Add":{"text":" n4D = [-alpha, zero, zero, zero]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107929"}},{"Add":{"text":" AB4m.g4DD_ito_BSSN_or_ADM(inputvars)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107970"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:107971"}},{"Add":{"text":" gamma4DD = ixp.zerorank2(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108007"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108031"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108059"}},{"Add":{"text":" gamma4DD[mu][nu] = AB4m.g4DD[mu][nu] + n4D[mu] * n4D[nu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108128"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108129"}},{"Add":{"text":" # Step 2.b: If expression for components of T4UU not given, declare T4UU here","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108211"}},{"Add":{"text":" if custom_T4UU == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108239"}},{"Add":{"text":" T4UU = ixp.declarerank2(\"T4UU\",\"sym01\",DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108293"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108303"}},{"Add":{"text":" T4UU = custom_T4UU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108330"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108331"}},{"Add":{"text":" # Step 2.c: Define BSSN source terms","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108372"}},{"Add":{"text":" global SDD,SD,S,rho","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108396"}},{"Add":{"text":" # Step 2.c.i: S_{ij} = gamma_{i mu} gamma_{j nu} T^{mu nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108459"}},{"Add":{"text":" SDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108485"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108508"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108535"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108567"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108603"}},{"Add":{"text":" SDD[i][j] += gamma4DD[i+1][mu] * gamma4DD[j+1][nu] * T4UU[mu][nu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108689"}},{"Add":{"text":" # Step 2.c.ii: S_{i} = -gamma_{i mu} n_{nu} T^{mu nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108747"}},{"Add":{"text":" SD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108772"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108795"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108823"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108855"}},{"Add":{"text":" SD[i] += - gamma4DD[i+1][mu] * n4D[nu] * T4UU[mu][nu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108925"}},{"Add":{"text":" # Step 2.c.iii: S = gamma^{ij} S_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108967"}},{"Add":{"text":" if inputvars == \"ADM\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:108994"}},{"Add":{"text":" gammaDD = ixp.declarerank2(\"gammaDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109049"}},{"Add":{"text":" gammaUU, dummydet = ixp.symm_matrix_inverter3x3(gammaDD) # Set gammaUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109129"}},{"Add":{"text":" elif inputvars == \"BSSN\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109159"}},{"Add":{"text":" import BSSN.ADM_in_terms_of_BSSN as AitoB # NRPy+: ADM quantities in terms of BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109262"}},{"Add":{"text":" AitoB.ADM_in_terms_of_BSSN()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109299"}},{"Add":{"text":" gammaUU = AitoB.gammaUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109331"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109332"}},{"Add":{"text":" S = zero","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109345"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109368"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109395"}},{"Add":{"text":" S += gammaUU[i][j] * SDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109438"}},{"Add":{"text":" # Step 2.c.iv: rho = n_{mu} n_{nu} T^{mu nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109487"}},{"Add":{"text":" rho = zero","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109502"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109526"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109554"}},{"Add":{"text":" rho += n4D[mu] * n4D[nu] * T4UU[mu][nu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109606"}},{"Add":{"text":" return SDD,SD,S,rho","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109630"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109631"}},{"Add":{"text":"# Step 3: Add BSSN stress-energy source terms to BSSN RHSs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109690"}},{"Add":{"text":"def BSSN_source_terms_for_BSSN_RHSs(custom_T4UU=None):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109745"}},{"Add":{"text":" global sourceterm_trK_rhs, sourceterm_a_rhsDD, sourceterm_lambda_rhsU, sourceterm_Lambdabar_rhsU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109846"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109847"}},{"Add":{"text":" # Step 3.a: Call BSSN_source_terms_ito_T4UU to get SDD, SD, S, & rho","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109920"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109921"}},{"Add":{"text":" if custom_T4UU == \"unrescaled BSSN source terms already given\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:109989"}},{"Add":{"text":" SDD = ixp.declarerank2(\"SDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110036"}},{"Add":{"text":" SD = ixp.declarerank1(\"SD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110072"}},{"Add":{"text":" S = sp.symbols(\"S\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110111"}},{"Add":{"text":" rho = sp.symbols(\"rho\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110154"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110164"}},{"Add":{"text":" SDD,SD,S,rho = stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(\"BSSN\", custom_T4UU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110271"}},{"Add":{"text":" PI = par.Cparameters(\"REAL\", thismodule, [\"PI\"], \"3.14159265358979323846264338327950288\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110365"}},{"Add":{"text":" alpha = sp.symbols(\"alpha\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110408"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110409"}},{"Add":{"text":" # Step 3.b: trK_rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110433"}},{"Add":{"text":" sourceterm_trK_rhs = 4 * PI * alpha * (rho + S)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110485"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110486"}},{"Add":{"text":" # Step 3.c: Abar_rhsDD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110514"}},{"Add":{"text":" # Step 3.c.i: Compute trace-free part of S_{ij}:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110567"}},{"Add":{"text":" import BSSN.BSSN_quantities as Bq","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110605"}},{"Add":{"text":" Bq.BSSN_basic_tensors() # Sets gammabarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110652"}},{"Add":{"text":" gammabarUU, dummydet = ixp.symm_matrix_inverter3x3(Bq.gammabarDD) # Set gammabarUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110740"}},{"Add":{"text":" tracefree_SDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110776"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110799"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110826"}},{"Add":{"text":" tracefree_SDD[i][j] = SDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110870"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110893"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110920"}},{"Add":{"text":" for k in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110951"}},{"Add":{"text":" for m in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:110986"}},{"Add":{"text":" tracefree_SDD[i][j] += -sp.Rational(1, 3) * Bq.gammabarDD[i][j] * gammabarUU[k][m] * SDD[k][m]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111101"}},{"Add":{"text":" # Step 3.c.ii: Define exp_m4phi = e^{-4 phi}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111150"}},{"Add":{"text":" Bq.phi_and_derivs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111174"}},{"Add":{"text":" # Step 3.c.iii: Evaluate stress-energy part of AbarDD's RHS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111238"}},{"Add":{"text":" sourceterm_a_rhsDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111279"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111302"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111329"}},{"Add":{"text":" Abar_rhsDDij = -8 * PI * alpha * Bq.exp_m4phi * tracefree_SDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111409"}},{"Add":{"text":" sourceterm_a_rhsDD[i][j] = Abar_rhsDDij / rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111478"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111479"}},{"Add":{"text":" # Step 3.d: Stress-energy part of Lambdabar_rhsU = stressenergy_Lambdabar_rhsU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111562"}},{"Add":{"text":" sourceterm_Lambdabar_rhsU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111610"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111633"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111660"}},{"Add":{"text":" sourceterm_Lambdabar_rhsU[i] += -16 * PI * alpha * gammabarUU[i][j] * SD[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111748"}},{"Add":{"text":" sourceterm_lambda_rhsU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111793"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111816"}},{"Add":{"text":" sourceterm_lambda_rhsU[i] = sourceterm_Lambdabar_rhsU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111894"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111895"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111896"}},{"Add":{"text":"# Step 4: Add BSSN stress-energy source terms to BSSN constraints","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:111962"}},{"Add":{"text":"def BSSN_source_terms_for_BSSN_constraints(custom_T4UU=None):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112024"}},{"Add":{"text":" global sourceterm_H, sourceterm_MU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112063"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112064"}},{"Add":{"text":" # Step 4.a: Call BSSN_source_terms_ito_T4UU to get SDD, SD, S, & rho","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112137"}},{"Add":{"text":" if custom_T4UU == \"unrescaled BSSN source terms already given\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112205"}},{"Add":{"text":" SDD = ixp.declarerank2(\"SDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112252"}},{"Add":{"text":" SD = ixp.declarerank1(\"SD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112288"}},{"Add":{"text":" S = sp.symbols(\"S\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112327"}},{"Add":{"text":" rho = sp.symbols(\"rho\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112370"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112380"}},{"Add":{"text":" SDD,SD,S,rho = stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(\"BSSN\", custom_T4UU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112487"}},{"Add":{"text":" PI = par.Cparameters(\"REAL\", thismodule, [\"PI\"], \"3.14159265358979323846264338327950288\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112581"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112582"}},{"Add":{"text":" # Step 4.b: Add source term to the Hamiltonian constraint H","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112646"}},{"Add":{"text":" sourceterm_H = -16 * PI * rho","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112680"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112681"}},{"Add":{"text":" # Step 4.c: Add source term to the momentum constraint M^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112744"}},{"Add":{"text":" # Step 4.c.i: Compute gammaUU in terms of BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112806"}},{"Add":{"text":" import BSSN.ADM_in_terms_of_BSSN as AitoB","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112852"}},{"Add":{"text":" AitoB.ADM_in_terms_of_BSSN() # Provides gammaUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112905"}},{"Add":{"text":" # Step 4.c.ii: Raise S_i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112934"}},{"Add":{"text":" SU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112959"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:112982"}},{"Add":{"text":" for j in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113009"}},{"Add":{"text":" SU[i] += AitoB.gammaUU[i][j] * SD[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113058"}},{"Add":{"text":" # Step 4.c.iii: Add source term to momentum constraint & rescale:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113128"}},{"Add":{"text":" sourceterm_MU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113164"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113187"}},{"Add":{"text":" sourceterm_MU[i] = -8 * PI * SU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113243"}}]}},{"FileAdd":{"meta":{"basename":"BrillLindquist.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/BrillLindquist.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module sets up Brill-Lindquist initial data in terms of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113327"}},{"Add":{"text":"# the variables used in BSSN_RHSs.py","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113364"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113365"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113396"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113439"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113440"}},{"Add":{"text":"# # Setting up Two Black Hole Initial Data, in Curvilinear Coordinates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113511"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113514"}},{"Add":{"text":"# ## This module sets up initial data for two black holes at rest in spherical coordinates, converts the initial data/basis to the desired CoordSystem, and then rescales all quantities according to the BSSNCurvilinear prescription.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113746"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:113749"}},{"Add":{"text":"# ### Brill-Lindquist initial data ([Brill & Lindquist, Phys. Rev. 131, 471, 1963](https://journals.aps.org/pr/abstract/10.1103/PhysRev.131.471); see also Eq. 1 of [Brandt & Br\\\"ugmann, arXiv:gr-qc/9711015v1](https://arxiv.org/pdf/gr-qc/9711015v1.pdf)) may be written in terms of the BSSN conformal factor and ADM extrinsic curvature as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114086"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114089"}},{"Add":{"text":"# $$\\psi = e^{\\phi} = 1 + \\sum_{i=1}^N \\frac{m_{(i)}}{2 \\left|\\vec{r}_{(i)} - \\vec{r}\\right|};\\quad K_{ij}=0.$$","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114201"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114204"}},{"Add":{"text":"# These data consist of $N$ nonspinning black holes initially at rest. This module restricts to the case of two such black holes, positioned along either the $x$ or $z$ axis. Here, we implement $N=2$.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114405"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114408"}},{"Add":{"text":"# **Inputs for $\\psi$**:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114433"}},{"Add":{"text":"# * The position and (bare) mass of black hole 1: $\\left(x_{(1)},y_{(1)},z_{(1)}\\right)$ and $m_{(1)}$, respectively","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114550"}},{"Add":{"text":"# * The position and (bare) mass of black hole 2: $\\left(x_{(2)},y_{(2)},z_{(2)}\\right)$ and $m_{(2)}$, respectively","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114667"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114670"}},{"Add":{"text":"# **Additional variables needed for spacetime evolution**:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114729"}},{"Add":{"text":"# * Desired coordinate system","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114759"}},{"Add":{"text":"# * Desired initial lapse $\\alpha$ and shift $\\beta^i$","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114814"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114817"}},{"Add":{"text":"# **Transformation to curvilinear coordinates**:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:114866"}},{"Add":{"text":"# * Once the above variables have been set in Cartesian coordinates, we will apply the appropriate coordinate transformations and tensor rescalings ([described in the BSSN NRPy+ tutorial module](Tutorial-BSSNCurvilinear.ipynb))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115094"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115095"}},{"Add":{"text":"# Step 1: Initialize core Python/NRPy+ modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115142"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115243"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115303"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115410"}},{"Add":{"text":"import BSSN.ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear as AtoB","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115482"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115483"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115505"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115506"}},{"Add":{"text":"BH1_posn_x, BH1_posn_y, BH1_posn_z = par.Cparameters(\"REAL\", thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115579"}},{"Add":{"text":" [\"BH1_posn_x\", \"BH1_posn_y\", \"BH1_posn_z\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115676"}},{"Add":{"text":" [0.0, 0.0, +0.5])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115747"}},{"Add":{"text":"BH1_mass = par.Cparameters(\"REAL\", thismodule, [\"BH1_mass\"], 1.0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115813"}},{"Add":{"text":"BH2_posn_x, BH2_posn_y, BH2_posn_z = par.Cparameters(\"REAL\", thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115886"}},{"Add":{"text":" [\"BH2_posn_x\", \"BH2_posn_y\", \"BH2_posn_z\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:115983"}},{"Add":{"text":" [0.0, 0.0, -0.5])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116054"}},{"Add":{"text":"BH2_mass = par.Cparameters(\"REAL\", thismodule, [\"BH2_mass\"], 1.0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116120"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116121"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116122"}},{"Add":{"text":"# ComputeADMGlobalsOnly == True will only set up the ADM global quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116198"}},{"Add":{"text":"# == False will perform the full ADM SphorCart->BSSN Curvi conversion","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116290"}},{"Add":{"text":"def BrillLindquist(ComputeADMGlobalsOnly = False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116341"}},{"Add":{"text":" global Cartxyz,gammaCartDD, KCartDD, alphaCart, betaCartU, BCartU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116411"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116416"}},{"Add":{"text":" # Step 2: Setting up Brill-Lindquist initial data","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116470"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116471"}},{"Add":{"text":" # Step 2.a: Set spatial dimension (must be 3 for BSSN)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116530"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116542"}},{"Add":{"text":" par.set_parval_from_str(\"grid::DIM\",DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116587"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116588"}},{"Add":{"text":" global Cartxyz, gammaCartDD, KCartDD, alphaCart, betaCartU, BCartU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116659"}},{"Add":{"text":" Cartxyz = ixp.declarerank1(\"Cartxyz\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116701"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116702"}},{"Add":{"text":" # Step 2.b: Set psi, the conformal factor:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116749"}},{"Add":{"text":" psi = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116773"}},{"Add":{"text":" psi += BH1_mass / ( 2 * sp.sqrt((Cartxyz[0]-BH1_posn_x)**2 + (Cartxyz[1]-BH1_posn_y)**2 + (Cartxyz[2]-BH1_posn_z)**2) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:116897"}},{"Add":{"text":" psi += BH2_mass / ( 2 * sp.sqrt((Cartxyz[0]-BH2_posn_x)**2 + (Cartxyz[1]-BH2_posn_y)**2 + (Cartxyz[2]-BH2_posn_z)**2) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117021"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117022"}},{"Add":{"text":" # Step 2.c: Set all needed ADM variables in Cartesian coordinates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117092"}},{"Add":{"text":" gammaCartDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117126"}},{"Add":{"text":" KCartDD = ixp.zerorank2() # K_{ij} = 0 for these initial data","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117196"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117221"}},{"Add":{"text":" gammaCartDD[i][i] = psi**4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117256"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117257"}},{"Add":{"text":" alphaCart = 1/psi**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117282"}},{"Add":{"text":" betaCartU = ixp.zerorank1() # We generally choose \\beta^i = 0 for these initial data","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117371"}},{"Add":{"text":" BCartU = ixp.zerorank1() # We generally choose B^i = 0 for these initial data","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117456"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117457"}},{"Add":{"text":" if ComputeADMGlobalsOnly == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117495"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117510"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117515"}},{"Add":{"text":" cf,hDD,lambdaU,aDD,trK,alpha,vetU,betU = \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117562"}},{"Add":{"text":" AtoB.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear(\"Cartesian\",Cartxyz, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117652"}},{"Add":{"text":" gammaCartDD,KCartDD,alphaCart,betaCartU,BCartU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117768"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117769"}},{"Add":{"text":" import BSSN.BSSN_ID_function_string as bIDf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117817"}},{"Add":{"text":" global returnfunction","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117843"}},{"Add":{"text":" returnfunction = bIDf.BSSN_ID_function_string(cf, hDD, lambdaU, aDD, trK, alpha, vetU, betU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:117940"}}]}},{"FileAdd":{"meta":{"basename":"Enforce_Detgammabar_Constraint.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/Enforce_Detgammabar_Constraint.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module implements the gammabar = gammahat constraint.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118038"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118039"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118070"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118113"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118114"}},{"Add":{"text":"# Step P1: import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118163"}},{"Add":{"text":"from outputC import * # NRPy+: Core C code output module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118232"}},{"Add":{"text":"import finite_difference as fin # NRPy+: Finite difference C code generation module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118318"}},{"Add":{"text":"import grid as gri # NRPy+: Functions having to do with numerical grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118405"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118515"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118583"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118687"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq # NRPy+: Computes useful BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118762"}},{"Add":{"text":"import os # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118859"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118860"}},{"Add":{"text":"def Enforce_Detgammabar_Constraint_symb_expressions():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118915"}},{"Add":{"text":" # Set spatial dimension (must be 3 for BSSN)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118964"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118976"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:118977"}},{"Add":{"text":" # Then we set the coordinate system for the numerical grid","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119040"}},{"Add":{"text":" rfm.reference_metric() # Create ReU, ReDD needed for rescaling B-L initial data, generating BSSN RHSs, etc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119153"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119154"}},{"Add":{"text":" # We will need the h_{ij} quantities defined within BSSN_RHSs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119220"}},{"Add":{"text":" # below when we enforce the gammahat=gammabar constraint","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119284"}},{"Add":{"text":" # Step 1: All barred quantities are defined in terms of BSSN rescaled gridfunctions,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119373"}},{"Add":{"text":" # which we declare here in case they haven't yet been declared elsewhere.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119459"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119460"}},{"Add":{"text":" Bq.declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119520"}},{"Add":{"text":" hDD = Bq.hDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119537"}},{"Add":{"text":" Bq.BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119565"}},{"Add":{"text":" gammabarDD = Bq.gammabarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119596"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119597"}},{"Add":{"text":" # First define the Kronecker delta:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119637"}},{"Add":{"text":" KroneckerDeltaDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119676"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119701"}},{"Add":{"text":" KroneckerDeltaDD[i][i] = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119748"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119749"}},{"Add":{"text":" # The detgammabar in BSSN_RHSs is set to detgammahat when BSSN_RHSs::detgbarOverdetghat_equals_one=True (default),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119868"}},{"Add":{"text":" # so we manually compute it here:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119909"}},{"Add":{"text":" dummygammabarUU, detgammabar = ixp.symm_matrix_inverter3x3(gammabarDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119984"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:119985"}},{"Add":{"text":" # Next apply the constraint enforcement equation above.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120045"}},{"Add":{"text":" hprimeDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120076"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120101"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120130"}},{"Add":{"text":" hprimeDD[i][j] = \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120161"}},{"Add":{"text":" (nrpyAbs(rfm.detgammahat) / detgammabar) ** (sp.Rational(1, 3)) * (KroneckerDeltaDD[i][j] + hDD[i][j]) \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120282"}},{"Add":{"text":" - KroneckerDeltaDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120323"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120324"}},{"Add":{"text":" enforce_detg_constraint_symb_expressions = [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120373"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"hDD00\"), rhs=hprimeDD[0][0]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120444"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"hDD01\"), rhs=hprimeDD[0][1]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120515"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"hDD02\"), rhs=hprimeDD[0][2]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120586"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"hDD11\"), rhs=hprimeDD[1][1]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120657"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"hDD12\"), rhs=hprimeDD[1][2]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120728"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"hDD22\"), rhs=hprimeDD[2][2])]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120799"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120800"}},{"Add":{"text":" return enforce_detg_constraint_symb_expressions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120852"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120853"}},{"Add":{"text":"def output_Enforce_Detgammabar_Constraint_Ccode(outdir=\"BSSN/\", exprs=\"\", Read_xxs=False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:120944"}},{"Add":{"text":" # Step 0: Check if outdir is string; error out if not.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121003"}},{"Add":{"text":" check_if_string__error_if_not(outdir,\"outdir\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121054"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121055"}},{"Add":{"text":" desc = \"Enforce det(gammabar) = det(gammahat) constraint.\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121118"}},{"Add":{"text":" name = \"enforce_detgammabar_constraint\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121162"}},{"Add":{"text":" params = \"const rfm_struct *restrict rfmstruct,const paramstruct *restrict params, REAL *restrict in_gfs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121272"}},{"Add":{"text":" loopopts = \"AllPoints,Enable_rfm_precompute\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121321"}},{"Add":{"text":" if Read_xxs:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121338"}},{"Add":{"text":" params = \"const paramstruct *restrict params, REAL *restrict xx[3], REAL *restrict in_gfs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121437"}},{"Add":{"text":" loopopts = \"AllPoints,Read_xxs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121477"}},{"Add":{"text":" outCfunction(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121495"}},{"Add":{"text":" outfile=os.path.join(outdir, name + \".h\"), desc=desc, name=name, params=params,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121583"}},{"Add":{"text":" body=fin.FD_outputC(\"returnstring\", exprs,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121634"}},{"Add":{"text":" params=\"outCverbose=False,preindent=1,includebraces=False\").replace(\"IDX4\", \"IDX4S\"),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121748"}},{"Add":{"text":" loopopts=loopopts)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121775"}}]}},{"FileAdd":{"meta":{"basename":"ID_ADM_SphorCart.h-ADM_Num_ID_validation","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/ID_ADM_SphorCart.h-ADM_Num_ID_validation","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121820"}},{"Add":{"text":"// This function takes as input either (x,y,z) or (r,th,ph) and outputs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121892"}},{"Add":{"text":"// all ADM quantities in the Cartesian or Spherical basis, respectively.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:121967"}},{"Add":{"text":"void ID_ADM_SphorCart(const REAL xyz_or_rthph[3], ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122018"}},{"Add":{"text":" REAL *gammaDD00,REAL *gammaDD01,REAL *gammaDD02,REAL *gammaDD11,REAL *gammaDD12,REAL *gammaDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122136"}},{"Add":{"text":" REAL *KDD00,REAL *KDD01,REAL *KDD02,REAL *KDD11,REAL *KDD12,REAL *KDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122230"}},{"Add":{"text":" REAL *alpha,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122264"}},{"Add":{"text":" REAL *betaU0,REAL *betaU1,REAL *betaU2,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122325"}},{"Add":{"text":" REAL *BU0,REAL *BU1,REAL *BU2) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122379"}},{"Add":{"text":" const REAL r = xyz_or_rthph[0];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122418"}},{"Add":{"text":" const REAL th = xyz_or_rthph[1];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122457"}},{"Add":{"text":" const REAL ph = xyz_or_rthph[2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122496"}},{"Add":{"text":" const double tmp0 = (1.0/4.0)*M;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122535"}},{"Add":{"text":" const double tmp1 = pow(M, 2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122572"}},{"Add":{"text":" const double tmp2 = pow(chi, 2)*tmp1;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122616"}},{"Add":{"text":" const double tmp3 = -tmp2;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122649"}},{"Add":{"text":" const double tmp4 = sqrt(tmp1 + tmp3);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122694"}},{"Add":{"text":" const double tmp5 = (1.0/4.0)*tmp4;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122736"}},{"Add":{"text":" const double tmp6 = cos(th);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122771"}},{"Add":{"text":" const double tmp7 = 1.0/r;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122804"}},{"Add":{"text":" const double tmp8 = (1.0/4.0)*tmp7*(M + tmp4) + 1;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122861"}},{"Add":{"text":" const double tmp9 = pow(r, 2)*pow(tmp8, 4);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122911"}},{"Add":{"text":" const double tmp10 = tmp2*pow(tmp6, 2) + tmp9;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:122964"}},{"Add":{"text":" const double tmp11 = r*pow(tmp8, 2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123007"}},{"Add":{"text":" const double tmp12 = -M + tmp11 + tmp4;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123053"}},{"Add":{"text":" const double tmp13 = tmp2 + tmp9;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123093"}},{"Add":{"text":" const double tmp14 = 2*tmp11;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123129"}},{"Add":{"text":" const double tmp15 = sin(th);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123165"}},{"Add":{"text":" const double tmp16 = pow(tmp15, 2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123207"}},{"Add":{"text":" const double tmp17 = tmp16*tmp2;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123246"}},{"Add":{"text":" const double tmp18 = pow(tmp13, 2) - tmp17*(-M*tmp14 + tmp13);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123315"}},{"Add":{"text":" const double tmp19 = 1.0/tmp10;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123353"}},{"Add":{"text":" const double tmp20 = tmp16*tmp19;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123393"}},{"Add":{"text":" const double tmp21 = pow(tmp10*tmp18, -1.0/2.0);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123448"}},{"Add":{"text":" const double tmp22 = pow(M, 4);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123486"}},{"Add":{"text":" *gammaDD00 = tmp10*pow(r + tmp0 + tmp5, 2)/(pow(r, 3)*tmp12);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123554"}},{"Add":{"text":" *gammaDD01 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123576"}},{"Add":{"text":" *gammaDD02 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123598"}},{"Add":{"text":" *gammaDD11 = tmp10;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123624"}},{"Add":{"text":" *gammaDD12 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123646"}},{"Add":{"text":" *gammaDD22 = tmp18*tmp20;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123678"}},{"Add":{"text":" *KDD00 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123696"}},{"Add":{"text":" *KDD01 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123714"}},{"Add":{"text":" *KDD02 = chi*tmp1*tmp20*tmp21*tmp8*(-pow(chi, 4)*tmp22 + 3*pow(r, 4)*pow(tmp8, 8) - tmp17*(tmp3 + tmp9) + 2*tmp2*tmp9)/sqrt(r*tmp12);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123854"}},{"Add":{"text":" *KDD11 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123872"}},{"Add":{"text":" *KDD12 = -pow(chi, 3)*tmp14*pow(tmp15, 3)*tmp19*tmp21*tmp22*tmp6*sqrt(tmp12*tmp7)*(r - tmp0 - tmp5);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123979"}},{"Add":{"text":" *KDD22 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:123997"}},{"Add":{"text":" *alpha = 1;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124015"}},{"Add":{"text":" *betaU0 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124034"}},{"Add":{"text":" *betaU1 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124053"}},{"Add":{"text":" *betaU2 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124072"}},{"Add":{"text":" *BU0 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124088"}},{"Add":{"text":" *BU1 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124104"}},{"Add":{"text":" *BU2 = 0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124120"}},{"Add":{"text":"}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124122"}}]}},{"FileAdd":{"meta":{"basename":"Psi4.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124179"}},{"Add":{"text":"# Tutorial-Psi4.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124204"}},{"Add":{"text":"# this module will construct a generic","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124245"}},{"Add":{"text":"# expression for \\psi_4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124271"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124272"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124303"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124346"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124347"}},{"Add":{"text":"# Step 1.a: import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124397"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124501"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124611"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124679"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124680"}},{"Add":{"text":"def Psi4(specify_tetrad=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124711"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124712"}},{"Add":{"text":" global psi4_im_pt, psi4_re_pt","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124746"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124747"}},{"Add":{"text":" # Step 1.b: Given the chosen coordinate system, set up","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124806"}},{"Add":{"text":" # corresponding reference metric and needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124864"}},{"Add":{"text":" # reference metric quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124908"}},{"Add":{"text":" # The following function call sets up the reference metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:124971"}},{"Add":{"text":" # and related quantities, including rescaling matrices ReDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125039"}},{"Add":{"text":" # ReU, and hatted quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125076"}},{"Add":{"text":" rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125103"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125104"}},{"Add":{"text":" # Step 1.c: Set spatial dimension (must be 3 for BSSN, as BSSN is","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125174"}},{"Add":{"text":" # a 3+1-dimensional decomposition of the general","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125237"}},{"Add":{"text":" # relativistic field equations)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125283"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125295"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125296"}},{"Add":{"text":" # Step 1.d: Import all ADM quantities as written in terms of BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125377"}},{"Add":{"text":" import BSSN.ADM_in_terms_of_BSSN as AB","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125420"}},{"Add":{"text":" AB.ADM_in_terms_of_BSSN()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125450"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125451"}},{"Add":{"text":" # Step 1.e: Set up tetrad vectors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125489"}},{"Add":{"text":" if specify_tetrad==True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125518"}},{"Add":{"text":" import BSSN.Psi4_tetrads as BP4t","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125559"}},{"Add":{"text":" BP4t.Psi4_tetrads()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125587"}},{"Add":{"text":" mre4U = BP4t.mre4U","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125614"}},{"Add":{"text":" mim4U = BP4t.mim4U","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125641"}},{"Add":{"text":" n4U = BP4t.n4U","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125666"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125676"}},{"Add":{"text":" # For code validation against NRPy+ psi_4 tutorial module (Tutorial-Psi4.ipynb);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125765"}},{"Add":{"text":" # ensures a more complete code validation.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125818"}},{"Add":{"text":" mre4U = ixp.declarerank1(\"mre4U\", DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125867"}},{"Add":{"text":" mim4U = ixp.declarerank1(\"mim4U\", DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125916"}},{"Add":{"text":" n4U = ixp.declarerank1(\"n4U\", DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125961"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:125962"}},{"Add":{"text":" # Step 2: Construct the (rank-4) Riemann curvature tensor associated with the ADM 3-metric:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126058"}},{"Add":{"text":" RDDDD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126086"}},{"Add":{"text":" gammaDDdDD = AB.gammaDDdDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126117"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126118"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126143"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126172"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126205"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126242"}},{"Add":{"text":" RDDDD[i][k][l][m] = sp.Rational(1, 2) * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126304"}},{"Add":{"text":" (gammaDDdDD[i][m][k][l] + gammaDDdDD[k][l][i][m] - gammaDDdDD[i][l][k][m] -","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126420"}},{"Add":{"text":" gammaDDdDD[k][m][i][l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126485"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126486"}},{"Add":{"text":" # ... then we add the term on the right:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126531"}},{"Add":{"text":" gammaDD = AB.gammaDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126556"}},{"Add":{"text":" GammaUDD = AB.GammaUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126583"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126584"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126609"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126638"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126671"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126708"}},{"Add":{"text":" for n in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126749"}},{"Add":{"text":" for p in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126794"}},{"Add":{"text":" RDDDD[i][k][l][m] += gammaDD[n][p] * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126861"}},{"Add":{"text":" (GammaUDD[n][k][l] * GammaUDD[p][i][m] - GammaUDD[n][k][m] * GammaUDD[p][i][l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126990"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:126991"}},{"Add":{"text":" # Step 3: Construct the (rank-4) tensor in term 1 of psi_4 (referring to Eq 5.1 in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127078"}},{"Add":{"text":" # Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127160"}},{"Add":{"text":" rank4term1DDDD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127197"}},{"Add":{"text":" KDD = AB.KDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127214"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127215"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127240"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127269"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127302"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127339"}},{"Add":{"text":" rank4term1DDDD[i][j][k][l] = RDDDD[i][j][k][l] + KDD[i][k] * KDD[l][j] - KDD[i][l] * KDD[k][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127454"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127455"}},{"Add":{"text":" # Step 4: Construct the (rank-3) tensor in term 2 of psi_4 (referring to Eq 5.1 in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127542"}},{"Add":{"text":" # Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127624"}},{"Add":{"text":" rank3term2DDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127660"}},{"Add":{"text":" KDDdD = AB.KDDdD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127681"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127682"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127707"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127736"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127769"}},{"Add":{"text":" rank3term2DDD[j][k][l] = sp.Rational(1, 2) * (KDDdD[j][k][l] - KDDdD[j][l][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127864"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127865"}},{"Add":{"text":" # ... then we construct the second term in this sum:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:127922"}},{"Add":{"text":" # \\Gamma^{p}_{j[k} K_{l]p} = \\frac{1}{2} (\\Gamma^{p}_{jk} K_{lp}-\\Gamma^{p}_{jl} K_{kp}):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128017"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128042"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128071"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128104"}},{"Add":{"text":" for p in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128141"}},{"Add":{"text":" rank3term2DDD[j][k][l] += sp.Rational(1, 2) * (","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128209"}},{"Add":{"text":" GammaUDD[p][j][k] * KDD[l][p] - GammaUDD[p][j][l] * KDD[k][p])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128304"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128305"}},{"Add":{"text":" # Finally, we multiply the term by $-8$:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128350"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128375"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128404"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128437"}},{"Add":{"text":" rank3term2DDD[j][k][l] *= sp.sympify(-8)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128494"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128495"}},{"Add":{"text":" # Step 5: Construct the (rank-2) tensor in term 3 of psi_4 (referring to Eq 5.1 in ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128583"}},{"Add":{"text":" # Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128665"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128666"}},{"Add":{"text":" # Step 5.1: Construct 3-Ricci tensor R_{ij} = gamma^{im} R_{ijml}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128736"}},{"Add":{"text":" RDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128762"}},{"Add":{"text":" gammaUU = AB.gammaUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128787"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128812"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128841"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128874"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128911"}},{"Add":{"text":" RDD[j][l] += gammaUU[i][m]*RDDDD[i][j][m][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128976"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:128977"}},{"Add":{"text":" # Step 5.2: Construct K^p_l = gamma^{pi} K_{il}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129029"}},{"Add":{"text":" KUD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129055"}},{"Add":{"text":" for p in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129080"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129109"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129142"}},{"Add":{"text":" KUD[p][l] += gammaUU[p][i]*KDD[i][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129195"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129196"}},{"Add":{"text":" # Step 5.3: Construct trK = gamma^{ij} K_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129246"}},{"Add":{"text":" trK = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129270"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129295"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129324"}},{"Add":{"text":" trK += gammaUU[i][j]*KDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129367"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129368"}},{"Add":{"text":" # Next we put these terms together to construct the entire term in parentheses:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129452"}},{"Add":{"text":" # +4 \\left(R_{jl} - K_{jp} K^p_l + K K_{jl} \\right),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129509"}},{"Add":{"text":" rank2term3DD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129544"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129569"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129598"}},{"Add":{"text":" rank2term3DD[j][l] = RDD[j][l] + trK*KDD[j][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129657"}},{"Add":{"text":" for p in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129690"}},{"Add":{"text":" rank2term3DD[j][l] += - KDD[j][p]*KUD[p][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129750"}},{"Add":{"text":" # Finally we multiply by +4:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129783"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129808"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129837"}},{"Add":{"text":" rank2term3DD[j][l] *= sp.sympify(4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129885"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129886"}},{"Add":{"text":" # Step 6: Construct real & imaginary parts of psi_4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:129942"}},{"Add":{"text":" # by contracting constituent rank 2, 3, and 4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130000"}},{"Add":{"text":" # tensors with input tetrads mre4U, mim4U, & n4U.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130062"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130063"}},{"Add":{"text":" def tetrad_product__Real_psi4(n, Mre, Mim, mu, nu, eta, delta):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130131"}},{"Add":{"text":" return +n[mu] * Mre[nu] * n[eta] * Mre[delta] - n[mu] * Mim[nu] * n[eta] * Mim[delta]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130225"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130226"}},{"Add":{"text":" def tetrad_product__Imag_psi4(n, Mre, Mim, mu, nu, eta, delta):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130294"}},{"Add":{"text":" return -n[mu] * Mre[nu] * n[eta] * Mim[delta] - n[mu] * Mim[nu] * n[eta] * Mre[delta]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130388"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130389"}},{"Add":{"text":" # We split psi_4 into three pieces, to expedite & possibly parallelize C code generation.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130483"}},{"Add":{"text":" psi4_re_pt = [sp.sympify(0),sp.sympify(0),sp.sympify(0)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130544"}},{"Add":{"text":" psi4_im_pt = [sp.sympify(0),sp.sympify(0),sp.sympify(0)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130605"}},{"Add":{"text":" # First term:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130623"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130648"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130677"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130710"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130747"}},{"Add":{"text":" psi4_re_pt[0] += rank4term1DDDD[i][j][k][l] * tetrad_product__Real_psi4(n4U, mre4U, mim4U,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130858"}},{"Add":{"text":" i + 1, j + 1,k + 1, l + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:130977"}},{"Add":{"text":" psi4_im_pt[0] += rank4term1DDDD[i][j][k][l] * tetrad_product__Imag_psi4(n4U, mre4U, mim4U,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131088"}},{"Add":{"text":" i + 1, j + 1, k + 1, l + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131208"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131209"}},{"Add":{"text":" # Second term:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131228"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131253"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131282"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131315"}},{"Add":{"text":" psi4_re_pt[1] += rank3term2DDD[j][k][l] * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131375"}},{"Add":{"text":" sp.Rational(1, 2) * (+tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, k + 1, l + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131493"}},{"Add":{"text":" - tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, k + 1, l + 1))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131613"}},{"Add":{"text":" psi4_im_pt[1] += rank3term2DDD[j][k][l] * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131673"}},{"Add":{"text":" sp.Rational(1, 2) * (+tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, k + 1, l + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131791"}},{"Add":{"text":" - tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, k + 1, l + 1))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131911"}},{"Add":{"text":" # Third term:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131929"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131954"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:131983"}},{"Add":{"text":" psi4_re_pt[2] += rank2term3DD[j][l] * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132035"}},{"Add":{"text":" (sp.Rational(1, 4) * (+tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, 0, l + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132146"}},{"Add":{"text":" - tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, 0, l + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132258"}},{"Add":{"text":" - tetrad_product__Real_psi4(n4U, mre4U, mim4U, 0, j + 1, l + 1, 0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132370"}},{"Add":{"text":" + tetrad_product__Real_psi4(n4U, mre4U, mim4U, j + 1, 0, l + 1, 0)))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132484"}},{"Add":{"text":" psi4_im_pt[2] += rank2term3DD[j][l] * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132536"}},{"Add":{"text":" (sp.Rational(1, 4) * (+tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, 0, l + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132647"}},{"Add":{"text":" - tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, 0, l + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132759"}},{"Add":{"text":" - tetrad_product__Imag_psi4(n4U, mre4U, mim4U, 0, j + 1, l + 1, 0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132871"}},{"Add":{"text":" + tetrad_product__Imag_psi4(n4U, mre4U, mim4U, j + 1, 0, l + 1, 0)))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:132985"}}]}},{"FileAdd":{"meta":{"basename":"Psi4Cartesianvalidation","metadata":1005},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation","context":[{"change":0,"pos":23}],"contents":[]}},{"FileAdd":{"meta":{"basename":"BSSN","metadata":1005},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation/BSSN","context":[{"change":0,"pos":133012}],"contents":[]}},{"FileAdd":{"meta":{"basename":"Psi4_tetrads.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation/BSSN/Psi4_tetrads.py","context":[{"change":0,"pos":133020}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133084"}},{"Add":{"text":"# Tutorial-Psi4_tetrads.ipynb,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133117"}},{"Add":{"text":"# this module will construct tetrads","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133156"}},{"Add":{"text":"# needed to compute \\psi_4 (as well as other","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133203"}},{"Add":{"text":"# Weyl scalars and invariants in principle)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133249"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133250"}},{"Add":{"text":"# Authors: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133282"}},{"Add":{"text":"# (zachetie **at** gmail **dot* com),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133329"}},{"Add":{"text":"# and Patrick Nelson","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133359"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133360"}},{"Add":{"text":"# Step 1.a: import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133410"}},{"Add":{"text":"import sympy as sp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133429"}},{"Add":{"text":"import NRPy_param_funcs as par","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133460"}},{"Add":{"text":"import indexedexp as ixp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133485"}},{"Add":{"text":"import grid as gri","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133504"}},{"Add":{"text":"import finite_difference as fin","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133536"}},{"Add":{"text":"import reference_metric as rfm","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133567"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133568"}},{"Add":{"text":"# Step 1.b: Initialize TetradChoice parameter","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133614"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133636"}},{"Add":{"text":"# Current option: QuasiKinnersley = choice made in Baker, Campanelli, and Lousto. PRD 65, 044001 (2002)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133740"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"TetradChoice\", \"QuasiKinnersley\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133831"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"UseCorrectUnitNormal\", \"False\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133920"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133921"}},{"Add":{"text":"def Psi4_tetrads():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133941"}},{"Add":{"text":" global l4U, n4U, mre4U, mim4U","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133975"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:133976"}},{"Add":{"text":" # Step 1.c: Check if tetrad choice is implemented:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134031"}},{"Add":{"text":" if par.parval_from_str(thismodule+\"::TetradChoice\") != \"QuasiKinnersley\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134109"}},{"Add":{"text":" print(\"ERROR: \"+thismodule+\"::TetradChoice = \"+par.parval_from_str(\"TetradChoice\")+\" currently unsupported!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134227"}},{"Add":{"text":" exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134243"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134244"}},{"Add":{"text":" # Step 1.d: Given the chosen coordinate system, set up","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134303"}},{"Add":{"text":" # corresponding reference metric and needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134361"}},{"Add":{"text":" # reference metric quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134405"}},{"Add":{"text":" # The following function call sets up the reference metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134468"}},{"Add":{"text":" # and related quantities, including rescaling matrices ReDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134536"}},{"Add":{"text":" # ReU, and hatted quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134573"}},{"Add":{"text":" rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134600"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134601"}},{"Add":{"text":" # Step 1.e: Set spatial dimension (must be 3 for BSSN, as BSSN is","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134671"}},{"Add":{"text":" # a 3+1-dimensional decomposition of the general","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134734"}},{"Add":{"text":" # relativistic field equations)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134780"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134792"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134793"}},{"Add":{"text":" # Step 1.f: Import all ADM quantities as written in terms of BSSN quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134874"}},{"Add":{"text":" # import BSSN.ADM_in_terms_of_BSSN as AB","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134919"}},{"Add":{"text":" # AB.ADM_in_terms_of_BSSN()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134951"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:134952"}},{"Add":{"text":" # Step 2.a: Declare the Cartesian x,y,z as input parameters","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135016"}},{"Add":{"text":" # and v_1^a, v_2^a, and v_3^a tetrads,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135069"}},{"Add":{"text":" # as well as detgamma and gammaUU from","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135122"}},{"Add":{"text":" # BSSN.ADM_in_terms_of_BSSN","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135164"}},{"Add":{"text":" x,y,z = gri.register_gridfunctions(\"AUX\",[\"x\",\"y\",\"z\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135224"}},{"Add":{"text":"# x, y, z = par.Cparameters(\"REAL\", thismodule, [\"x\", \"y\", \"z\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135289"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135290"}},{"Add":{"text":" v1UCart = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135320"}},{"Add":{"text":" v2UCart = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135350"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135351"}},{"Add":{"text":" gammaDD = ixp.declarerank2(\"gammaDD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135401"}},{"Add":{"text":" gammaUU,detgamma = ixp.symm_matrix_inverter3x3(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135461"}},{"Add":{"text":" # detgamma = AB.detgamma","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135490"}},{"Add":{"text":" # gammaUU = AB.gammaUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135517"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135518"}},{"Add":{"text":" # Step 2.b: Define v1U and v2U","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135553"}},{"Add":{"text":" v1UCart = [-y, x, sp.sympify(0)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135590"}},{"Add":{"text":" v2UCart = [x, y, z]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135614"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135615"}},{"Add":{"text":" v1U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135641"}},{"Add":{"text":" v2U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135667"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135692"}},{"Add":{"text":" v1U[i] = v1UCart[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135720"}},{"Add":{"text":" v2U[i] = v2UCart[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135748"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135749"}},{"Add":{"text":" # # Step 2.c: Construct the Jacobian d x_Cart^i / d xx^j","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135810"}},{"Add":{"text":" # Jac_dUCart_dDrfmUD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135853"}},{"Add":{"text":" # for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135880"}},{"Add":{"text":" # for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135911"}},{"Add":{"text":" # Jac_dUCart_dDrfmUD[i][j] = sp.diff(rfm.xxCart[i], rfm.xx[j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135986"}},{"Add":{"text":" #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:135992"}},{"Add":{"text":" # # Step 2.d: Invert above Jacobian to get needed d xx^j / d x_Cart^i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136066"}},{"Add":{"text":" # Jac_dUrfm_dDCartUD, dummyDET = ixp.generic_matrix_inverter3x3(Jac_dUCart_dDrfmUD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136154"}},{"Add":{"text":" #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136160"}},{"Add":{"text":" # # Step 2.e: Transform v1U and v2U from the Cartesian to the xx^i basis","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136237"}},{"Add":{"text":" # v1U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136265"}},{"Add":{"text":" # v2U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136293"}},{"Add":{"text":" # for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136320"}},{"Add":{"text":" # for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136351"}},{"Add":{"text":" # v1U[i] += Jac_dUrfm_dDCartUD[i][j] * v1UCart[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136413"}},{"Add":{"text":" # v2U[i] += Jac_dUrfm_dDCartUD[i][j] * v2UCart[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136475"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136476"}},{"Add":{"text":" # Step 2.f: Define the rank-3 version of the Levi-Civita symbol. Amongst","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136553"}},{"Add":{"text":" # other uses, this is needed for the construction of the approximate","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136634"}},{"Add":{"text":" # quasi-Kinnersley tetrad.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136673"}},{"Add":{"text":" def define_LeviCivitaSymbol_rank3(DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136720"}},{"Add":{"text":" if DIM == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136742"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136787"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136788"}},{"Add":{"text":" LeviCivitaSymbol = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136831"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136832"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136861"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136894"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:136931"}},{"Add":{"text":" # From https://codegolf.stackexchange.com/questions/160359/levi-civita-symbol :","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137031"}},{"Add":{"text":" LeviCivitaSymbol[i][j][k] = (i - j) * (j - k) * (k - i) / 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137111"}},{"Add":{"text":" return LeviCivitaSymbol","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137143"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137144"}},{"Add":{"text":" # Step 2.g: Define v3U","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137171"}},{"Add":{"text":" v3U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137197"}},{"Add":{"text":" LeviCivitaSymbolDDD = define_LeviCivitaSymbol_rank3(DIM=3)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137260"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137285"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137314"}},{"Add":{"text":" for c in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137347"}},{"Add":{"text":" for d in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137384"}},{"Add":{"text":" v3U[a] += sp.sqrt(detgamma) * gammaUU[a][d] * LeviCivitaSymbolDDD[d][b][c] * v1U[b] * v2U[c]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137497"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137498"}},{"Add":{"text":" # Step 2.h: Define omega_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137532"}},{"Add":{"text":" omegaDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137562"}},{"Add":{"text":" #gammaDD = AB.gammaDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137588"}},{"Add":{"text":" def v_vectorDU(v1U,v2U,v3U, i,a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137627"}},{"Add":{"text":" if i==0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137644"}},{"Add":{"text":" return v1U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137670"}},{"Add":{"text":" elif i==1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137689"}},{"Add":{"text":" return v2U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137715"}},{"Add":{"text":" elif i==2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137734"}},{"Add":{"text":" return v3U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137760"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137774"}},{"Add":{"text":" print(\"ERROR: unknown vector!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137818"}},{"Add":{"text":" exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137838"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137839"}},{"Add":{"text":" def update_omega(omegaDD, i,j, v1U,v2U,v3U,gammaDD):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137896"}},{"Add":{"text":" omegaDD[i][j] = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137934"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137963"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:137996"}},{"Add":{"text":" omegaDD[i][j] += v_vectorDU(v1U,v2U,v3U, i,a)*v_vectorDU(v1U,v2U,v3U, j,b)*gammaDD[a][b]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138101"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138102"}},{"Add":{"text":" # Step 2.i: Define e^a_i. Note that:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138143"}},{"Add":{"text":" # omegaDD[0][0] = \\omega_{11} above; ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138195"}},{"Add":{"text":" # omegaDD[1][1] = \\omega_{22} above, etc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138251"}},{"Add":{"text":" # First e_1^a: Orthogonalize & normalize:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138297"}},{"Add":{"text":" e1U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138323"}},{"Add":{"text":" update_omega(omegaDD, 0,0, v1U,v2U,v3U,gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138375"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138400"}},{"Add":{"text":" e1U[a] = v1U[a]/sp.sqrt(omegaDD[0][0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138447"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138448"}},{"Add":{"text":" # Next e_2^a: First orthogonalize:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138487"}},{"Add":{"text":" e2U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138513"}},{"Add":{"text":" update_omega(omegaDD, 0,1, e1U,v2U,v3U,gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138565"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138590"}},{"Add":{"text":" e2U[a] = (v2U[a] - omegaDD[0][1]*e1U[a])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138639"}},{"Add":{"text":" # Then normalize:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138661"}},{"Add":{"text":" update_omega(omegaDD, 1,1, e1U,e2U,v3U,gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138713"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138738"}},{"Add":{"text":" e2U[a] /= sp.sqrt(omegaDD[1][1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138779"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138780"}},{"Add":{"text":" # Next e_3^a: First orthogonalize:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138819"}},{"Add":{"text":" e3U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138845"}},{"Add":{"text":" update_omega(omegaDD, 0,2, e1U,e2U,v3U,gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138897"}},{"Add":{"text":" update_omega(omegaDD, 1,2, e1U,e2U,v3U,gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138949"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:138974"}},{"Add":{"text":" e3U[a] = (v3U[a] - omegaDD[0][2]*e1U[a] - omegaDD[1][2]*e2U[a])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139046"}},{"Add":{"text":" # Then normalize:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139068"}},{"Add":{"text":" update_omega(omegaDD, 2,2, e1U,e2U,e3U,gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139120"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139145"}},{"Add":{"text":" e3U[a] /= sp.sqrt(omegaDD[2][2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139186"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139187"}},{"Add":{"text":" # Step 2.j: Construct l^mu, n^mu, and m^mu, based on r^mu, theta^mu, phi^mu, and u^mu:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139278"}},{"Add":{"text":" r4U = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139313"}},{"Add":{"text":" u4U = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139348"}},{"Add":{"text":" theta4U = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139383"}},{"Add":{"text":" phi4U = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139418"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139419"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139444"}},{"Add":{"text":" r4U[ a+1] = e2U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139474"}},{"Add":{"text":" theta4U[a+1] = e3U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139504"}},{"Add":{"text":" phi4U[ a+1] = e1U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139534"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139535"}},{"Add":{"text":" # FIXME? assumes alpha=1, beta^i = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139576"}},{"Add":{"text":" if par.parval_from_str(thismodule+\"::UseCorrectUnitNormal\") == \"False\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139652"}},{"Add":{"text":" u4U[0] = 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139671"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139681"}},{"Add":{"text":" # Eq. 2.116 in Baumgarte & Shapiro:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139725"}},{"Add":{"text":" # n^mu = {1/alpha, -beta^i/alpha}. Note that n_mu = {alpha,0}, so n^mu n_mu = -1.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139816"}},{"Add":{"text":" import BSSN.BSSN_quantities as Bq","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139858"}},{"Add":{"text":" Bq.declare_BSSN_gridfunctions_if_not_declared_already()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139922"}},{"Add":{"text":" Bq.BSSN_basic_tensors()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139954"}},{"Add":{"text":" u4U[0] = 1/Bq.alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:139982"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140011"}},{"Add":{"text":" u4U[i+1] = -Bq.betaU[i]/Bq.alpha","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140056"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140057"}},{"Add":{"text":" l4U = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140088"}},{"Add":{"text":" n4U = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140119"}},{"Add":{"text":" mre4U = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140153"}},{"Add":{"text":" mim4U = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140187"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140188"}},{"Add":{"text":" isqrt2 = 1/sp.sqrt(2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140214"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140238"}},{"Add":{"text":" l4U[mu] = isqrt2*(u4U[mu] + r4U[mu])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140285"}},{"Add":{"text":" n4U[mu] = isqrt2*(u4U[mu] - r4U[mu])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140332"}},{"Add":{"text":" mre4U[mu] = isqrt2*theta4U[mu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140371"}},{"Add":{"text":" mim4U[mu] = isqrt2* phi4U[mu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140410"}}]}},{"FileAdd":{"meta":{"basename":"__init__.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation/BSSN/__init__.py","context":[{"change":0,"pos":133020}],"contents":[]}},{"FileAdd":{"meta":{"basename":"Tutorial-Psi4-Cartesian_validation.ipynb","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation/Tutorial-Psi4-Cartesian_validation.ipynb","context":[{"change":0,"pos":133012}],"contents":[{"Add":{"text":"{","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140472"}},{"Add":{"text":" \"cells\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140484"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140488"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140516"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140535"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140550"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140649"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140884"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:140894"}},{"Add":{"text":" \"# Start-to-Finish validation of $\\\\psi_4$ in curvilinear coordinates against Cartesian formulation provided by [Patrick Nelson's Weyl scalars & invariants in Cartesian coordinates module](../../Tutorial-WeylScalarsInvariants-Cartesian.ipynb)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141145"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141155"}},{"Add":{"text":" \"### Author: Zach Etienne\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141189"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141199"}},{"Add":{"text":" \"**This module exists as a modification of [the NRPy+ $\\\\psi_4$ in curvilinear coordinates module](../../Tutorial-Psi4.ipynb), writing all spacetime quantities in terms of ADM variables and their derivatives directly.**\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141453"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141463"}},{"Add":{"text":" \"## A Note on Notation\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141494"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141504"}},{"Add":{"text":" \"As is standard in NRPy+, \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141539"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141549"}},{"Add":{"text":" \"* Greek indices range from 0 to 3, inclusive, with the zeroth component denoting the temporal (time) component.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141670"}},{"Add":{"text":" \"* Latin indices range from 0 to 2, inclusive, with the zeroth component denoting the first spatial component.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141789"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:141799"}},{"Add":{"text":" \"As a corollary, any expressions involving mixed Greek and Latin indices will need to offset one set of indices by one: A Latin index in a four-vector will be incremented and a Greek index in a three-vector will be decremented (however, the latter case does not occur in this tutorial module).\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142101"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142111"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142137"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142147"}},{"Add":{"text":" \"# Introduction, Table of Contents\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142190"}},{"Add":{"text":" \"$$\\\\label{toc}$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142216"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142226"}},{"Add":{"text":" \"This module constructs $\\\\psi_4$, a quantity that is immensely useful when extracting gravitational wave content from a numerical relativity simulation. $\\\\psi_4$ is related to the gravitational wave strain via\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142446"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142456"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142468"}},{"Add":{"text":" \"\\\\psi_4 = \\\\ddot{h}_+ - i \\\\ddot{h}_\\\\times.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142522"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142534"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142544"}},{"Add":{"text":" \"We construct $\\\\psi_4$ from the standard ADM spatial metric $\\\\gamma_{ij}$ and extrinsic curvature $K_{ij}$, and their derivatives. The full expression is given by Eq. 5.1 in [Baker, Campanelli, Lousto (2001)](https://arxiv.org/pdf/gr-qc/0104063.pdf):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142805"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142815"}},{"Add":{"text":" \"\\\\begin{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142839"}},{"Add":{"text":" \"\\\\psi_4 &= \\\\left[ {R}_{ijkl}+2K_{i[k}K_{l]j}\\\\right]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142902"}},{"Add":{"text":" \"{n}^i\\\\bar{m}^j{n}^k\\\\bar{m}^l \\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:142948"}},{"Add":{"text":" \"& -8\\\\left[ K_{j[k,l]}+{\\\\Gamma }_{j[k}^pK_{l]p}\\\\right]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143014"}},{"Add":{"text":" \"{n}^{[0}\\\\bar{m}^{j]}{n}^k\\\\bar{m}^l \\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143065"}},{"Add":{"text":" \"& +4\\\\left[ {R}_{jl}-K_{jp}K_l^p+KK_{jl}\\\\right]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143123"}},{"Add":{"text":" \"{n}^{[0}\\\\bar{m}^{j]}{n}^{[0}\\\\bar{m}^{l]},\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143176"}},{"Add":{"text":" \"\\\\end{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143198"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143208"}},{"Add":{"text":" \"Note that $\\\\psi_4$ is imaginary, with the imaginary components originating from the tetrad vector $m^\\\\mu$. This module does not specify a tetrad; instead it only constructs the above expression leaving $m^\\\\mu$ and $n^\\\\mu$ unspecified. The [next module on tetrads defines these tetrad quantities](Tutorial-Psi4_tetrads.ipynb) (currently only a quasi-Kinnersley tetrad is supported).\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143603"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143613"}},{"Add":{"text":" \"**This tutorial module is organized as follows:**\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143672"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143682"}},{"Add":{"text":" \"1. [Step 1](#initializenrpy): Initialize needed NRPy+ modules\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143753"}},{"Add":{"text":" \"1. [Step 2](#riemann): Constructing the 3-Riemann tensor $R_{ik\\\\ell m}$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143835"}},{"Add":{"text":" \"1. [Step 3](#termone): Constructing the rank-4 tensor in Term 1 of $\\\\psi_4$: $R_{ijkl} + 2 K_{i[k} K_{l]j}$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:143953"}},{"Add":{"text":" \"1. [Step 4](#termtwo): Constructing the rank-3 tensor in Term 2 of $\\\\psi_4$: $-8 \\\\left(K_{j[k,l]} + \\\\Gamma^{p}_{j[k} K_{l]p} \\\\right)$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144100"}},{"Add":{"text":" \"1. [Step 5](#termthree): Constructing the rank-2 tensor in term 3 of $\\\\psi_4$: $+4 \\\\left(R_{jl} - K_{jp} K^p_l + K K_{jl} \\\\right)$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144243"}},{"Add":{"text":" \"1. [Step 6](#psifour): Constructing $\\\\psi_4$ through contractions of the above terms with arbitrary tetrad vectors $n^\\\\mu$ and $m^\\\\mu$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144390"}},{"Add":{"text":" \"1. [Step 7](#code_validation): Code Validation against BSSN.Psi4 NRPy+ module\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144477"}},{"Add":{"text":" \"1. [Step 8](#latex_pdf_output): Output this notebook to $\\\\LaTeX$-formatted PDF\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144563"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144568"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144573"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144577"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144605"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144624"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144639"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144676"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144686"}},{"Add":{"text":" \"# Step 1: Initialize core NRPy+ modules \\\\[Back to [top](#toc)\\\\]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144761"}},{"Add":{"text":" \"$$\\\\label{initializenrpy}$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144798"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144808"}},{"Add":{"text":" \"Let's start by importing all the needed modules from NRPy+:\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144874"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144879"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144884"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144888"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144912"}},{"Add":{"text":" \"execution_count\": 1,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144937"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144956"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144974"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:144989"}},{"Add":{"text":" \"# Step 1.a: import all needed modules from NRPy+:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145048"}},{"Add":{"text":" \"import sympy as sp\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145076"}},{"Add":{"text":" \"from outputC import *\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145107"}},{"Add":{"text":" \"import NRPy_param_funcs as par\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145147"}},{"Add":{"text":" \"import indexedexp as ixp\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145181"}},{"Add":{"text":" \"import grid as gri\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145209"}},{"Add":{"text":" \"import finite_difference as fin\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145250"}},{"Add":{"text":" \"import reference_metric as rfm\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145290"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145300"}},{"Add":{"text":" \"# Step 1.b: Set the coordinate system for the numerical grid\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145370"}},{"Add":{"text":" \"par.set_parval_from_str(\\\"reference_metric::CoordSystem\\\",\\\"Cartesian\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145452"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145462"}},{"Add":{"text":" \"# Step 1.c: Given the chosen coordinate system, set up \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145527"}},{"Add":{"text":" \"# corresponding reference metric and needed\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145590"}},{"Add":{"text":" \"# reference metric quantities\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145639"}},{"Add":{"text":" \"# The following function call sets up the reference metric\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145707"}},{"Add":{"text":" \"# and related quantities, including rescaling matrices ReDD,\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145780"}},{"Add":{"text":" \"# ReU, and hatted quantities.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145822"}},{"Add":{"text":" \"rfm.reference_metric()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145854"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145864"}},{"Add":{"text":" \"# Step 1.d: Set spatial dimension (must be 3 for BSSN, as BSSN is \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:145940"}},{"Add":{"text":" \"# a 3+1-dimensional decomposition of the general \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146009"}},{"Add":{"text":" \"# relativistic field equations)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146060"}},{"Add":{"text":" \"DIM = 3\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146077"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146087"}},{"Add":{"text":" \"# Step 1.e: Import all ADM quantities as written in terms of BSSN quantities\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146173"}},{"Add":{"text":" \"# import BSSN.ADM_in_terms_of_BSSN as AB\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146223"}},{"Add":{"text":" \"# AB.ADM_in_terms_of_BSSN()\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146257"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146262"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146267"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146271"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146299"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146318"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146333"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146363"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146373"}},{"Add":{"text":" \"# Step 2: Constructing the 3-Riemann tensor $R_{ik\\\\ell m}$ \\\\[Back to [top](#toc)\\\\]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146468"}},{"Add":{"text":" \"$$\\\\label{riemann}$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146498"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146508"}},{"Add":{"text":" \"Analogously to Christoffel symbols, the Riemann tensor is a measure of the curvature of an $N$-dimensional manifold. Thus the 3-Riemann tensor is not simply a projection of the 4-Riemann tensor (see e.g., Eq. 2.7 of [Campanelli *et al* (1998)](https://arxiv.org/pdf/gr-qc/9803058.pdf) for the relation between 4-Riemann and 3-Riemann), as $N$-dimensional Riemann tensors are meant to define a notion of curvature given only the associated $N$-dimensional metric. \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146981"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:146991"}},{"Add":{"text":" \"So, given the ADM 3-metric, the Riemann tensor in arbitrary dimension is given by the 3-dimensional version of Eq. 1.19 in Baumgarte & Shapiro's *Numerical Relativity*. I.e.,\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147175"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147185"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147197"}},{"Add":{"text":" \"R^i_{jkl} = \\\\partial_k \\\\Gamma^{i}_{jl} - \\\\partial_l \\\\Gamma^{i}_{jk} + \\\\Gamma^i_{mk} \\\\Gamma^m_{jl} - \\\\Gamma^{i}_{ml} \\\\Gamma^{m}_{jk},\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147347"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147359"}},{"Add":{"text":" \"where $\\\\Gamma^i_{jk}$ is the Christoffel symbol associated with the 3-metric $\\\\gamma_{ij}$:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147462"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147472"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147484"}},{"Add":{"text":" \"\\\\Gamma^l_{ij} = \\\\frac{1}{2} \\\\gamma^{lk} \\\\left(\\\\gamma_{ki,j} + \\\\gamma_{kj,i} - \\\\gamma_{ij,k} \\\\right) \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147602"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147614"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147624"}},{"Add":{"text":" \"Notice that this equation for the Riemann tensor is equivalent to the equation given in the Wikipedia article on [Formulas in Riemannian geometry](https://en.wikipedia.org/w/index.php?title=List_of_formulas_in_Riemannian_geometry&oldid=882667524):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147881"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147891"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147903"}},{"Add":{"text":" \"R^\\\\ell{}_{ijk}=\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:147929"}},{"Add":{"text":" \"\\\\partial_j \\\\Gamma^\\\\ell{}_{ik}-\\\\partial_k\\\\Gamma^\\\\ell{}_{ij}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148003"}},{"Add":{"text":" \"+\\\\Gamma^\\\\ell{}_{js}\\\\Gamma_{ik}^s-\\\\Gamma^\\\\ell{}_{ks}\\\\Gamma^s{}_{ij},\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148086"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148098"}},{"Add":{"text":" \"with the replacements $i\\\\to \\\\ell$, $j\\\\to i$, $k\\\\to j$, $l\\\\to k$, and $s\\\\to m$. Wikipedia also provides a simpler form in terms of second-derivatives of three-metric itself (using the definition of Christoffel symbol), so that we need not define derivatives of the Christoffel symbol:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148397"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148407"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148419"}},{"Add":{"text":" \"R_{ik\\\\ell m}=\\\\frac{1}{2}\\\\left(\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148462"}},{"Add":{"text":" \"\\\\gamma_{im,k\\\\ell} \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148492"}},{"Add":{"text":" \"+ \\\\gamma_{k\\\\ell,im}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148523"}},{"Add":{"text":" \"- \\\\gamma_{i\\\\ell,km}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148554"}},{"Add":{"text":" \"- \\\\gamma_{km,i\\\\ell} \\\\right)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148594"}},{"Add":{"text":" \"+\\\\gamma_{np} \\\\left(\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148625"}},{"Add":{"text":" \"\\\\Gamma^n{}_{k\\\\ell} \\\\Gamma^p{}_{im} - \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148675"}},{"Add":{"text":" \"\\\\Gamma^n{}_{km} \\\\Gamma^p{}_{i\\\\ell} \\\\right).\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148732"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148744"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148754"}},{"Add":{"text":" \"First we construct the term on the left:\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148801"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148806"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148811"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148815"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148839"}},{"Add":{"text":" \"execution_count\": 2,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148864"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148883"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148901"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:148916"}},{"Add":{"text":" \"# Step 2: Construct the (rank-4) Riemann curvature tensor associated with the ADM 3-metric:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149017"}},{"Add":{"text":" \"RDDDD = ixp.zerorank4()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149050"}},{"Add":{"text":" \"gammaDD = ixp.register_gridfunctions_for_single_rank2(\\\"AUX\\\",\\\"gammaDD\\\", \\\"sym01\\\") # The AUX or EVOL designation is *not*\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149184"}},{"Add":{"text":" \" # used in diagnostic modules.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149303"}},{"Add":{"text":" \"kDD = ixp.register_gridfunctions_for_single_rank2(\\\"AUX\\\",\\\"kDD\\\", \\\"sym01\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149390"}},{"Add":{"text":" \"gammaDD_dD = ixp.declarerank3(\\\"gammaDD_dD\\\",\\\"sym01\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149455"}},{"Add":{"text":" \"gammaDD_dDD = ixp.declarerank4(\\\"gammaDD_dDD\\\",\\\"sym01_sym23\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149528"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149538"}},{"Add":{"text":" \"# gammaDD_dDD = AB.gammaDD_dDD\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149578"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149588"}},{"Add":{"text":" \"for i in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149618"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149652"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149690"}},{"Add":{"text":" \" for m in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149732"}},{"Add":{"text":" \" RDDDD[i][k][l][m] = sp.Rational(1,2) * \\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149799"}},{"Add":{"text":" \" (gammaDD_dDD[i][m][k][l] + gammaDD_dDD[k][l][i][m] - gammaDD_dDD[i][l][k][m] - gammaDD_dDD[k][m][i][l])\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149929"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149934"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149939"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149943"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149971"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:149990"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150005"}},{"Add":{"text":" \"... then we add the term on the right:\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150050"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150055"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150060"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150064"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150088"}},{"Add":{"text":" \"execution_count\": 3,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150113"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150132"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150150"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150165"}},{"Add":{"text":" \"# ... then we add the term on the right:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150215"}},{"Add":{"text":" \"# Define the Christoffel symbols\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150257"}},{"Add":{"text":" \"GammaUDD = ixp.zerorank3(DIM)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150296"}},{"Add":{"text":" \"gammaUU,gammadetdummy = ixp.symm_matrix_inverter3x3(gammaDD)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150366"}},{"Add":{"text":" \"for i in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150396"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150430"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150468"}},{"Add":{"text":" \" for m in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150510"}},{"Add":{"text":" \" GammaUDD[i][k][l] += (sp.Rational(1,2))*gammaUU[i][m]*\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150592"}},{"Add":{"text":" \" (gammaDD_dD[m][k][l] + gammaDD_dD[m][l][k] - gammaDD_dD[k][l][m])\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150704"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150714"}},{"Add":{"text":" \"for i in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150744"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150778"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150816"}},{"Add":{"text":" \" for m in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150858"}},{"Add":{"text":" \" for n in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150904"}},{"Add":{"text":" \" for p in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:150954"}},{"Add":{"text":" \" RDDDD[i][k][l][m] += gammaDD[n][p] * \\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151027"}},{"Add":{"text":" \" (GammaUDD[n][k][l]*GammaUDD[p][i][m] - GammaUDD[n][k][m]*GammaUDD[p][i][l])\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151137"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151142"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151147"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151151"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151179"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151198"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151213"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151243"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151253"}},{"Add":{"text":" \"# Step 3: Constructing the rank-4 tensor in Term 1 of $\\\\psi_4$: $R_{ijkl} + 2 K_{i[k} K_{l]j}$ \\\\[Back to [top](#toc)\\\\]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151384"}},{"Add":{"text":" \"$$\\\\label{termone}$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151414"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151424"}},{"Add":{"text":" \"Following Eq. 5.1 in [Baker, Campanelli, Lousto (2001)](https://arxiv.org/pdf/gr-qc/0104063.pdf), the rank-4 tensor in the first term of $\\\\psi_4$ is given by\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151592"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151602"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151614"}},{"Add":{"text":" \"R_{ijkl} + 2 K_{i[k} K_{l]j} = R_{ijkl} + K_{ik} K_{lj} - K_{il} K_{kj}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151695"}},{"Add":{"text":" \"$$\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151704"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151709"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151714"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151718"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151742"}},{"Add":{"text":" \"execution_count\": 4,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151767"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151786"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151804"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151819"}},{"Add":{"text":" \"# Step 3: Construct the (rank-4) tensor in term 1 of psi_4 (referring to Eq 5.1 in \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151912"}},{"Add":{"text":" \"# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:151999"}},{"Add":{"text":" \"rank4term1 = ixp.zerorank4()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152037"}},{"Add":{"text":" \"# kDD = AB.kDD\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152061"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152071"}},{"Add":{"text":" \"for i in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152101"}},{"Add":{"text":" \" for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152135"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152173"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152215"}},{"Add":{"text":" \" rank4term1[i][j][k][l] = RDDDD[i][j][k][l] + kDD[i][k]*kDD[l][j] - kDD[i][l]*kDD[k][j]\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152324"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152329"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152334"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152338"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152366"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152385"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152400"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152430"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152440"}},{"Add":{"text":" \"# Step 4: Constructing the rank-3 tensor in Term 2 of $\\\\psi_4$: $-8 \\\\left(K_{j[k,l]} + \\\\Gamma^{p}_{j[k} K_{l]p} \\\\right)$ \\\\[Back to [top](#toc)\\\\]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152600"}},{"Add":{"text":" \"$$\\\\label{termtwo}$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152630"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152640"}},{"Add":{"text":" \"Following Eq. 5.1 in [Baker, Campanelli, Lousto (2001)](https://arxiv.org/pdf/gr-qc/0104063.pdf), the rank-3 tensor in the second term of $\\\\psi_4$ is given by\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152809"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152819"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152831"}},{"Add":{"text":" \"-8 \\\\left(K_{j[k,l]} + \\\\Gamma^{p}_{j[k} K_{l]p} \\\\right)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152898"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:152910"}},{"Add":{"text":" \"First let's construct the first term in this sum: $K_{j[k,l]} = \\\\frac{1}{2} (K_{jk,l} - K_{jl,k})$:\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153017"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153022"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153027"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153031"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153055"}},{"Add":{"text":" \"execution_count\": 5,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153080"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153099"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153117"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153132"}},{"Add":{"text":" \"# Step 4: Construct the (rank-3) tensor in term 2 of psi_4 (referring to Eq 5.1 in \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153225"}},{"Add":{"text":" \"# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153312"}},{"Add":{"text":" \"rank3term2 = ixp.zerorank3()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153350"}},{"Add":{"text":" \"# kDD_dD = AB.kDD_dD\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153380"}},{"Add":{"text":" \"kDD_dD = ixp.declarerank3(\\\"kDD_dD\\\",\\\"sym01\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153437"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153447"}},{"Add":{"text":" \"for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153477"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153511"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153549"}},{"Add":{"text":" \" rank3term2[j][k][l] = sp.Rational(1,2)*(kDD_dD[j][k][l] - kDD_dD[j][l][k])\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153642"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153647"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153652"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153656"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153684"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153703"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153718"}},{"Add":{"text":" \"... then we construct the second term in this sum: $\\\\Gamma^{p}_{j[k} K_{l]p} = \\\\frac{1}{2} (\\\\Gamma^{p}_{jk} K_{lp}-\\\\Gamma^{p}_{jl} K_{kp})$:\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153869"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153874"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153879"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153883"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153907"}},{"Add":{"text":" \"execution_count\": 6,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153932"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153951"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153969"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:153984"}},{"Add":{"text":" \"# ... then we construct the second term in this sum: \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154047"}},{"Add":{"text":" \"# \\\\Gamma^{p}_{j[k} K_{l]p} = \\\\frac{1}{2} (\\\\Gamma^{p}_{jk} K_{lp}-\\\\Gamma^{p}_{jl} K_{kp}):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154151"}},{"Add":{"text":" \"for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154181"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154215"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154253"}},{"Add":{"text":" \" for p in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154295"}},{"Add":{"text":" \" rank3term2[j][k][l] += sp.Rational(1,2)*(GammaUDD[p][j][k]*kDD[l][p] - GammaUDD[p][j][l]*kDD[k][p])\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154417"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154422"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154427"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154431"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154459"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154478"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154493"}},{"Add":{"text":" \"Finally, we multiply the term by $-8$:\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154538"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154543"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154548"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154552"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154576"}},{"Add":{"text":" \"execution_count\": 7,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154601"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154620"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154638"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154653"}},{"Add":{"text":" \"# Finally, we multiply the term by $-8$:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154703"}},{"Add":{"text":" \"for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154733"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154767"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154805"}},{"Add":{"text":" \" rank3term2[j][k][l] *= sp.sympify(-8)\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154861"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154866"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154871"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154875"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154903"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154922"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154937"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154969"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:154979"}},{"Add":{"text":" \"# Step 5: Constructing the rank-2 tensor in term 3 of $\\\\psi_4$: $+4 \\\\left(R_{jl} - K_{jp} K^p_l + K K_{jl} \\\\right)$ \\\\[Back to [top](#toc)\\\\]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155133"}},{"Add":{"text":" \"$$\\\\label{termthree}$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155165"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155175"}},{"Add":{"text":" \"Following Eq. 5.1 in [Baker, Campanelli, Lousto (2001)](https://arxiv.org/pdf/gr-qc/0104063.pdf), the rank-2 tensor in the third term of $\\\\psi_4$ is given by\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155343"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155353"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155365"}},{"Add":{"text":" \"+4 \\\\left(R_{jl} - K_{jp} K^p_l + K K_{jl} \\\\right),\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155427"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155439"}},{"Add":{"text":" \"where\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155454"}},{"Add":{"text":" \"\\\\begin{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155478"}},{"Add":{"text":" \"R_{jl} &= R^i_{jil} \\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155512"}},{"Add":{"text":" \"&= \\\\gamma^{im} R_{ijml} \\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155551"}},{"Add":{"text":" \"K &= K^i_i \\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155576"}},{"Add":{"text":" \"&= \\\\gamma^{im} K_{im}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155608"}},{"Add":{"text":" \"\\\\end{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155630"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155640"}},{"Add":{"text":" \"Let's build the components of this term: $R_{jl}$, $K^p_l$, and $K$, as defined above:\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155733"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155738"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155743"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155747"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155771"}},{"Add":{"text":" \"execution_count\": 8,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155796"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155815"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155833"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155848"}},{"Add":{"text":" \"# Step 5: Construct the (rank-2) tensor in term 3 of psi_4 (referring to Eq 5.1 in \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:155941"}},{"Add":{"text":" \"# Baker, Campanelli, Lousto (2001); https://arxiv.org/pdf/gr-qc/0104063.pdf\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156028"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156038"}},{"Add":{"text":" \"# Step 5.1: Construct 3-Ricci tensor R_{ij} = gamma^{im} R_{ijml}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156113"}},{"Add":{"text":" \"RDD = ixp.zerorank2()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156144"}},{"Add":{"text":" \"for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156174"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156208"}},{"Add":{"text":" \" for i in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156246"}},{"Add":{"text":" \" for m in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156288"}},{"Add":{"text":" \" RDD[j][l] += gammaUU[i][m]*RDDDD[i][j][m][l]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156358"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156368"}},{"Add":{"text":" \"# Step 5.2: Construct K^p_l = gamma^{pi} K_{il}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156425"}},{"Add":{"text":" \"KUD = ixp.zerorank2()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156456"}},{"Add":{"text":" \"for p in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156486"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156520"}},{"Add":{"text":" \" for i in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156558"}},{"Add":{"text":" \" KUD[p][l] += gammaUU[p][i]*kDD[i][l]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156616"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156626"}},{"Add":{"text":" \"# Step 5.3: Construct trK = gamma^{ij} K_{ij}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156681"}},{"Add":{"text":" \"trK = sp.sympify(0)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156710"}},{"Add":{"text":" \"for i in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156740"}},{"Add":{"text":" \" for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156774"}},{"Add":{"text":" \" trK += gammaUU[i][j]*kDD[i][j]\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156819"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156824"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156829"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156833"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156861"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156880"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156895"}},{"Add":{"text":" \"Next we put these terms together to construct the entire term:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156967"}},{"Add":{"text":" \"$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:156979"}},{"Add":{"text":" \"+4 \\\\left(R_{jl} - K_{jp} K^p_l + K K_{jl} \\\\right),\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157041"}},{"Add":{"text":" \"$$\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157050"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157055"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157060"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157064"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157088"}},{"Add":{"text":" \"execution_count\": 9,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157113"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157132"}},{"Add":{"text":" \"outputs\": [],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157150"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157165"}},{"Add":{"text":" \"# Next we put these terms together to construct the entire term in parentheses:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157254"}},{"Add":{"text":" \"# +4 \\\\left(R_{jl} - K_{jp} K^p_l + K K_{jl} \\\\right),\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157318"}},{"Add":{"text":" \"rank2term3 = ixp.zerorank2()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157356"}},{"Add":{"text":" \"for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157386"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157420"}},{"Add":{"text":" \" rank2term3[j][l] = RDD[j][l] + trK*kDD[j][l]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157482"}},{"Add":{"text":" \" for p in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157520"}},{"Add":{"text":" \" rank2term3[j][l] += - kDD[j][p]*KUD[p][l]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157583"}},{"Add":{"text":" \"# Finally we multiply by +4:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157621"}},{"Add":{"text":" \"for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157651"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157685"}},{"Add":{"text":" \" rank2term3[j][l] *= sp.sympify(4)\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157733"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157738"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157743"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157747"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157775"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157794"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157809"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157839"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:157849"}},{"Add":{"text":" \"# Step 6: Constructing $\\\\psi_4$ through contractions of the above terms with an arbitrary tetrad vectors $m^\\\\mu$ and $n^\\\\mu$ \\\\[Back to [top](#toc)\\\\]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158012"}},{"Add":{"text":" \"$$\\\\label{psifour}$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158042"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158052"}},{"Add":{"text":" \"Eq. 5.1 in [Baker, Campanelli, Lousto (2001)](https://arxiv.org/pdf/gr-qc/0104063.pdf) writes $\\\\psi_4$ (which is complex) as the contraction of each of the above terms with products of tetrad vectors:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158263"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158273"}},{"Add":{"text":" \"\\\\begin{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158297"}},{"Add":{"text":" \"\\\\psi_4 &= \\\\left[ {R}_{ijkl}+2K_{i[k}K_{l]j}\\\\right]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158360"}},{"Add":{"text":" \"{n}^i\\\\bar{m}^j{n}^k\\\\bar{m}^l \\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158406"}},{"Add":{"text":" \"& -8\\\\left[ K_{j[k,l]}+{\\\\Gamma }_{j[k}^pK_{l]p}\\\\right]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158472"}},{"Add":{"text":" \"{n}^{[0}\\\\bar{m}^{j]}{n}^k\\\\bar{m}^l \\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158523"}},{"Add":{"text":" \"& +4\\\\left[ {R}_{jl}-K_{jp}K_l^p+KK_{jl}\\\\right]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158581"}},{"Add":{"text":" \"{n}^{[0}\\\\bar{m}^{j]}{n}^{[0}\\\\bar{m}^{l]},\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158634"}},{"Add":{"text":" \"\\\\end{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158656"}},{"Add":{"text":" \"where $\\\\bar{m}^\\\\mu$ is the complex conjugate of $m^\\\\mu$, and $n^\\\\mu$ is real. The third term is given by\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158774"}},{"Add":{"text":" \"\\\\begin{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158798"}},{"Add":{"text":" \"{n}^{[0}\\\\bar{m}^{j]}{n}^{[0}\\\\bar{m}^{l]}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158850"}},{"Add":{"text":" \"&= \\\\frac{1}{2}({n}^{0}\\\\bar{m}^{j} - {n}^{j}\\\\bar{m}^{0} )\\\\frac{1}{2}({n}^{0}\\\\bar{m}^{l} - {n}^{l}\\\\bar{m}^{0} )\\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:158979"}},{"Add":{"text":" \"&= \\\\frac{1}{4}({n}^{0}\\\\bar{m}^{j} - {n}^{j}\\\\bar{m}^{0} )({n}^{0}\\\\bar{m}^{l} - {n}^{l}\\\\bar{m}^{0} )\\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159096"}},{"Add":{"text":" \"&= \\\\frac{1}{4}({n}^{0}\\\\bar{m}^{j}{n}^{0}\\\\bar{m}^{l} - {n}^{j}\\\\bar{m}^{0}{n}^{0}\\\\bar{m}^{l} - {n}^{0}\\\\bar{m}^{j}{n}^{l}\\\\bar{m}^{0} + {n}^{j}\\\\bar{m}^{0}{n}^{l}\\\\bar{m}^{0})\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159285"}},{"Add":{"text":" \"\\\\end{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159307"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159317"}},{"Add":{"text":" \"Only $m^\\\\mu$ is complex, so we can separate the real and imaginary parts of $\\\\psi_4$ by hand, defining $M^\\\\mu$ to now be the real part of $\\\\bar{m}^\\\\mu$ and $\\\\mathcal{M}^\\\\mu$ to be the imaginary part. All of the above products are of the form ${n}^\\\\mu\\\\bar{m}^\\\\nu{n}^\\\\eta\\\\bar{m}^\\\\delta$, so let's evalute the real and imaginary parts of this product once, for all such terms:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159713"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159723"}},{"Add":{"text":" \"\\\\begin{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159747"}},{"Add":{"text":" \"{n}^\\\\mu\\\\bar{m}^\\\\nu{n}^\\\\eta\\\\bar{m}^\\\\delta\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159803"}},{"Add":{"text":" \"&= {n}^\\\\mu(M^\\\\nu - i \\\\mathcal{M}^\\\\nu){n}^\\\\eta(M^\\\\delta - i \\\\mathcal{M}^\\\\delta) \\\\\\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159904"}},{"Add":{"text":" \"&= \\\\left({n}^\\\\mu M^\\\\nu {n}^\\\\eta M^\\\\delta -\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:159961"}},{"Add":{"text":" \"{n}^\\\\mu \\\\mathcal{M}^\\\\nu {n}^\\\\eta \\\\mathcal{M}^\\\\delta \\\\right)+\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160038"}},{"Add":{"text":" \"i \\\\left(\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160057"}},{"Add":{"text":" \"-{n}^\\\\mu M^\\\\nu {n}^\\\\eta \\\\mathcal{M}^\\\\delta\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160114"}},{"Add":{"text":" \"-{n}^\\\\mu \\\\mathcal{M}^\\\\nu {n}^\\\\eta M^\\\\delta\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160171"}},{"Add":{"text":" \"\\\\right)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160189"}},{"Add":{"text":" \"\\\\end{align}\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160211"}},{"Add":{"text":" \"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160220"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160225"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160230"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160234"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160258"}},{"Add":{"text":" \"execution_count\": 10,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160284"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160303"}},{"Add":{"text":" \"outputs\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160319"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160325"}},{"Add":{"text":" \"name\": \"stdout\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160348"}},{"Add":{"text":" \"output_type\": \"stream\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160378"}},{"Add":{"text":" \"text\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160393"}},{"Add":{"text":" \"initialize_param() minor warning: Did nothing; already initialized parameter reference_metric::M_PI\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160504"}},{"Add":{"text":" \"initialize_param() minor warning: Did nothing; already initialized parameter reference_metric::xmin\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160615"}},{"Add":{"text":" \"initialize_param() minor warning: Did nothing; already initialized parameter reference_metric::xmax\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160726"}},{"Add":{"text":" \"initialize_param() minor warning: Did nothing; already initialized parameter reference_metric::ymin\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160837"}},{"Add":{"text":" \"initialize_param() minor warning: Did nothing; already initialized parameter reference_metric::ymax\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:160948"}},{"Add":{"text":" \"initialize_param() minor warning: Did nothing; already initialized parameter reference_metric::zmin\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161059"}},{"Add":{"text":" \"initialize_param() minor warning: Did nothing; already initialized parameter reference_metric::zmax\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161169"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161176"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161182"}},{"Add":{"text":" ],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161188"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161203"}},{"Add":{"text":" \"# mre4U = ixp.declarerank1(\\\"mre4U\\\",DIM=4)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161256"}},{"Add":{"text":" \"# mim4U = ixp.declarerank1(\\\"mim4U\\\",DIM=4)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161309"}},{"Add":{"text":" \"# n4U = ixp.declarerank1(\\\"n4U\\\" ,DIM=4)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161362"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161372"}},{"Add":{"text":" \"import BSSN.Psi4_tetrads as P4t\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161413"}},{"Add":{"text":" \"P4t.Psi4_tetrads()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161441"}},{"Add":{"text":" \"mre4U = P4t.mre4U\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161468"}},{"Add":{"text":" \"mim4U = P4t.mim4U\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161495"}},{"Add":{"text":" \"n4U = P4t.n4U\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161518"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161528"}},{"Add":{"text":" \"def tetrad_product__Real_psi4(n,Mre,Mim, mu,nu,eta,delta):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161597"}},{"Add":{"text":" \" return +n[mu]*Mre[nu]*n[eta]*Mre[delta] - n[mu]*Mim[nu]*n[eta]*Mim[delta]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161684"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161694"}},{"Add":{"text":" \"def tetrad_product__Imag_psi4(n,Mre,Mim, mu,nu,eta,delta):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161763"}},{"Add":{"text":" \" return -n[mu]*Mre[nu]*n[eta]*Mim[delta] - n[mu]*Mim[nu]*n[eta]*Mre[delta]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161850"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161860"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161870"}},{"Add":{"text":" \"psi4_re = sp.sympify(0)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161903"}},{"Add":{"text":" \"psi4_im = sp.sympify(0)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161936"}},{"Add":{"text":" \"# First term:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161959"}},{"Add":{"text":" \"for i in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:161989"}},{"Add":{"text":" \" for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162023"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162061"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162103"}},{"Add":{"text":" \" psi4_re += rank4term1[i][j][k][l]*tetrad_product__Real_psi4(n4U,mre4U,mim4U, i+1,j+1,k+1,l+1)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162222"}},{"Add":{"text":" \" psi4_im += rank4term1[i][j][k][l]*tetrad_product__Imag_psi4(n4U,mre4U,mim4U, i+1,j+1,k+1,l+1)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162341"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162351"}},{"Add":{"text":" \"# Second term:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162375"}},{"Add":{"text":" \"for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162405"}},{"Add":{"text":" \" for k in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162439"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162477"}},{"Add":{"text":" \" psi4_re += rank3term2[j][k][l] * \\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162534"}},{"Add":{"text":" \" sp.Rational(1,2)*(+tetrad_product__Real_psi4(n4U,mre4U,mim4U, 0,j+1,k+1,l+1)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162643"}},{"Add":{"text":" \" -tetrad_product__Real_psi4(n4U,mre4U,mim4U, j+1,0,k+1,l+1) )\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162754"}},{"Add":{"text":" \" psi4_im += rank3term2[j][k][l] * \\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162811"}},{"Add":{"text":" \" sp.Rational(1,2)*(+tetrad_product__Imag_psi4(n4U,mre4U,mim4U, 0,j+1,k+1,l+1)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:162920"}},{"Add":{"text":" \" -tetrad_product__Imag_psi4(n4U,mre4U,mim4U, j+1,0,k+1,l+1) )\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163031"}},{"Add":{"text":" \"# Third term:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163054"}},{"Add":{"text":" \"for j in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163084"}},{"Add":{"text":" \" for l in range(DIM):\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163118"}},{"Add":{"text":" \" psi4_re += rank2term3[j][l] * \\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163168"}},{"Add":{"text":" \" (sp.Rational(1,4)*(+tetrad_product__Real_psi4(n4U,mre4U,mim4U, 0,j+1,0,l+1)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163276"}},{"Add":{"text":" \" -tetrad_product__Real_psi4(n4U,mre4U,mim4U, j+1,0,0,l+1)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163384"}},{"Add":{"text":" \" -tetrad_product__Real_psi4(n4U,mre4U,mim4U, 0,j+1,l+1,0)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163492"}},{"Add":{"text":" \" +tetrad_product__Real_psi4(n4U,mre4U,mim4U, j+1,0,l+1,0)))\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163602"}},{"Add":{"text":" \" psi4_im += rank2term3[j][l] * \\\\\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163652"}},{"Add":{"text":" \" (sp.Rational(1,4)*(+tetrad_product__Imag_psi4(n4U,mre4U,mim4U, 0,j+1,0,l+1)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163760"}},{"Add":{"text":" \" -tetrad_product__Imag_psi4(n4U,mre4U,mim4U, j+1,0,0,l+1)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163868"}},{"Add":{"text":" \" -tetrad_product__Imag_psi4(n4U,mre4U,mim4U, 0,j+1,l+1,0)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:163976"}},{"Add":{"text":" \" +tetrad_product__Imag_psi4(n4U,mre4U,mim4U, j+1,0,l+1,0)))\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164083"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164088"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164093"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164097"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164125"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164144"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164159"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164197"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164207"}},{"Add":{"text":" \"# Step 6: Code validation against BSSN.Psi4 NRPy+ module \\\\[Back to [top](#toc)\\\\]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164299"}},{"Add":{"text":" \"$$\\\\label{code_validation}$$\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164337"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164347"}},{"Add":{"text":" \"As a code validation check, we verify agreement in the SymPy expressions for the RHSs of the BSSN equations between\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164472"}},{"Add":{"text":" \"1. this tutorial and \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164503"}},{"Add":{"text":" \"2. the NRPy+ BSSN.Psi4 module.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164543"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164553"}},{"Add":{"text":" \"By default, we compare all quantities in Spherical coordinates, though other coordinate systems may be chosen.\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164670"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164675"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164680"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164684"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164708"}},{"Add":{"text":" \"execution_count\": 11,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164734"}},{"Add":{"text":" \"metadata\": {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164751"}},{"Add":{"text":" \"scrolled\": true","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164772"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164778"}},{"Add":{"text":" \"outputs\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164794"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164800"}},{"Add":{"text":" \"name\": \"stdout\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164823"}},{"Add":{"text":" \"output_type\": \"stream\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164853"}},{"Add":{"text":" \"text\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164868"}},{"Add":{"text":" \"STARTING NEW\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164892"}},{"Add":{"text":" \"Wrote to file \\\"Psi4_new.h\\\"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164932"}},{"Add":{"text":" \"FINISHED NEW\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164956"}},{"Add":{"text":" \"STARTING OLD\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:164980"}},{"Add":{"text":" \"Wrote to file \\\"Psi4_old.h\\\"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165020"}},{"Add":{"text":" \"FINISHED OLD\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165043"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165050"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165056"}},{"Add":{"text":" ],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165062"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165077"}},{"Add":{"text":" \"outCparams = \\\"preindent=1,outCfileaccess=w,outCverbose=False,includebraces=False\\\"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165170"}},{"Add":{"text":" \"print(\\\"STARTING NEW\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165203"}},{"Add":{"text":" \"fin.FD_outputC(\\\"Psi4_new.h\\\", lhrh(lhs=\\\"psi4_real\\\", rhs=psi4_im), outCparams)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165293"}},{"Add":{"text":" \"print(\\\"FINISHED NEW\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165326"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165336"}},{"Add":{"text":" \"gri.glb_gridfcs_list = []\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165371"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165381"}},{"Add":{"text":" \"import WeylScal4NRPy.WeylScalars_Cartesian as W4\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165439"}},{"Add":{"text":" \"W4.WeylScalars_Cartesian()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165475"}},{"Add":{"text":" \"print(\\\"STARTING OLD\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165508"}},{"Add":{"text":" \"fin.FD_outputC(\\\"Psi4_old.h\\\", lhrh(lhs=\\\"psi4_real\\\", rhs=W4.psi4i), outCparams)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165599"}},{"Add":{"text":" \"print(\\\"FINISHED OLD\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165632"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165642"}},{"Add":{"text":" \"# print(\\\"FullSimplify[\\\"+str(sp.mathematica_code(psi4_re-W4.psi4r))+\\\"]\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165727"}},{"Add":{"text":" \"# with open(\\\"math.txt\\\",\\\"w\\\") as file:\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165777"}},{"Add":{"text":" \"# file.write(\\\"FullSimplify[\\\"+str(sp.mathematica_code(psi4_re-W4.psi4r))+\\\"]\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165871"}},{"Add":{"text":" \" \\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165885"}},{"Add":{"text":" \"# # Call the BSSN_RHSs() function from within the\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165944"}},{"Add":{"text":" \"# # BSSN/BSSN_RHSs.py module,\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:165992"}},{"Add":{"text":" \"# # which should do exactly the same as in Steps 1-16 above.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166071"}},{"Add":{"text":" \"# print(\\\"vvv Ignore the minor warnings below. vvv\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166134"}},{"Add":{"text":" \"# import BSSN.Psi4 as BP4\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166169"}},{"Add":{"text":" \"# BP4.Psi4()\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166191"}},{"Add":{"text":" \"# print(\\\"^^^ Ignore the minor warnings above. ^^^\\\\n\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166257"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166267"}},{"Add":{"text":" \"# print(\\\"Consistency check between this tutorial and BSSN.Psi4 NRPy+ module: ALL SHOULD BE ZERO.\\\")\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166377"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166387"}},{"Add":{"text":" \"# print(\\\"psi4_im - BP4.psi4_im = \\\" + str(psi4_im - BP4.psi4_im))\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166463"}},{"Add":{"text":" \"# print(\\\"psi4_re - BP4.psi4_re = \\\" + str(psi4_re - BP4.psi4_re))\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166536"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166541"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166546"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166550"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166574"}},{"Add":{"text":" \"execution_count\": 12,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166600"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166619"}},{"Add":{"text":" \"outputs\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166635"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166641"}},{"Add":{"text":" \"name\": \"stdout\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166664"}},{"Add":{"text":" \"output_type\": \"stream\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166694"}},{"Add":{"text":" \"text\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166709"}},{"Add":{"text":" \"GOOD: 9.858968807130199e-16 : 1.678026634904849e-08 1.678026634904847e-08\\r\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166795"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166802"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166808"}},{"Add":{"text":" ],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166814"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166829"}},{"Add":{"text":" \"!gcc -O2 psi4_tester.c -o psi4_tester -lm\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166880"}},{"Add":{"text":" \"!./psi4_tester 4 4 4\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166907"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166912"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166917"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166921"}},{"Add":{"text":" \"cell_type\": \"markdown\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166949"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166968"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:166983"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167022"}},{"Add":{"text":" \"\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167032"}},{"Add":{"text":" \"# Step 7: Output this notebook to $\\\\LaTeX$-formatted PDF file \\\\[Back to [top](#toc)\\\\]\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167130"}},{"Add":{"text":" \"$$\\\\label{latex_pdf_output}$$\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167166"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167171"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167176"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167180"}},{"Add":{"text":" \"cell_type\": \"code\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167204"}},{"Add":{"text":" \"execution_count\": 13,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167230"}},{"Add":{"text":" \"metadata\": {},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167249"}},{"Add":{"text":" \"outputs\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167265"}},{"Add":{"text":" {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167271"}},{"Add":{"text":" \"name\": \"stdout\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167294"}},{"Add":{"text":" \"output_type\": \"stream\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167324"}},{"Add":{"text":" \"text\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167339"}},{"Add":{"text":" \"[NbConvertApp] Converting notebook Tutorial-Psi4.ipynb to latex\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167414"}},{"Add":{"text":" \"[NbConvertApp] Writing 61056 bytes to Tutorial-Psi4.tex\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167481"}},{"Add":{"text":" \"This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167590"}},{"Add":{"text":" \" restricted \\\\write18 enabled.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167632"}},{"Add":{"text":" \"entering extended mode\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167666"}},{"Add":{"text":" \"This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167775"}},{"Add":{"text":" \" restricted \\\\write18 enabled.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167817"}},{"Add":{"text":" \"entering extended mode\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167851"}},{"Add":{"text":" \"This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex)\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:167960"}},{"Add":{"text":" \" restricted \\\\write18 enabled.\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168002"}},{"Add":{"text":" \"entering extended mode\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168035"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168042"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168048"}},{"Add":{"text":" ],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168054"}},{"Add":{"text":" \"source\": [","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168069"}},{"Add":{"text":" \"!jupyter nbconvert --to latex --template latex_nrpy_style.tplx --log-level='WARN' Tutorial-Psi4.ipynb\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168180"}},{"Add":{"text":" \"!pdflatex -interaction=batchmode Tutorial-Psi4.tex\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168240"}},{"Add":{"text":" \"!pdflatex -interaction=batchmode Tutorial-Psi4.tex\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168300"}},{"Add":{"text":" \"!pdflatex -interaction=batchmode Tutorial-Psi4.tex\\n\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168360"}},{"Add":{"text":" \"!rm -f Tut*.out Tut*.aux Tut*.log\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168400"}},{"Add":{"text":" ]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168405"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168409"}},{"Add":{"text":" ],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168413"}},{"Add":{"text":" \"metadata\": {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168428"}},{"Add":{"text":" \"kernelspec\": {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168446"}},{"Add":{"text":" \"display_name\": \"Python 2\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168477"}},{"Add":{"text":" \"language\": \"python\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168502"}},{"Add":{"text":" \"name\": \"python2\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168523"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168528"}},{"Add":{"text":" \"language_info\": {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168549"}},{"Add":{"text":" \"codemirror_mode\": {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168573"}},{"Add":{"text":" \"name\": \"ipython\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168596"}},{"Add":{"text":" \"version\": 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168613"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168619"}},{"Add":{"text":" \"file_extension\": \".py\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168647"}},{"Add":{"text":" \"mimetype\": \"text/x-python\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168679"}},{"Add":{"text":" \"name\": \"python\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168700"}},{"Add":{"text":" \"nbconvert_exporter\": \"python\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168735"}},{"Add":{"text":" \"pygments_lexer\": \"ipython2\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168768"}},{"Add":{"text":" \"version\": \"2.7.13\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168791"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168795"}},{"Add":{"text":" },","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168799"}},{"Add":{"text":" \"nbformat\": 4,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168815"}},{"Add":{"text":" \"nbformat_minor\": 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168836"}},{"Add":{"text":"}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168838"}}]}},{"FileAdd":{"meta":{"basename":"WeylScal4NRPy","metadata":1005},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation/WeylScal4NRPy","context":[{"change":0,"pos":133012}],"contents":[]}},{"FileAdd":{"meta":{"basename":"WeylScalars_Cartesian.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation/WeylScal4NRPy/WeylScalars_Cartesian.py","context":[{"change":0,"pos":168856}],"contents":[{"Add":{"text":"# This code calculates the Weyl scalars psi0, psi1, psi2, psi3, and psi4. It does so by following the paper","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:168992"}},{"Add":{"text":"# Baker, Campanelli, and Lousto. PRD 65, 044001 (2002), gr-qc/0104063 and the example set by the Kranc-","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169096"}},{"Add":{"text":"# generated ETK thorn which can be found at https://bitbucket.org/einsteintoolkit/einsteinanalysis/src","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169199"}},{"Add":{"text":"# Step 1: import all needed modules from NRPy+:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169247"}},{"Add":{"text":"import NRPy_param_funcs as par","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169278"}},{"Add":{"text":"import indexedexp as ixp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169303"}},{"Add":{"text":"import grid as gri","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169322"}},{"Add":{"text":"import finite_difference as fin","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169354"}},{"Add":{"text":"from outputC import *","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169376"}},{"Add":{"text":"import sympy as sp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169395"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169396"}},{"Add":{"text":"# Step 2: Initialize WeylScalars parameters","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169440"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169462"}},{"Add":{"text":"# Current option: Approx_QuasiKinnersley = choice made in Baker, Campanelli, and Lousto. PRD 65, 044001 (2002)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169573"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char *\", thismodule, \"TetradChoice\", \"Approx_QuasiKinnersley\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169673"}},{"Add":{"text":"# This controls what gets output. Acceptable values are \"psi4_only\", \"all_psis\", and \"all_psis_and_invariants\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169784"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char *\", thismodule, \"output_scalars\", \"all_psis_and_invariants\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169887"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169888"}},{"Add":{"text":"# Step 3: Define the rank-3 version of the Levi-Civita symbol. Amongst","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:169959"}},{"Add":{"text":"# other possible uses, this is needed for the construction of the approximate ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170046"}},{"Add":{"text":"# quasi-Kinnersley tetrad.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170081"}},{"Add":{"text":"def define_LeviCivitaSymbol_rank3(DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170124"}},{"Add":{"text":" if DIM == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170142"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170183"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170184"}},{"Add":{"text":" LeviCivitaSymbol = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170223"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170224"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170249"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170278"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170311"}},{"Add":{"text":" # From https://codegolf.stackexchange.com/questions/160359/levi-civita-symbol :","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170407"}},{"Add":{"text":" LeviCivitaSymbol[i][j][k] = (i - j) * (j - k) * (k - i) / 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170483"}},{"Add":{"text":" return LeviCivitaSymbol","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170511"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170512"}},{"Add":{"text":"# Step 1: Call BSSNs. This module computes many different quantities related to the metric,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170604"}},{"Add":{"text":"# many of which will be essential here. We must first change to our desired coordinate","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170699"}},{"Add":{"text":"# system, however.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170726"}},{"Add":{"text":"def WeylScalars_Cartesian():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170755"}},{"Add":{"text":" # We do not need the barred or hatted quantities calculated when using Cartesian coordinates.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170853"}},{"Add":{"text":" # Instead, we declare the PHYSICAL metric and extrinsic curvature as grid functions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:170942"}},{"Add":{"text":" gammaDD = ixp.register_gridfunctions_for_single_rank2(\"AUX\",\"gammaDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171026"}},{"Add":{"text":" kDD = ixp.register_gridfunctions_for_single_rank2(\"AUX\",\"kDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171102"}},{"Add":{"text":" gammaUU, detgamma = ixp.symm_matrix_inverter3x3(gammaDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171163"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171168"}},{"Add":{"text":" output_scalars = par.parval_from_str(\"output_scalars\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171227"}},{"Add":{"text":" global psi4r,psi4i,psi3r,psi3i,psi2r,psi2i,psi1r,psi1i,psi0r,psi0i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171298"}},{"Add":{"text":"# if output_scalars is \"all_psis_and_invariants\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171351"}},{"Add":{"text":"# psi4r,psi4i,psi3r,psi3i,psi2r,psi2i,psi1r,psi1i,psi0r,psi0i = sp.symbols(\"psi4r psi4i\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171447"}},{"Add":{"text":"# psi3r psi3i\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171543"}},{"Add":{"text":"# psi2r psi2i\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171639"}},{"Add":{"text":"# psi1r psi1i\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171735"}},{"Add":{"text":"# psi0r psi0i\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171832"}},{"Add":{"text":" # elif output_scalars is \"all_psis\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171872"}},{"Add":{"text":" psi4r,psi4i,psi3r,psi3i,psi2r,psi2i,psi1r,psi1i,psi0r,psi0i = gri.register_gridfunctions(\"AUX\",[\"psi4r\",\"psi4i\",\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:171990"}},{"Add":{"text":" \"psi3r\",\"psi3i\",\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172108"}},{"Add":{"text":" \"psi2r\",\"psi2i\",\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172226"}},{"Add":{"text":" \"psi1r\",\"psi1i\",\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172344"}},{"Add":{"text":" \"psi0r\",\"psi0i\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172462"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172463"}},{"Add":{"text":" # Step 2a: Set spatial dimension (must be 3 for BSSN)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172521"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172533"}},{"Add":{"text":" par.set_parval_from_str(\"grid::DIM\",DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172578"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172579"}},{"Add":{"text":" # Step 2b: Set the coordinate system to Cartesian","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172633"}},{"Add":{"text":" x,y,z = gri.register_gridfunctions(\"AUX\",[\"x\",\"y\",\"z\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172693"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172694"}},{"Add":{"text":" # Step 2c: Set which tetrad is used; at the moment, only one supported option","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172776"}},{"Add":{"text":" if par.parval_from_str(\"WeylScal4NRPy.WeylScalars_Cartesian::TetradChoice\") == \"Approx_QuasiKinnersley\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172885"}},{"Add":{"text":" # Step 3a: Choose 3 orthogonal vectors. Here, we choose one in the azimuthal ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:172971"}},{"Add":{"text":" # direction, one in the radial direction, and the cross product of the two. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173065"}},{"Add":{"text":" # Eqs 5.6, 5.7 in https://arxiv.org/pdf/gr-qc/0104063.pdf:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173132"}},{"Add":{"text":" # v_1^a &= [-y,x,0] \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173163"}},{"Add":{"text":" # v_2^a &= [x,y,z] \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173193"}},{"Add":{"text":" # v_3^a &= {\\rm det}(g)^{1/2} g^{ad} \\epsilon_{dbc} v_1^b v_2^c,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173266"}},{"Add":{"text":" v1U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173296"}},{"Add":{"text":" v2U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173326"}},{"Add":{"text":" v3U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173356"}},{"Add":{"text":" v1U[0] = -y","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173376"}},{"Add":{"text":" v1U[1] = x","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173395"}},{"Add":{"text":" v1U[2] = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173426"}},{"Add":{"text":" v2U[0] = x","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173445"}},{"Add":{"text":" v2U[1] = y","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173464"}},{"Add":{"text":" v2U[2] = z","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173483"}},{"Add":{"text":" LeviCivitaSymbol_rank3 = define_LeviCivitaSymbol_rank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173548"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173577"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173610"}},{"Add":{"text":" for c in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173647"}},{"Add":{"text":" for d in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173688"}},{"Add":{"text":" v3U[a] += sp.sqrt(detgamma) * gammaUU[a][d] * LeviCivitaSymbol_rank3[d][b][c] * v1U[b] *v2U[c]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173807"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173808"}},{"Add":{"text":" # Step 3b: Gram-Schmidt orthonormalization of the vectors.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173875"}},{"Add":{"text":" # The w_i^a vectors here are used to temporarily hold values on the way to the final vectors e_i^a","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:173982"}},{"Add":{"text":" # e_1^a &= \\frac{v_1^a}{\\omega_{11}} \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174030"}},{"Add":{"text":" # e_2^a &= \\frac{v_2^a - \\omega_{12} e_1^a}{\\omega_{22}} \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174098"}},{"Add":{"text":" # e_3^a &= \\frac{v_3^a - \\omega_{13} e_1^a - \\omega_{23} e_2^a}{\\omega_{33}}, \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174187"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174196"}},{"Add":{"text":" # Normalize the first vector","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174233"}},{"Add":{"text":" w1U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174263"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174292"}},{"Add":{"text":" w1U[a] = v1U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174320"}},{"Add":{"text":" omega11 = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174352"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174381"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174414"}},{"Add":{"text":" omega11 += w1U[a] * w1U[b] * gammaDD[a][b]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174473"}},{"Add":{"text":" e1U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174503"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174532"}},{"Add":{"text":" e1U[a] = w1U[a] / sp.sqrt(omega11)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174579"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174580"}},{"Add":{"text":" # Subtract off the portion of the first vector along the second, then normalize","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174668"}},{"Add":{"text":" omega12 = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174700"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174729"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174762"}},{"Add":{"text":" omega12 += e1U[a] * v2U[b] * gammaDD[a][b]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174821"}},{"Add":{"text":" w2U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174851"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174880"}},{"Add":{"text":" w2U[a] = v2U[a] - omega12*e1U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174925"}},{"Add":{"text":" omega22 = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174957"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:174986"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175019"}},{"Add":{"text":" omega22 += w2U[a] * w2U[b] *gammaDD[a][b]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175077"}},{"Add":{"text":" e2U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175107"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175136"}},{"Add":{"text":" e2U[a] = w2U[a] / sp.sqrt(omega22)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175183"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175184"}},{"Add":{"text":" # Subtract off the portion of the first and second vectors along the third, then normalize","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175283"}},{"Add":{"text":" omega13 = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175315"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175344"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175377"}},{"Add":{"text":" omega13 += e1U[a] * v3U[b] * gammaDD[a][b]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175436"}},{"Add":{"text":" omega23 = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175468"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175497"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175530"}},{"Add":{"text":" omega23 += e2U[a] * v3U[b] * gammaDD[a][b]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175589"}},{"Add":{"text":" w3U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175619"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175648"}},{"Add":{"text":" w3U[a] = v3U[a] - omega13*e1U[a] - omega23*e2U[a]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175710"}},{"Add":{"text":" omega33 = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175742"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175771"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175804"}},{"Add":{"text":" omega33 += w3U[a] * w3U[b] * gammaDD[a][b]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175863"}},{"Add":{"text":" e3U = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175893"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175922"}},{"Add":{"text":" e3U[a] = w3U[a] / sp.sqrt(omega33)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175969"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:175970"}},{"Add":{"text":" # Step 3c: Construct the tetrad itself.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176018"}},{"Add":{"text":" # Eqs. 5.6:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176038"}},{"Add":{"text":" # l^a &= \\frac{1}{\\sqrt{2}} e_2^a \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176083"}},{"Add":{"text":" # n^a &= -\\frac{1}{\\sqrt{2}} e_2^a \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176129"}},{"Add":{"text":" # m^a &= \\frac{1}{\\sqrt{2}} (e_3^a + i e_1^a) \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176186"}},{"Add":{"text":" # \\overset{*}{m}{}^a &= \\frac{1}{\\sqrt{2}} (e_3^a - i e_1^a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176255"}},{"Add":{"text":" isqrt2 = 1/sp.sqrt(2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176285"}},{"Add":{"text":" ltetU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176317"}},{"Add":{"text":" ntetU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176349"}},{"Add":{"text":" #mtetU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176382"}},{"Add":{"text":" #mtetccU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176417"}},{"Add":{"text":" remtetU = ixp.zerorank1() # SymPy does not like trying to take the real/imaginary parts of such a","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176523"}},{"Add":{"text":" immtetU = ixp.zerorank1() # complicated expression as the Weyl scalars, so we will do it ourselves.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176631"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176660"}},{"Add":{"text":" ltetU[i] = isqrt2 * e2U[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176699"}},{"Add":{"text":" ntetU[i] = -isqrt2 * e2U[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176739"}},{"Add":{"text":" remtetU[i] = isqrt2 * e3U[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176780"}},{"Add":{"text":" immtetU[i] = isqrt2 * e1U[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176821"}},{"Add":{"text":" nn = isqrt2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176841"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176842"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176852"}},{"Add":{"text":" print(\"Error: TetradChoice == \"+par.parval_from_str(\"TetradChoice\")+\" unsupported!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176945"}},{"Add":{"text":" exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176961"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:176962"}},{"Add":{"text":" gammaDD_dD = ixp.declarerank3(\"gammaDD_dD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177018"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177019"}},{"Add":{"text":" # Define the Christoffel symbols","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177056"}},{"Add":{"text":" GammaUDD = ixp.zerorank3(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177090"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177115"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177144"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177177"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177214"}},{"Add":{"text":" GammaUDD[i][k][l] += (sp.Rational(1,2))*gammaUU[i][m]*\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177290"}},{"Add":{"text":" (gammaDD_dD[m][k][l] + gammaDD_dD[m][l][k] - gammaDD_dD[k][l][m])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177397"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177398"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177399"}},{"Add":{"text":" # Step 4b: Declare and construct the Riemann curvature tensor:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177466"}},{"Add":{"text":" # R_{abcd} = \\frac{1}{2} (\\gamma_{ad,cb}+\\gamma_{bc,da}-\\gamma_{ac,bd}-\\gamma_{bd,ac}) ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177558"}},{"Add":{"text":" # + \\gamma_{je} \\Gamma^{j}_{bc}\\Gamma^{e}_{ad} - \\gamma_{je} \\Gamma^{j}_{bd} \\Gamma^{e}_{ac}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177666"}},{"Add":{"text":" gammaDD_dDD = ixp.declarerank4(\"gammaDD_dDD\",\"sym01_sym23\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177730"}},{"Add":{"text":" RiemannDDDD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177764"}},{"Add":{"text":" for a in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177789"}},{"Add":{"text":" for b in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177818"}},{"Add":{"text":" for c in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177851"}},{"Add":{"text":" for d in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177888"}},{"Add":{"text":" RiemannDDDD[a][b][c][d] = (gammaDD_dDD[a][d][c][b] + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:177963"}},{"Add":{"text":" gammaDD_dDD[b][c][d][a] - \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178038"}},{"Add":{"text":" gammaDD_dDD[a][c][b][d] - \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178113"}},{"Add":{"text":" gammaDD_dDD[b][d][a][c]) / 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178189"}},{"Add":{"text":" for e in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178230"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178275"}},{"Add":{"text":" RiemannDDDD[a][b][c][d] += gammaDD[j][e] * GammaUDD[j][b][c] * GammaUDD[e][a][d] - \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178389"}},{"Add":{"text":" gammaDD[j][e] * GammaUDD[j][b][d] * GammaUDD[e][a][c]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178499"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178500"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178501"}},{"Add":{"text":" # Step 4c: We also need the extrinsic curvature tensor $K_{ij}$. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178571"}},{"Add":{"text":" # In Cartesian coordinates, we already made the components gridfunctions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178649"}},{"Add":{"text":" # We will, however, need to calculate the trace of K seperately:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178718"}},{"Add":{"text":" trK = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178742"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178767"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178796"}},{"Add":{"text":" trK += gammaUU[i][j] * kDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178841"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178842"}},{"Add":{"text":" # Step 5: Build the formula for \\psi_4.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178886"}},{"Add":{"text":" # Gauss equation: involving the Riemann tensor and extrinsic curvature.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:178962"}},{"Add":{"text":" # GaussDDDD[i][j][k][l] =& R_{ijkl} + 2K_{i[k}K_{l]j}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179020"}},{"Add":{"text":" GaussDDDD = ixp.zerorank4()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179052"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179077"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179106"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179139"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179176"}},{"Add":{"text":" GaussDDDD[i][j][k][l] = RiemannDDDD[i][j][k][l] + kDD[i][k]*kDD[l][j] - kDD[i][l]*kDD[k][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179288"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179289"}},{"Add":{"text":" # Codazzi equation: involving partial derivatives of the extrinsic curvature. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179372"}},{"Add":{"text":" # We will first need to declare derivatives of kDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179427"}},{"Add":{"text":" # CodazziDDD[j][k][l] =& -2 (K_{j[k,l]} + \\Gamma^p_{j[k} K_{l]p})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179497"}},{"Add":{"text":" kDD_dD = ixp.declarerank3(\"kDD_dD\",\"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179545"}},{"Add":{"text":" CodazziDDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179578"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179603"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179632"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179665"}},{"Add":{"text":" CodazziDDD[j][k][l] = kDD_dD[j][l][k] - kDD_dD[j][k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179737"}},{"Add":{"text":" for p in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179774"}},{"Add":{"text":" CodazziDDD[j][k][l] += GammaUDD[p][j][l]*kDD[k][p] - GammaUDD[p][j][k]*kDD[l][p]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179875"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179876"}},{"Add":{"text":" # Another piece. While not associated with any particular equation,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:179948"}},{"Add":{"text":" # this is still useful for organizational purposes.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180004"}},{"Add":{"text":" # RojoDD[j][l]} = & R_{jl} - K_{jp} K^p_l + KK_{jl} \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180063"}},{"Add":{"text":" # = & \\gamma^{pd} R_{jpld} - K_{jp} K^p_l + KK_{jl}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180133"}},{"Add":{"text":" RojoDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180162"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180187"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180216"}},{"Add":{"text":" RojoDD[j][l] = trK*kDD[j][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180257"}},{"Add":{"text":" for p in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180290"}},{"Add":{"text":" for d in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180327"}},{"Add":{"text":" RojoDD[j][l] += gammaUU[p][d]*RiemannDDDD[j][p][l][d] - kDD[j][p]*gammaUU[p][d]*kDD[d][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180437"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180438"}},{"Add":{"text":" # Now we can calculate $\\psi_4$ itself! We assume l^0 = n^0 = \\frac{1}{\\sqrt{2}} ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180524"}},{"Add":{"text":" # and m^0 = \\overset{*}{m}{}^0 = 0 to simplify these equations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180592"}},{"Add":{"text":" # We calculate the Weyl scalars as defined in https://arxiv.org/abs/gr-qc/0104063","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180678"}},{"Add":{"text":" # In terms of the above-defined quantites, the psis are defined as:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180750"}},{"Add":{"text":" # \\psi_4 =&\\ (\\text{GaussDDDD[i][j][k][l]}) n^i \\overset{*}{m}{}^j n^k \\overset{*}{m}{}^l \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180847"}},{"Add":{"text":" # &+2 (\\text{CodazziDDD[j][k][l]}) n^{0} \\overset{*}{m}{}^{j} n^k \\overset{*}{m}{}^l \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:180947"}},{"Add":{"text":" # &+ (\\text{RojoDD[j][l]}) n^{0} \\overset{*}{m}{}^{j} n^{0} \\overset{*}{m}{}^{l}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181041"}},{"Add":{"text":" # \\psi_3 =&\\ (\\text{GaussDDDD[i][j][k][l]}) l^i n^j \\overset{*}{m}{}^k n^l \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181123"}},{"Add":{"text":" # &+ (\\text{CodazziDDD[j][k][l]}) (l^{0} n^{j} \\overset{*}{m}{}^k n^l - l^{j} n^{0} \\overset{*}{m}{}^k n^l - l^k n^j\\overset{*}{m}{}^l n^0) \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181278"}},{"Add":{"text":" # &- (\\text{RojoDD[j][l]}) l^{0} n^{j} \\overset{*}{m}{}^l n^0 - l^{j} n^{0} \\overset{*}{m}{}^l n^0 \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181392"}},{"Add":{"text":" # \\psi_2 =&\\ (\\text{GaussDDDD[i][j][k][l]}) l^i m^j \\overset{*}{m}{}^k n^l \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181474"}},{"Add":{"text":" # &+ (\\text{CodazziDDD[j][k][l]}) (l^{0} m^{j} \\overset{*}{m}{}^k n^l - l^{j} m^{0} \\overset{*}{m}{}^k n^l - l^k m^l \\overset{*}{m}{}^l n^0) \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181630"}},{"Add":{"text":" # &- (\\text{RojoDD[j][l]}) l^0 m^j \\overset{*}{m}{}^l n^0 \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181703"}},{"Add":{"text":" # \\psi_1 =&\\ (\\text{GaussDDDD[i][j][k][l]}) n^i l^j m^k l^l \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181770"}},{"Add":{"text":" # &+ (\\text{CodazziDDD[j][k][l]}) (n^{0} l^{j} m^k l^l - n^{j} l^{0} m^k l^l - n^k l^l m^j l^0) \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181881"}},{"Add":{"text":" # &- (\\text{RojoDD[j][l]}) (n^{0} l^{j} m^l l^0 - n^{j} l^{0} m^l l^0) \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:181967"}},{"Add":{"text":" # \\psi_0 =&\\ (\\text{GaussDDDD[i][j][k][l]}) l^i m^j l^k m^l \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182034"}},{"Add":{"text":" # &+2 (\\text{CodazziDDD[j][k][l]}) (l^0 m^j l^k m^l + l^k m^l l^0 m^j) \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182120"}},{"Add":{"text":" # &+ (\\text{RojoDD[j][l]}) l^0 m^j l^0 m^j. \\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182179"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182180"}},{"Add":{"text":" psi4r = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182206"}},{"Add":{"text":" psi4i = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182232"}},{"Add":{"text":" psi3r = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182258"}},{"Add":{"text":" psi3i = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182284"}},{"Add":{"text":" psi2r = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182310"}},{"Add":{"text":" psi2i = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182336"}},{"Add":{"text":" psi1r = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182362"}},{"Add":{"text":" psi1i = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182388"}},{"Add":{"text":" psi0r = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182414"}},{"Add":{"text":" psi0i = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182440"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182465"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182494"}},{"Add":{"text":" psi4r += RojoDD[j][l] * nn * nn * (remtetU[j]*remtetU[l]-immtetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182586"}},{"Add":{"text":" psi4i += RojoDD[j][l] * nn * nn * (-remtetU[j]*immtetU[l]-immtetU[j]*remtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182679"}},{"Add":{"text":" psi3r +=-RojoDD[j][l] * nn * nn * (ntetU[j]-ltetU[j]) * remtetU[l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182758"}},{"Add":{"text":" psi3i += RojoDD[j][l] * nn * nn * (ntetU[j]-ltetU[j]) * immtetU[l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182837"}},{"Add":{"text":" psi2r +=-RojoDD[j][l] * nn * nn * (remtetU[l]*remtetU[j]+immtetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:182929"}},{"Add":{"text":" psi2i +=-RojoDD[j][l] * nn * nn * (immtetU[l]*remtetU[j]-remtetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183021"}},{"Add":{"text":" psi1r += RojoDD[j][l] * nn * nn * (ntetU[j]*remtetU[l]-ltetU[j]*remtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183109"}},{"Add":{"text":" psi1i += RojoDD[j][l] * nn * nn * (ntetU[j]*immtetU[l]-ltetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183197"}},{"Add":{"text":" psi0r += RojoDD[j][l] * nn * nn * (remtetU[j]*remtetU[l]-immtetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183289"}},{"Add":{"text":" psi0i += RojoDD[j][l] * nn * nn * (remtetU[j]*immtetU[l]+immtetU[j]*remtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183381"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183382"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183407"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183436"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183469"}},{"Add":{"text":" psi4r += 2 * CodazziDDD[j][k][l] * ntetU[k] * nn * (remtetU[j]*remtetU[l]-immtetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183582"}},{"Add":{"text":" psi4i += 2 * CodazziDDD[j][k][l] * ntetU[k] * nn * (-remtetU[j]*immtetU[l]-immtetU[j]*remtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183696"}},{"Add":{"text":" psi3r += 1 * CodazziDDD[j][k][l] * nn * ((ntetU[j]-ltetU[j])*remtetU[k]*ntetU[l]-remtetU[j]*ltetU[k]*ntetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183823"}},{"Add":{"text":" psi3i +=-1 * CodazziDDD[j][k][l] * nn * ((ntetU[j]-ltetU[j])*immtetU[k]*ntetU[l]-immtetU[j]*ltetU[k]*ntetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:183950"}},{"Add":{"text":" psi2r += 1 * CodazziDDD[j][k][l] * nn * (ntetU[l]*(remtetU[j]*remtetU[k]+immtetU[j]*immtetU[k])-ltetU[k]*(remtetU[j]*remtetU[l]+immtetU[j]*immtetU[l]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184118"}},{"Add":{"text":" psi2i += 1 * CodazziDDD[j][k][l] * nn * (ntetU[l]*(immtetU[j]*remtetU[k]-remtetU[j]*immtetU[k])-ltetU[k]*(remtetU[j]*immtetU[l]-immtetU[j]*remtetU[l]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184286"}},{"Add":{"text":" psi1r += 1 * CodazziDDD[j][k][l] * nn * (ltetU[j]*remtetU[k]*ltetU[l]-remtetU[j]*ntetU[k]*ltetU[l]-ntetU[j]*remtetU[k]*ltetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184431"}},{"Add":{"text":" psi1i += 1 * CodazziDDD[j][k][l] * nn * (ltetU[j]*immtetU[k]*ltetU[l]-immtetU[j]*ntetU[k]*ltetU[l]-ntetU[j]*immtetU[k]*ltetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184576"}},{"Add":{"text":" psi0r += 2 * CodazziDDD[j][k][l] * nn * ltetU[k]*(remtetU[j]*remtetU[l]-immtetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184687"}},{"Add":{"text":" psi0i += 2 * CodazziDDD[j][k][l] * nn * ltetU[k]*(remtetU[j]*immtetU[l]+immtetU[j]*remtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184798"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184799"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184800"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184825"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184854"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184887"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:184924"}},{"Add":{"text":" psi4r += GaussDDDD[i][j][k][l] * ntetU[i] * ntetU[k] * (remtetU[j]*remtetU[l]-immtetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185045"}},{"Add":{"text":" psi4i += GaussDDDD[i][j][k][l] * ntetU[i] * ntetU[k] * (-remtetU[j]*immtetU[l]-immtetU[j]*remtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185167"}},{"Add":{"text":" psi3r += GaussDDDD[i][j][k][l] * ltetU[i] * ntetU[j] * remtetU[k] * ntetU[l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185264"}},{"Add":{"text":" psi3i +=-GaussDDDD[i][j][k][l] * ltetU[i] * ntetU[j] * immtetU[k] * ntetU[l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185361"}},{"Add":{"text":" psi2r += GaussDDDD[i][j][k][l] * ltetU[i] * ntetU[l] * (remtetU[j]*remtetU[k]+immtetU[j]*immtetU[k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185482"}},{"Add":{"text":" psi2i += GaussDDDD[i][j][k][l] * ltetU[i] * ntetU[l] * (immtetU[j]*remtetU[k]-remtetU[j]*immtetU[k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185603"}},{"Add":{"text":" psi1r += GaussDDDD[i][j][k][l] * ntetU[i] * ltetU[j] * remtetU[k] * ltetU[l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185700"}},{"Add":{"text":" psi1i += GaussDDDD[i][j][k][l] * ntetU[i] * ltetU[j] * immtetU[k] * ltetU[l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185797"}},{"Add":{"text":" psi0r += GaussDDDD[i][j][k][l] * ltetU[i] * ltetU[k] * (remtetU[j]*remtetU[l]-immtetU[j]*immtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:185918"}},{"Add":{"text":" psi0i += GaussDDDD[i][j][k][l] * ltetU[i] * ltetU[k] * (remtetU[j]*immtetU[l]+immtetU[j]*remtetU[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186039"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186040"}}]}},{"FileAdd":{"meta":{"basename":"__init__.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation/WeylScal4NRPy/__init__.py","context":[{"change":0,"pos":168856}],"contents":[]}},{"FileAdd":{"meta":{"basename":"psi4_tester.c","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/Psi4Cartesianvalidation/psi4_tester.c","context":[{"change":0,"pos":133012}],"contents":[{"Add":{"text":"#include ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186093"}},{"Add":{"text":"#include ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186111"}},{"Add":{"text":"#include ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186131"}},{"Add":{"text":"#include ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186153"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186154"}},{"Add":{"text":"/* EVOLVED VARIABLES: */","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186179"}},{"Add":{"text":"#define NUM_AUX_GFS 15","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186202"}},{"Add":{"text":"#define KDD00GF 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186220"}},{"Add":{"text":"#define KDD01GF 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186238"}},{"Add":{"text":"#define KDD02GF 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186256"}},{"Add":{"text":"#define KDD11GF 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186274"}},{"Add":{"text":"#define KDD12GF 4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186292"}},{"Add":{"text":"#define KDD22GF 5","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186310"}},{"Add":{"text":"#define GAMMADD00GF 6","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186332"}},{"Add":{"text":"#define GAMMADD01GF 7","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186354"}},{"Add":{"text":"#define GAMMADD02GF 8","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186376"}},{"Add":{"text":"#define GAMMADD11GF 9","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186398"}},{"Add":{"text":"#define GAMMADD12GF 10","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186421"}},{"Add":{"text":"#define GAMMADD22GF 11","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186444"}},{"Add":{"text":"#define XGF 12","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186459"}},{"Add":{"text":"#define YGF 13","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186474"}},{"Add":{"text":"#define ZGF 14","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186489"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186490"}},{"Add":{"text":"#define REAL double","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186510"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186511"}},{"Add":{"text":"#define NGHOSTS 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186529"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186530"}},{"Add":{"text":"// Cartesian coordinates parameters","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186566"}},{"Add":{"text":"const REAL xmin = -10.,xmax=10.;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186599"}},{"Add":{"text":"const REAL ymin = -10.,ymax=10.;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186632"}},{"Add":{"text":"const REAL zmin = -10.,zmax=10.;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186665"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186666"}},{"Add":{"text":"#define IDX4(g,i,j,k) \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186690"}},{"Add":{"text":"( (i) + Nxx_plus_2NGHOSTS[0] * ( (j) + Nxx_plus_2NGHOSTS[1] * ( (k) + Nxx_plus_2NGHOSTS[2] * (g) ) ) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186793"}},{"Add":{"text":"#define IDX3(i,j,k) ( (i) + Nxx_plus_2NGHOSTS[0] * ( (j) + Nxx_plus_2NGHOSTS[1] * (k) ) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186883"}},{"Add":{"text":"// Assuming idx = IDX3(i,j,k). Much faster if idx can be reused over and over:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:186962"}},{"Add":{"text":"#define IDX4pt(g,idx) ( (idx) + (Nxx_plus_2NGHOSTS[0]*Nxx_plus_2NGHOSTS[1]*Nxx_plus_2NGHOSTS[2]) * (g) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187069"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187070"}},{"Add":{"text":"int main(int argc, const char *argv[]) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187111"}},{"Add":{"text":" // Step 0a: Read command-line input, error out if nonconformant","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187177"}},{"Add":{"text":" if((argc != 4) || atoi(argv[1]) < NGHOSTS || atoi(argv[2]) < NGHOSTS || atoi(argv[3]) < 2 /* FIXME; allow for axisymmetric sims */) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187313"}},{"Add":{"text":" fprintf(stderr,\"Error: Expected three command-line arguments: ./BrillLindquist_Playground Nx0 Nx1 Nx2,\\n\");","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187425"}},{"Add":{"text":" fprintf(stderr,\"where Nx[0,1,2] is the number of grid points in the 0, 1, and 2 directions.\\n\");","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187526"}},{"Add":{"text":" fprintf(stderr,\"Nx[] MUST BE larger than NGHOSTS (= %d)\\n\",NGHOSTS);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187599"}},{"Add":{"text":" exit(1);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187612"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187616"}},{"Add":{"text":" // Step 0b: Set up numerical grid structure, first in space...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187681"}},{"Add":{"text":" const int Nxx[3] = { atoi(argv[1]), atoi(argv[2]), atoi(argv[3]) };","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187751"}},{"Add":{"text":" if(Nxx[0]%2 != 0 || Nxx[1]%2 != 0 || Nxx[2]%2 != 0) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187807"}},{"Add":{"text":" fprintf(stderr,\"Error: Cannot guarantee a proper cell-centered grid if number of grid cells not set to even number.\\n\");","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:187932"}},{"Add":{"text":" fprintf(stderr,\" For example, in case of angular directions, proper symmetry zones will not exist.\\n\");","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188046"}},{"Add":{"text":" exit(1);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188059"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188063"}},{"Add":{"text":" const int Nxx_plus_2NGHOSTS[3] = { Nxx[0]+2*NGHOSTS, Nxx[1]+2*NGHOSTS, Nxx[2]+2*NGHOSTS };","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188156"}},{"Add":{"text":" const int Nxx_plus_2NGHOSTS_tot = Nxx_plus_2NGHOSTS[0]*Nxx_plus_2NGHOSTS[1]*Nxx_plus_2NGHOSTS[2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188256"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188257"}},{"Add":{"text":" REAL *aux_gfs_new = (REAL *)malloc(sizeof(REAL) * NUM_AUX_GFS * Nxx_plus_2NGHOSTS_tot);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188348"}},{"Add":{"text":" REAL *aux_gfs_old = (REAL *)malloc(sizeof(REAL) * NUM_AUX_GFS * Nxx_plus_2NGHOSTS_tot);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188439"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188440"}},{"Add":{"text":" // Step 0d: Set up space and time coordinates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188488"}},{"Add":{"text":" // Step 0d.i: Set \\Delta x^i on uniform grids.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188537"}},{"Add":{"text":" REAL xxmin[3],xxmax[3];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188563"}},{"Add":{"text":" xxmin[0] = xmin;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188582"}},{"Add":{"text":" xxmin[1] = ymin;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188601"}},{"Add":{"text":" xxmin[2] = zmin;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188620"}},{"Add":{"text":" xxmax[0] = xmax;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188639"}},{"Add":{"text":" xxmax[1] = ymax;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188658"}},{"Add":{"text":" xxmax[2] = zmax;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188677"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188678"}},{"Add":{"text":" REAL dxx[3];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188693"}},{"Add":{"text":" for(int i=0;i<3;i++) dxx[i] = (xxmax[i] - xxmin[i]) / ((REAL)Nxx[i]);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188765"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188766"}},{"Add":{"text":" // Step 0d.ii: Set up uniform coordinate grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188815"}},{"Add":{"text":" REAL *xx[3];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188830"}},{"Add":{"text":" for(int i=0;i<3;i++) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188855"}},{"Add":{"text":" xx[i] = (REAL *)malloc(sizeof(REAL)*Nxx_plus_2NGHOSTS[i]);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:188918"}},{"Add":{"text":" for(int j=0;jBSSN Curvi conversion","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201527"}},{"Add":{"text":"def ShiftedKerrSchild(ComputeADMGlobalsOnly = False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201581"}},{"Add":{"text":" global Sph_r_th_ph,r,th,ph, rho2, gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201665"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201670"}},{"Add":{"text":" # All gridfunctions will be written in terms of spherical coordinates (r, th, ph):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201757"}},{"Add":{"text":" r,th,ph = sp.symbols('r th ph', real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201804"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201805"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201817"}},{"Add":{"text":" par.set_parval_from_str(\"grid::DIM\",DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201862"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201863"}},{"Add":{"text":" # Auxiliary variables:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201890"}},{"Add":{"text":" rho2 = sp.symbols('rho2', real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201931"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:201936"}},{"Add":{"text":" # Step 1: Define rho^2, alpha, beta^(r_{KS}), beta^(theta), beta^(phi), gamma_{r_{KS}theta}, gamma_{theta\\phi}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202051"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202052"}},{"Add":{"text":" # r_{KS} = r + r0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202074"}},{"Add":{"text":" rKS = r+r0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202089"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202090"}},{"Add":{"text":" # rho^2 = rKS^2 + a^2*cos^2(theta)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202129"}},{"Add":{"text":" rho2 = rKS*rKS + a*a*sp.cos(th)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202168"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202169"}},{"Add":{"text":" # alpha = 1/sqrt{1 + M*rKS/rho^2}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202207"}},{"Add":{"text":" alphaSph = 1/(sp.sqrt(1 + 2*M*rKS/rho2))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202252"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202253"}},{"Add":{"text":" # Initialize the shift vector, \\beta^i, to zero.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202306"}},{"Add":{"text":" betaSphU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202337"}},{"Add":{"text":" # beta^r = alpha^2*2Mr/rho^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202370"}},{"Add":{"text":" betaSphU[0] = alphaSph*alphaSph*2*M*rKS/rho2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202419"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202420"}},{"Add":{"text":" # Time derivative of shift vector beta^i, B^i, is zero.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202480"}},{"Add":{"text":" BSphU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202508"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202509"}},{"Add":{"text":" # Step 2: Define and construct nonzero components gamma_{r_{KS}r_{KS}}$, gamma_{r_{KS}phi},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202605"}},{"Add":{"text":" # gamma_{thetatheta}, gamma_{phiphi}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202654"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202655"}},{"Add":{"text":" # Initialize \\gamma_{ij} to zero.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202693"}},{"Add":{"text":" gammaSphDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202726"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202727"}},{"Add":{"text":" # gammaDD{rKS rKS} = 1 +2M*rKS/rho^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202768"}},{"Add":{"text":" gammaSphDD[0][0] = 1 + 2*M*rKS/rho2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202808"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202809"}},{"Add":{"text":" # gammaDD{rKS phi} = -a*gammaDD{r r}*sin^2(theta)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202863"}},{"Add":{"text":" gammaSphDD[0][2] = gammaSphDD[2][0] = -a*gammaSphDD[0][0]*sp.sin(th)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202939"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202940"}},{"Add":{"text":" # gammaDD{theta theta} = rho^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:202975"}},{"Add":{"text":" gammaSphDD[1][1] = rho2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203003"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203004"}},{"Add":{"text":" # gammaDD{phi phi} = (rKS^2 + a^2 + 2Mr/rho^2*a^2*sin^2(theta))*sin^2(theta)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203085"}},{"Add":{"text":" gammaSphDD[2][2] = (rKS*rKS + a*a + 2*M*rKS*a*a*sp.sin(th)**2/rho2)*sp.sin(th)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203171"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203176"}},{"Add":{"text":" # Step 3: Define useful quantities A, B, C","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203223"}},{"Add":{"text":" # A = (a^2*cos^2(2theta) + a^2 + 2r^2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203266"}},{"Add":{"text":" A = (a*a*sp.cos(2*th) + a*a + 2*rKS*rKS)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203311"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203312"}},{"Add":{"text":" # B = A + 4M*rKS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203333"}},{"Add":{"text":" B = A + 4*M*rKS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203353"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203354"}},{"Add":{"text":" # D = \\sqrt(2M*rKS/(a^2cos^2(theta) + rKS^2) + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203408"}},{"Add":{"text":" D = sp.sqrt(2*M*rKS/(a*a*sp.cos(th)**2 + rKS*rKS) + 1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203467"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203484"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203489"}},{"Add":{"text":" # Step 4: Define the extrinsic curvature in spherical polar coordinates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203565"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203566"}},{"Add":{"text":" # Establish the 3x3 zero-matrix","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203602"}},{"Add":{"text":" KSphDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203631"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203632"}},{"Add":{"text":" # *** Fill in the nonzero components ***","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203677"}},{"Add":{"text":" # *** This will create an upper-triangular matrix ***","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203735"}},{"Add":{"text":" # K_{r r} = D(A+2Mr)/(A^2*B)[4M(a^2*cos(2theta) + a^2 - 2r^2)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203802"}},{"Add":{"text":" KSphDD[0][0] = D*(A+2*M*rKS)/(A*A*B)*(4*M*(a*a*sp.cos(2*th)+a*a-2*rKS*rKS))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203882"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203883"}},{"Add":{"text":" # K_{r theta} = D/(AB)[8a^2*Mr*sin(theta)cos(theta)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:203940"}},{"Add":{"text":" KSphDD[0][1] = KSphDD[1][0] = D/(A*B)*(8*a*a*M*rKS*sp.sin(th)*sp.cos(th))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204018"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204019"}},{"Add":{"text":" # K_{r phi} = D/A^2[-2aMsin^2(theta)(a^2cos(2theta)+a^2-2r^2)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204086"}},{"Add":{"text":" KSphDD[0][2] = KSphDD[2][0] = D/(A*A)*(-2*a*M*sp.sin(th)**2*(a*a*sp.cos(2*th)+a*a-2*rKS*rKS))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204185"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204186"}},{"Add":{"text":" # K_{theta theta} = D/B[4Mr^2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204221"}},{"Add":{"text":" KSphDD[1][1] = D/B*(4*M*rKS*rKS)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204258"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204259"}},{"Add":{"text":" # K_{theta phi} = D/(AB)*(-8*a^3*Mr*sin^3(theta)cos(theta))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204323"}},{"Add":{"text":" KSphDD[1][2] = KSphDD[2][1] = D/(A*B)*(-8*a**3*M*rKS*sp.sin(th)**3*sp.cos(th))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204406"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204407"}},{"Add":{"text":" # K_{phi phi} = D/(A^2*B)[2Mr*sin^2(theta)(a^4(M+3r)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204464"}},{"Add":{"text":" # +4a^2r^2(2r-M)+4a^2r*cos(2theta)(a^2+r(M+2r))+8r^5)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204525"}},{"Add":{"text":" KSphDD[2][2] = D/(A*A*B)*(2*M*rKS*sp.sin(th)**2*(a**4*(rKS-M)*sp.cos(4*th)\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204605"}},{"Add":{"text":" + a**4*(M+3*rKS)+4*a*a*rKS*rKS*(2*rKS-M)\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204675"}},{"Add":{"text":" + 4*a*a*rKS*sp.cos(2*th)*(a*a + rKS*(M + 2*rKS)) + 8*rKS**5)) ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204775"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204780"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204785"}},{"Add":{"text":" if ComputeADMGlobalsOnly == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204823"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204838"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204843"}},{"Add":{"text":" # Validated against original SENR: ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204883"}},{"Add":{"text":" #print(sp.mathematica_code(gammaSphDD[1][1]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204933"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204934"}},{"Add":{"text":" Sph_r_th_ph = [r,th,ph]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:204962"}},{"Add":{"text":" cf,hDD,lambdaU,aDD,trK,alpha,vetU,betU = \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205009"}},{"Add":{"text":" AtoB.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear(\"Spherical\", Sph_r_th_ph, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205104"}},{"Add":{"text":" gammaSphDD,KSphDD,alphaSph,betaSphU,BSphU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205215"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205216"}},{"Add":{"text":" import BSSN.BSSN_ID_function_string as bIDf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205264"}},{"Add":{"text":" global returnfunction","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205290"}},{"Add":{"text":" returnfunction = bIDf.BSSN_ID_function_string(cf, hDD, lambdaU, aDD, trK, alpha, vetU, betU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205387"}}]}},{"FileAdd":{"meta":{"basename":"StaticTrumpet.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/StaticTrumpet.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module sets up Static Trumpet initial data in terms of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205469"}},{"Add":{"text":"# the variables used in BSSN_RHSs.py","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205506"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205507"}},{"Add":{"text":"# Authors: Terrence Pierre Jacques, terrencepierrej **at** gmail **dot** com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205584"}},{"Add":{"text":"# Zachariah B. Etienne, zachetie **at** gmail **dot** com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205651"}},{"Add":{"text":"# Ian Ruchlin","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205674"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:205675"}},{"Add":{"text":"# ## This module sets up initial data for a static trumpet geometry in spherical coordinates. We can convert from spherical to any coordinate system defined in [reference_metric.py](../edit/reference_metric.py) (e.g., SinhSpherical, Cylindrical, Cartesian, etc.) using the [Exact ADM Spherical-to-BSSNCurvilinear converter module](Tutorial-ADM_Initial_Data-Converting_Exact_ADM_Spherical_or_Cartesian_to_BSSNCurvilinear.ipynb)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206102"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206105"}},{"Add":{"text":"# ### NRPy+ Source Code for this module: [BSSN/BrillLindquist.py](../edit/BSSN/BrillLindquist.py)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206203"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206206"}},{"Add":{"text":"# **All quantities have been validated against the [original SENR code](https://bitbucket.org/zach_etienne/nrpy).**","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206349"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206350"}},{"Add":{"text":"# ### Here we set up Static Trumpet initial data ([Dennison and Baumgarte, 2014](https://arxiv.org/abs/1403.5484)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206466"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206469"}},{"Add":{"text":"# Description of Static Trumpet geometry. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206512"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206515"}},{"Add":{"text":"# **Inputs for initial data**:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206546"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206549"}},{"Add":{"text":"# * The black hole mass $M$.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206578"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206581"}},{"Add":{"text":"# **Additional variables needed for spacetime evolution**:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206640"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206643"}},{"Add":{"text":"# * Desired coordinate system","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206673"}},{"Add":{"text":"# * Desired initial lapse $\\alpha$ and shift $\\beta^i$. We will choose our gauge conditions as $\\alpha=1$ and $\\beta^i=B^i=0$. $\\alpha = \\psi^{-2}$ will yield much better behavior, but the conformal factor $\\psi$ depends on the desired *destination* coordinate system (which may not be spherical coordinates).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206983"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:206984"}},{"Add":{"text":"# Step 1: Initialize core Python/NRPy+ modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207031"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207132"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207192"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207299"}},{"Add":{"text":"import BSSN.ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear as AtoB","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207371"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207372"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207394"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207395"}},{"Add":{"text":"# Input parameters:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207415"}},{"Add":{"text":"M = par.Cparameters(\"REAL\", thismodule, [\"M\"], [1.0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207469"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207470"}},{"Add":{"text":"# ComputeADMGlobalsOnly == True will only set up the ADM global quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207546"}},{"Add":{"text":"# == False will perform the full ADM SphorCart->BSSN Curvi conversion","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207638"}},{"Add":{"text":"def StaticTrumpet(ComputeADMGlobalsOnly = False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207688"}},{"Add":{"text":" global Sph_r_th_ph,r,th,ph, gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207766"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207771"}},{"Add":{"text":" # All gridfunctions will be written in terms of spherical coordinates (r, th, ph):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207858"}},{"Add":{"text":" r,th,ph = sp.symbols('r th ph', real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207905"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207906"}},{"Add":{"text":" # Step 0: Set spatial dimension (must be 3 for BSSN)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207963"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:207975"}},{"Add":{"text":" par.set_parval_from_str(\"grid::DIM\",DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208020"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208021"}},{"Add":{"text":" # Step 1: Set psi, the conformal factor:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208066"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208067"}},{"Add":{"text":" # Auxiliary variables:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208094"}},{"Add":{"text":" psi0 = sp.symbols('psi0', real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208135"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208140"}},{"Add":{"text":" # *** The StaticTrumpet conformal factor ***","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208189"}},{"Add":{"text":" # Dennison and Baumgarte (2014) Eq. 13","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208232"}},{"Add":{"text":" # https://arxiv.org/pdf/1403.5484.pdf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208274"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208279"}},{"Add":{"text":" # psi = sqrt{1 + M/r }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208306"}},{"Add":{"text":" psi0 = sp.sqrt(1 + M/r)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208334"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208339"}},{"Add":{"text":" # *** The physical spatial metric in spherical basis ***","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208400"}},{"Add":{"text":" # Set the upper-triangle of the matrix...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208446"}},{"Add":{"text":" # Eq. 15","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208459"}},{"Add":{"text":" # gamma_{ij} = psi^4 * eta_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208495"}},{"Add":{"text":" # eta_00 = 1, eta_11 = r^2, eta_22 = r^2 * sin^2 (theta) ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208557"}},{"Add":{"text":" gammaSphDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208590"}},{"Add":{"text":" gammaSphDD[0][0] = psi0**4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208621"}},{"Add":{"text":" gammaSphDD[1][1] = psi0**4 * r**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208659"}},{"Add":{"text":" gammaSphDD[2][2] = psi0**4 * r**2*sp.sin(th)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208711"}},{"Add":{"text":" # ... then apply symmetries to get the other components","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208771"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208776"}},{"Add":{"text":" # *** The physical trace-free extrinsic curvature in spherical basis ***","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208853"}},{"Add":{"text":" # Set the upper-triangle of the matrix...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208899"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208900"}},{"Add":{"text":" # Eq.19 and 20","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208919"}},{"Add":{"text":" KSphDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208948"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208949"}},{"Add":{"text":" # K_{rr} = M / r^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:208972"}},{"Add":{"text":" KSphDD[0][0] = -M / r**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209001"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209002"}},{"Add":{"text":" # K_{theta theta} = K_{phi phi} / sin^2 theta = M","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209056"}},{"Add":{"text":" KSphDD[1][1] = M","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209077"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209078"}},{"Add":{"text":" KSphDD[2][2] = M * sp.sin(th)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209115"}},{"Add":{"text":" # ... then apply symmetries to get the other components","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209175"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209180"}},{"Add":{"text":" # Lapse function and shift vector","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209218"}},{"Add":{"text":" # Eq. 15","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209231"}},{"Add":{"text":" # alpha = r / (r+M)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209255"}},{"Add":{"text":" alphaSph = r / (r + M)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209282"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209283"}},{"Add":{"text":" betaSphU = ixp.zerorank1() ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209315"}},{"Add":{"text":" # beta^r = Mr / (r + M)^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209345"}},{"Add":{"text":" betaSphU[0] = M*r / (r + M)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209380"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209385"}},{"Add":{"text":" BSphU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209416"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209417"}},{"Add":{"text":" if ComputeADMGlobalsOnly == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209455"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209470"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209475"}},{"Add":{"text":" # Validated against original SENR: ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209515"}},{"Add":{"text":" #print(sp.mathematica_code(gammaSphDD[1][1]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209565"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209566"}},{"Add":{"text":" Sph_r_th_ph = [r,th,ph]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209594"}},{"Add":{"text":" cf,hDD,lambdaU,aDD,trK,alpha,vetU,betU = \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209641"}},{"Add":{"text":" AtoB.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear(\"Spherical\", Sph_r_th_ph, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209736"}},{"Add":{"text":" gammaSphDD,KSphDD,alphaSph,betaSphU,BSphU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209847"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209848"}},{"Add":{"text":" import BSSN.BSSN_ID_function_string as bIDf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209896"}},{"Add":{"text":" global returnfunction","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:209922"}},{"Add":{"text":" returnfunction = bIDf.BSSN_ID_function_string(cf, hDD, lambdaU, aDD, trK, alpha, vetU, betU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210019"}}]}},{"FileAdd":{"meta":{"basename":"T4UUmunu_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/T4UUmunu_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module performs the conversion of T^{mu nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210137"}},{"Add":{"text":"# in Spherical or Cartesian coordinates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210177"}},{"Add":{"text":"# given as *numerical* expressions (i.e., given as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210228"}},{"Add":{"text":"# numerical values with fixed floating-point precision;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210284"}},{"Add":{"text":"# e.g., in the case of an initial data solver), to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210335"}},{"Add":{"text":"# rescaled BSSN stress-energy source terms.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210379"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210380"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210411"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210454"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210455"}},{"Add":{"text":"# Step P1: Import needed modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210488"}},{"Add":{"text":"from outputC import * # NRPy+: Core C code output module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210557"}},{"Add":{"text":"import finite_difference as fin # NRPy+: Finite difference C code generation module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210643"}},{"Add":{"text":"import grid as gri # NRPy+: Functions having to do with numerical grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210730"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210840"}},{"Add":{"text":"import reference_metric as rfm # NRPy+: Reference metric support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:210908"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211012"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211075"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq # NRPy+: This module depends on the parameter EvolvedConformalFactor_cf,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211182"}},{"Add":{"text":" # which is defined in BSSN.BSSN_quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211266"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211363"}},{"Add":{"text":"import BSSN.BSSN_RHSs as bssnrhs # NRPy+: BSSN RHS quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211426"}},{"Add":{"text":"import loop as lp # NRPy+: Helper module for writing C-code loops","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211492"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211493"}},{"Add":{"text":"def T4UUmunu_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear(CoordType_in,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211572"}},{"Add":{"text":" Tmunu_input_function_name,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211661"}},{"Add":{"text":" pointer_to_ID_inputs=False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211752"}},{"Add":{"text":" # The ADM & BSSN formalisms only work in 3D; they are 3+1 decompositions of Einstein's equations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211854"}},{"Add":{"text":" # To implement axisymmetry or spherical symmetry, simply set all spatial derivatives in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:211949"}},{"Add":{"text":" # the relevant angular directions to zero; DO NOT SET DIM TO ANYTHING BUT 3.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212033"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212034"}},{"Add":{"text":" # Step 0: Set spatial dimension (must be 3 for BSSN)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212091"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212103"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212104"}},{"Add":{"text":" # Step 1: Define the input variables: the 4D stress-energy tensor, and the ADM 3-metric, lapse, & shift:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212213"}},{"Add":{"text":" T4SphorCartUU = ixp.declarerank2(\"T4SphorCartUU\", \"sym01\", DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212283"}},{"Add":{"text":" gammaSphorCartDD = ixp.declarerank2(\"gammaSphorCartDD\", \"sym01\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212352"}},{"Add":{"text":" alphaSphorCart = sp.symbols(\"alphaSphorCart\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212402"}},{"Add":{"text":" betaSphorCartU = ixp.declarerank1(\"betaSphorCartU\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212458"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212459"}},{"Add":{"text":" # Step 2: All Tmunu initial data quantities are functions of xx0,xx1,xx2, but","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212541"}},{"Add":{"text":" # in the Spherical or Cartesian basis.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212592"}},{"Add":{"text":" # We first define the BSSN stress-energy source terms in the Spherical","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212675"}},{"Add":{"text":" # or Cartesian basis, respectively.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212723"}},{"Add":{"text":" # To get \\gamma_{\\mu \\nu} = gammabar4DD[mu][nu], we'll need to construct the 4-metric, using Eq. 2.122 in B&S:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212838"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212839"}},{"Add":{"text":" # S_{ij} = \\gamma_{i \\mu} \\gamma_{j \\nu} T^{\\mu \\nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212896"}},{"Add":{"text":" # S_{i} = -\\gamma_{i\\mu} n_\\nu T^{\\mu\\nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212943"}},{"Add":{"text":" # S = \\gamma^{ij} S_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:212977"}},{"Add":{"text":" # rho = n_\\mu n_\\nu T^{\\mu\\nu},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213016"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213017"}},{"Add":{"text":" # where","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213029"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213030"}},{"Add":{"text":" # \\gamma_{\\mu\\nu} = g_{\\mu\\nu} + n_\\mu n_\\nu","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213079"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213080"}},{"Add":{"text":" # and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213090"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213091"}},{"Add":{"text":" # n_mu = {-\\alpha,0,0,0},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213121"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213122"}},{"Add":{"text":" # Step 2.1: Construct the 4-metric based on the input ADM quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213196"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213197"}},{"Add":{"text":" # This is provided by Eq 4.47 in [Gourgoulhon](https://arxiv.org/pdf/gr-qc/0703035.pdf):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213290"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213291"}},{"Add":{"text":" # g_{tt} = -\\alpha^2 + \\beta^k \\beta_k","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213334"}},{"Add":{"text":" # g_{ti} = \\beta_i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213357"}},{"Add":{"text":" # g_{ij} = \\gamma_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213384"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213385"}},{"Add":{"text":" # Eq. 2.121 in B&S","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213408"}},{"Add":{"text":" betaSphorCartD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213445"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213470"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213499"}},{"Add":{"text":" betaSphorCartD[i] += gammaSphorCartDD[i][j] * betaSphorCartU[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213575"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213576"}},{"Add":{"text":" # Now compute the beta contraction.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213616"}},{"Add":{"text":" beta2 = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213642"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213667"}},{"Add":{"text":" beta2 += betaSphorCartU[i] * betaSphorCartD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213722"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213723"}},{"Add":{"text":" # Eq. 2.122 in B&S","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213746"}},{"Add":{"text":" g4SphorCartDD = ixp.zerorank2(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213787"}},{"Add":{"text":" g4SphorCartDD[0][0] = -alphaSphorCart ** 2 + beta2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213842"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213867"}},{"Add":{"text":" g4SphorCartDD[i + 1][0] = g4SphorCartDD[0][i + 1] = betaSphorCartD[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213945"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213970"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:213999"}},{"Add":{"text":" g4SphorCartDD[i + 1][j + 1] = gammaSphorCartDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214064"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214065"}},{"Add":{"text":" # Step 2.2: Construct \\gamma_{mu nu} = g_{mu nu} + n_mu n_nu:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214131"}},{"Add":{"text":" n4SphorCartD = ixp.zerorank1(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214171"}},{"Add":{"text":" n4SphorCartD[0] = -alphaSphorCart","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214209"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214210"}},{"Add":{"text":" gamma4SphorCartDD = ixp.zerorank2(DIM=4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214255"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214279"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214307"}},{"Add":{"text":" gamma4SphorCartDD[mu][nu] = g4SphorCartDD[mu][nu] + n4SphorCartD[mu] * n4SphorCartD[nu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214407"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214408"}},{"Add":{"text":" # Step 2.3: We now have all we need to construct the BSSN source","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214477"}},{"Add":{"text":" # terms in the current basis (Spherical or Cartesian):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214546"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214547"}},{"Add":{"text":" # S_{ij} = \\gamma_{i \\mu} \\gamma_{j \\nu} T^{\\mu \\nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214604"}},{"Add":{"text":" # S_{i} = -\\gamma_{i\\mu} n_\\nu T^{\\mu\\nu}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214651"}},{"Add":{"text":" # S = \\gamma^{ij} S_{ij}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214685"}},{"Add":{"text":" # rho = n_\\mu n_\\nu T^{\\mu\\nu},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214724"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214725"}},{"Add":{"text":" SSphorCartDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214760"}},{"Add":{"text":" SSphorCartD = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214795"}},{"Add":{"text":" SSphorCart = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214828"}},{"Add":{"text":" rhoSphorCart = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214861"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214862"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214887"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214916"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214948"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:214984"}},{"Add":{"text":" SSphorCartDD[i][j] += gamma4SphorCartDD[i + 1][mu] * gamma4SphorCartDD[j + 1][nu] * T4SphorCartUU[mu][nu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215110"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215111"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215136"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215164"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215196"}},{"Add":{"text":" SSphorCartD[i] += -gamma4SphorCartDD[i + 1][mu] * n4SphorCartD[nu] * T4SphorCartUU[mu][nu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215303"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215304"}},{"Add":{"text":" gammaSphorCartUU, gammaDET = ixp.symm_matrix_inverter3x3(gammaSphorCartDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215383"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215408"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215437"}},{"Add":{"text":" SSphorCart += gammaSphorCartUU[i][j] * SSphorCartDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215507"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215508"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215532"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215560"}},{"Add":{"text":" rhoSphorCart += n4SphorCartD[mu] * n4SphorCartD[nu] * T4SphorCartUU[mu][nu]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215648"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215649"}},{"Add":{"text":" # Step 3: Perform basis conversion to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215691"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215692"}},{"Add":{"text":" # Make sure that rfm.reference_metric() has been called.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215753"}},{"Add":{"text":" # We'll need the variables it defines throughout this module.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215822"}},{"Add":{"text":" if rfm.have_already_called_reference_metric_function == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215889"}},{"Add":{"text":" print(\"Error. Called Tmunu_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear() without\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:215988"}},{"Add":{"text":" print(\" first setting up reference metric, by calling rfm.reference_metric().\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216082"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216102"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216103"}},{"Add":{"text":" # Step 1: All input quantities are in terms of r,th,ph or x,y,z. We want them in terms","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216194"}},{"Add":{"text":" # of xx0,xx1,xx2, so here we call sympify_integers__replace_rthph() to replace","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216285"}},{"Add":{"text":" # r,th,ph or x,y,z, respectively, with the appropriate functions of xx0,xx1,xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216377"}},{"Add":{"text":" # as defined for this particular reference metric in reference_metric.py's","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216464"}},{"Add":{"text":" # xxSph[] or xxCart[], respectively:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216513"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_oID_xx = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216549"}},{"Add":{"text":" if CoordType_in == \"Spherical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216585"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_oID_xx = rfm.xxSph","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216632"}},{"Add":{"text":" elif CoordType_in == \"Cartesian\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216670"}},{"Add":{"text":" r_th_ph_or_Cart_xyz_oID_xx = rfm.xxCart","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216718"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216728"}},{"Add":{"text":" print(\"Error: Can only convert ADM Cartesian or Spherical initial data to BSSN Curvilinear coords.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216837"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216857"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216858"}},{"Add":{"text":" # Next apply Jacobian transformations to convert into the (xx0,xx1,xx2) basis","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216940"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:216941"}},{"Add":{"text":" # alpha is a scalar, so no Jacobian transformation is necessary.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217010"}},{"Add":{"text":" alpha = alphaSphorCart","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217037"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217038"}},{"Add":{"text":" Jac_dUSphorCart_dDrfmUD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217084"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217109"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217138"}},{"Add":{"text":" Jac_dUSphorCart_dDrfmUD[i][j] = sp.diff(r_th_ph_or_Cart_xyz_oID_xx[i], rfm.xx[j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217232"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217233"}},{"Add":{"text":" Jac_dUrfm_dDSphorCartUD, dummyDET = ixp.generic_matrix_inverter3x3(Jac_dUSphorCart_dDrfmUD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217329"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217330"}},{"Add":{"text":" betaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217358"}},{"Add":{"text":" BU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217383"}},{"Add":{"text":" gammaSphorCartDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217422"}},{"Add":{"text":" KDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217448"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217473"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217502"}},{"Add":{"text":" betaU[i] += Jac_dUrfm_dDSphorCartUD[i][j] * betaSphorCartU[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217576"}},{"Add":{"text":" BU[i] += Jac_dUrfm_dDSphorCartUD[i][j] * BSphorCartU[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217644"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217677"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217714"}},{"Add":{"text":" gammaSphorCartDD[i][j] += Jac_dUSphorCart_dDrfmUD[k][i] * Jac_dUSphorCart_dDrfmUD[l][j] * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217826"}},{"Add":{"text":" gammaSphorCartDD[k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:217886"}},{"Add":{"text":" KDD[i][j] += Jac_dUSphorCart_dDrfmUD[k][i] * Jac_dUSphorCart_dDrfmUD[l][j] * KSphorCartDD[k][l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218002"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218003"}},{"Add":{"text":" # Step 3: All ADM quantities were input into this function in the Spherical or Cartesian","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218096"}},{"Add":{"text":" # basis, as functions of r,th,ph or x,y,z, respectively. In Steps 1 and 2 above,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218189"}},{"Add":{"text":" # we converted them to the xx0,xx1,xx2 basis, and as functions of xx0,xx1,xx2.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218280"}},{"Add":{"text":" # Here we convert ADM quantities to their BSSN Curvilinear counterparts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218365"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218366"}},{"Add":{"text":" # Step 3.1: Convert ADM $\\gamma_{ij}$ to BSSN $\\bar{\\gamma}_{ij}$:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218437"}},{"Add":{"text":" # We have (Eqs. 2 and 3 of [Ruchlin *et al.*](https://arxiv.org/pdf/1712.07658.pdf)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218529"}},{"Add":{"text":" # \\bar{\\gamma}_{i j} = \\left(\\frac{\\bar{\\gamma}}{\\gamma}\\right)^{1/3} \\gamma_{ij}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218616"}},{"Add":{"text":" gammaSphorCartUU, gammaDET = ixp.symm_matrix_inverter3x3(gammaSphorCartDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218695"}},{"Add":{"text":" gammabarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218728"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218753"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218782"}},{"Add":{"text":" gammabarDD[i][j] = (rfm.detgammahat / gammaDET) ** (sp.Rational(1, 3)) * gammaSphorCartDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218890"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218891"}},{"Add":{"text":" # Step 3.2: Convert the extrinsic curvature $K_{ij}$ to the trace-free extrinsic","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:218976"}},{"Add":{"text":" # curvature $\\bar{A}_{ij}$, plus the trace of the extrinsic curvature $K$,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219065"}},{"Add":{"text":" # where (Eq. 3 of [Baumgarte *et al.*](https://arxiv.org/pdf/1211.6632.pdf)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219157"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219158"}},{"Add":{"text":" # K = \\gamma^{ij} K_{ij}, and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219192"}},{"Add":{"text":" # \\bar{A}_{ij} &= \\left(\\frac{\\bar{\\gamma}}{\\gamma}\\right)^{1/3} \\left(K_{ij} - \\frac{1}{3} \\gamma_{ij} K \\right)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219310"}},{"Add":{"text":" trK = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219334"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219359"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219388"}},{"Add":{"text":" trK += gammaSphorCartUU[i][j] * KDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219442"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219443"}},{"Add":{"text":" AbarDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219472"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219497"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219526"}},{"Add":{"text":" AbarDD[i][j] = (rfm.detgammahat / gammaDET) ** (sp.Rational(1, 3)) * (","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219609"}},{"Add":{"text":" KDD[i][j] - sp.Rational(1, 3) * gammaSphorCartDD[i][j] * trK)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219695"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219696"}},{"Add":{"text":" # Step 3.3: Set the conformal factor variable $\\texttt{cf}$, which is set","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219774"}},{"Add":{"text":" # by the \"BSSN_RHSs::EvolvedConformalFactor_cf\" parameter. For example if","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219862"}},{"Add":{"text":" # \"EvolvedConformalFactor_cf\" is set to \"phi\", we can use Eq. 3 of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:219943"}},{"Add":{"text":" # [Ruchlin *et al.*](https://arxiv.org/pdf/1712.07658.pdf),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220017"}},{"Add":{"text":" # which in arbitrary coordinates is written:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220076"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220077"}},{"Add":{"text":" # \\phi = \\frac{1}{12} \\log\\left(\\frac{\\gamma}{\\bar{\\gamma}}\\right).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220149"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220150"}},{"Add":{"text":" # Alternatively if \"BSSN_RHSs::EvolvedConformalFactor_cf\" is set to \"chi\", then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220234"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220235"}},{"Add":{"text":" # \\chi = e^{-4 \\phi} = \\exp\\left(-4 \\frac{1}{12} \\left(\\frac{\\gamma}{\\bar{\\gamma}}\\right)\\right)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220336"}},{"Add":{"text":" # = \\exp\\left(-\\frac{1}{3} \\log\\left(\\frac{\\gamma}{\\bar{\\gamma}}\\right)\\right) = \\left(\\frac{\\gamma}{\\bar{\\gamma}}\\right)^{-1/3}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220475"}},{"Add":{"text":" #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220481"}},{"Add":{"text":" # Finally if \"BSSN_RHSs::EvolvedConformalFactor_cf\" is set to \"W\", then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220557"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220558"}},{"Add":{"text":" # W = e^{-2 \\phi} = \\exp\\left(-2 \\frac{1}{12} \\log\\left(\\frac{\\gamma}{\\bar{\\gamma}}\\right)\\right) =","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220662"}},{"Add":{"text":" # \\exp\\left(-\\frac{1}{6} \\log\\left(\\frac{\\gamma}{\\bar{\\gamma}}\\right)\\right) =","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220745"}},{"Add":{"text":" # \\left(\\frac{\\gamma}{\\bar{\\gamma}}\\right)^{-1/6}.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220800"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220801"}},{"Add":{"text":" # First compute gammabarDET:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220834"}},{"Add":{"text":" gammabarUU, gammabarDET = ixp.symm_matrix_inverter3x3(gammabarDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220904"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220905"}},{"Add":{"text":" cf = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220928"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220929"}},{"Add":{"text":" if par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"phi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:220995"}},{"Add":{"text":" cf = sp.Rational(1, 12) * sp.log(gammaDET / gammabarDET)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221060"}},{"Add":{"text":" elif par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"chi\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221128"}},{"Add":{"text":" cf = (gammaDET / gammabarDET) ** (-sp.Rational(1, 3))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221190"}},{"Add":{"text":" elif par.parval_from_str(\"EvolvedConformalFactor_cf\") == \"W\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221256"}},{"Add":{"text":" cf = (gammaDET / gammabarDET) ** (-sp.Rational(1, 6))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221318"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221328"}},{"Add":{"text":" print(\"Error EvolvedConformalFactor_cf type = \\\"\" + par.parval_from_str(\"EvolvedConformalFactor_cf\") + \"\\\" unknown.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221454"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221474"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221475"}},{"Add":{"text":" # Step 4: Rescale tensorial quantities according to the prescription described in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221561"}},{"Add":{"text":" # the [BSSN in curvilinear coordinates tutorial module](Tutorial-BSSNCurvilinear.ipynb)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221661"}},{"Add":{"text":" # (also [Ruchlin *et al.*](https://arxiv.org/pdf/1712.07658.pdf)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221740"}},{"Add":{"text":" #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221746"}},{"Add":{"text":" # h_{ij} &= (\\bar{\\gamma}_{ij} - \\hat{\\gamma}_{ij})/\\text{ReDD[i][j]}\\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221822"}},{"Add":{"text":" # a_{ij} &= \\bar{A}_{ij}/\\text{ReDD[i][j]}\\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221871"}},{"Add":{"text":" # \\lambda^i &= \\bar{\\Lambda}^i/\\text{ReU[i]}\\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221922"}},{"Add":{"text":" # \\mathcal{V}^i &= \\beta^i/\\text{ReU[i]}\\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:221969"}},{"Add":{"text":" # \\mathcal{B}^i &= B^i/\\text{ReU[i]}\\\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222012"}},{"Add":{"text":" hDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222042"}},{"Add":{"text":" aDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222072"}},{"Add":{"text":" vetU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222102"}},{"Add":{"text":" betU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222132"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222157"}},{"Add":{"text":" vetU[i] = betaU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222205"}},{"Add":{"text":" betU[i] = BU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222253"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222282"}},{"Add":{"text":" hDD[i][j] = (gammabarDD[i][j] - rfm.ghatDD[i][j]) / rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222361"}},{"Add":{"text":" aDD[i][j] = AbarDD[i][j] / rfm.ReDD[i][j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222440"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222441"}},{"Add":{"text":" # Step 5: Output all ADM-to-BSSN expressions to a C function. This function","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222521"}},{"Add":{"text":" # must first call the ID_ADM_SphorCart() defined above. Using these","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222601"}},{"Add":{"text":" # Spherical or Cartesian data, it sets up all quantities needed for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222681"}},{"Add":{"text":" # BSSNCurvilinear initial data, *except* $\\lambda^i$, which must be","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222761"}},{"Add":{"text":" # computed from numerical data using finite-difference derivatives.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222841"}},{"Add":{"text":" with open(\"BSSN/ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs.h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:222931"}},{"Add":{"text":" file.write(\"void ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs(const REAL xx0xx1xx2[3],\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223035"}},{"Add":{"text":" if pointer_to_ID_inputs == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223076"}},{"Add":{"text":" file.write(\"ID_inputs *other_inputs,\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223127"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223141"}},{"Add":{"text":" file.write(\"ID_inputs other_inputs,\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223191"}},{"Add":{"text":" file.write(\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223214"}},{"Add":{"text":" REAL *hDD00,REAL *hDD01,REAL *hDD02,REAL *hDD11,REAL *hDD12,REAL *hDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223307"}},{"Add":{"text":" REAL *aDD00,REAL *aDD01,REAL *aDD02,REAL *aDD11,REAL *aDD12,REAL *aDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223400"}},{"Add":{"text":" REAL *trK, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223432"}},{"Add":{"text":" REAL *vetU0,REAL *vetU1,REAL *vetU2,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223489"}},{"Add":{"text":" REAL *betU0,REAL *betU1,REAL *betU2,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223546"}},{"Add":{"text":" REAL *alpha, REAL *cf) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223592"}},{"Add":{"text":" REAL gammaSphorCartDD00,gammaSphorCartDD01,gammaSphorCartDD02,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223661"}},{"Add":{"text":" gammaSphorCartDD11,gammaSphorCartDD12,gammaSphorCartDD22;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223730"}},{"Add":{"text":" REAL KSphorCartDD00,KSphorCartDD01,KSphorCartDD02,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223787"}},{"Add":{"text":" KSphorCartDD11,KSphorCartDD12,KSphorCartDD22;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223844"}},{"Add":{"text":" REAL alphaSphorCart,betaSphorCartU0,betaSphorCartU1,betaSphorCartU2;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223919"}},{"Add":{"text":" REAL BSphorCartU0,BSphorCartU1,BSphorCartU2;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:223970"}},{"Add":{"text":" const REAL xx0 = xx0xx1xx2[0];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224007"}},{"Add":{"text":" const REAL xx1 = xx0xx1xx2[1];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224044"}},{"Add":{"text":" const REAL xx2 = xx0xx1xx2[2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224081"}},{"Add":{"text":" REAL xyz_or_rthph[3];\\n\"\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224115"}},{"Add":{"text":" outCparams = \"preindent=1,outCfileaccess=a,outCverbose=False,includebraces=False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224201"}},{"Add":{"text":" outputC(r_th_ph_or_Cart_xyz_oID_xx[0:3], [\"xyz_or_rthph[0]\", \"xyz_or_rthph[1]\", \"xyz_or_rthph[2]\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224305"}},{"Add":{"text":" \"BSSN/ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs.h\", outCparams + \",CSE_enable=False\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224413"}},{"Add":{"text":" with open(\"BSSN/ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs.h\", \"a\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224503"}},{"Add":{"text":" file.write(\" \"+ADM_input_function_name+\"\"\"(xyz_or_rthph, other_inputs,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224587"}},{"Add":{"text":" &gammaSphorCartDD00,&gammaSphorCartDD01,&gammaSphorCartDD02,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224670"}},{"Add":{"text":" &gammaSphorCartDD11,&gammaSphorCartDD12,&gammaSphorCartDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224753"}},{"Add":{"text":" &KSphorCartDD00,&KSphorCartDD01,&KSphorCartDD02,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224824"}},{"Add":{"text":" &KSphorCartDD11,&KSphorCartDD12,&KSphorCartDD22,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224895"}},{"Add":{"text":" &alphaSphorCart,&betaSphorCartU0,&betaSphorCartU1,&betaSphorCartU2,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:224985"}},{"Add":{"text":" &BSphorCartU0,&BSphorCartU1,&BSphorCartU2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225051"}},{"Add":{"text":" // Next compute all rescaled BSSN curvilinear quantities:\\n\"\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225123"}},{"Add":{"text":" outCparams = \"preindent=1,outCfileaccess=a,outCverbose=False,includebraces=False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225209"}},{"Add":{"text":" outputC([hDD[0][0], hDD[0][1], hDD[0][2], hDD[1][1], hDD[1][2], hDD[2][2],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225288"}},{"Add":{"text":" aDD[0][0], aDD[0][1], aDD[0][2], aDD[1][1], aDD[1][2], aDD[2][2],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225367"}},{"Add":{"text":" trK, vetU[0], vetU[1], vetU[2], betU[0], betU[1], betU[2],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225439"}},{"Add":{"text":" alpha, cf],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225464"}},{"Add":{"text":" [\"*hDD00\", \"*hDD01\", \"*hDD02\", \"*hDD11\", \"*hDD12\", \"*hDD22\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225537"}},{"Add":{"text":" \"*aDD00\", \"*aDD01\", \"*aDD02\", \"*aDD11\", \"*aDD12\", \"*aDD22\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225610"}},{"Add":{"text":" \"*trK\", \"*vetU0\", \"*vetU1\", \"*vetU2\", \"*betU0\", \"*betU1\", \"*betU2\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225691"}},{"Add":{"text":" \"*alpha\", \"*cf\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225722"}},{"Add":{"text":" \"BSSN/ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs.h\", params=outCparams)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225815"}},{"Add":{"text":" with open(\"BSSN/ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs.h\", \"a\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225905"}},{"Add":{"text":" file.write(\"}\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225931"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225932"}},{"Add":{"text":" # Step 5.A: Output the driver function for the above","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:225989"}},{"Add":{"text":" # function ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226068"}},{"Add":{"text":" # Next write the driver function for ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226164"}},{"Add":{"text":" with open(\"BSSN/ID_BSSN__ALL_BUT_LAMBDAs.h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226227"}},{"Add":{"text":" file.write(\"void ID_BSSN__ALL_BUT_LAMBDAs(const int Nxx_plus_2NGHOSTS[3],REAL *xx[3],\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226323"}},{"Add":{"text":" if pointer_to_ID_inputs == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226364"}},{"Add":{"text":" file.write(\"ID_inputs *other_inputs,\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226415"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226429"}},{"Add":{"text":" file.write(\"ID_inputs other_inputs,\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226479"}},{"Add":{"text":" file.write(\"REAL *in_gfs) {\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226519"}},{"Add":{"text":" file.write(lp.loop([\"i2\", \"i1\", \"i0\"], [\"0\", \"0\", \"0\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226583"}},{"Add":{"text":" [\"Nxx_plus_2NGHOSTS[2]\", \"Nxx_plus_2NGHOSTS[1]\", \"Nxx_plus_2NGHOSTS[0]\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226684"}},{"Add":{"text":" [\"1\", \"1\", \"1\"], [\"#pragma omp parallel for\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226757"}},{"Add":{"text":" \" const REAL xx2 = xx[2][i2];\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226837"}},{"Add":{"text":" \" const REAL xx1 = xx[1][i1];\"], \"\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226926"}},{"Add":{"text":" \"\"\"const REAL xx0 = xx[0][i0];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:226984"}},{"Add":{"text":"const int idx = IDX3(i0,i1,i2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227016"}},{"Add":{"text":"const REAL xx0xx1xx2[3] = {xx0,xx1,xx2};","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227057"}},{"Add":{"text":"ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs(xx0xx1xx2,other_inputs,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227133"}},{"Add":{"text":" &in_gfs[IDX4pt(HDD00GF,idx)],&in_gfs[IDX4pt(HDD01GF,idx)],&in_gfs[IDX4pt(HDD02GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227241"}},{"Add":{"text":" &in_gfs[IDX4pt(HDD11GF,idx)],&in_gfs[IDX4pt(HDD12GF,idx)],&in_gfs[IDX4pt(HDD22GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227349"}},{"Add":{"text":" &in_gfs[IDX4pt(ADD00GF,idx)],&in_gfs[IDX4pt(ADD01GF,idx)],&in_gfs[IDX4pt(ADD02GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227457"}},{"Add":{"text":" &in_gfs[IDX4pt(ADD11GF,idx)],&in_gfs[IDX4pt(ADD12GF,idx)],&in_gfs[IDX4pt(ADD22GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227565"}},{"Add":{"text":" &in_gfs[IDX4pt(TRKGF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227613"}},{"Add":{"text":" &in_gfs[IDX4pt(VETU0GF,idx)],&in_gfs[IDX4pt(VETU1GF,idx)],&in_gfs[IDX4pt(VETU2GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227721"}},{"Add":{"text":" &in_gfs[IDX4pt(BETU0GF,idx)],&in_gfs[IDX4pt(BETU1GF,idx)],&in_gfs[IDX4pt(BETU2GF,idx)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227829"}},{"Add":{"text":" &in_gfs[IDX4pt(ALPHAGF,idx)],&in_gfs[IDX4pt(CFGF,idx)]);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227906"}},{"Add":{"text":"\"\"\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227912"}},{"Add":{"text":" file.write(\"}\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227938"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:227939"}},{"Add":{"text":" # Step 6: Compute $\\bar{\\Lambda}^i$ (Eqs. 4 and 5 of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228000"}},{"Add":{"text":" # [Baumgarte *et al.*](https://arxiv.org/pdf/1211.6632.pdf)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228078"}},{"Add":{"text":" # from finite-difference derivatives of rescaled metric","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228150"}},{"Add":{"text":" # quantities $h_{ij}$:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228189"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228190"}},{"Add":{"text":" # \\bar{\\Lambda}^i = \\bar{\\gamma}^{jk}\\left(\\bar{\\Gamma}^i_{jk} - \\hat{\\Gamma}^i_{jk}\\right).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228291"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228292"}},{"Add":{"text":" # The reference_metric.py module provides us with analytic expressions for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228375"}},{"Add":{"text":" # $\\hat{\\Gamma}^i_{jk}$, so here we need only compute","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228445"}},{"Add":{"text":" # finite-difference expressions for $\\bar{\\Gamma}^i_{jk}$, based on","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228529"}},{"Add":{"text":" # the values for $h_{ij}$ provided in the initial data. Once","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228606"}},{"Add":{"text":" # $\\bar{\\Lambda}^i$ has been computed, we apply the usual rescaling","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228690"}},{"Add":{"text":" # procedure:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228719"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228720"}},{"Add":{"text":" # \\lambda^i = \\bar{\\Lambda}^i/\\text{ReU[i]},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228773"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228774"}},{"Add":{"text":" # and then output the result to a C file using the NRPy+","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228839"}},{"Add":{"text":" # finite-difference C output routine.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228893"}},{"Add":{"text":" # We will need all BSSN gridfunctions to be defined, as well as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:228965"}},{"Add":{"text":" # expressions for gammabarDD_dD in terms of exact derivatives of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229042"}},{"Add":{"text":" # the rescaling matrix and finite-difference derivatives of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229114"}},{"Add":{"text":" # hDD's.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229135"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229136"}},{"Add":{"text":" gammabarDD = bssnrhs.gammabarDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229176"}},{"Add":{"text":" gammabarUU, gammabarDET = ixp.symm_matrix_inverter3x3(gammabarDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229250"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229251"}},{"Add":{"text":" gammabarDD_dD = bssnrhs.gammabarDD_dD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229297"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229298"}},{"Add":{"text":" # Next compute Christoffel symbols \\bar{\\Gamma}^i_{jk}:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229362"}},{"Add":{"text":" GammabarUDD = ixp.zerorank3()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229400"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229429"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229462"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229499"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229540"}},{"Add":{"text":" GammabarUDD[i][j][k] += sp.Rational(1, 2) * gammabarUU[i][l] * (gammabarDD_dD[l][j][k] +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229653"}},{"Add":{"text":" gammabarDD_dD[l][k][j] -","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229766"}},{"Add":{"text":" gammabarDD_dD[j][k][l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229878"}},{"Add":{"text":" # Next evaluate \\bar{\\Lambda}^i, based on GammabarUDD above and GammahatUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:229962"}},{"Add":{"text":" # (from the reference metric):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230007"}},{"Add":{"text":" LambdabarU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230044"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230073"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230106"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230143"}},{"Add":{"text":" LambdabarU[i] += gammabarUU[j][k] * (GammabarUDD[i][j][k] - rfm.GammahatUDD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230249"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230250"}},{"Add":{"text":" # Finally apply rescaling:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230285"}},{"Add":{"text":" # lambda^i = Lambdabar^i/\\text{ReU[i]}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230332"}},{"Add":{"text":" lambdaU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230366"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230395"}},{"Add":{"text":" lambdaU[i] = LambdabarU[i] / rfm.ReU[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230447"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230448"}},{"Add":{"text":" outCparams = \"preindent=1,outCfileaccess=a,outCverbose=False,includebraces=False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230538"}},{"Add":{"text":" lambdaU_expressions = [lhrh(lhs=gri.gfaccess(\"in_gfs\", \"lambdaU0\"), rhs=lambdaU[0]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230631"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"lambdaU1\"), rhs=lambdaU[1]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230724"}},{"Add":{"text":" lhrh(lhs=gri.gfaccess(\"in_gfs\", \"lambdaU2\"), rhs=lambdaU[2])]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230817"}},{"Add":{"text":" lambdaU_expressions_FDout = fin.FD_outputC(\"returnstring\", lambdaU_expressions, outCparams)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230917"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230918"}},{"Add":{"text":" with open(\"BSSN/ID_BSSN_lambdas.h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:230976"}},{"Add":{"text":" file.write(\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231003"}},{"Add":{"text":"void ID_BSSN_lambdas(const int Nxx[3],const int Nxx_plus_2NGHOSTS[3],REAL *xx[3],const REAL dxx[3],REAL *in_gfs) {\\n\"\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231124"}},{"Add":{"text":" file.write(lp.loop([\"i2\", \"i1\", \"i0\"], [\"NGHOSTS\", \"NGHOSTS\", \"NGHOSTS\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231210"}},{"Add":{"text":" [\"NGHOSTS+Nxx[2]\", \"NGHOSTS+Nxx[1]\", \"NGHOSTS+Nxx[0]\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231297"}},{"Add":{"text":" [\"1\", \"1\", \"1\"], [\"const REAL invdx0 = 1.0/dxx[0];\\n\" +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231384"}},{"Add":{"text":" \"const REAL invdx1 = 1.0/dxx[1];\\n\" +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231471"}},{"Add":{"text":" \"const REAL invdx2 = 1.0/dxx[2];\\n\" +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231558"}},{"Add":{"text":" \"#pragma omp parallel for\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231635"}},{"Add":{"text":" \" const REAL xx2 = xx[2][i2];\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231719"}},{"Add":{"text":" \" const REAL xx1 = xx[1][i1];\"], \"\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231812"}},{"Add":{"text":" \"const REAL xx0 = xx[0][i0];\\n\" + lambdaU_expressions_FDout))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231905"}},{"Add":{"text":" file.write(\"}\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:231935"}}]}},{"FileAdd":{"meta":{"basename":"UIUCBlackHole.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/UIUCBlackHole.py","context":[{"change":0,"pos":23}],"contents":[{"Add":{"text":"# This module sets up UIUC Black Hole initial data in terms of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232019"}},{"Add":{"text":"# the variables used in BSSN_RHSs.py","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232056"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232057"}},{"Add":{"text":"# Authors: Zachariah B. Etienne, zachetie **at** gmail **dot** com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232124"}},{"Add":{"text":"# Terrence Pierre Jacques, terrencepierrej **at** gmail **dot** com ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232204"}},{"Add":{"text":"# Ian Ruchlin","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232227"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232228"}},{"Add":{"text":"# ## This module sets up initial data for a merging black hole system in spherical coordinates. We can convert from spherical to any coordinate system defined in [reference_metric.py](../edit/reference_metric.py) (e.g., SinhSpherical, Cylindrical, Cartesian, etc.) using the [Exact ADM Spherical-to-BSSNCurvilinear converter module](Tutorial-ADM_Initial_Data-Converting_Exact_ADM_Spherical_or_Cartesian_to_BSSNCurvilinear.ipynb)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232657"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232660"}},{"Add":{"text":"# ### Here we set up UIUC Black Hole initial data ([Liu, Etienne, & Shapiro, PRD 80 121503, 2009](https://arxiv.org/abs/1001.4077)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232793"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:232796"}},{"Add":{"text":"# UIUC black holes have the advantage of finite coordinate radius in the maximal spin limit. It is therefore excellent for studying very highly spinning black holes. This module sets the UIUC black hole at the origin. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233015"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233018"}},{"Add":{"text":"# **Inputs for initial data**:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233049"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233052"}},{"Add":{"text":"# * The black hole mass $M$.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233081"}},{"Add":{"text":"# * The dimensionless spin parameter $\\chi = a/M$","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233131"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233134"}},{"Add":{"text":"# **Additional variables needed for spacetime evolution**:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233193"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233196"}},{"Add":{"text":"# * Desired coordinate system","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233226"}},{"Add":{"text":"# * Desired initial lapse $\\alpha$ and shift $\\beta^i$. We will choose our gauge conditions as $\\alpha=1$ and $\\beta^i=B^i=0$. $\\alpha = \\psi^{-2}$ will yield much better behavior, but the conformal factor $\\psi$ depends on the desired *destination* coordinate system (which may not be spherical coordinates).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233536"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233537"}},{"Add":{"text":"# Step P0: Load needed modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233568"}},{"Add":{"text":"import sympy as sp # SymPy: The Python computer algebra package upon which NRPy+ depends","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233669"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233729"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233836"}},{"Add":{"text":"import BSSN.ADM_Exact_Spherical_or_Cartesian_to_BSSNCurvilinear as AtoB","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233908"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233909"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233931"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233932"}},{"Add":{"text":"# The UIUC initial data represent a Kerr black hole with mass M","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:233996"}},{"Add":{"text":"# and dimensionless spin chi in UIUC quasi-isotropic coordinates,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234063"}},{"Add":{"text":"# see https://arxiv.org/abs/1001.4077","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234103"}},{"Add":{"text":"# Input parameters:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234123"}},{"Add":{"text":"M, chi = par.Cparameters(\"REAL\", thismodule, [\"M\", \"chi\"], [1.0, 0.99])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234195"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234196"}},{"Add":{"text":"# ComputeADMGlobalsOnly == True will only set up the ADM global quantities.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234272"}},{"Add":{"text":"# == False will perform the full ADM SphorCart->BSSN Curvi conversion","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234364"}},{"Add":{"text":"def UIUCBlackHole(ComputeADMGlobalsOnly = False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234414"}},{"Add":{"text":" global Sph_r_th_ph,r,th,ph, gammaSphDD, KSphDD, alphaSph, betaSphU, BSphU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234492"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234497"}},{"Add":{"text":" # All gridfunctions will be written in terms of spherical coordinates (r, th, ph):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234584"}},{"Add":{"text":" r,th,ph = sp.symbols('r th ph', real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234631"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234632"}},{"Add":{"text":" # Step 0: Set spatial dimension (must be 3 for BSSN)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234689"}},{"Add":{"text":" DIM = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234701"}},{"Add":{"text":" par.set_parval_from_str(\"grid::DIM\",DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234746"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234751"}},{"Add":{"text":" # Step 1: Set psi, the conformal factor:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234796"}},{"Add":{"text":" # Spin per unit mass","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234821"}},{"Add":{"text":" a = M*chi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234835"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234836"}},{"Add":{"text":" # Defined under equation 1 in Liu, Etienne, & Shapiro (2009) https://arxiv.org/pdf/1001.4077.pdf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234937"}},{"Add":{"text":" # Boyer - Lindquist outer horizon","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:234975"}},{"Add":{"text":" rp = M + sp.sqrt(M**2 - a**2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235009"}},{"Add":{"text":" # Boyer - Lindquist inner horizon","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235047"}},{"Add":{"text":" rm = M - sp.sqrt(M**2 - a**2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235081"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235086"}},{"Add":{"text":" # Boyer - Lindquist radius in terms of UIUC radius","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235141"}},{"Add":{"text":" # Eq. 11","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235154"}},{"Add":{"text":" # r_{BL} = r * ( 1 + r_+ / 4r )^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235192"}},{"Add":{"text":" rBL = r*(1 + rp / (4*r))**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235224"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235229"}},{"Add":{"text":" # Expressions found below Eq. 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235265"}},{"Add":{"text":" # Sigma = r_{BL}^2 + a^2 cos^2 theta","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235306"}},{"Add":{"text":" SIG = rBL**2 + a**2*sp.cos(th)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235344"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235345"}},{"Add":{"text":" # Delta = r_{BL}^2 - 2Mr_{BL} + a^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235385"}},{"Add":{"text":" DEL = rBL**2 - 2*M*rBL + a**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235419"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235420"}},{"Add":{"text":" # A = (r_{BL}^2 + a^2)^2 - Delta a^2 sin^2 theta","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235473"}},{"Add":{"text":" AA = (rBL**2 + a**2)**2 - DEL*a**2*sp.sin(th)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235526"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235527"}},{"Add":{"text":" # *** The ADM 3-metric in spherical basis ***","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235577"}},{"Add":{"text":" gammaSphDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235610"}},{"Add":{"text":" # Declare the nonzero components of the 3-metric ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235664"}},{"Add":{"text":" # (Eq. 13 of Liu, Etienne, & Shapiro, https://arxiv.org/pdf/1001.4077.pdf):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235744"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235745"}},{"Add":{"text":" # ds^2 = Sigma (r + r_+/4)^2 / ( r^3 (r_{BL} - r_- ) * dr^2 + ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235812"}},{"Add":{"text":" # Sigma d theta^2 + (A sin^2 theta) / Sigma * d\\phi^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235886"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235887"}},{"Add":{"text":" gammaSphDD[0][0] = ((SIG*(r + rp/4)**2)/(r**3*(rBL - rm)))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235950"}},{"Add":{"text":" gammaSphDD[1][1] = SIG","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:235977"}},{"Add":{"text":" gammaSphDD[2][2] = AA/SIG*sp.sin(th)**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236021"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236022"}},{"Add":{"text":" # *** The physical trace-free extrinsic curvature in spherical basis ***","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236099"}},{"Add":{"text":" # Nonzero components of the extrinsic curvature K, given by","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236163"}},{"Add":{"text":" # Eq. 14 of Liu, Etienne, & Shapiro, https://arxiv.org/pdf/1001.4077.pdf:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236241"}},{"Add":{"text":" KSphDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236274"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236275"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236276"}},{"Add":{"text":" # K_{r phi} = K_{phi r} = (Ma sin^2 theta) / (Sigma sqrt{A Sigma}) *","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236349"}},{"Add":{"text":" # [3r^4_{BL} + 2a^2 r^2_{BL} - a^4 - a^2 (r^2_{BL} - a^2) sin^2 theta] *","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236430"}},{"Add":{"text":" # (1 + r_+ / 4r) (1 / sqrt{r(r_{BL} - r_-)})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236483"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236484"}},{"Add":{"text":" KSphDD[0][2] = KSphDD[2][0] = (M*a*sp.sin(th)**2)/(SIG*sp.sqrt(AA*SIG))*\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236562"}},{"Add":{"text":" (3*rBL**4 + 2*a**2*rBL**2 - a**4- a**2*(rBL**2 - a**2)*\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236639"}},{"Add":{"text":" sp.sin(th)**2)*(1 + rp/(4*r))*1/sp.sqrt(r*(rBL - rm))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236714"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236719"}},{"Add":{"text":" # Components of the extrinsic curvature K, given by","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236775"}},{"Add":{"text":" # Eq. 15 of Liu, Etienne, & Shapiro, https://arxiv.org/pdf/1001.4077.pdf:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236853"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236854"}},{"Add":{"text":" # K_{theta phi} = K_{phi theta} = -(2a^3 Mr_{BL} cos theta sin^3 theta) / ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:236933"}},{"Add":{"text":" # (Sigma sqrt{A Sigma}) x (r - r_+ / 4) sqrt{(r_{BL} - r_-) / r }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237011"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237012"}},{"Add":{"text":" KSphDD[1][2] = KSphDD[2][1] = -((2*a**3*M*rBL*sp.cos(th)*sp.sin(th)**3)/ \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237091"}},{"Add":{"text":" (SIG*sp.sqrt(AA*SIG)))*(r - rp/4)*sp.sqrt((rBL - rm)/r)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237167"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237168"}},{"Add":{"text":" alphaSph = sp.sympify(1) # We generally choose alpha = 1/psi**2 (psi = BSSN conformal factor) for these initial data","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237291"}},{"Add":{"text":" betaSphU = ixp.zerorank1() # We generally choose \\beta^i = 0 for these initial data","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237379"}},{"Add":{"text":" BSphU = ixp.zerorank1() # We generally choose B^i = 0 for these initial data","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237463"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237464"}},{"Add":{"text":" if ComputeADMGlobalsOnly == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237502"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237517"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237522"}},{"Add":{"text":" # Validated against original SENR: KSphDD[0][2], KSphDD[1][2], gammaSphDD[2][2], gammaSphDD[0][0], gammaSphDD[1][1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237642"}},{"Add":{"text":" #print(sp.mathematica_code(gammaSphDD[1][1]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237692"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237693"}},{"Add":{"text":" Sph_r_th_ph = [r,th,ph]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237721"}},{"Add":{"text":" cf,hDD,lambdaU,aDD,trK,alpha,vetU,betU = \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237768"}},{"Add":{"text":" AtoB.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear(\"Spherical\", Sph_r_th_ph, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237863"}},{"Add":{"text":" gammaSphDD,KSphDD,alphaSph,betaSphU,BSphU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237974"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:237975"}},{"Add":{"text":" import BSSN.BSSN_ID_function_string as bIDf","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238023"}},{"Add":{"text":" global returnfunction","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238049"}},{"Add":{"text":" returnfunction = bIDf.BSSN_ID_function_string(cf, hDD, lambdaU, aDD, trK, alpha, vetU, betU)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238146"}}]}},{"FileAdd":{"meta":{"basename":"__init__.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/__init__.py","context":[{"change":0,"pos":23}],"contents":[]}},{"FileAdd":{"meta":{"basename":"tests","metadata":1005},"path":"BaikalX/doc/nrpytutorial/BSSN/tests","context":[{"change":0,"pos":23}],"contents":[]}},{"FileAdd":{"meta":{"basename":"__init__.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/tests/__init__.py","context":[{"change":0,"pos":238171}],"contents":[]}},{"FileAdd":{"meta":{"basename":"test_BSSN.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/tests/test_BSSN.py","context":[{"change":0,"pos":238171}],"contents":[{"Add":{"text":"from UnitTesting.create_test import create_test","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238251"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238252"}},{"Add":{"text":"def test_ADMBSSN_tofrom_4metric():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238287"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238288"}},{"Add":{"text":" module = 'BSSN.ADMBSSN_tofrom_4metric'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238331"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238332"}},{"Add":{"text":" module_name = 'ADMBSSN_tofrom_4metric'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238375"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238376"}},{"Add":{"text":" function_and_global_dict = {'g4DD_ito_BSSN_or_ADM(\\\"ADM\\\")': ['g4DD'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238451"}},{"Add":{"text":" 'g4UU_ito_BSSN_or_ADM(\\\"ADM\\\")': ['g4UU'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238526"}},{"Add":{"text":" 'BSSN_or_ADM_ito_g4DD(\\\"ADM\\\")': ['gammaDD', 'betaU', 'alpha']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238622"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238623"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238686"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238687"}},{"Add":{"text":"def test_ADMBSSN_tofrom_4metric_BSSN():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238727"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238728"}},{"Add":{"text":" module = 'BSSN.ADMBSSN_tofrom_4metric'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238771"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238772"}},{"Add":{"text":" module_name = 'ADMBSSN_tofrom_4metric'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238815"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238816"}},{"Add":{"text":" function_and_global_dict = {'g4DD_ito_BSSN_or_ADM(\\\"BSSN\\\")': ['g4DD'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238892"}},{"Add":{"text":" 'g4UU_ito_BSSN_or_ADM(\\\"BSSN\\\")': ['g4UU'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:238968"}},{"Add":{"text":" 'BSSN_or_ADM_ito_g4DD(\\\"BSSN\\\")': ['hDD', 'cf', 'vetU', 'alpha']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239066"}},{"Add":{"text":" rfm_init_string = '''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239092"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239126"}},{"Add":{"text":"import reference_metric as rfm","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239157"}},{"Add":{"text":"rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239180"}},{"Add":{"text":"rfm.ref_metric__hatted_quantities()'''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239219"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239220"}},{"Add":{"text":" initialization_string_dict = {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239255"}},{"Add":{"text":" 'g4DD_ito_BSSN_or_ADM(\\\"BSSN\\\")': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239314"}},{"Add":{"text":" 'g4UU_ito_BSSN_or_ADM(\\\"BSSN\\\")': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239373"}},{"Add":{"text":" 'BSSN_or_ADM_ito_g4DD(\\\"BSSN\\\")': rfm_init_string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239431"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239437"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239438"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict, logging_level='INFO', initialization_string_dict=initialization_string_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239578"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239579"}},{"Add":{"text":"def test_BSSN_stress_energy_source_terms():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239623"}},{"Add":{"text":" module = 'BSSN.BSSN_stress_energy_source_terms'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239675"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239676"}},{"Add":{"text":" module_name = 'BSSN_stress_energy_source_terms'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239728"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239729"}},{"Add":{"text":" function_and_global_dict = {'stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(\\\"ADM\\\")': ['SDD','SD','S','rho'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239860"}},{"Add":{"text":" 'stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(\\\"BSSN\\\")': ['SDD','SD','S','rho'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:239992"}},{"Add":{"text":" 'BSSN_source_terms_for_BSSN_RHSs()': ['sourceterm_trK_rhs', 'sourceterm_a_rhsDD', 'sourceterm_lambda_rhsU', 'sourceterm_Lambdabar_rhsU']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240162"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240163"}},{"Add":{"text":" rfm_init_string = '''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240189"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240223"}},{"Add":{"text":"import reference_metric as rfm","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240254"}},{"Add":{"text":"rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240277"}},{"Add":{"text":"rfm.ref_metric__hatted_quantities()'''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240316"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240317"}},{"Add":{"text":" initialization_string_dict = {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240352"}},{"Add":{"text":" 'stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(\\\"ADM\\\")': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240452"}},{"Add":{"text":" 'stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars(\\\"BSSN\\\")': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240553"}},{"Add":{"text":" 'BSSN_source_terms_for_BSSN_RHSs()': rfm_init_string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240614"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240620"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240621"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict, logging_level='INFO', initialization_string_dict=initialization_string_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240761"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240762"}},{"Add":{"text":"def test_ADM_in_terms_of_BSSN():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240795"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240796"}},{"Add":{"text":" module = 'BSSN.ADM_in_terms_of_BSSN'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240837"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240838"}},{"Add":{"text":" module_name = 'ADM_in_terms_of_BSSN'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240879"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:240880"}},{"Add":{"text":" function_and_global_dict = {'ADM_in_terms_of_BSSN()': ['gammaDD', 'gammaDDdD', 'gammaDDdDD', 'gammaUU', 'detgamma', ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241001"}},{"Add":{"text":" 'GammaUDD', 'KDD', 'KDDdD']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241089"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241090"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241153"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241154"}},{"Add":{"text":"def test_BSSN_in_terms_of_ADM():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241187"}},{"Add":{"text":" module = 'BSSN.BSSN_in_terms_of_ADM'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241228"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241229"}},{"Add":{"text":" module_name = 'BSSN_in_terms_of_ADM'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241270"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241271"}},{"Add":{"text":" function_and_global_dict = {'gammabarDD_hDD(gammaDD=None)': ['gammabarDD','hDD'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241357"}},{"Add":{"text":" 'trK_AbarDD_aDD(gammaDD=None,KDD=None)': ['trK','AbarDD','aDD'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241454"}},{"Add":{"text":" 'LambdabarU_lambdaU__exact_gammaDD(gammaDD=None)': ['LambdabarU','lambdaU'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241563"}},{"Add":{"text":" 'cf_from_gammaDD(gammaDD=None)': ['cf'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241636"}},{"Add":{"text":" 'betU_vetU(betaU=None,BU=None)': ['vetU','betU']","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241717"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241751"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241752"}},{"Add":{"text":" rfm_init_string = '''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241778"}},{"Add":{"text":"import BSSN.BSSN_quantities as Bq","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241812"}},{"Add":{"text":"import reference_metric as rfm","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241843"}},{"Add":{"text":"rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241866"}},{"Add":{"text":"rfm.ref_metric__hatted_quantities()'''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241905"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241906"}},{"Add":{"text":" initialization_string_dict = {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241941"}},{"Add":{"text":" 'gammabarDD_hDD(gammaDD=None)': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:241998"}},{"Add":{"text":" 'trK_AbarDD_aDD(gammaDD=None,KDD=None)': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242064"}},{"Add":{"text":" 'LambdabarU_lambdaU__exact_gammaDD(gammaDD=None)': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242140"}},{"Add":{"text":" 'cf_from_gammaDD(gammaDD=None)': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242198"}},{"Add":{"text":" 'betU_vetU(betaU=None,BU=None)': rfm_init_string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242255"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242261"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242262"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict, logging_level='INFO', initialization_string_dict=initialization_string_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242402"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242403"}},{"Add":{"text":"def test_BrillLindquist():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242430"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242431"}},{"Add":{"text":" module = 'BSSN.BrillLindquist'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242466"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242467"}},{"Add":{"text":" module_name = 'BrillLindquist'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242502"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242503"}},{"Add":{"text":" function_and_global_dict = {'BrillLindquist(ComputeADMGlobalsOnly=True)': ['alphaCart', 'betaCartU', 'BCartU',","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242618"}},{"Add":{"text":" 'gammaCartDD', 'KCartDD']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242724"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242725"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242788"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242789"}},{"Add":{"text":"def test_constraints():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242813"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242814"}},{"Add":{"text":" module = 'BSSN.BSSN_constraints'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242851"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242852"}},{"Add":{"text":" module_name = 'BSSN_constraints'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242889"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242894"}},{"Add":{"text":" function_and_global_dict = {'BSSN_constraints()': ['H', 'MU']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242961"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:242962"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243025"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243026"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243027"}},{"Add":{"text":"def test_Psi4():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243044"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243045"}},{"Add":{"text":" module = 'BSSN.Psi4'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243070"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243071"}},{"Add":{"text":" module_name = 'Psi4'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243096"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243101"}},{"Add":{"text":" function_and_global_dict = {'Psi4(specify_tetrad=False)': ['psi4_re_pt', 'psi4_im_pt']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243193"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243194"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243257"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243258"}},{"Add":{"text":"def test_Psi4_tetrads():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243283"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243284"}},{"Add":{"text":" module = 'BSSN.Psi4_tetrads'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243317"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243318"}},{"Add":{"text":" module_name = 'Psi4_tetrads'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243351"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243356"}},{"Add":{"text":" function_and_global_dict = {'Psi4_tetrads()': ['l4U', 'n4U', 'mre4U', 'mim4U']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243440"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243441"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243504"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243505"}},{"Add":{"text":"def test_quantities():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243528"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243529"}},{"Add":{"text":" module = 'BSSN.BSSN_quantities'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243565"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243566"}},{"Add":{"text":" module_name = 'BSSN_quantities'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243602"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243607"}},{"Add":{"text":" function_and_global_dict = {'declare_BSSN_gridfunctions_if_not_declared_already()': ['hDD', 'aDD', 'lambdaU', 'vetU', 'betU', 'trK', 'cf', 'alpha'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243760"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243761"}},{"Add":{"text":" 'BSSN_basic_tensors()': ['gammabarDD', 'AbarDD', 'LambdabarU', 'betaU', 'BU'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243872"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:243873"}},{"Add":{"text":" 'gammabar__inverse_and_derivs()': ['gammabarUU', 'gammabarDD_dD', 'gammabarDD_dupD', 'gammabarDD_dDD', 'GammabarUDD'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244024"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244025"}},{"Add":{"text":" 'detgammabar_and_derivs()': ['detgammabar', 'detgammabar_dD', 'detgammabar_dDD'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244139"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244140"}},{"Add":{"text":" 'AbarUU_AbarUD_trAbar_AbarDD_dD()': ['AbarUU', 'AbarUD', 'trAbar', 'AbarDD_dD', 'AbarDD_dupD'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244268"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244269"}},{"Add":{"text":" 'RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU()': ['RbarDD', 'DGammaUDD', 'gammabarDD_dHatD', 'DGammaU'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244409"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244410"}},{"Add":{"text":" 'betaU_derivs()': ['betaU_dD', 'betaU_dupD', 'betaU_dDD'],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244501"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244502"}},{"Add":{"text":" 'phi_and_derivs()': ['phi_dD', 'phi_dupD', 'phi_dDD', 'exp_m4phi', 'phi_dBarD', 'phi_dBarDD']","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244628"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244662"}},{"Add":{"text":" rfm_init_string = '''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244688"}},{"Add":{"text":"import reference_metric as rfm","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244719"}},{"Add":{"text":"rfm.reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244742"}},{"Add":{"text":"rfm.ref_metric__hatted_quantities()'''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244781"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244782"}},{"Add":{"text":" initialization_string_dict = {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244817"}},{"Add":{"text":" 'BSSN_basic_tensors()': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244866"}},{"Add":{"text":" 'gammabar__inverse_and_derivs()': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244925"}},{"Add":{"text":" 'detgammabar_and_derivs()': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:244978"}},{"Add":{"text":" 'AbarUU_AbarUD_trAbar_AbarDD_dD()': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245039"}},{"Add":{"text":" 'RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU()': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245116"}},{"Add":{"text":" 'betaU_derivs()': rfm_init_string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245159"}},{"Add":{"text":" 'phi_and_derivs()': rfm_init_string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245203"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245209"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245210"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict, logging_level='INFO', initialization_string_dict=initialization_string_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245350"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245351"}},{"Add":{"text":"def test_RHSs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245368"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245369"}},{"Add":{"text":" module = 'BSSN.BSSN_RHSs'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245399"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245400"}},{"Add":{"text":" module_name = 'BSSN_RHSs'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245430"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245435"}},{"Add":{"text":" function_and_global_dict = {'BSSN_RHSs()': ['cf_rhs', 'trK_rhs', 'lambda_rhsU', 'a_rhsDD', 'h_rhsDD']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245542"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245543"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245606"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245607"}},{"Add":{"text":"def test_gauge_RHSs():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245630"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245631"}},{"Add":{"text":" module = 'BSSN.BSSN_gauge_RHSs'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245667"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245668"}},{"Add":{"text":" module_name = 'gauge_RHSs'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245699"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245704"}},{"Add":{"text":" function_and_global_dict = {'BSSN_gauge_RHSs()': ['alpha_rhs', 'bet_rhsU', 'vet_rhsU']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245796"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245797"}},{"Add":{"text":" bssn_rhs_init_string = '''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245828"}},{"Add":{"text":"import BSSN.BSSN_RHSs as rhs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245857"}},{"Add":{"text":"rhs.BSSN_RHSs()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245873"}},{"Add":{"text":"'''","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245877"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245878"}},{"Add":{"text":" initialization_string_dict = { 'BSSN_gauge_RHSs()': bssn_rhs_init_string }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245957"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:245958"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict, initialization_string_dict=initialization_string_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246076"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246077"}},{"Add":{"text":"def test_ShiftedKerrSchild():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246107"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246108"}},{"Add":{"text":" module = 'BSSN.ShiftedKerrSchild'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246146"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246147"}},{"Add":{"text":" module_name = 'ShiftedKerrSchild'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246185"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246190"}},{"Add":{"text":" function_and_global_dict = {'ShiftedKerrSchild(ComputeADMGlobalsOnly=True)': ['alphaSph', 'betaSphU', 'BSphU',","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246305"}},{"Add":{"text":" 'gammaSphDD', 'KSphDD']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246414"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246415"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246478"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246479"}},{"Add":{"text":"def test_StaticTrumpet():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246505"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246506"}},{"Add":{"text":" module = 'BSSN.StaticTrumpet'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246540"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246541"}},{"Add":{"text":" module_name = 'StaticTrumpet'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246575"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246580"}},{"Add":{"text":" function_and_global_dict = {'StaticTrumpet(ComputeADMGlobalsOnly=True)': ['alphaSph', 'betaSphU', 'BSphU',","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246691"}},{"Add":{"text":" 'gammaSphDD', 'KSphDD']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246796"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246797"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246860"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246861"}},{"Add":{"text":"def test_T4UUmunu_vars():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246887"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246888"}},{"Add":{"text":" module = 'BSSN.BSSN_T4UUmunu_vars'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246927"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246928"}},{"Add":{"text":" module_name = 'T4UUmunu_vars'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246962"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:246967"}},{"Add":{"text":" function_and_global_dict = {'define_BSSN_T4UUmunu_rescaled_source_terms()': ['rho', 'S', 'sD', 'sDD']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247074"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247075"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247138"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247139"}},{"Add":{"text":"def test_UIUCBlackHole():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247165"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247166"}},{"Add":{"text":" module = 'BSSN.UIUCBlackHole'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247200"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247201"}},{"Add":{"text":" module_name = 'UIUCBlackHole'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247235"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247240"}},{"Add":{"text":" function_and_global_dict = {'UIUCBlackHole(ComputeADMGlobalsOnly=True)': ['alphaSph', 'betaSphU', 'BSphU',","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247351"}},{"Add":{"text":" 'gammaSphDD', 'KSphDD']}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247456"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247457"}},{"Add":{"text":" create_test(module, module_name, function_and_global_dict)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247520"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247521"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247522"}},{"Add":{"text":"if __name__ == '__main__':","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247549"}},{"Add":{"text":" import sys","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247564"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247565"}},{"Add":{"text":" if len(sys.argv) <= 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247592"}},{"Add":{"text":" failed_functions = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247622"}},{"Add":{"text":" for fun in dir():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247648"}},{"Add":{"text":" if fun[0:5] == 'test_':","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247684"}},{"Add":{"text":" print('\\nTesting ' + str(fun) + '...\\n')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247741"}},{"Add":{"text":" try:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247762"}},{"Add":{"text":" exec(fun + '()')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247799"}},{"Add":{"text":" except SystemExit:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247834"}},{"Add":{"text":" failed_functions.append(fun)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247883"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247884"}},{"Add":{"text":" if failed_functions != []:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247919"}},{"Add":{"text":" import sys, os","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:247946"}},{"Add":{"text":" with open(os.path.join('UnitTesting', 'failed_tests.txt'), 'a') as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248031"}},{"Add":{"text":" for function in failed_functions:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248081"}},{"Add":{"text":" file.write(sys.argv[0] + ': ' + str(function) + '\\n')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248155"}},{"Add":{"text":" exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248175"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248176"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248186"}},{"Add":{"text":" globals()[sys.argv[4]]()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248219"}}]}},{"FileAdd":{"meta":{"basename":"trusted_values_dict.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/BSSN/tests/trusted_values_dict.py","context":[{"change":0,"pos":238171}],"contents":[{"Add":{"text":"from mpmath import mpf, mp, mpc","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248278"}},{"Add":{"text":"from UnitTesting.standard_constants import precision","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248331"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248332"}},{"Add":{"text":"mp.dps = precision","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248351"}},{"Add":{"text":"trusted_values_dict = {}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248376"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248377"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:248404"}},{"Add":{"text":"trusted_values_dict['ADM_in_terms_of_BSSN__ADM_in_terms_of_BSSN__globals'] = {'gammaDD[0][0]': mpf('8.84684305820134422150597858207921'), 'gammaDD[0][1]': mpf('3.350018689599008046165002833204'), 'gammaDD[0][2]': mpf('0.194795767378908960688399288371257'), 'gammaDD[1][0]': mpf('3.350018689599008046165002833204'), 'gammaDD[1][1]': mpf('1.92752387150314689143948714387062'), 'gammaDD[1][2]': mpf('0.617514215490828029162196536408385'), 'gammaDD[2][0]': mpf('0.194795767378908960688399288371257'), 'gammaDD[2][1]': mpf('0.617514215490828029162196536408385'), 'gammaDD[2][2]': mpf('0.440219517017598275317485123438443'), 'gammaDDdD[0][0][0]': mpf('-39.2181788667717063214934687853284'), 'gammaDDdD[0][0][1]': mpf('-43.5347678242827125179031665798782'), 'gammaDDdD[0][0][2]': mpf('-43.5448629253377323761214222661368'), 'gammaDDdD[0][1][0]': mpf('-3.82269337582904325002653701794443'), 'gammaDDdD[0][1][1]': mpf('-15.8371132982064951265352981022794'), 'gammaDDdD[0][1][2]': mpf('-13.0007465813467278947970267824292'), 'gammaDDdD[0][2][0]': mpf('-0.218013883809053119477949934634148'), 'gammaDDdD[0][2][1]': mpf('0.785829885135145904482804685445781'), 'gammaDDdD[0][2][2]': mpf('-0.581351677673311207621301361731265'), 'gammaDDdD[1][0][0]': mpf('-3.82269337582904325002653701794443'), 'gammaDDdD[1][0][1]': mpf('-15.8371132982064951265352981022794'), 'gammaDDdD[1][0][2]': mpf('-13.0007465813467278947970267824292'), 'gammaDDdD[1][1][0]': mpf('1.02077344056659026570129696849467'), 'gammaDDdD[1][1][1]': mpf('-9.20007419968800686893912169288767'), 'gammaDDdD[1][1][2]': mpf('-8.15422339233949609213151393845906'), 'gammaDDdD[1][2][0]': mpf('0.357104131772599372488808535542396'), 'gammaDDdD[1][2][1]': mpf('-1.65079628886562588602648974576529'), 'gammaDDdD[1][2][2]': mpf('-2.86344337379037596725739579107855'), 'gammaDDdD[2][0][0]': mpf('-0.218013883809053119477949934634148'), 'gammaDDdD[2][0][1]': mpf('0.785829885135145904482804685445781'), 'gammaDDdD[2][0][2]': mpf('-0.581351677673311207621301361731265'), 'gammaDDdD[2][1][0]': mpf('0.357104131772599372488808535542396'), 'gammaDDdD[2][1][1]': mpf('-1.65079628886562588602648974576529'), 'gammaDDdD[2][1][2]': mpf('-2.86344337379037596725739579107855'), 'gammaDDdD[2][2][0]': mpf('0.195001221087943638085807308270354'), 'gammaDDdD[2][2][1]': mpf('-0.410311324085430408983791626770926'), 'gammaDDdD[2][2][2]': mpf('-1.92276041454685421458861940256278'), 'gammaDDdDD[0][0][0][0]': mpf('225.398957517527156513326956764229'), 'gammaDDdDD[0][0][0][1]': mpf('288.140070211252996184124719294385'), 'gammaDDdDD[0][0][0][2]': mpf('281.623967129510091655495816474147'), 'gammaDDdDD[0][0][1][0]': mpf('288.140070211252996184124719294385'), 'gammaDDdDD[0][0][1][1]': mpf('337.948619849001134211864646627346'), 'gammaDDdDD[0][0][1][2]': mpf('322.481152355898457651315654723053'), 'gammaDDdDD[0][0][2][0]': mpf('281.623967129510091655495816474147'), 'gammaDDdDD[0][0][2][1]': mpf('322.481152355898457651315654723053'), 'gammaDDdDD[0][0][2][2]': mpf('293.564334950019576720032123379472'), 'gammaDDdDD[0][1][0][0]': mpf('3.64051177720082509234617335007875'), 'gammaDDdDD[0][1][0][1]': mpf('50.4627675517741918630578752181752'), 'gammaDDdDD[0][1][0][2]': mpf('46.1357119642924033983593968867937'), 'gammaDDdDD[0][1][1][0]': mpf('50.4627675517741918630578752181752'), 'gammaDDdDD[0][1][1][1]': mpf('119.02655264345724986788778186216'), 'gammaDDdDD[0][1][1][2]': mpf('100.654984059470512047205484497294'), 'gammaDDdDD[0][1][2][0]': mpf('46.1357119642924033983593968867937'), 'gammaDDdDD[0][1][2][1]': mpf('100.654984059470512047205484497294'), 'gammaDDdDD[0][1][2][2]': mpf('77.760445818040255191531604261198'), 'gammaDDdDD[0][2][0][0]': mpf('0.375532488603708956700281774274923'), 'gammaDDdDD[0][2][0][1]': mpf('0.678340756727625343658227489853017'), 'gammaDDdDD[0][2][0][2]': mpf('2.78948049995862477035881653480892'), 'gammaDDdDD[0][2][1][0]': mpf('0.678340756727625343658227489853017'), 'gammaDDdDD[0][2][1][1]': mpf('-6.12617437316042868416067368255866'), 'gammaDDdDD[0][2][1][2]': mpf('-1.75847734950653146320336447142805'), 'gammaDDdDD[0][2][2][0]': mpf('2.78948049995862477035881653480892'), 'gammaDDdDD[0][2][2][1]': mpf('-1.75847734950653146320336447142805'), 'gammaDDdDD[0][2][2][2]': mpf('2.73521309266304236084886214346027'), 'gammaDDdDD[1][0][0][0]': mpf('3.64051177720082509234617335007875'), 'gammaDDdDD[1][0][0][1]': mpf('50.4627675517741918630578752181752'), 'gammaDDdDD[1][0][0][2]': mpf('46.1357119642924033983593968867937'), 'gammaDDdDD[1][0][1][0]': mpf('50.4627675517741918630578752181752'), 'gammaDDdDD[1][0][1][1]': mpf('119.02655264345724986788778186216'), 'gammaDDdDD[1][0][1][2]': mpf('100.654984059470512047205484497294'), 'gammaDDdDD[1][0][2][0]': mpf('46.1357119642924033983593968867937'), 'gammaDDdDD[1][0][2][1]': mpf('100.654984059470512047205484497294'), 'gammaDDdDD[1][0][2][2]': mpf('77.760445818040255191531604261198'), 'gammaDDdDD[1][1][0][0]': mpf('-9.92106187379982562603610831325235'), 'gammaDDdDD[1][1][0][1]': mpf('15.825454310362637536048355653535'), 'gammaDDdDD[1][1][0][2]': mpf('14.4039518436611112501034205835319'), 'gammaDDdDD[1][1][1][0]': mpf('15.825454310362637536048355653535'), 'gammaDDdDD[1][1][1][1]': mpf('70.6517225129821789456736189152217'), 'gammaDDdDD[1][1][1][2]': mpf('61.9035794546980075683100782914809'), 'gammaDDdDD[1][1][2][0]': mpf('14.4039518436611112501034205835319'), 'gammaDDdDD[1][1][2][1]': mpf('61.9035794546980075683100782914809'), 'gammaDDdDD[1][1][2][2]': mpf('50.8579841651123380242828623654651'), 'gammaDDdDD[1][2][0][0]': mpf('-3.34089527571068728373797749836677'), 'gammaDDdDD[1][2][0][1]': mpf('5.5335349427183318693808176585407'), 'gammaDDdDD[1][2][0][2]': mpf('4.51408779818567722405331676792284'), 'gammaDDdDD[1][2][1][0]': mpf('5.5335349427183318693808176585407'), 'gammaDDdDD[1][2][1][1]': mpf('9.66395575640457553089340537573125'), 'gammaDDdDD[1][2][1][2]': mpf('15.1141997261213981599250387014752'), 'gammaDDdDD[1][2][2][0]': mpf('4.51408779818567722405331676792284'), 'gammaDDdDD[1][2][2][1]': mpf('15.1141997261213981599250387014752'), 'gammaDDdDD[1][2][2][2]': mpf('19.0650383126789942251109383834193'), 'gammaDDdDD[2][0][0][0]': mpf('0.375532488603708956700281774274923'), 'gammaDDdDD[2][0][0][1]': mpf('0.678340756727625343658227489853017'), 'gammaDDdDD[2][0][0][2]': mpf('2.78948049995862477035881653480892'), 'gammaDDdDD[2][0][1][0]': mpf('0.678340756727625343658227489853017'), 'gammaDDdDD[2][0][1][1]': mpf('-6.12617437316042868416067368255866'), 'gammaDDdDD[2][0][1][2]': mpf('-1.75847734950653146320336447142805'), 'gammaDDdDD[2][0][2][0]': mpf('2.78948049995862477035881653480892'), 'gammaDDdDD[2][0][2][1]': mpf('-1.75847734950653146320336447142805'), 'gammaDDdDD[2][0][2][2]': mpf('2.73521309266304236084886214346027'), 'gammaDDdDD[2][1][0][0]': mpf('-3.34089527571068728373797749836677'), 'gammaDDdDD[2][1][0][1]': mpf('5.5335349427183318693808176585407'), 'gammaDDdDD[2][1][0][2]': mpf('4.51408779818567722405331676792284'), 'gammaDDdDD[2][1][1][0]': mpf('5.5335349427183318693808176585407'), 'gammaDDdDD[2][1][1][1]': mpf('9.66395575640457553089340537573125'), 'gammaDDdDD[2][1][1][2]': mpf('15.1141997261213981599250387014752'), 'gammaDDdDD[2][1][2][0]': mpf('4.51408779818567722405331676792284'), 'gammaDDdDD[2][1][2][1]': mpf('15.1141997261213981599250387014752'), 'gammaDDdDD[2][1][2][2]': mpf('19.0650383126789942251109383834193'), 'gammaDDdDD[2][2][0][0]': mpf('-2.52353147414316377574820905559147'), 'gammaDDdDD[2][2][0][1]': mpf('4.53575664377867062493942188091689'), 'gammaDDdDD[2][2][0][2]': mpf('3.56377908834306629097560544110174'), 'gammaDDdDD[2][2][1][0]': mpf('4.5357566437786706249394218809232'), 'gammaDDdDD[2][2][1][1]': mpf('1.84054709164445852274067505481422'), 'gammaDDdDD[2][2][1][2]': mpf('7.16074940759453707759590964424542'), 'gammaDDdDD[2][2][2][0]': mpf('3.56377908834306629097560544110174'), 'gammaDDdDD[2][2][2][1]': mpf('7.16074940759453707759590964424542'), 'gammaDDdDD[2][2][2][2]': mpf('12.0437865836043923259359609593463'), 'gammaUU[0][0]': mpf('-6.28938129956539035233976956863059'), 'gammaUU[0][1]': mpf('18.2330938347990520861338232067731'), 'gammaUU[0][2]': mpf('-22.7932869645533398576110813493934'), 'gammaUU[1][0]': mpf('18.2330938347990520861338232067731'), 'gammaUU[1][1]': mpf('-51.9160225808937703970803496330078'), 'gammaUU[1][2]': mpf('64.7566755861571412059499249935555'), 'gammaUU[2][0]': mpf('-22.7932869645533398576110813493934'), 'gammaUU[2][1]': mpf('64.7566755861571412059499249935555'), 'gammaUU[2][2]': mpf('-78.479328065890663873188546288808'), 'detgamma': mpf('-0.0742854979156755661927481235463981'), 'GammaUDD[0][0][0]': mpf('-40.7797584599095266200402578142104'), 'GammaUDD[0][0][1]': mpf('-14.9811790250568026018422503217171'), 'GammaUDD[0][0][2]': mpf('12.2823492767347497337333129446469'), 'GammaUDD[0][1][0]': mpf('-14.9811790250568026018422503217171'), 'GammaUDD[0][1][1]': mpf('-36.3609505192780257845662292664448'), 'GammaUDD[0][1][2]': mpf('-30.1270719072420555274502961949333'), 'GammaUDD[0][2][0]': mpf('12.2823492767347497337333129446469'), 'GammaUDD[0][2][1]': mpf('-30.1270719072420555274502961949333'), 'GammaUDD[0][2][2]': mpf('-22.2862334550824046529070435685497'), 'GammaUDD[1][0][0]': mpf('106.641099858555951710230668316931'), 'GammaUDD[1][0][1]': mpf('34.5648661443104393199809718733873'), 'GammaUDD[1][0][2]': mpf('-42.0625759749969397716067483012153'), 'GammaUDD[1][1][0]': mpf('34.5648661443104393199809718733873'), 'GammaUDD[1][1][1]': mpf('97.8702478474345566909160962391556'), 'GammaUDD[1][1][2]': mpf('83.7688065067695141694849527164939'), 'GammaUDD[1][2][0]': mpf('-42.0625759749969397716067483012153'), 'GammaUDD[1][2][1]': mpf('83.7688065067695141694849527164939'), 'GammaUDD[1][2][2]': mpf('63.37436120121238471219216463813'), 'GammaUDD[2][0][0]': mpf('-82.5821023178249589056509375957706'), 'GammaUDD[2][0][1]': mpf('-25.7920996188850360970982778501415'), 'GammaUDD[2][0][2]': mpf('53.7895042071558641126267308366467'), 'GammaUDD[2][1][0]': mpf('-25.7920996188850360970982778501415'), 'GammaUDD[2][1][1]': mpf('-115.685453925551790074619499114864'), 'GammaUDD[2][1][2]': mpf('-104.640881703073552107006493456468'), 'GammaUDD[2][2][0]': mpf('53.7895042071558641126267308366467'), 'GammaUDD[2][2][1]': mpf('-104.640881703073552107006493456468'), 'GammaUDD[2][2][2]': mpf('-81.2201272697658198766768439312511'), 'KDD[0][0]': mpf('2.52635313601760623671007177930783'), 'KDD[0][1]': mpf('2.82898873912114767238892405861643'), 'KDD[0][2]': mpf('0.381578303862588400274173947157554'), 'KDD[1][0]': mpf('2.82898873912114767238892405861643'), 'KDD[1][1]': mpf('0.775186746770488740436250426070358'), 'KDD[1][2]': mpf('0.547222495805151738810645787512339'), 'KDD[2][0]': mpf('0.381578303862588400274173947157554'), 'KDD[2][1]': mpf('0.547222495805151738810645787512339'), 'KDD[2][2]': mpf('0.23987159265969208367518412563801'), 'KDDdD[0][0][0]': mpf('-6.98418007348680855492680452748596'), 'KDDdD[0][0][1]': mpf('-4.90357255070945013899614827846758'), 'KDDdD[0][0][2]': mpf('-9.51091715630967778721956190135931'), 'KDDdD[0][1][0]': mpf('-4.23975060495945983382577294248919'), 'KDDdD[0][1][1]': mpf('-13.8610965865853556038884955897668'), 'KDDdD[0][1][2]': mpf('-10.9245220106877969893233753184212'), 'KDDdD[0][2][0]': mpf('0.673882280969017838122158707807608'), 'KDDdD[0][2][1]': mpf('-0.152233642969041739842056712724457'), 'KDDdD[0][2][2]': mpf('-0.869578101320992405108114411360838'), 'KDDdD[1][0][0]': mpf('-4.23975060495945983382577294248919'), 'KDDdD[1][0][1]': mpf('-13.8610965865853556038884955897668'), 'KDDdD[1][0][2]': mpf('-10.9245220106877969893233753184212'), 'KDDdD[1][1][0]': mpf('0.830817678793678957257737618165166'), 'KDDdD[1][1][1]': mpf('-3.44366499994735267064814741173414'), 'KDDdD[1][1][2]': mpf('-3.27432266931077674480141080049683'), 'KDDdD[1][2][0]': mpf('0.708601442458893682779601967212525'), 'KDDdD[1][2][1]': mpf('-1.5539589956391283812811555376677'), 'KDDdD[1][2][2]': mpf('-2.26158238807310704211409034124987'), 'KDDdD[2][0][0]': mpf('0.673882280969017838122158707807608'), 'KDDdD[2][0][1]': mpf('-0.152233642969041739842056712724457'), 'KDDdD[2][0][2]': mpf('-0.869578101320992405108114411360838'), 'KDDdD[2][1][0]': mpf('0.708601442458893682779601967212525'), 'KDDdD[2][1][1]': mpf('-1.5539589956391283812811555376677'), 'KDDdD[2][1][2]': mpf('-2.26158238807310704211409034124987'), 'KDDdD[2][2][0]': mpf('0.424502981369425679158130440942863'), 'KDDdD[2][2][1]': mpf('-0.116489737786019245029640728668932'), 'KDDdD[2][2][2]': mpf('-1.03790663578070485250054725692471')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:260933"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:260934"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:260961"}},{"Add":{"text":"trusted_values_dict['BrillLindquist__BrillLindquist__ComputeADMGlobalsOnly=True__globals'] = {'alphaCart': mpf('0.343480750893445797669295337903236'), 'betaCartU[0]': mpf('0.0'), 'betaCartU[1]': mpf('0.0'), 'betaCartU[2]': mpf('0.0'), 'BCartU[0]': mpf('0.0'), 'BCartU[1]': mpf('0.0'), 'BCartU[2]': mpf('0.0'), 'gammaCartDD[0][0]': mpf('8.47608284216415538664572854966934'), 'gammaCartDD[0][1]': mpf('0.0'), 'gammaCartDD[0][2]': mpf('0.0'), 'gammaCartDD[1][0]': mpf('0.0'), 'gammaCartDD[1][1]': mpf('8.47608284216415538664572854966934'), 'gammaCartDD[1][2]': mpf('0.0'), 'gammaCartDD[2][0]': mpf('0.0'), 'gammaCartDD[2][1]': mpf('0.0'), 'gammaCartDD[2][2]': mpf('8.47608284216415538664572854966934'), 'KCartDD[0][0]': mpf('0.0'), 'KCartDD[0][1]': mpf('0.0'), 'KCartDD[0][2]': mpf('0.0'), 'KCartDD[1][0]': mpf('0.0'), 'KCartDD[1][1]': mpf('0.0'), 'KCartDD[1][2]': mpf('0.0'), 'KCartDD[2][0]': mpf('0.0'), 'KCartDD[2][1]': mpf('0.0'), 'KCartDD[2][2]': mpf('0.0')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:261922"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:261923"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:261950"}},{"Add":{"text":"trusted_values_dict['Psi4__Psi4__specify_tetrad=False__globals'] = {'psi4_re_pt[0]': mpf('-11.4627408385133346012203475168749'), 'psi4_re_pt[1]': mpf('-35.6806714906029645727316589574499'), 'psi4_re_pt[2]': mpf('-3374.92496104893019517395960329346'), 'psi4_im_pt[0]': mpf('7.17626585537563385139665194926662'), 'psi4_im_pt[1]': mpf('103.321768247585408574682983348206'), 'psi4_im_pt[2]': mpf('-1785.88265198482805325630868693525')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:262382"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:262383"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:262410"}},{"Add":{"text":"trusted_values_dict['Psi4_tetrads__Psi4_tetrads__globals'] = {'l4U[0]': mpf('0.707106781186547524400844362104785'), 'l4U[1]': mpf('0.238900425354320344832613106016182'), 'l4U[2]': mpf('0.0'), 'l4U[3]': mpf('-0.105712695337363311625493077156009'), 'n4U[0]': mpf('0.707106781186547524400844362104785'), 'n4U[1]': mpf('-0.238900425354320344832613106016182'), 'n4U[2]': mpf('0.0'), 'n4U[3]': mpf('0.105712695337363311625493077156009'), 'mre4U[0]': mpf('0.0'), 'mre4U[1]': mpc(real='0.0', imag='1.78934738466770903997371533478145'), 'mre4U[2]': mpc(real='0.0', imag='-5.09490051820905343049616931239143'), 'mre4U[3]': mpc(real='0.0', imag='6.3550480872706263113514069118537'), 'mim4U[0]': mpf('0.0'), 'mim4U[1]': mpf('0.0'), 'mim4U[2]': mpf('0.0'), 'mim4U[3]': mpf('1.06573776541005837815518683742699')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:263209"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:263210"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:263237"}},{"Add":{"text":"trusted_values_dict['BSSN_RHSs__BSSN_RHSs__globals'] = {'cf_rhs': mpf('3.77382093789289698643326794257121'), 'trK_rhs': mpf('4897.15010872261926255101979442461'), 'lambda_rhsU[0]': mpf('-932925.380251880280514928387377418'), 'lambda_rhsU[1]': mpf('1067214.31502612160105983520112858'), 'lambda_rhsU[2]': mpf('-634521.485102957628967190217797872'), 'a_rhsDD[0][0]': mpf('140611.691921936258075248177043018'), 'a_rhsDD[0][1]': mpf('129610.009549628960496251001913799'), 'a_rhsDD[0][2]': mpf('12478.2048292408067063007598939149'), 'a_rhsDD[1][0]': mpf('129610.009549628960496251001913218'), 'a_rhsDD[1][1]': mpf('190869.710957991947993273525242575'), 'a_rhsDD[1][2]': mpf('127861.933393387548396211650851467'), 'a_rhsDD[2][0]': mpf('12478.2048292408067063007598938196'), 'a_rhsDD[2][1]': mpf('127861.933393387548396211650851428'), 'a_rhsDD[2][2]': mpf('200379.251226055957975675818299921'), 'h_rhsDD[0][0]': mpf('26.0204338410819173136453286914799'), 'h_rhsDD[0][1]': mpf('25.0575733174708969733897611044168'), 'h_rhsDD[0][2]': mpf('11.7768556092635889801475757434684'), 'h_rhsDD[1][0]': mpf('25.0575733174708969733897611044168'), 'h_rhsDD[1][1]': mpf('40.8921058052569946189333312205232'), 'h_rhsDD[1][2]': mpf('39.8230119150907530884376958638246'), 'h_rhsDD[2][0]': mpf('11.7768556092635889801475757434684'), 'h_rhsDD[2][1]': mpf('39.8230119150907530884376958638246'), 'h_rhsDD[2][2]': mpf('72.3354550710637207030251571354033')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:264665"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:264666"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:264693"}},{"Add":{"text":"trusted_values_dict['ShiftedKerrSchild__ShiftedKerrSchild__ComputeADMGlobalsOnly=True__globals'] = {'alphaSph': mpf('0.764992222074068488402374263959388'), 'betaSphU[0]': mpf('0.414786900166179080948286822502086'), 'betaSphU[1]': mpf('0.0'), 'betaSphU[2]': mpf('0.0'), 'BSphU[0]': mpf('0.0'), 'BSphU[1]': mpf('0.0'), 'BSphU[2]': mpf('0.0'), 'gammaSphDD[0][0]': mpf('1.70877924688282501671697638255698'), 'gammaSphDD[0][1]': mpf('0.0'), 'gammaSphDD[0][2]': mpf('-0.34407721284779690446451905546302'), 'gammaSphDD[1][0]': mpf('0.0'), 'gammaSphDD[1][1]': mpf('0.83749814889950038479162273698221'), 'gammaSphDD[1][2]': mpf('0.0'), 'gammaSphDD[2][0]': mpf('-0.34407721284779690446451905546302'), 'gammaSphDD[2][1]': mpf('0.0'), 'gammaSphDD[2][2]': mpf('0.428211355345928897234853289336263'), 'KSphDD[0][0]': mpf('-0.608416975836176206520434449342952'), 'KSphDD[0][1]': mpf('0.0707242913409545835190603089766082'), 'KSphDD[0][2]': mpf('0.0772829375209889643435925308431919'), 'KSphDD[1][0]': mpf('0.0707242913409545835190603089766082'), 'KSphDD[1][1]': mpf('0.457311525223526834585984744200641'), 'KSphDD[1][2]': mpf('-0.0142409366743087039035851689662884'), 'KSphDD[2][0]': mpf('0.0772829375209889643435925308431919'), 'KSphDD[2][1]': mpf('-0.0142409366743087039035851689662884'), 'KSphDD[2][2]': mpf('0.189536302720822065090385756720081')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:266029"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:266030"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:266057"}},{"Add":{"text":"trusted_values_dict['StaticTrumpet__StaticTrumpet__ComputeADMGlobalsOnly=True__globals'] = {'alphaSph': mpf('0.47901157071628237535174768234896'), 'betaSphU[0]': mpf('0.249559485836202384477547321977731'), 'betaSphU[1]': mpf('0.0'), 'betaSphU[2]': mpf('0.0'), 'BSphU[0]': mpf('0.0'), 'BSphU[1]': mpf('0.0'), 'BSphU[2]': mpf('0.0'), 'gammaSphDD[0][0]': mpf('4.35820838377928180149222863568597'), 'gammaSphDD[0][1]': mpf('0.0'), 'gammaSphDD[0][2]': mpf('0.0'), 'gammaSphDD[1][0]': mpf('0.0'), 'gammaSphDD[1][1]': mpf('0.456231514782622374769913065861258'), 'gammaSphDD[1][2]': mpf('0.0'), 'gammaSphDD[2][0]': mpf('0.0'), 'gammaSphDD[2][1]': mpf('0.0'), 'gammaSphDD[2][2]': mpf('0.19552817796951759898685705719116'), 'KSphDD[0][0]': mpf('-3.36157982955715545881983739302993'), 'KSphDD[0][1]': mpf('0.0'), 'KSphDD[0][2]': mpf('0.0'), 'KSphDD[1][0]': mpf('0.0'), 'KSphDD[1][1]': mpf('0.351901176504010315682080545229837'), 'KSphDD[1][2]': mpf('0.0'), 'KSphDD[2][0]': mpf('0.0'), 'KSphDD[2][1]': mpf('0.0'), 'KSphDD[2][2]': mpf('0.150815087598546495698285048292878')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:267119"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:267120"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:267147"}},{"Add":{"text":"trusted_values_dict['T4UUmunu_vars__define_BSSN_T4UUmunu_rescaled_source_terms__globals'] = {'rho': mpf('0.318351756980246647366072920704028'), 'S': mpf('0.41672759971301631676254828562378'), 'sD[0]': mpf('0.139936033700502671095478035567794'), 'sD[1]': mpf('0.724042932336828037875875452300534'), 'sD[2]': mpf('0.634678894759461820207491200562799'), 'sDD[0][0]': mpf('0.975581143777359494073664336610818'), 'sDD[0][1]': mpf('0.319506043115684978950241657003062'), 'sDD[0][2]': mpf('0.843707417334013110021828651952092'), 'sDD[1][0]': mpf('0.319506043115684978950241657003062'), 'sDD[1][1]': mpf('0.535419446395211107159184393822215'), 'sDD[1][2]': mpf('0.697293983830049590721955610206351'), 'sDD[2][0]': mpf('0.843707417334013110021828651952092'), 'sDD[2][1]': mpf('0.697293983830049590721955610206351'), 'sDD[2][2]': mpf('0.0883241044811280406889864025288261')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:268012"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:268013"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:268040"}},{"Add":{"text":"trusted_values_dict['UIUCBlackHole__UIUCBlackHole__ComputeADMGlobalsOnly=True__globals'] = {'alphaSph': mpf('1.0'), 'betaSphU[0]': mpf('0.0'), 'betaSphU[1]': mpf('0.0'), 'betaSphU[2]': mpf('0.0'), 'BSphU[0]': mpf('0.0'), 'BSphU[1]': mpf('0.0'), 'BSphU[2]': mpf('0.0'), 'gammaSphDD[0][0]': mpf('5.88800397535091508054696345959799'), 'gammaSphDD[0][1]': mpf('0.0'), 'gammaSphDD[0][2]': mpf('0.0'), 'gammaSphDD[1][0]': mpf('0.0'), 'gammaSphDD[1][1]': mpf('0.49579570354855419371061261468577'), 'gammaSphDD[1][2]': mpf('0.0'), 'gammaSphDD[2][0]': mpf('0.0'), 'gammaSphDD[2][1]': mpf('0.0'), 'gammaSphDD[2][2]': mpf('0.239531368774223457427342816780148'), 'KSphDD[0][0]': mpf('0.0'), 'KSphDD[0][1]': mpf('0.0'), 'KSphDD[0][2]': mpf('0.516384223238703786717270771044344'), 'KSphDD[1][0]': mpf('0.0'), 'KSphDD[1][1]': mpf('0.0'), 'KSphDD[1][2]': mpf('-0.00263738331117854302766878470676251'), 'KSphDD[2][0]': mpf('0.516384223238703786717270771044344'), 'KSphDD[2][1]': mpf('-0.00263738331117854302766878470676251'), 'KSphDD[2][2]': mpf('0.0')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269077"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269078"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269105"}},{"Add":{"text":"trusted_values_dict['BSSN_constraints__BSSN_constraints__globals'] = {'H': mpf('-743404.980107555200155796229460404'), 'MU[0]': mpf('180487.187683651511140228998931702'), 'MU[1]': mpf('-212737.320962133501867845763983593'), 'MU[2]': mpf('117663.393460122555345796445578668')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269381"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269382"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269409"}},{"Add":{"text":"trusted_values_dict['gauge_RHSs__BSSN_gauge_RHSs__globals'] = {'alpha_rhs': mpf('4.55215595841202287904255791161233'), 'bet_rhsU[0]': mpf('-699763.514938021371061944114376614'), 'bet_rhsU[1]': mpf('800493.882262268190058064264269136'), 'bet_rhsU[2]': mpf('-475937.852585205029810577745084266'), 'vet_rhsU[0]': mpf('-202.50075396040237046126314033238'), 'vet_rhsU[1]': mpf('243.191035932372271446347823729945'), 'vet_rhsU[2]': mpf('-122.639420805832850593976051533138')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269879"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269880"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:269907"}},{"Add":{"text":"trusted_values_dict['BSSN_quantities__declare_BSSN_gridfunctions_if_not_declared_already__globals'] = {'hDD[0][0]': mpf('0.00450974412619198350427041077637114'), 'hDD[0][1]': mpf('0.923519781999295741314881524886005'), 'hDD[0][2]': mpf('0.120267555611392129577552623231895'), 'hDD[1][0]': mpf('0.923519781999295741314881524886005'), 'hDD[1][1]': mpf('0.290125263019792467567015137319686'), 'hDD[1][2]': mpf('0.925654825647319157155834545847028'), 'hDD[2][0]': mpf('0.120267555611392129577552623231895'), 'hDD[2][1]': mpf('0.925654825647319157155834545847028'), 'hDD[2][2]': mpf('0.477887576370744082687735954095842'), 'aDD[0][0]': mpf('0.142813553146530880511022587597836'), 'aDD[0][1]': mpf('0.647457955584693545247887414006982'), 'aDD[0][2]': mpf('0.21834217753528206706903347367188'), 'aDD[1][0]': mpf('0.647457955584693545247887414006982'), 'aDD[1][1]': mpf('0.333850909184938648976981312443968'), 'aDD[1][2]': mpf('0.687554902414082569350739504443482'), 'aDD[2][0]': mpf('0.21834217753528206706903347367188'), 'aDD[2][1]': mpf('0.687554902414082569350739504443482'), 'aDD[2][2]': mpf('0.593368548750377144962442343967268'), 'lambdaU[0]': mpf('0.562783861711218968970626974623883'), 'lambdaU[1]': mpf('0.664424004972256732060031936271116'), 'lambdaU[2]': mpf('0.26459724357734237809580690736766'), 'vetU[0]': mpf('0.696603667756184763426574590994278'), 'vetU[1]': mpf('0.602357411405810894144963185681263'), 'vetU[2]': mpf('0.850413289206002676046125543507515'), 'betU[0]': mpf('0.0391630274878592699039359104062896'), 'betU[1]': mpf('0.0690677340046900178904820677416865'), 'betU[2]': mpf('0.210433354840527941931327404745389'), 'trK': mpf('0.430179315304250131646313093369827'), 'cf': mpf('0.336963542644043156926159099384677'), 'alpha': mpf('0.574476527200906694758941739564762')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:271695"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:271696"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:271723"}},{"Add":{"text":"trusted_values_dict['BSSN_quantities__BSSN_basic_tensors__globals'] = {'gammabarDD[0][0]': mpf('1.00450974412619198350427041077637'), 'gammabarDD[0][1]': mpf('0.380375959488448974007020456949004'), 'gammabarDD[0][2]': mpf('0.0221179741925291571131550303027706'), 'gammabarDD[1][0]': mpf('0.380375959488448974007020456949004'), 'gammabarDD[1][1]': mpf('0.218859597510979935870263689587696'), 'gammabarDD[1][2]': mpf('0.0701152990412707885651168831120483'), 'gammabarDD[2][0]': mpf('0.0221179741925291571131550303027706'), 'gammabarDD[2][1]': mpf('0.0701152990412707885651168831120483'), 'gammabarDD[2][2]': mpf('0.0499844737257731260766363781664902'), 'AbarDD[0][0]': mpf('0.142813553146530880511022587597836'), 'AbarDD[0][1]': mpf('0.266672621295452871655360256826897'), 'AbarDD[0][2]': mpf('0.0401545256600238301157730952990965'), 'AbarDD[1][0]': mpf('0.266672621295452871655360256826897'), 'AbarDD[1][1]': mpf('0.056635179317288849494133380201829'), 'AbarDD[1][2]': mpf('0.0520800154164839604018649639497029'), 'AbarDD[2][0]': mpf('0.0401545256600238301157730952990965'), 'AbarDD[2][1]': mpf('0.0520800154164839604018649639497029'), 'AbarDD[2][2]': mpf('0.0200686541445511291805537698984873'), 'LambdabarU[0]': mpf('0.562783861711218968970626974623883'), 'LambdabarU[1]': mpf('1.61316375791018207963945540610151'), 'LambdabarU[2]': mpf('1.43876032359725990511334321483131'), 'betaU[0]': mpf('0.696603667756184763426574590994278'), 'betaU[1]': mpf('1.46247146117037299492483621025343'), 'betaU[2]': mpf('4.6241634365771266519514488292252'), 'BU[0]': mpf('0.0391630274878592699039359104062896'), 'BU[1]': mpf('0.167690457454195833796083765751675'), 'BU[2]': mpf('1.14424155600667335640923075733714')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:273424"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:273425"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:273452"}},{"Add":{"text":"trusted_values_dict['BSSN_quantities__gammabar__inverse_and_derivs__globals'] = {'gammabarUU[0][0]': mpf('-55.3913683921929939892608290454462'), 'gammabarUU[0][1]': mpf('160.581139770070431806627488067463'), 'gammabarUU[0][2]': mpf('-200.743331495864219543840762334583'), 'gammabarUU[1][0]': mpf('160.581139770070431806627488067463'), 'gammabarUU[1][1]': mpf('-457.230909570455507522618494885285'), 'gammabarUU[1][2]': mpf('570.320147944349793491547665601545'), 'gammabarUU[2][0]': mpf('-200.743331495864219543840762334583'), 'gammabarUU[2][1]': mpf('570.320147944349793491547665601545'), 'gammabarUU[2][2]': mpf('-691.177266096096440977423920582226'), 'gammabarDD_dD[0][0][0]': mpf('0.113376527866793974652637189137749'), 'gammabarDD_dD[0][0][1]': mpf('0.597031746016325581827288715430768'), 'gammabarDD_dD[0][0][2]': mpf('0.0326900992587932925914628867758438'), 'gammabarDD_dD[0][1][0]': mpf('1.29509849818179299105146594183329'), 'gammabarDD_dD[0][1][1]': mpf('0.29966757015887334440305520963308'), 'gammabarDD_dD[0][1][2]': mpf('0.408456984468846210692212242298237'), 'gammabarDD_dD[0][2][0]': mpf('0.0757914276030065310563752344719272'), 'gammabarDD_dD[0][2][1]': mpf('0.211213637778013737361842492406609'), 'gammabarDD_dD[0][2][2]': mpf('0.043576970886389692140854474231034'), 'gammabarDD_dD[1][0][0]': mpf('1.29509849818179299105146594183329'), 'gammabarDD_dD[1][0][1]': mpf('0.29966757015887334440305520963308'), 'gammabarDD_dD[1][0][2]': mpf('0.408456984468846210692212242298237'), 'gammabarDD_dD[1][1][0]': mpf('1.11081293166050470517099765479562'), 'gammabarDD_dD[1][1][1]': mpf('0.162456880553023991817285210787008'), 'gammabarDD_dD[1][1][2]': mpf('0.158500072577490769771706912461303'), 'gammabarDD_dD[1][2][0]': mpf('0.359283025128967082047900286877992'), 'gammabarDD_dD[1][2][1]': mpf('0.199267454573993880968860334987007'), 'gammabarDD_dD[1][2][2]': mpf('0.0222668035023729125133168779194776'), 'gammabarDD_dD[2][0][0]': mpf('0.0757914276030065310563752344719272'), 'gammabarDD_dD[2][0][1]': mpf('0.211213637778013737361842492406609'), 'gammabarDD_dD[2][0][2]': mpf('0.043576970886389692140854474231034'), 'gammabarDD_dD[2][1][0]': mpf('0.359283025128967082047900286877992'), 'gammabarDD_dD[2][1][1]': mpf('0.199267454573993880968860334987007'), 'gammabarDD_dD[2][1][2]': mpf('0.0222668035023729125133168779194776'), 'gammabarDD_dD[2][2][0]': mpf('0.249364796420989096924555910811589'), 'gammabarDD_dD[2][2][1]': mpf('0.229090281001197346827970614026702'), 'gammabarDD_dD[2][2][2]': mpf('0.0293354706024628609686096695909266'), 'gammabarDD_dupD[0][0][0]': mpf('0.37728180260573840332227746330318'), 'gammabarDD_dupD[0][0][1]': mpf('0.670267766719132906949596417689463'), 'gammabarDD_dupD[0][0][2]': mpf('0.781414536731840470018539690499892'), 'gammabarDD_dupD[0][1][0]': mpf('1.27559379975272638197786370234481'), 'gammabarDD_dupD[0][1][1]': mpf('0.270519930552051576420169894439394'), 'gammabarDD_dupD[0][1][2]': mpf('0.126974122612752350149982986405959'), 'gammabarDD_dupD[0][2][0]': mpf('0.160014994496667253968983142186692'), 'gammabarDD_dupD[0][2][1]': mpf('0.159417776511127717981289959174267'), 'gammabarDD_dupD[0][2][2]': mpf('0.0914222006910319288079363366980038'), 'gammabarDD_dupD[1][0][0]': mpf('1.27559379975272638197786370234481'), 'gammabarDD_dupD[1][0][1]': mpf('0.270519930552051576420169894439394'), 'gammabarDD_dupD[1][0][2]': mpf('0.126974122612752350149982986405959'), 'gammabarDD_dupD[1][1][0]': mpf('1.11565554836934532567070034274662'), 'gammabarDD_dupD[1][1][1]': mpf('0.0225054491023032484277595044174296'), 'gammabarDD_dupD[1][1][2]': mpf('0.148236212186685765996028318648501'), 'gammabarDD_dupD[1][2][0]': mpf('0.38244111267429014279462120452751'), 'gammabarDD_dupD[1][2][1]': mpf('0.19605291006032265256196166097098'), 'gammabarDD_dupD[1][2][2]': mpf('0.000359393084847625499631216495471881'), 'gammabarDD_dupD[2][0][0]': mpf('0.160014994496667253968983142186692'), 'gammabarDD_dupD[2][0][1]': mpf('0.159417776511127717981289959174267'), 'gammabarDD_dupD[2][0][2]': mpf('0.0914222006910319288079363366980038'), 'gammabarDD_dupD[2][1][0]': mpf('0.38244111267429014279462120452751'), 'gammabarDD_dupD[2][1][1]': mpf('0.19605291006032265256196166097098'), 'gammabarDD_dupD[2][1][2]': mpf('0.000359393084847625499631216495471881'), 'gammabarDD_dupD[2][2][0]': mpf('0.255124908396158921845552323395099'), 'gammabarDD_dupD[2][2][1]': mpf('0.210716113114337146067597109416175'), 'gammabarDD_dupD[2][2][2]': mpf('0.01339819778908501331879521055357'), 'gammabarDD_dDD[0][0][0][0]': mpf('0.185845801018537204463143552857218'), 'gammabarDD_dDD[0][0][0][1]': mpf('0.41265964722127601582712941308273'), 'gammabarDD_dDD[0][0][0][2]': mpf('0.37985477211695328758622736131656'), 'gammabarDD_dDD[0][0][1][0]': mpf('0.41265964722127601582712941308273'), 'gammabarDD_dDD[0][0][1][1]': mpf('0.689211123606880748937442149326671'), 'gammabarDD_dDD[0][0][1][2]': mpf('0.0048337295380591616122956111212261'), 'gammabarDD_dDD[0][0][2][0]': mpf('0.37985477211695328758622736131656'), 'gammabarDD_dDD[0][0][2][1]': mpf('0.0048337295380591616122956111212261'), 'gammabarDD_dDD[0][0][2][2]': mpf('0.538905401817390661278750485507771'), 'gammabarDD_dDD[0][1][0][0]': mpf('2.17695434404486827829573669497839'), 'gammabarDD_dDD[0][1][0][1]': mpf('0.737845818275736881995111390979058'), 'gammabarDD_dDD[0][1][0][2]': mpf('1.27821731904689736052853767370668'), 'gammabarDD_dDD[0][1][1][0]': mpf('0.737845818275736881995111390979058'), 'gammabarDD_dDD[0][1][1][1]': mpf('0.0572033349261599444767919389310414'), 'gammabarDD_dDD[0][1][1][2]': mpf('0.114449372510356573992423216972657'), 'gammabarDD_dDD[0][1][2][0]': mpf('1.27821731904689736052853767370668'), 'gammabarDD_dDD[0][1][2][1]': mpf('0.114449372510356573992423216972657'), 'gammabarDD_dDD[0][1][2][2]': mpf('0.336172859503064373361339781168181'), 'gammabarDD_dDD[0][2][0][0]': mpf('0.149593239036693143279810874442325'), 'gammabarDD_dDD[0][2][0][1]': mpf('0.670365627630913964987374237749722'), 'gammabarDD_dDD[0][2][0][2]': mpf('0.178979216891036880951181191336912'), 'gammabarDD_dDD[0][2][1][0]': mpf('0.670365627630913964987374237749722'), 'gammabarDD_dDD[0][2][1][1]': mpf('0.659480314934221443474116011063672'), 'gammabarDD_dDD[0][2][1][2]': mpf('0.211927554805221158936564646974544'), 'gammabarDD_dDD[0][2][2][0]': mpf('0.178979216891036880951181191336912'), 'gammabarDD_dDD[0][2][2][1]': mpf('0.211927554805221158936564646974544'), 'gammabarDD_dDD[0][2][2][2]': mpf('0.0131768891907001501822079393602128'), 'gammabarDD_dDD[1][0][0][0]': mpf('2.17695434404486827829573669497839'), 'gammabarDD_dDD[1][0][0][1]': mpf('0.737845818275736881995111390979058'), 'gammabarDD_dDD[1][0][0][2]': mpf('1.27821731904689736052853767370668'), 'gammabarDD_dDD[1][0][1][0]': mpf('0.737845818275736881995111390979058'), 'gammabarDD_dDD[1][0][1][1]': mpf('0.0572033349261599444767919389310414'), 'gammabarDD_dDD[1][0][1][2]': mpf('0.114449372510356573992423216972657'), 'gammabarDD_dDD[1][0][2][0]': mpf('1.27821731904689736052853767370668'), 'gammabarDD_dDD[1][0][2][1]': mpf('0.114449372510356573992423216972657'), 'gammabarDD_dDD[1][0][2][2]': mpf('0.336172859503064373361339781168181'), 'gammabarDD_dDD[1][1][0][0]': mpf('3.2125897978005476278879035565663'), 'gammabarDD_dDD[1][1][0][1]': mpf('0.89598315374067949012654219762452'), 'gammabarDD_dDD[1][1][0][2]': mpf('0.820646830703092166810003596680962'), 'gammabarDD_dDD[1][1][1][0]': mpf('0.89598315374067949012654219762452'), 'gammabarDD_dDD[1][1][1][1]': mpf('0.168996792900712596062122767009282'), 'gammabarDD_dDD[1][1][1][2]': mpf('0.0473971971696919594315542625878797'), 'gammabarDD_dDD[1][1][2][0]': mpf('0.820646830703092166810003596680962'), 'gammabarDD_dDD[1][1][2][1]': mpf('0.0473971971696919594315542625878797'), 'gammabarDD_dDD[1][1][2][2]': mpf('0.12968746168617386620955233939796'), 'gammabarDD_dDD[1][2][0][0]': mpf('1.04180796862731772248736459987955'), 'gammabarDD_dDD[1][2][0][1]': mpf('1.02777187626693600280637544109045'), 'gammabarDD_dDD[1][2][0][2]': mpf('0.138815878772543536594426398853965'), 'gammabarDD_dDD[1][2][1][0]': mpf('1.02777187626693600280637544109045'), 'gammabarDD_dDD[1][2][1][1]': mpf('0.205354158028681326149566579067253'), 'gammabarDD_dDD[1][2][1][2]': mpf('0.051702758215965343443390702033079'), 'gammabarDD_dDD[1][2][2][0]': mpf('0.138815878772543536594426398853965'), 'gammabarDD_dDD[1][2][2][1]': mpf('0.051702758215965343443390702033079'), 'gammabarDD_dDD[1][2][2][2]': mpf('0.0737488709653608336887200438662802'), 'gammabarDD_dDD[2][0][0][0]': mpf('0.149593239036693143279810874442325'), 'gammabarDD_dDD[2][0][0][1]': mpf('0.670365627630913964987374237749722'), 'gammabarDD_dDD[2][0][0][2]': mpf('0.178979216891036880951181191336912'), 'gammabarDD_dDD[2][0][1][0]': mpf('0.670365627630913964987374237749722'), 'gammabarDD_dDD[2][0][1][1]': mpf('0.659480314934221443474116011063672'), 'gammabarDD_dDD[2][0][1][2]': mpf('0.211927554805221158936564646974544'), 'gammabarDD_dDD[2][0][2][0]': mpf('0.178979216891036880951181191336912'), 'gammabarDD_dDD[2][0][2][1]': mpf('0.211927554805221158936564646974544'), 'gammabarDD_dDD[2][0][2][2]': mpf('0.0131768891907001501822079393602128'), 'gammabarDD_dDD[2][1][0][0]': mpf('1.04180796862731772248736459987955'), 'gammabarDD_dDD[2][1][0][1]': mpf('1.02777187626693600280637544109045'), 'gammabarDD_dDD[2][1][0][2]': mpf('0.138815878772543536594426398853965'), 'gammabarDD_dDD[2][1][1][0]': mpf('1.02777187626693600280637544109045'), 'gammabarDD_dDD[2][1][1][1]': mpf('0.205354158028681326149566579067253'), 'gammabarDD_dDD[2][1][1][2]': mpf('0.051702758215965343443390702033079'), 'gammabarDD_dDD[2][1][2][0]': mpf('0.138815878772543536594426398853965'), 'gammabarDD_dDD[2][1][2][1]': mpf('0.051702758215965343443390702033079'), 'gammabarDD_dDD[2][1][2][2]': mpf('0.0737488709653608336887200438662802'), 'gammabarDD_dDD[2][2][0][0]': mpf('0.66508879899869765324495129089009'), 'gammabarDD_dDD[2][2][0][1]': mpf('1.15812919014671874295450095368265'), 'gammabarDD_dDD[2][2][0][2]': mpf('0.165896787206516112586624167221097'), 'gammabarDD_dDD[2][2][1][0]': mpf('1.15812919014671874295450095368285'), 'gammabarDD_dDD[2][2][1][1]': mpf('0.533174868302490566724214906488119'), 'gammabarDD_dDD[2][2][1][2]': mpf('0.131976505361826978863691234258533'), 'gammabarDD_dDD[2][2][2][0]': mpf('0.165896787206516112586624167221097'), 'gammabarDD_dDD[2][2][2][1]': mpf('0.131976505361826978863691234258533'), 'gammabarDD_dDD[2][2][2][2]': mpf('0.010262022536939967495395958633956'), 'GammabarUDD[0][0][0]': mpf('144.958869354596952650223295197696'), 'GammabarUDD[0][0][1]': mpf('56.3884081838815055298106227619069'), 'GammabarUDD[0][0][2]': mpf('18.7492848883834673075437947835502'), 'GammabarUDD[0][1][0]': mpf('56.3884081838815055298106227619069'), 'GammabarUDD[0][1][1]': mpf('3.11678651957992149533502697995063'), 'GammabarUDD[0][1][2]': mpf('-17.4797246150434126590734188209953'), 'GammabarUDD[0][2][0]': mpf('18.7492848883834673075437947835502'), 'GammabarUDD[0][2][1]': mpf('-17.4797246150434126590734188209953'), 'GammabarUDD[0][2][2]': mpf('-13.2700699776147156200210831819353'), 'GammabarUDD[1][0][0]': mpf('-412.661847055574875860384479574194'), 'GammabarUDD[1][0][1]': mpf('-159.805737735924117067707092684796'), 'GammabarUDD[1][0][2]': mpf('-53.4969391010037688000184007256669'), 'GammabarUDD[1][1][0]': mpf('-159.805737735924117067707092684796'), 'GammabarUDD[1][1][1]': mpf('-9.75864522872634062530478027925608'), 'GammabarUDD[1][1][2]': mpf('49.998503864403681839928229922025'), 'GammabarUDD[1][2][0]': mpf('-53.4969391010037688000184007256669'), 'GammabarUDD[1][2][1]': mpf('49.998503864403681839928229922025'), 'GammabarUDD[1][2][2]': mpf('37.5338109651112817021709810969423'), 'GammabarUDD[2][0][0]': mpf('515.903374261971431760645349581284'), 'GammabarUDD[2][0][1]': mpf('200.835355938522818161227492367693'), 'GammabarUDD[2][0][2]': mpf('69.2403025140953793071085058377914'), 'GammabarUDD[2][1][0]': mpf('200.835355938522818161227492367693'), 'GammabarUDD[2][1][1]': mpf('14.7107829316252639239815376245426'), 'GammabarUDD[2][1][2]': mpf('-60.1086414978290381532119255024356'), 'GammabarUDD[2][2][0]': mpf('69.2403025140953793071085058377914'), 'GammabarUDD[2][2][1]': mpf('-60.1086414978290381532119255024356'), 'GammabarUDD[2][2][2]': mpf('-46.4848263107765220270562375920812')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:285739"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:285740"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:285767"}},{"Add":{"text":"trusted_values_dict['BSSN_quantities__detgammabar_and_derivs__globals'] = {'detgammabar': mpf('0.00573756266880972544377979111558305'), 'detgammabar_dD[0]': mpf('0.0557212146869903791885764536246544'), 'detgammabar_dD[1]': mpf('0.0229955254712656127315158404877634'), 'detgammabar_dD[2]': mpf('0.0'), 'detgammabar_dDD[0][0]': mpf('0.405858804349815958396163363914466'), 'detgammabar_dDD[0][1]': mpf('0.223324551832801915665195788045795'), 'detgammabar_dDD[0][2]': mpf('0.0'), 'detgammabar_dDD[1][0]': mpf('0.223324551832801915665195788045795'), 'detgammabar_dDD[1][1]': mpf('0.0346066538274459059495911839041824'), 'detgammabar_dDD[1][2]': mpf('0.0'), 'detgammabar_dDD[2][0]': mpf('0.0'), 'detgammabar_dDD[2][1]': mpf('0.0'), 'detgammabar_dDD[2][2]': mpf('0.0')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:286530"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:286531"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:286558"}},{"Add":{"text":"trusted_values_dict['BSSN_quantities__AbarUU_AbarUD_trAbar_AbarDD_dD__globals'] = {'AbarUU[0][0]': mpf('-4501.35489903001232813737257379218'), 'AbarUU[0][1]': mpf('12891.1260926920183373060745066027'), 'AbarUU[0][2]': mpf('-16048.8656589832488120714141642617'), 'AbarUU[1][0]': mpf('12891.1260926920183373060745066027'), 'AbarUU[1][1]': mpf('-36915.8909445128919893699783581937'), 'AbarUU[1][2]': mpf('45960.7552497439495397460051934269'), 'AbarUU[2][0]': mpf('-16048.8656589832488120714141642617'), 'AbarUU[2][1]': mpf('45960.7552497439495397460051934269'), 'AbarUU[2][2]': mpf('-57214.0298282929626166132996415947'), 'AbarUD[0][0]': mpf('26.8512020837293036423215049007785'), 'AbarUD[0][1]': mpf('-16.1315355594965963827373776014512'), 'AbarUD[0][2]': mpf('2.11020561975821049709560254567513'), 'AbarUD[1][0]': mpf('-76.096867038514101536679331070774'), 'AbarUD[1][1]': mpf('46.6295210174394985755149432015637'), 'AbarUD[1][2]': mpf('-5.91897552114475146319310921096151'), 'AbarUD[2][0]': mpf('95.6660051214531525255013492129713'), 'AbarUD[2][1]': mpf('-57.2290892443011388753856943624776'), 'AbarUD[2][2]': mpf('7.77053133578485609602163485965202'), 'trAbar': mpf('81.251254436953658313858082961098'), 'AbarDD_dD[0][0][0]': mpf('0.33721198437911092948837676885887'), 'AbarDD_dD[0][0][1]': mpf('0.679909473427153132618627751071472'), 'AbarDD_dD[0][0][2]': mpf('0.327242304499680503049319213459967'), 'AbarDD_dD[0][1][0]': mpf('0.733454489269375682720410108340373'), 'AbarDD_dD[0][1][1]': mpf('0.0564054522687123879076101957745309'), 'AbarDD_dD[0][1][2]': mpf('0.288952399746149364416592105125356'), 'AbarDD_dD[0][2][0]': mpf('0.259134566883295043505905621463171'), 'AbarDD_dD[0][2][1]': mpf('0.18566392834089806327031028199579'), 'AbarDD_dD[0][2][2]': mpf('0.10947288045690455436180777612326'), 'AbarDD_dD[1][0][0]': mpf('0.733454489269375682720410108340373'), 'AbarDD_dD[1][0][1]': mpf('0.0564054522687123879076101957745309'), 'AbarDD_dD[1][0][2]': mpf('0.288952399746149364416592105125356'), 'AbarDD_dD[1][1][0]': mpf('0.300852467812027766391019475297803'), 'AbarDD_dD[1][1][1]': mpf('0.0145399155791957464680340380309724'), 'AbarDD_dD[1][1][2]': mpf('0.0395378448600819201304333750185868'), 'AbarDD_dD[1][2][0]': mpf('0.300398363998209101604122555846344'), 'AbarDD_dD[1][2][1]': mpf('0.119537195366846939854213812053404'), 'AbarDD_dD[1][2][2]': mpf('0.04721114477346884448153824722088'), 'AbarDD_dD[2][0][0]': mpf('0.259134566883295043505905621463171'), 'AbarDD_dD[2][0][1]': mpf('0.18566392834089806327031028199579'), 'AbarDD_dD[2][0][2]': mpf('0.10947288045690455436180777612326'), 'AbarDD_dD[2][1][0]': mpf('0.300398363998209101604122555846344'), 'AbarDD_dD[2][1][1]': mpf('0.119537195366846939854213812053404'), 'AbarDD_dD[2][1][2]': mpf('0.04721114477346884448153824722088'), 'AbarDD_dD[2][2][0]': mpf('0.128416701185305713723338911303584'), 'AbarDD_dD[2][2][1]': mpf('0.091211183233673576891878621321523'), 'AbarDD_dD[2][2][2]': mpf('0.0124213262600154053715160803941519'), 'AbarDD_dupD[0][0][0]': mpf('0.769930872140056510311012516467599'), 'AbarDD_dupD[0][0][1]': mpf('0.406856967532203017690051183308242'), 'AbarDD_dupD[0][0][2]': mpf('0.034573833670986209298803260026034'), 'AbarDD_dupD[0][1][0]': mpf('0.799078538941273777740809109133389'), 'AbarDD_dupD[0][1][1]': mpf('0.111116568306179455959424903906438'), 'AbarDD_dupD[0][1][2]': mpf('0.377511909918297386621098531539175'), 'AbarDD_dupD[0][2][0]': mpf('0.214500608396807435491964973223518'), 'AbarDD_dupD[0][2][1]': mpf('0.115344958017771695940477015182743'), 'AbarDD_dupD[0][2][2]': mpf('0.122244734709826544219416183615818'), 'AbarDD_dupD[1][0][0]': mpf('0.799078538941273777740809109133389'), 'AbarDD_dupD[1][0][1]': mpf('0.111116568306179455959424903906438'), 'AbarDD_dupD[1][0][2]': mpf('0.377511909918297386621098531539175'), 'AbarDD_dupD[1][1][0]': mpf('0.435501861817190390787863358691289'), 'AbarDD_dupD[1][1][1]': mpf('0.116623980226106608051172387504808'), 'AbarDD_dupD[1][1][2]': mpf('0.0029262421496022085618519737385143'), 'AbarDD_dupD[1][2][0]': mpf('0.319628992953124375855747562860006'), 'AbarDD_dupD[1][2][1]': mpf('0.154649167361595245816006653565866'), 'AbarDD_dupD[1][2][2]': mpf('0.0691883280846439197601862955001518'), 'AbarDD_dupD[2][0][0]': mpf('0.214500608396807435491964973223518'), 'AbarDD_dupD[2][0][1]': mpf('0.115344958017771695940477015182743'), 'AbarDD_dupD[2][0][2]': mpf('0.122244734709826544219416183615818'), 'AbarDD_dupD[2][1][0]': mpf('0.319628992953124375855747562860006'), 'AbarDD_dupD[2][1][1]': mpf('0.154649167361595245816006653565866'), 'AbarDD_dupD[2][1][2]': mpf('0.0691883280846439197601862955001518'), 'AbarDD_dupD[2][2][0]': mpf('0.102626201407641450303174373971461'), 'AbarDD_dupD[2][2][1]': mpf('0.102313858934520263961250056659667'), 'AbarDD_dupD[2][2][2]': mpf('0.00853496939586718772700035856415055')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:291384"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:291385"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:291412"}},{"Add":{"text":"trusted_values_dict['BSSN_quantities__RicciBar__gammabarDD_dHatD__DGammaUDD__DGammaU__globals'] = {'RbarDD[0][0]': mpf('-41245.2193607369706612392062712087'), 'RbarDD[0][1]': mpf('-13279.8476666719541384124392490902'), 'RbarDD[0][2]': mpf('-13136.4852727140129778266912775021'), 'RbarDD[1][0]': mpf('-13279.8476666719541384124392490142'), 'RbarDD[1][1]': mpf('17572.3339460500557245822009043625'), 'RbarDD[1][2]': mpf('-4983.05391806650925004378740779'), 'RbarDD[2][0]': mpf('-13136.485272714012977826691277452'), 'RbarDD[2][1]': mpf('-4983.05391806650925004378740779404'), 'RbarDD[2][2]': mpf('-5521.17554758589382532917232982535'), 'DGammaUDD[0][0][0]': mpf('144.958869354596952650223295197696'), 'DGammaUDD[0][0][1]': mpf('56.3884081838815055298106227619069'), 'DGammaUDD[0][0][2]': mpf('18.7492848883834673075437947835502'), 'DGammaUDD[0][1][0]': mpf('56.3884081838815055298106227619069'), 'DGammaUDD[0][1][1]': mpf('3.52866287231487465035648484008052'), 'DGammaUDD[0][1][2]': mpf('-17.4797246150434126590734188209953'), 'DGammaUDD[0][2][0]': mpf('18.7492848883834673075437947835502'), 'DGammaUDD[0][2][1]': mpf('-17.4797246150434126590734188209953'), 'DGammaUDD[0][2][2]': mpf('-13.1879541513368329697779753752397'), 'DGammaUDD[1][0][0]': mpf('-412.661847055574875860384479574194'), 'DGammaUDD[1][0][1]': mpf('-162.233650854411671297209410338331'), 'DGammaUDD[1][0][2]': mpf('-53.4969391010037688000184007256669'), 'DGammaUDD[1][1][0]': mpf('-162.233650854411671297209410338331'), 'DGammaUDD[1][1][1]': mpf('-9.75864522872634062530478027925608'), 'DGammaUDD[1][1][2]': mpf('49.998503864403681839928229922025'), 'DGammaUDD[1][2][0]': mpf('-53.4969391010037688000184007256669'), 'DGammaUDD[1][2][1]': mpf('49.998503864403681839928229922025'), 'DGammaUDD[1][2][2]': mpf('37.9333377581165059513560056676581'), 'DGammaUDD[2][0][0]': mpf('515.903374261971431760645349581284'), 'DGammaUDD[2][0][1]': mpf('200.835355938522818161227492367693'), 'DGammaUDD[2][0][2]': mpf('66.8123893956078250776061881842562'), 'DGammaUDD[2][1][0]': mpf('200.835355938522818161227492367693'), 'DGammaUDD[2][1][1]': mpf('14.7107829316252639239815376245426'), 'DGammaUDD[2][1][2]': mpf('-62.1125869707275593077009803716383'), 'DGammaUDD[2][2][0]': mpf('66.8123893956078250776061881842562'), 'DGammaUDD[2][2][1]': mpf('-62.1125869707275593077009803716383'), 'DGammaUDD[2][2][2]': mpf('-46.4848263107765220270562375920812'), 'gammabarDD_dHatD[0][0][0]': mpf('0.113376527866793974652637189137749'), 'gammabarDD_dHatD[0][0][1]': mpf('-1.25000781798226590080247433434124'), 'gammabarDD_dHatD[0][0][2]': mpf('-0.0747109401340281274447427294117478'), 'gammabarDD_dHatD[0][1][0]': mpf('0.371578716182497249736584416947285'), 'gammabarDD_dHatD[0][1][1]': mpf('0.182029291952476074147915289630397'), 'gammabarDD_dHatD[0][1][2]': mpf('0.193899915867061900813055159582757'), 'gammabarDD_dHatD[0][2][0]': mpf('0.0220909079065958210382724263781314'), 'gammabarDD_dHatD[0][2][1]': mpf('-0.00334343082377057251731459030886539'), 'gammabarDD_dHatD[0][2][2]': mpf('0.156675546280700493851442555008333'), 'gammabarDD_dHatD[1][0][0]': mpf('0.371578716182497249736584416947285'), 'gammabarDD_dHatD[1][0][1]': mpf('0.182029291952476074147915289630397'), 'gammabarDD_dHatD[1][0][2]': mpf('0.193899915867061900813055159582757'), 'gammabarDD_dHatD[1][1][0]': mpf('0.0480687558528761896352673763644066'), 'gammabarDD_dHatD[1][1][1]': mpf('0.475792606277345313962293654458942'), 'gammabarDD_dHatD[1][1][2]': mpf('-0.122514399611870464853979699604412'), 'gammabarDD_dHatD[1][2][0]': mpf('0.0188153164310087189522141894729995'), 'gammabarDD_dHatD[1][2][1]': mpf('0.0678700890196179934569006598920808'), 'gammabarDD_dHatD[1][2][2]': mpf('0.0407758029860071575845246674537359'), 'gammabarDD_dHatD[2][0][0]': mpf('0.0220909079065958210382724263781314'), 'gammabarDD_dHatD[2][0][1]': mpf('-0.00334343082377057251731459030886539'), 'gammabarDD_dHatD[2][0][2]': mpf('0.156675546280700493851442555008333'), 'gammabarDD_dHatD[2][1][0]': mpf('0.0188153164310087189522141894729995'), 'gammabarDD_dHatD[2][1][1]': mpf('0.0678700890196179934569006598920808'), 'gammabarDD_dHatD[2][1][2]': mpf('0.0407758029860071575845246674537359'), 'gammabarDD_dHatD[2][2][0]': mpf('0.00664887746198699878899292414052604'), 'gammabarDD_dHatD[2][2][1]': mpf('0.0287579613252410813496304259029699'), 'gammabarDD_dHatD[2][2][2]': mpf('0.0889938231884100782604806662221182'), 'DGammaU[0]': mpf('-9883.50614138972832359869160635136'), 'DGammaU[1]': mpf('27506.4846155065370543113398270077'), 'DGammaU[2]': mpf('-36345.2254745846641825231815918191')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:295977"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:295978"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:296005"}},{"Add":{"text":"trusted_values_dict['BSSN_quantities__betaU_derivs__globals'] = {'betaU_dD[0][0]': mpf('0.192243539484738046319023396790726'), 'betaU_dD[0][1]': mpf('0.754980728051157679026061941840453'), 'betaU_dD[0][2]': mpf('0.586123078895915305963626451557502'), 'betaU_dD[1][0]': mpf('-3.18830793589382952185971488180311'), 'betaU_dD[1][1]': mpf('0.922655491152517150129828380218527'), 'betaU_dD[1][2]': mpf('2.402141784188005363245692498957'), 'betaU_dD[2][0]': mpf('-8.9043744551685352332500234492703'), 'betaU_dD[2][1]': mpf('-4.62598533129686961830418682100716'), 'betaU_dD[2][2]': mpf('3.76687640853700760943325487483147'), 'betaU_dupD[0][0]': mpf('0.659472189904469763277461424877401'), 'betaU_dupD[0][1]': mpf('0.948628367838908470588421550928615'), 'betaU_dupD[0][2]': mpf('0.669133180747105038577160485147033'), 'betaU_dupD[1][0]': mpf('-1.60394693865713402126230258890783'), 'betaU_dupD[1][1]': mpf('1.41044106421919101151961432862351'), 'betaU_dupD[1][2]': mpf('0.406302118865459317620854482607423'), 'betaU_dupD[2][0]': mpf('-6.34070058470575134851313539411892'), 'betaU_dupD[2][1]': mpf('-8.20689620375936786515281493126901'), 'betaU_dupD[2][2]': mpf('3.95742743877129970876759452390656'), 'betaU_dDD[0][0][0]': mpf('0.693440743164982609236801636143355'), 'betaU_dDD[0][0][1]': mpf('0.474644061200962252833335242030444'), 'betaU_dDD[0][0][2]': mpf('0.248757440072191138291657352965558'), 'betaU_dDD[0][1][0]': mpf('0.474644061200962252833335242030444'), 'betaU_dDD[0][1][1]': mpf('0.0806331535826826373281051019148435'), 'betaU_dDD[0][1][2]': mpf('0.906200949230643648668603873375105'), 'betaU_dDD[0][2][0]': mpf('0.248757440072191138291657352965558'), 'betaU_dDD[0][2][1]': mpf('0.906200949230643648668603873375105'), 'betaU_dDD[0][2][2]': mpf('0.256446105879290064955000616464531'), 'betaU_dDD[1][0][0]': mpf('17.6480807195419839436961496336133'), 'betaU_dDD[1][0][1]': mpf('-0.521955208304153160154395471306198'), 'betaU_dDD[1][0][2]': mpf('-3.59469879181060009166143907294526'), 'betaU_dDD[1][1][0]': mpf('-0.521955208304153160154395471306198'), 'betaU_dDD[1][1][1]': mpf('0.390333580442849126669804861962297'), 'betaU_dDD[1][1][2]': mpf('1.03879140080831086038810101219714'), 'betaU_dDD[1][2][0]': mpf('-3.59469879181060009166143907294526'), 'betaU_dDD[1][2][1]': mpf('1.03879140080831086038810101219714'), 'betaU_dDD[1][2][2]': mpf('0.429021139775372473874225378432791'), 'betaU_dDD[2][0][0]': mpf('47.7279356778735564316328362884232'), 'betaU_dDD[2][0][1]': mpf('11.3305777369963646737013674981541'), 'betaU_dDD[2][0][2]': mpf('-9.09922406127764796777495296898437'), 'betaU_dDD[2][1][0]': mpf('11.3305777369963646737013674981541'), 'betaU_dDD[2][1][1]': mpf('24.3353794441474582057173283509946'), 'betaU_dDD[2][1][2]': mpf('-3.95193536311042053355897439286505'), 'betaU_dDD[2][2][0]': mpf('-9.09922406127764796777495296898437'), 'betaU_dDD[2][2][1]': mpf('-3.95193536311042053355897439286505'), 'betaU_dDD[2][2][2]': mpf('0.749372685256775991946308530989456')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:298975"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:298976"}},{"Add":{"text":"# Generated on: 2019-08-09","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:299003"}},{"Add":{"text":"trusted_values_dict['BSSN_quantities__phi_and_derivs__globals'] = {'phi_dD[0]': mpf('-1.13647037353523967950954390927125'), 'phi_dD[1]': mpf('-1.37882238967032079487109408639122'), 'phi_dD[2]': mpf('-1.23865565471203051564572756374677'), 'phi_dupD[0]': mpf('-1.30437304716054772824033366627827'), 'phi_dupD[1]': mpf('-0.387439729438011521402787682064875'), 'phi_dupD[2]': mpf('-1.286536248178407847990777607347'), 'phi_dDD[0][0]': mpf('1.41350298031869520561660429447829'), 'phi_dDD[0][1]': mpf('2.60287661327406578686593533352924'), 'phi_dDD[0][2]': mpf('2.40978752502737233244962940835342'), 'phi_dDD[1][0]': mpf('2.60287661327406578686593533352924'), 'phi_dDD[1][1]': mpf('3.41285382262798172893551850424285'), 'phi_dDD[1][2]': mpf('3.0612083554957324225454264680395'), 'phi_dDD[2][0]': mpf('2.40978752502737233244962940835342'), 'phi_dDD[2][1]': mpf('3.0612083554957324225454264680395'), 'phi_dDD[2][2]': mpf('2.10516420696710843004822415147254'), 'exp_m4phi': mpf('0.113544429071223891132192393151795'), 'phi_dBarD[0]': mpf('-1.13647037353523967950954390927125'), 'phi_dBarD[1]': mpf('-1.37882238967032079487109408639122'), 'phi_dBarD[2]': mpf('-1.23865565471203051564572756374677'), 'phi_dBarDD[0][0]': mpf('236.194201114655255326559793477184'), 'phi_dBarDD[0][1]': mpf('95.1087520363466622986255911257178'), 'phi_dBarDD[0][2]': mpf('35.7199091574093810655803917372351'), 'phi_dBarDD[1][0]': mpf('95.1087520363466622986255911257178'), 'phi_dBarDD[1][1]': mpf('11.7211452920461024221333792078154'), 'phi_dBarDD[1][2]': mpf('-22.3188329171420787008183405055411'), 'phi_dBarDD[2][0]': mpf('35.7199091574093810655803917372351'), 'phi_dBarDD[2][1]': mpf('-22.3188329171420787008183405055411'), 'phi_dBarDD[2][2]': mpf('-18.8021112171325449817326637076808')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:300762"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:300763"}},{"Add":{"text":"# Generated on: 2019-09-03","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:300790"}},{"Add":{"text":"trusted_values_dict['BrillLindquist__BrillLindquist__ComputeADMGlobalsOnly_True__globals'] = {'alphaCart': mpf('0.343480750893445797669295337903236'), 'betaCartU[0]': mpf('0.0'), 'betaCartU[1]': mpf('0.0'), 'betaCartU[2]': mpf('0.0'), 'BCartU[0]': mpf('0.0'), 'BCartU[1]': mpf('0.0'), 'BCartU[2]': mpf('0.0'), 'gammaCartDD[0][0]': mpf('8.47608284216415538664572854966934'), 'gammaCartDD[0][1]': mpf('0.0'), 'gammaCartDD[0][2]': mpf('0.0'), 'gammaCartDD[1][0]': mpf('0.0'), 'gammaCartDD[1][1]': mpf('8.47608284216415538664572854966934'), 'gammaCartDD[1][2]': mpf('0.0'), 'gammaCartDD[2][0]': mpf('0.0'), 'gammaCartDD[2][1]': mpf('0.0'), 'gammaCartDD[2][2]': mpf('8.47608284216415538664572854966934'), 'KCartDD[0][0]': mpf('0.0'), 'KCartDD[0][1]': mpf('0.0'), 'KCartDD[0][2]': mpf('0.0'), 'KCartDD[1][0]': mpf('0.0'), 'KCartDD[1][1]': mpf('0.0'), 'KCartDD[1][2]': mpf('0.0'), 'KCartDD[2][0]': mpf('0.0'), 'KCartDD[2][1]': mpf('0.0'), 'KCartDD[2][2]': mpf('0.0')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:301751"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:301752"}},{"Add":{"text":"# Generated on: 2019-09-03","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:301779"}},{"Add":{"text":"trusted_values_dict['Psi4__Psi4__specify_tetrad_False__globals'] = {'psi4_re_pt[0]': mpf('-11.4627408385133346012203475168749'), 'psi4_re_pt[1]': mpf('-35.6806714906029645727316589574499'), 'psi4_re_pt[2]': mpf('-3374.92496104893019517395960329346'), 'psi4_im_pt[0]': mpf('7.17626585537563385139665194926662'), 'psi4_im_pt[1]': mpf('103.321768247585408574682983348206'), 'psi4_im_pt[2]': mpf('-1785.88265198482805325630868693525')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:302211"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:302212"}},{"Add":{"text":"# Generated on: 2019-09-03","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:302239"}},{"Add":{"text":"trusted_values_dict['ShiftedKerrSchild__ShiftedKerrSchild__ComputeADMGlobalsOnly_True__globals'] = {'alphaSph': mpf('0.764992222074068488402374263959388'), 'betaSphU[0]': mpf('0.414786900166179080948286822502086'), 'betaSphU[1]': mpf('0.0'), 'betaSphU[2]': mpf('0.0'), 'BSphU[0]': mpf('0.0'), 'BSphU[1]': mpf('0.0'), 'BSphU[2]': mpf('0.0'), 'gammaSphDD[0][0]': mpf('1.70877924688282501671697638255698'), 'gammaSphDD[0][1]': mpf('0.0'), 'gammaSphDD[0][2]': mpf('-0.34407721284779690446451905546302'), 'gammaSphDD[1][0]': mpf('0.0'), 'gammaSphDD[1][1]': mpf('0.83749814889950038479162273698221'), 'gammaSphDD[1][2]': mpf('0.0'), 'gammaSphDD[2][0]': mpf('-0.34407721284779690446451905546302'), 'gammaSphDD[2][1]': mpf('0.0'), 'gammaSphDD[2][2]': mpf('0.428211355345928897234853289336263'), 'KSphDD[0][0]': mpf('-0.608416975836176206520434449342952'), 'KSphDD[0][1]': mpf('0.0707242913409545835190603089766082'), 'KSphDD[0][2]': mpf('0.0772829375209889643435925308431919'), 'KSphDD[1][0]': mpf('0.0707242913409545835190603089766082'), 'KSphDD[1][1]': mpf('0.457311525223526834585984744200641'), 'KSphDD[1][2]': mpf('-0.0142409366743087039035851689662884'), 'KSphDD[2][0]': mpf('0.0772829375209889643435925308431919'), 'KSphDD[2][1]': mpf('-0.0142409366743087039035851689662884'), 'KSphDD[2][2]': mpf('0.189536302720822065090385756720081')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:303575"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:303576"}},{"Add":{"text":"# Generated on: 2019-09-03","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:303603"}},{"Add":{"text":"trusted_values_dict['StaticTrumpet__StaticTrumpet__ComputeADMGlobalsOnly_True__globals'] = {'alphaSph': mpf('0.47901157071628237535174768234896'), 'betaSphU[0]': mpf('0.249559485836202384477547321977731'), 'betaSphU[1]': mpf('0.0'), 'betaSphU[2]': mpf('0.0'), 'BSphU[0]': mpf('0.0'), 'BSphU[1]': mpf('0.0'), 'BSphU[2]': mpf('0.0'), 'gammaSphDD[0][0]': mpf('4.35820838377928180149222863568597'), 'gammaSphDD[0][1]': mpf('0.0'), 'gammaSphDD[0][2]': mpf('0.0'), 'gammaSphDD[1][0]': mpf('0.0'), 'gammaSphDD[1][1]': mpf('0.456231514782622374769913065861258'), 'gammaSphDD[1][2]': mpf('0.0'), 'gammaSphDD[2][0]': mpf('0.0'), 'gammaSphDD[2][1]': mpf('0.0'), 'gammaSphDD[2][2]': mpf('0.19552817796951759898685705719116'), 'KSphDD[0][0]': mpf('-3.36157982955715545881983739302993'), 'KSphDD[0][1]': mpf('0.0'), 'KSphDD[0][2]': mpf('0.0'), 'KSphDD[1][0]': mpf('0.0'), 'KSphDD[1][1]': mpf('0.351901176504010315682080545229837'), 'KSphDD[1][2]': mpf('0.0'), 'KSphDD[2][0]': mpf('0.0'), 'KSphDD[2][1]': mpf('0.0'), 'KSphDD[2][2]': mpf('0.150815087598546495698285048292878')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:304665"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:304666"}},{"Add":{"text":"# Generated on: 2019-09-03","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:304693"}},{"Add":{"text":"trusted_values_dict['UIUCBlackHole__UIUCBlackHole__ComputeADMGlobalsOnly_True__globals'] = {'alphaSph': mpf('1.0'), 'betaSphU[0]': mpf('0.0'), 'betaSphU[1]': mpf('0.0'), 'betaSphU[2]': mpf('0.0'), 'BSphU[0]': mpf('0.0'), 'BSphU[1]': mpf('0.0'), 'BSphU[2]': mpf('0.0'), 'gammaSphDD[0][0]': mpf('5.88800397535091508054696345959799'), 'gammaSphDD[0][1]': mpf('0.0'), 'gammaSphDD[0][2]': mpf('0.0'), 'gammaSphDD[1][0]': mpf('0.0'), 'gammaSphDD[1][1]': mpf('0.49579570354855419371061261468577'), 'gammaSphDD[1][2]': mpf('0.0'), 'gammaSphDD[2][0]': mpf('0.0'), 'gammaSphDD[2][1]': mpf('0.0'), 'gammaSphDD[2][2]': mpf('0.239531368774223457427342816780148'), 'KSphDD[0][0]': mpf('0.0'), 'KSphDD[0][1]': mpf('0.0'), 'KSphDD[0][2]': mpf('0.516384223238703786717270771044344'), 'KSphDD[1][0]': mpf('0.0'), 'KSphDD[1][1]': mpf('0.0'), 'KSphDD[1][2]': mpf('-0.00263738331117854302766878470676251'), 'KSphDD[2][0]': mpf('0.516384223238703786717270771044344'), 'KSphDD[2][1]': mpf('-0.00263738331117854302766878470676251'), 'KSphDD[2][2]': mpf('0.0')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:305730"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:305731"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:305758"}},{"Add":{"text":"trusted_values_dict['ADMBSSN_tofrom_4metric__g4DD_ito_BSSN_or_ADM___ADM___globals'] = {'g4DD[0][0]': mpf('1.42770464273047624140299713522594'), 'g4DD[0][1]': mpf('0.813388473397507463814385913308194'), 'g4DD[0][2]': mpf('0.652706348793296836714132090802973'), 'g4DD[0][3]': mpf('1.22429414375154980405074869244046'), 'g4DD[1][0]': mpf('0.813388473397507463814385913308194'), 'g4DD[1][1]': mpf('0.657497767033916602485987823456526'), 'g4DD[1][2]': mpf('0.0577387051674528306577371949970257'), 'g4DD[1][3]': mpf('0.391026617743468030141684721456841'), 'g4DD[2][0]': mpf('0.652706348793296836714132090802973'), 'g4DD[2][1]': mpf('0.0577387051674528306577371949970257'), 'g4DD[2][2]': mpf('0.14235077874207879844448143558111'), 'g4DD[2][3]': mpf('0.723120760610660329170684690325288'), 'g4DD[3][0]': mpf('1.22429414375154980405074869244046'), 'g4DD[3][1]': mpf('0.391026617743468030141684721456841'), 'g4DD[3][2]': mpf('0.723120760610660329170684690325288'), 'g4DD[3][3]': mpf('0.919283767179900235255729512573453')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:306771"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:306772"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:306799"}},{"Add":{"text":"trusted_values_dict['ADMBSSN_tofrom_4metric__g4UU_ito_BSSN_or_ADM___ADM___globals'] = {'g4UU[0][0]': mpf('-3.03008926847944211197781568780977'), 'g4UU[0][1]': mpf('2.25487680174746330097911429618154'), 'g4UU[0][2]': mpf('0.88396408821931067329277382962707'), 'g4UU[0][3]': mpf('2.38097417962378184338842987036543'), 'g4UU[1][0]': mpf('2.25487680174746330097911429618154'), 'g4UU[1][1]': mpf('-0.109478866681308257858746913532804'), 'g4UU[1][2]': mpf('-1.57673807708112257475456728613969'), 'g4UU[1][3]': mpf('-1.71617440778374167644096697698262'), 'g4UU[2][0]': mpf('0.88396408821931067329277382962707'), 'g4UU[2][1]': mpf('-1.57673807708112257475456728613969'), 'g4UU[2][2]': mpf('-2.06437348264308527564608946533953'), 'g4UU[2][3]': mpf('1.11728919891515454886216209391363'), 'g4UU[3][0]': mpf('2.38097417962378184338842987036543'), 'g4UU[3][1]': mpf('-1.71617440778374167644096697698262'), 'g4UU[3][2]': mpf('1.11728919891515454886216209391363'), 'g4UU[3][3]': mpf('-2.23203972375107587678882970577398')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:307807"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:307808"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:307835"}},{"Add":{"text":"trusted_values_dict['ADMBSSN_tofrom_4metric__BSSN_or_ADM_ito_g4DD___ADM___globals'] = {'gammaDD[0][0]': mpf('0.498904274895148658330867874610703'), 'gammaDD[0][1]': mpf('0.252497897757109623917415319738211'), 'gammaDD[0][2]': mpf('0.501283702587057011790250271587865'), 'gammaDD[1][0]': mpf('0.252497897757109623917415319738211'), 'gammaDD[1][1]': mpf('0.974132307468977720610325832240051'), 'gammaDD[1][2]': mpf('0.788410581529429888014703919907333'), 'gammaDD[2][0]': mpf('0.501283702587057011790250271587865'), 'gammaDD[2][1]': mpf('0.788410581529429888014703919907333'), 'gammaDD[2][2]': mpf('0.909148885640877257863223803724395'), 'betaU[0]': mpf('9.06694959302922007806468735643867'), 'betaU[1]': mpf('6.98967266398671524153764426039564'), 'betaU[2]': mpf('-10.826763784327769115585618700949'), 'alpha': mpf('2.9281812371251576982173791733214')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:308687"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:308688"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:308715"}},{"Add":{"text":"trusted_values_dict['ADMBSSN_tofrom_4metric__g4DD_ito_BSSN_or_ADM___BSSN___globals'] = {'g4DD[0][0]': mpf('33.9316040782510563053933745757657'), 'g4DD[0][1]': mpf('11.962817515445852455324947838214'), 'g4DD[0][2]': mpf('8.00807061586371404752271503878887'), 'g4DD[0][3]': mpf('3.0744393577022965271968636933869'), 'g4DD[1][0]': mpf('11.962817515445852455324947838214'), 'g4DD[1][1]': mpf('8.84684305820134422150597858207921'), 'g4DD[1][2]': mpf('3.350018689599008046165002833204'), 'g4DD[1][3]': mpf('0.194795767378908960688399288371257'), 'g4DD[2][0]': mpf('8.00807061586371404752271503878887'), 'g4DD[2][1]': mpf('3.350018689599008046165002833204'), 'g4DD[2][2]': mpf('1.92752387150314689143948714387062'), 'g4DD[2][3]': mpf('0.617514215490828029162196536408385'), 'g4DD[3][0]': mpf('3.0744393577022965271968636933869'), 'g4DD[3][1]': mpf('0.194795767378908960688399288371257'), 'g4DD[3][2]': mpf('0.617514215490828029162196536408385'), 'g4DD[3][3]': mpf('0.440219517017598275317485123438443')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:309712"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:309713"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:309740"}},{"Add":{"text":"trusted_values_dict['ADMBSSN_tofrom_4metric__g4UU_ito_BSSN_or_ADM___BSSN___globals'] = {'g4UU[0][0]': mpf('-3.03008926847944211197781568780977'), 'g4UU[0][1]': mpf('2.11077129805143422596450042497429'), 'g4UU[0][2]': mpf('4.4314190799497963375295703643971'), 'g4UU[0][3]': mpf('14.0116280048673688065179881220934'), 'g4UU[1][0]': mpf('2.11077129805143422596450042497429'), 'g4UU[1][1]': mpf('-7.75975232758250248342057473161043'), 'g4UU[1][2]': mpf('15.146151050341286192891709193053'), 'g4UU[1][3]': mpf('-32.5538384239792224249547239894336'), 'g4UU[2][0]': mpf('4.4314190799497963375295703643971'), 'g4UU[2][1]': mpf('15.146151050341286192891709193053'), 'g4UU[2][2]': mpf('-58.3968465178062189938977785341917'), 'g4UU[2][3]': mpf('44.2650695045030422092937754418837'), 'g4UU[3][0]': mpf('14.0116280048673688065179881220934'), 'g4UU[3][1]': mpf('-32.5538384239792224249547239894336'), 'g4UU[3][2]': mpf('44.2650695045030422092937754418837'), 'g4UU[3][3]': mpf('-143.271385972918464696654248758534')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:310742"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:310743"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:310770"}},{"Add":{"text":"trusted_values_dict['ADMBSSN_tofrom_4metric__BSSN_or_ADM_ito_g4DD___BSSN___globals'] = {'hDD[0][0]': mpf('-0.707823822038679430924860360088691'), 'hDD[0][1]': mpf('0.359019871168498611582168252151222'), 'hDD[0][2]': mpf('1.59629921830030516363312220121092'), 'hDD[1][0]': mpf('0.359019871168498611582168252151222'), 'hDD[1][1]': mpf('2.36288339604623268350851551662764'), 'hDD[1][2]': mpf('6.09559777405440062117804245902213'), 'hDD[2][0]': mpf('1.59629921830030516363312220121092'), 'hDD[2][1]': mpf('6.09559777405440062117804245902213'), 'hDD[2][2]': mpf('14.7423246171918635049100138961082'), 'cf': mpf('0.765268415331718015781674002095462'), 'vetU[0]': mpf('9.06694959302922007806468735643867'), 'vetU[1]': mpf('2.87888088365405202711159845187769'), 'vetU[2]': mpf('-1.99111124153992461429422443718632'), 'alpha': mpf('2.9281812371251576982173791733214')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:311630"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:311631"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:311658"}},{"Add":{"text":"trusted_values_dict['BSSN_stress_energy_source_terms__stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars___ADM___globals'] = {'SDD[0][0]': mpf('1.80029784665212934056799078226269'), 'SDD[0][1]': mpf('1.39659583030126451047804795612856'), 'SDD[0][2]': mpf('3.00811244695977724176245476191804'), 'SDD[1][0]': mpf('1.39659583030126451047804795612856'), 'SDD[1][1]': mpf('1.22494659231382375810150001831715'), 'SDD[1][2]': mpf('2.50094687070838058316104348117154'), 'SDD[2][0]': mpf('3.00811244695977724176245476191804'), 'SDD[2][1]': mpf('2.50094687070838058316104348117154'), 'SDD[2][2]': mpf('5.32511755805920028174659119741427'), 'SD[0]': mpf('0.608341733349877488954095315599777'), 'SD[1]': mpf('0.470565344820866964820125587278172'), 'SD[2]': mpf('1.12342071849067535252360437426405'), 'S': mpf('5.51886985348101528899497640423697'), 'rho': mpf('0.128468170910047767321502802016049')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:312557"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:312558"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:312585"}},{"Add":{"text":"trusted_values_dict['BSSN_stress_energy_source_terms__stress_energy_source_terms_ito_T4UU_and_ADM_or_BSSN_metricvars___BSSN___globals'] = {'SDD[0][0]': mpf('340.54483250614325553458020093047'), 'SDD[0][1]': mpf('193.449779818371076633319750276679'), 'SDD[0][2]': mpf('59.7673665437832411953316595668582'), 'SDD[1][0]': mpf('193.449779818371076633319750276679'), 'SDD[1][1]': mpf('109.367007247314914388974035339596'), 'SDD[1][2]': mpf('33.5362683001178984597875112467598'), 'SDD[2][0]': mpf('59.7673665437832411953316595668582'), 'SDD[2][1]': mpf('33.5362683001178984597875112467598'), 'SDD[2][2]': mpf('10.1607088644086656351007264098463'), 'SD[0]': mpf('8.31158076395254821775662660137348'), 'SD[1]': mpf('4.46081177450846137199550370457638'), 'SD[2]': mpf('1.24975530738365002814654512794839'), 'S': mpf('56.0590719290101215802838899642879'), 'rho': mpf('0.128468170910047767321502802016049')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:313482"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:313483"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:313510"}},{"Add":{"text":"trusted_values_dict['BSSN_stress_energy_source_terms__BSSN_source_terms_for_BSSN_RHSs__globals'] = {'sourceterm_trK_rhs': mpf('34.481947192059905389281900539522'), 'sourceterm_a_rhsDD[0][0]': mpf('-24.4205232684807096387985845039797'), 'sourceterm_a_rhsDD[0][1]': mpf('-44.274626076606489686511882243972'), 'sourceterm_a_rhsDD[0][2]': mpf('-42.5329213202643698441006620646304'), 'sourceterm_a_rhsDD[1][0]': mpf('-44.274626076606489686511882243972'), 'sourceterm_a_rhsDD[1][1]': mpf('-60.2567558996127088470902295335831'), 'sourceterm_a_rhsDD[1][2]': mpf('-40.4716414381018667155368392378324'), 'sourceterm_a_rhsDD[2][0]': mpf('-42.5329213202643698441006620646304'), 'sourceterm_a_rhsDD[2][1]': mpf('-40.4716414381018667155368392378324'), 'sourceterm_a_rhsDD[2][2]': mpf('-7.97163159314560426073123653904653'), 'sourceterm_lambda_rhsU[0]': mpf('-12.4024163649413169626935281713898'), 'sourceterm_lambda_rhsU[1]': mpf('-7.90926902901598263785587714011605'), 'sourceterm_lambda_rhsU[2]': mpf('-5.32437139197028910868095764281183'), 'sourceterm_Lambdabar_rhsU[0]': mpf('-12.4024163649413169626935281713898'), 'sourceterm_Lambdabar_rhsU[1]': mpf('-19.2030180331952244454789590045448'), 'sourceterm_Lambdabar_rhsU[2]': mpf('-28.9515272468210212098860497720561')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:314767"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:314768"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:314795"}},{"Add":{"text":"trusted_values_dict['BSSN_in_terms_of_ADM__gammabarDD_hDD__gammaDD_None__globals'] = {'gammabarDD[0][0]': mpc(real='0.0934311617845273723048649117117748', imag='0.161827519220989063386539896782779'), 'gammabarDD[0][1]': mpc(real='0.00820473402984368653523272740812899', imag='0.0142110162022786069846436163288672'), 'gammabarDD[0][2]': mpc(real='0.0555653159846578106884074088611669', imag='0.0962419504240464018796075151840341'), 'gammabarDD[1][0]': mpc(real='0.00820473402984368653523272740812899', imag='0.0142110162022786069846436163288672'), 'gammabarDD[1][1]': mpc(real='0.0202282035098053057653455510944696', imag='0.035036276224825878278235080642844'), 'gammabarDD[1][2]': mpc(real='0.102756261940095613982570910138747', imag='0.177979066476101677185539529091329'), 'gammabarDD[2][0]': mpc(real='0.0555653159846578106884074088611669', imag='0.0962419504240464018796075151840341'), 'gammabarDD[2][1]': mpc(real='0.102756261940095613982570910138747', imag='0.177979066476101677185539529091329'), 'gammabarDD[2][2]': mpc(real='0.1306312426956797445587454831184', imag='0.226259949404778087922451845770411'), 'hDD[0][0]': mpc(real='-0.906568838215472627695135088288225', imag='0.161827519220989063386539896782779'), 'hDD[0][1]': mpc(real='0.0199203813847587431207220021178728', imag='0.0345031126645514094053446285670361'), 'hDD[0][2]': mpc(real='0.302139096107031490667793605098268', imag='0.523320265410314511278500049229478'), 'hDD[1][0]': mpc(real='0.0199203813847587431207220021178728', imag='0.0345031126645514094053446285670361'), 'hDD[1][1]': mpc(real='-0.880759552378340582201587949384702', imag='0.206530513597969589412173263553996'), 'hDD[1][2]': mpc(real='1.35657739510377672864649412076687', imag='2.34966097271918039623983531782869'), 'hDD[2][0]': mpc(real='0.302139096107031490667793605098268', imag='0.523320265410314511278500049229478'), 'hDD[2][1]': mpc(real='1.35657739510377672864649412076687', imag='2.34966097271918039623983531782869'), 'hDD[2][2]': mpc(real='2.86236517613411134419720838195644', imag='6.68981272244899649592753121396527')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:316862"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:316863"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:316890"}},{"Add":{"text":"trusted_values_dict['BSSN_in_terms_of_ADM__trK_AbarDD_aDD__gammaDD_None_KDD_None__globals'] = {'trK': mpf('1.2095765123256476836242095293423'), 'AbarDD[0][0]': mpc(real='0.0386623707004693575872700250783964', imag='0.0669651903942752452225661841112014'), 'AbarDD[0][1]': mpc(real='0.0197082770012822795779872109278585', imag='0.0341357370958621092471574343107932'), 'AbarDD[0][2]': mpc(real='-0.0116599231388074490306516750592891', imag='-0.0201955792887624809017754756723662'), 'AbarDD[1][0]': mpc(real='0.0197082770012822795779872109278585', imag='0.0341357370958621092471574343107932'), 'AbarDD[1][1]': mpc(real='0.0523135333085628650984233445342397', imag='0.0906096976138776738496360962926701'), 'AbarDD[1][2]': mpc(real='0.0274023107443551947048909767090663', imag='0.0474621944540137424839443269775074'), 'AbarDD[2][0]': mpc(real='-0.0116599231388074490306516750592891', imag='-0.0201955792887624809017754756723662'), 'AbarDD[2][1]': mpc(real='0.0274023107443551947048909767090663', imag='0.0474621944540137424839443269775074'), 'AbarDD[2][2]': mpc(real='0.0773121459494762602870920886743988', imag='0.133908564826673265324430417422263'), 'aDD[0][0]': mpc(real='0.0386623707004693575872700250783964', imag='0.0669651903942752452225661841112014'), 'aDD[0][1]': mpc(real='0.0478499842741998068773590091495862', imag='0.0828786039042858496683763291912328'), 'aDD[0][2]': mpc(real='-0.0634013966339984497144754982400627', imag='-0.109814440240911720403360618547595'), 'aDD[1][0]': mpc(real='0.0478499842741998068773590091495862', imag='0.0828786039042858496683763291912328'), 'aDD[1][1]': mpc(real='0.308375834035874929472953454023809', imag='0.534122612376563332681200790830189'), 'aDD[1][2]': mpc(real='0.361762433038608999247287556499941', imag='0.626590914292604606039560621866258'), 'aDD[2][0]': mpc(real='-0.0634013966339984497144754982400627', imag='-0.109814440240911720403360618547595'), 'aDD[2][1]': mpc(real='0.361762433038608999247287556499941', imag='0.626590914292604606039560621866258'), 'aDD[2][2]': mpc(real='2.28588302495977568895568765583448', imag='3.95926553938956793388115329435095')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:319000"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:319001"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:319028"}},{"Add":{"text":"trusted_values_dict['BSSN_in_terms_of_ADM__LambdabarU_lambdaU__exact_gammaDD__gammaDD_None__globals'] = {'LambdabarU[0]': mpc(real='-4.74783841908033465983862697612494', imag='8.22349736797463570781019370770082'), 'LambdabarU[1]': mpc(real='12.33620224866062287105705763679', imag='-21.3669290671256320024440356064588'), 'LambdabarU[2]': mpc(real='-15.5391046195871584956194055848755', imag='26.9145187052532079974298540037125'), 'lambdaU[0]': mpc(real='-4.74783841908033465983862697612494', imag='8.22349736797463570781019370770082'), 'lambdaU[1]': mpc(real='5.08098998877906549154204185470007', imag='-8.80053281331416137334144877968356'), 'lambdaU[2]': mpc(real='-2.85774091943449803920884733088315', imag='4.949752467329147975760861299932')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:319774"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:319775"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:319802"}},{"Add":{"text":"trusted_values_dict['BSSN_in_terms_of_ADM__cf_from_gammaDD__gammaDD_None__globals'] = {'cf': mpc(real='0.461683509914074474700385053438367', imag='-0.266553098729302162528398412177921')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:319989"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:319990"}},{"Add":{"text":"# Generated on: 2019-10-08","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320017"}},{"Add":{"text":"trusted_values_dict['BSSN_in_terms_of_ADM__betU_vetU__betaU_None_BU_None__globals'] = {'vetU[0]': mpf('0.744161838795925789646901193918893'), 'vetU[1]': mpf('0.120156164503744952492307520976668'), 'vetU[2]': mpf('0.144509409106853504997322208612039'), 'betU[0]': mpf('0.53440111094236486533048946512281'), 'betU[1]': mpf('0.216739633922006111369610208272842'), 'betU[2]': mpf('0.00830060552287044152590411578016158')}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320435"}}]}},{"FileAdd":{"meta":{"basename":"LICENSE","metadata":420},"path":"BaikalX/doc/nrpytutorial/LICENSE","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"BSD 2-Clause License","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320468"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320469"}},{"Add":{"text":"Copyright (c) 2018, Zachariah Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320507"}},{"Add":{"text":"All rights reserved.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320528"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320529"}},{"Add":{"text":"Redistribution and use in source and binary forms, with or without","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320596"}},{"Add":{"text":"modification, are permitted provided that the following conditions are met:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320672"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320673"}},{"Add":{"text":"* Redistributions of source code must retain the above copyright notice, this","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320751"}},{"Add":{"text":" list of conditions and the following disclaimer.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320802"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320803"}},{"Add":{"text":"* Redistributions in binary form must reproduce the above copyright notice,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320879"}},{"Add":{"text":" this list of conditions and the following disclaimer in the documentation","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:320955"}},{"Add":{"text":" and/or other materials provided with the distribution.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321012"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321013"}},{"Add":{"text":"THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321089"}},{"Add":{"text":"AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321163"}},{"Add":{"text":"IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321242"}},{"Add":{"text":"DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321319"}},{"Add":{"text":"FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321394"}},{"Add":{"text":"DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321469"}},{"Add":{"text":"SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321544"}},{"Add":{"text":"CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321622"}},{"Add":{"text":"OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321700"}},{"Add":{"text":"OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321769"}}]}},{"FileAdd":{"meta":{"basename":"NRPy_logo.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/NRPy_logo.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"def print_logo(print_to_stdout=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321824"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321825"}},{"Add":{"text":" logo_str = \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321844"}},{"Add":{"text":"ooooo ooo ooooooooo. ooooooooo. 88","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321902"}},{"Add":{"text":"`888b. `8' `888 `Y88. `888 `Y88. 888888 ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:321964"}},{"Add":{"text":" 8 `88b. 8 888 .d88' 888 .d88' oooo ooo 88","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322022"}},{"Add":{"text":" 8 `88b. 8 888ooo88P' 888ooo88P' `88. .8'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322074"}},{"Add":{"text":" 8 `88b.8 888`88b. 888 `88..8'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322125"}},{"Add":{"text":" 8 `888 888 `88b. 888 `888'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322175"}},{"Add":{"text":"o8o `8 o888o o888o o888o .8'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322224"}},{"Add":{"text":" .o..P'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322272"}},{"Add":{"text":" NRPy+: Python-based Code Generation `Y8P'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322319"}},{"Add":{"text":" for Numerical Relativity... and Beyond!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322362"}},{"Add":{"text":" - homepage: http://blackholesathome.net","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322403"}},{"Add":{"text":" - download: https://github.com/zachetienne/nrpytutorial","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322460"}},{"Add":{"text":"\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322464"}},{"Add":{"text":" if print_to_stdout==True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322494"}},{"Add":{"text":" print(logo_str)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322518"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322528"}},{"Add":{"text":" return logo_str","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322552"}}]}},{"FileAdd":{"meta":{"basename":"NRPy_param_funcs.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/NRPy_param_funcs.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322621"}},{"Add":{"text":"# Tutorial-Coutput__Parameter_Interface.ipynb","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322669"}},{"Add":{"text":"# this core NRPy+ module is used for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322708"}},{"Add":{"text":"# initializing, storing, and recalling","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322749"}},{"Add":{"text":"# parameters.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322765"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322766"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322797"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322840"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322841"}},{"Add":{"text":"import sympy as sp # Import SymPy","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322893"}},{"Add":{"text":"import os, sys # Standard Python: OS-independent system functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:322981"}},{"Add":{"text":"from collections import namedtuple # Standard Python: Enable namedtuple data type","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323065"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323066"}},{"Add":{"text":"glb_params_list = [] # = where we store NRPy+ parameters and default values of parameters. A list of named tuples","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323181"}},{"Add":{"text":"glb_paramsvals_list = [] # = where we store NRPy+ parameter values.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323250"}},{"Add":{"text":"glb_param = namedtuple('glb_param', 'type module parname defaultval')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323321"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323322"}},{"Add":{"text":"glb_Cparams_list = [] # = where we store C runtime parameters and default values of parameters. A list of named tuples","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323442"}},{"Add":{"text":"glb_Cparam = namedtuple('glb_Cparam','type module parname defaultval')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323513"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323514"}},{"Add":{"text":"veryverbose = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323534"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323535"}},{"Add":{"text":"def initialize_param(input):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323564"}},{"Add":{"text":" if get_params_idx(input) == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323600"}},{"Add":{"text":" glb_params_list.append(input)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323638"}},{"Add":{"text":" glb_paramsvals_list.append(input.defaultval)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323691"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323701"}},{"Add":{"text":" if veryverbose == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323733"}},{"Add":{"text":" print(\"initialize_param() minor warning: Did nothing; already initialized parameter \"+input.module+\"::\"+input.parname)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323864"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323865"}},{"Add":{"text":"def initialize_Cparam(input):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323895"}},{"Add":{"text":" if get_params_idx(input,Cparam=True) == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323943"}},{"Add":{"text":" glb_Cparams_list.append(input)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323982"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:323992"}},{"Add":{"text":" if veryverbose == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324024"}},{"Add":{"text":" print(\"initialize_Cparam() minor warning: Did nothing; already initialized parameter \"+input.module+\"::\"+input.parname)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324156"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324157"}},{"Add":{"text":"# Given the named tuple `input` and list of named tuples `params`,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324224"}},{"Add":{"text":"# defined according to namedtuple('param', 'type module name defaultval'),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324302"}},{"Add":{"text":"# where in the case of `input`, defaultval need not be set,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324365"}},{"Add":{"text":"# return the list index of `params` that matches `input`.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324426"}},{"Add":{"text":"# On error returns -1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324448"}},{"Add":{"text":"def get_params_idx(input,Cparam=False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324488"}},{"Add":{"text":" # inspired by: https://stackoverflow.com/questions/2917372/how-to-search-a-list-of-tuples-in-python:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324593"}},{"Add":{"text":" if Cparam==False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324615"}},{"Add":{"text":" list = [i for i, v in enumerate(glb_params_list)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324672"}},{"Add":{"text":" if (input.type==\"ignoretype\" or input.type==v[0]) and input.module == v[1] and input.parname == v[2]]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324790"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324800"}},{"Add":{"text":" list = [i for i, v in enumerate(glb_Cparams_list) if input.parname == v[2]]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324884"}},{"Add":{"text":" if list == []:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324903"}},{"Add":{"text":" return -1 # No match found => error out!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324952"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324962"}},{"Add":{"text":" if len(list) > 1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:324988"}},{"Add":{"text":" print(\"Error: Found multiple parameters matching \"+str(input))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325063"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325087"}},{"Add":{"text":" return list.pop() # pop() returns the index","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325139"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325140"}},{"Add":{"text":"def get_params_value(input):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325169"}},{"Add":{"text":" idx = get_params_idx(input)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325201"}},{"Add":{"text":" if idx < 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325217"}},{"Add":{"text":" print(\"Error: could not find a parameter matching:\",input)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325284"}},{"Add":{"text":" print(\"Full list of modules:\\n\",glb_params_list)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325341"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325361"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325371"}},{"Add":{"text":" return glb_paramsvals_list[idx]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325411"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325412"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325414"}},{"Add":{"text":"def idx_from_str(varname,modname=\"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325452"}},{"Add":{"text":" if \"::\" in varname:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325476"}},{"Add":{"text":" splitstring = re.split('::', varname)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325522"}},{"Add":{"text":" modname=splitstring[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325553"}},{"Add":{"text":" varname=splitstring[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325584"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325593"}},{"Add":{"text":" # inspired by: https://stackoverflow.com/questions/2917372/how-to-search-a-list-of-tuples-in-python: ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325702"}},{"Add":{"text":" if modname == \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325724"}},{"Add":{"text":" list = [i for i, v in enumerate(glb_params_list) if v[2] == varname]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325801"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325811"}},{"Add":{"text":" list = [i for i, v in enumerate(glb_params_list) if (v[1] == modname and v[2] == varname)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325910"}},{"Add":{"text":" if list == []:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:325929"}},{"Add":{"text":" print(\"Error: Could not find a parameter matching \\\"\"+varname+\"\\\" in \",glb_params_list)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326025"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326045"}},{"Add":{"text":" if len(list) > 1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326067"}},{"Add":{"text":" print(\"Error: Found more than one parameter named \\\"\"+varname+\"\\\". Use get_params_value() instead.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326176"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326196"}},{"Add":{"text":" return list.pop()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326218"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326219"}},{"Add":{"text":"def parval_from_str(string):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326248"}},{"Add":{"text":" return glb_paramsvals_list[idx_from_str(string)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326301"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326302"}},{"Add":{"text":"def set_parval_from_str(string,value):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326341"}},{"Add":{"text":" glb_paramsvals_list[idx_from_str(string)] = value","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326395"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326396"}},{"Add":{"text":"# parse_param_string__set__params_and_paramsvars:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326446"}},{"Add":{"text":"# Summary: This function parses a string like this","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326497"}},{"Add":{"text":"# module::variablename=value","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326526"}},{"Add":{"text":"# into its component parts: module,variablename,value","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326580"}},{"Add":{"text":"# then hunts for module,variablename in the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326624"}},{"Add":{"text":"# params list. When it finds the matching index in the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326679"}},{"Add":{"text":"# list \"idx\", it sets paramsvals[idx] = value.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326726"}},{"Add":{"text":"# Usage comment: This function parses both parameter file","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326784"}},{"Add":{"text":"# inputs as well as parameter inputs from the command","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326840"}},{"Add":{"text":"# line. You should set filename = \"\" if reading from the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326899"}},{"Add":{"text":"# command line. This ensures the error messages are","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326953"}},{"Add":{"text":"# appropriate for the context.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326986"}},{"Add":{"text":"import re","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:326996"}},{"Add":{"text":"def set_paramsvals_value(line,filename=\"\", FindMainModuleMode=False):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327066"}},{"Add":{"text":" MainModuleFound = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327093"}},{"Add":{"text":" if FindMainModuleMode == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327128"}},{"Add":{"text":" MainModuleFound = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327160"}},{"Add":{"text":" # First remove carriage return and leading whitespace:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327219"}},{"Add":{"text":" stripped_line_of_text = line.strip()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327260"}},{"Add":{"text":" # Only process lines that do NOT start with a hash","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327315"}},{"Add":{"text":" if not stripped_line_of_text.startswith(\"#\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327365"}},{"Add":{"text":" # Valid lines take the form:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327402"}},{"Add":{"text":" # module::variable = value # Comment here","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327455"}},{"Add":{"text":" # Thus, using the delimiters \"::\", \"=\", and \"#\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327512"}},{"Add":{"text":" # with the regex split command, the first three","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327568"}},{"Add":{"text":" # items in single_param_def will be [module, variablename, value]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327642"}},{"Add":{"text":" single_param_def = re.split('::|=|#', stripped_line_of_text)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327711"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327712"}},{"Add":{"text":" # First verify that single_param_def has at least 3 parts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327779"}},{"Add":{"text":" if len(single_param_def) < 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327817"}},{"Add":{"text":" if filename != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327848"}},{"Add":{"text":" print(\"Error: the line \" + line + \" in parameter file \" + filename + \" is not in the form\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:327956"}},{"Add":{"text":" print(\"\\\"module::variable = value\\\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328010"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328028"}},{"Add":{"text":" print(\"Error: the command-line argument \" + stripped_line_of_text + \" is not in the form\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328135"}},{"Add":{"text":" print(\"\\\"module::variable=value\\\" <-- NOTICE NO SPACES ALLOWED!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328219"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328243"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328244"}},{"Add":{"text":" # Next remove all leading/trailing whitespace from single_param_def","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328320"}},{"Add":{"text":" for i in range(len(single_param_def)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328367"}},{"Add":{"text":" single_param_def[i] = single_param_def[i].strip()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328429"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328430"}},{"Add":{"text":" if FindMainModuleMode == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328470"}},{"Add":{"text":" # Next find the parameter in the params list and set","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328535"}},{"Add":{"text":" # the corresponding element in paramsvals to the value.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328603"}},{"Add":{"text":" idx = get_params_idx(glb_param(\"ignoretype\", single_param_def[0], single_param_def[1], \"ignoredefval\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328719"}},{"Add":{"text":" # If parameter is not found, print useful error message, then exit:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328799"}},{"Add":{"text":" if idx == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328825"}},{"Add":{"text":" if filename != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328860"}},{"Add":{"text":" print(\"Error: when reading line \\\"\" + line + \"\\\" in parameter file \\\"\" + filename + \"\\\":\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328971"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:328993"}},{"Add":{"text":" print(\"Error: when parsing command-line argument \\\"\" + stripped_line_of_text + \"\\\":\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329099"}},{"Add":{"text":" print(\"\\t\\tcould not find parameter \\\"\"+ single_param_def[1] + \"\\\" in \\\"\"+single_param_def[0]+\"\\\" module.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329223"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329251"}},{"Add":{"text":" # If parameter is found at index idx, set paramsval[idx] to the value specified in the file.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329356"}},{"Add":{"text":" partype = glb_params_list[idx].type","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329404"}},{"Add":{"text":" if partype == \"bool\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329438"}},{"Add":{"text":" if single_param_def[2] == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329488"}},{"Add":{"text":" glb_paramsvals_list[idx] = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329540"}},{"Add":{"text":" elif single_param_def[2] == \"False\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329593"}},{"Add":{"text":" glb_paramsvals_list[idx] = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329646"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329668"}},{"Add":{"text":" print(\"Error: \\\"bool\\\" type can only take values of \\\"True\\\" or \\\"False\\\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329764"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329796"}},{"Add":{"text":" elif partype == \"int\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329831"}},{"Add":{"text":" glb_paramsvals_list[idx] = int(single_param_def[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329899"}},{"Add":{"text":" elif partype == \"REAL\" or \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329939"}},{"Add":{"text":" partype == \"char\" or \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:329978"}},{"Add":{"text":" partype == \"char *\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330015"}},{"Add":{"text":" glb_paramsvals_list[idx] = single_param_def[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330078"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330096"}},{"Add":{"text":" print(\"Error: type \\\"\"+partype+\"\\\" on variable \\\"\"+ glb_params_list[idx].parname +\"\\\" is unsupported.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330216"}},{"Add":{"text":" print(\"Supported types include: bool, int, REAL, REALARRAY, char, and char *\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330311"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330339"}},{"Add":{"text":" elif FindMainModuleMode == True and MainModuleFound == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330409"}},{"Add":{"text":" if single_param_def[0] == \"NRPy\" and single_param_def[1] == \"MainModule\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330495"}},{"Add":{"text":" idx = get_params_idx(glb_param(\"ignoretype\", single_param_def[0], single_param_def[1], \"ignoredefval\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330615"}},{"Add":{"text":" if idx == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330645"}},{"Add":{"text":" print(\"Critical error: NRPy::MainModule is uninitialized!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330725"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330757"}},{"Add":{"text":" glb_paramsvals_list[idx] = single_param_def[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330820"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330821"}},{"Add":{"text":"def Cparameters(type,module,names,defaultvals,assumption=\"Real\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330887"}},{"Add":{"text":" output = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330903"}},{"Add":{"text":" # if names is not a list, make it a list, to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:330952"}},{"Add":{"text":" # simplify the remainder of this routine.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331003"}},{"Add":{"text":" if not isinstance(names,list):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331038"}},{"Add":{"text":" names = [names]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331062"}},{"Add":{"text":" defaultval_list = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331087"}},{"Add":{"text":" if not isinstance(defaultvals,list):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331128"}},{"Add":{"text":" for i in range(len(names)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331164"}},{"Add":{"text":" defaultval_list.append(defaultvals)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331212"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331222"}},{"Add":{"text":" # If defaultvals *is* a list, then make sure it has the same number of elements as \"names\".","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331322"}},{"Add":{"text":" if len(defaultvals) != len(names):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331365"}},{"Add":{"text":" print(\"Error in Cparameters(): Was provided a list of variables:\\n\"+str(names)+\"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331462"}},{"Add":{"text":" print(\"and a list of their default values:\\n\"+str(defaultvals)+\"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331543"}},{"Add":{"text":" print(\"but the lists have different lengths (\"+str(len(names))+\" != \"+str(len(defaultvals))+\")\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331654"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331678"}},{"Add":{"text":" defaultval_list = defaultvals","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331716"}},{"Add":{"text":" for i in range(len(names)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331748"}},{"Add":{"text":" initialize_Cparam(glb_Cparam(type, module, names[i], defaultval_list[i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331830"}},{"Add":{"text":" if assumption == \"Real\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331863"}},{"Add":{"text":" tmp = sp.Symbol(names[i], real=True) # Assumes all Cparameters are real.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331948"}},{"Add":{"text":" elif assumption == \"RealPositive\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:331991"}},{"Add":{"text":" tmp = sp.Symbol(names[i], real=True, positive=True) # Assumes all Cparameters are real and positive.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332104"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332118"}},{"Add":{"text":" print(\"Error: assumption \"+str(assumption)+\" not supported.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332192"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332216"}},{"Add":{"text":" output.append(tmp)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332243"}},{"Add":{"text":" if len(names) == 1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332267"}},{"Add":{"text":" return output[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332292"}},{"Add":{"text":" return output","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332310"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332311"}},{"Add":{"text":"def generate_Cparameters_Ccodes(directory=\"./\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332360"}},{"Add":{"text":" # Step 1: Check that Cparams types are supported.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332414"}},{"Add":{"text":" for i in range(len(glb_Cparams_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332457"}},{"Add":{"text":" partype = glb_Cparams_list[i].type","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332500"}},{"Add":{"text":" if partype != \"bool\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332535"}},{"Add":{"text":" partype != \"#define\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332573"}},{"Add":{"text":" partype != \"char\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332608"}},{"Add":{"text":" partype != \"int\" and \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332642"}},{"Add":{"text":" partype != \"REAL\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332672"}},{"Add":{"text":" print(\"Error: parameter \"+glb_Cparams_list[i].module+\"::\"+glb_Cparams_list[i].parname+\" has unsupported type: \\\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332798"}},{"Add":{"text":" + glb_Cparams_list[i].type + \"\\\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332851"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332875"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332876"}},{"Add":{"text":" # Step 2: Generate C code to declare C paramstruct; ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332933"}},{"Add":{"text":" # output to \"declare_Cparameters_struct.h\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:332988"}},{"Add":{"text":" with open(os.path.join(directory,\"declare_Cparameters_struct.h\"), \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333072"}},{"Add":{"text":" file.write(\"typedef struct __paramstruct__ {\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333129"}},{"Add":{"text":" for i in range(len(glb_Cparams_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333176"}},{"Add":{"text":" if glb_Cparams_list[i].type != \"#define\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333230"}},{"Add":{"text":" if glb_Cparams_list[i].type == \"char\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333285"}},{"Add":{"text":" Ctype = \"char *\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333322"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333344"}},{"Add":{"text":" Ctype = glb_Cparams_list[i].type","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333397"}},{"Add":{"text":" file.write(Ctype + \" \" + glb_Cparams_list[i].parname + \";\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333475"}},{"Add":{"text":" file.write(\"} paramstruct;\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333514"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333515"}},{"Add":{"text":" # Step 3: Generate C code to set all elements in ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333569"}},{"Add":{"text":" # C paramstruct to default values; output to ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333627"}},{"Add":{"text":" # \"set_Cparameters_default.h\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333669"}},{"Add":{"text":" with open(os.path.join(directory,\"set_Cparameters_default.h\"), \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333750"}},{"Add":{"text":" for i in range(len(glb_Cparams_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333797"}},{"Add":{"text":" if glb_Cparams_list[i].type != \"#define\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333851"}},{"Add":{"text":" Coutput = \"params.\" + glb_Cparams_list[i].parname","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333917"}},{"Add":{"text":" if isinstance(glb_Cparams_list[i].defaultval, (bool,int,float)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:333998"}},{"Add":{"text":" Coutput += \" = \" + str(glb_Cparams_list[i].defaultval).lower() + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334089"}},{"Add":{"text":" elif glb_Cparams_list[i].type == \"char\" and isinstance(glb_Cparams_list[i].defaultval, (str)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334200"}},{"Add":{"text":" Coutput += \" = \\\"\" + str(glb_Cparams_list[i].defaultval).lower() + \"\\\";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334295"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334317"}},{"Add":{"text":" Coutput += \" = \" + str(glb_Cparams_list[i].defaultval) + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334400"}},{"Add":{"text":" file.write(Coutput)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334436"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334437"}},{"Add":{"text":" # Step 4: Generate C code to set C parameter constants ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334497"}},{"Add":{"text":" # (i.e., all ints != -12345678 and REALs != 1e300); ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334562"}},{"Add":{"text":" # output to filename \"set_Cparameters.h\" if SIMD_enable==False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334637"}},{"Add":{"text":" # or \"set_Cparameters-SIMD.h\" if SIMD_enable==True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334700"}},{"Add":{"text":" # Step 4.a: Output non-SIMD version, set_Cparameters.h","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334759"}},{"Add":{"text":" def gen_set_Cparameters(pointerEnable=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334808"}},{"Add":{"text":" returnstring = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334834"}},{"Add":{"text":" for i in range(len(glb_Cparams_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334881"}},{"Add":{"text":" if glb_Cparams_list[i].type == \"char\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334932"}},{"Add":{"text":" Ctype = \"char *\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334965"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:334983"}},{"Add":{"text":" Ctype = glb_Cparams_list[i].type","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335032"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335045"}},{"Add":{"text":" pointer = \"->\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335072"}},{"Add":{"text":" if pointerEnable==False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335109"}},{"Add":{"text":" pointer = \".\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335139"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335156"}},{"Add":{"text":" if not ((Ctype == \"REAL\" and glb_Cparams_list[i].defaultval == 1e300) or Ctype == \"#define\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335262"}},{"Add":{"text":" Coutput = \"const \"+Ctype+\" \"+glb_Cparams_list[i].parname+\" = \"+\"params\"+pointer+glb_Cparams_list[i].parname + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335394"}},{"Add":{"text":" returnstring += Coutput","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335434"}},{"Add":{"text":" return returnstring","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335462"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335471"}},{"Add":{"text":" with open(os.path.join(directory,\"set_Cparameters.h\"), \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335544"}},{"Add":{"text":" file.write(gen_set_Cparameters(pointerEnable=True))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335604"}},{"Add":{"text":" with open(os.path.join(directory,\"set_Cparameters-nopointer.h\"), \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335687"}},{"Add":{"text":" file.write(gen_set_Cparameters(pointerEnable=False))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335748"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335749"}},{"Add":{"text":" # Step 4.b: Output SIMD version, set_Cparameters-SIMD.h","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335809"}},{"Add":{"text":" with open(os.path.join(directory,\"set_Cparameters-SIMD.h\"), \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335887"}},{"Add":{"text":" for i in range(len(glb_Cparams_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335934"}},{"Add":{"text":" if glb_Cparams_list[i].type == \"char\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:335985"}},{"Add":{"text":" Ctype = \"char *\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336018"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336036"}},{"Add":{"text":" Ctype = glb_Cparams_list[i].type","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336085"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336086"}},{"Add":{"text":" parname = glb_Cparams_list[i].parname","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336136"}},{"Add":{"text":" if Ctype == \"REAL\" and glb_Cparams_list[i].defaultval != 1e300:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336212"}},{"Add":{"text":" Coutput = \"const REAL NOSIMD\" + parname + \" = \" + \"params->\" + glb_Cparams_list[i].parname + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336339"}},{"Add":{"text":" Coutput += \"const REAL_SIMD_ARRAY \" + parname + \" = ConstSIMD(NOSIMD\" + parname + \");\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336444"}},{"Add":{"text":" file.write(Coutput)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336480"}},{"Add":{"text":" elif glb_Cparams_list[i].defaultval != 1e300 and Ctype !=\"#define\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336560"}},{"Add":{"text":" Coutput = \"const \"+Ctype+\" \"+parname + \" = \" + \"params->\" + glb_Cparams_list[i].parname + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336672"}},{"Add":{"text":" file.write(Coutput)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336708"}}]}},{"FileAdd":{"meta":{"basename":"README.md","metadata":420},"path":"BaikalX/doc/nrpytutorial/README.md","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# NRPy+, SENRv2, and the NRPy+ Jupyter Tutorial","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336769"}},{"Add":{"text":"[![Build Status](https://travis-ci.org/zachetienne/nrpytutorial.svg?branch=master)](https://travis-ci.org/zachetienne/nrpytutorial)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:336901"}},{"Add":{"text":"[![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/zachetienne/nrpytutorial/master?filepath=NRPyPlus_Tutorial.ipynb)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337038"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337039"}},{"Add":{"text":"This repository houses","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337062"}},{"Add":{"text":"* [The newest version of NRPy+: Python-Based Code Generation for Numerical Relativity... and Beyond](https://arxiv.org/abs/1712.07658),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337198"}},{"Add":{"text":"* The second version of SENR, the Simple, Efficient Numerical Relativity code (see the \"Colliding Black Holes\" Start-to-Finish tutorial module), and ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337348"}},{"Add":{"text":"* The NRPy+ Jupyter Tutorial: An Introduction to Python-Based Code Generation for Numerical Relativity... and Beyond!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337466"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337467"}},{"Add":{"text":"To explore the NRPy+ tutorial without downloading, check out the [NRPy+ tutorial mybinder](https://mybinder.org/v2/gh/zachetienne/nrpytutorial/master?filepath=NRPyPlus_Tutorial.ipynb).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337652"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337653"}},{"Add":{"text":"If you would like to explore the NRPy+ tutorial on your local computer, you'll need to install Python, Jupyter, Sympy, and Matplotlib. Once they are installed, [you may find this useful](https://jupyter-notebook-beginner-guide.readthedocs.io/en/latest/execute.html)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337919"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:337920"}},{"Add":{"text":"In certain circumstances, developers may wish to execute one of these Jupyter notebooks from the command line. For example, when the notebook constructs an [Einstein Toolkit](https://einsteintoolkit.org) thorn. In such a case, the following command should be useful:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338187"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338188"}},{"Add":{"text":"jupyter nbconvert --to notebook --inplace --execute --ExecutePreprocessor.timeout=-1 [Jupyter notebook file]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338297"}}]}},{"FileAdd":{"meta":{"basename":"SIMD","metadata":1005},"path":"BaikalX/doc/nrpytutorial/SIMD","context":[{"change":0,"pos":15}],"contents":[]}},{"FileAdd":{"meta":{"basename":"SIMD_intrinsics.h","metadata":420},"path":"BaikalX/doc/nrpytutorial/SIMD/SIMD_intrinsics.h","context":[{"change":0,"pos":338306}],"contents":[{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338328"}},{"Add":{"text":"// If compiled with AVX512F SIMD instructions enabled:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338383"}},{"Add":{"text":"#ifdef __AVX512F__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338402"}},{"Add":{"text":"#include ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338425"}},{"Add":{"text":"#define REAL_SIMD_ARRAY __m512d","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338457"}},{"Add":{"text":"#define SIMD_width 8 // 8 doubles per loop iteration","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338510"}},{"Add":{"text":"#define ReadSIMD(a) _mm512_loadu_pd(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338549"}},{"Add":{"text":"#define WriteSIMD(a,b) _mm512_storeu_pd(a,(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338596"}},{"Add":{"text":"#define ConstSIMD(a) _mm512_set1_pd(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338635"}},{"Add":{"text":"#define AddSIMD(a,b) _mm512_add_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338679"}},{"Add":{"text":"#define SubSIMD(a,b) _mm512_sub_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338723"}},{"Add":{"text":"#define MulSIMD(a,b) _mm512_mul_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338767"}},{"Add":{"text":"#define DivSIMD(a,b) _mm512_div_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338811"}},{"Add":{"text":"#define ExpSIMD(a) _mm512_exp_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338849"}},{"Add":{"text":"#define SinSIMD(a) _mm512_sin_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338887"}},{"Add":{"text":"#define CosSIMD(a) _mm512_cos_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338925"}},{"Add":{"text":"// All AVX512 chips have FMA enabled","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:338962"}},{"Add":{"text":"#define FusedMulAddSIMD(a,b,c) _mm512_fmadd_pd((a),(b),(c))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339022"}},{"Add":{"text":"#define FusedMulSubSIMD(a,b,c) _mm512_fmsub_pd((a),(b),(c))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339082"}},{"Add":{"text":"// In the case of 512-bit SIMD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339114"}},{"Add":{"text":"// The result from this comparison is: result[i] = (a OP b) ? 1 : 0, stored in an 8-bit mask array.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339217"}},{"Add":{"text":"// Then if result==1 we set upwind = 0+1, and if result==0 we set upwind = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339297"}},{"Add":{"text":"#define UPWIND_ALG(a) _mm512_mask_add_pd(upwind_Integer_0, _mm512_cmp_pd_mask( (a) , upwind_Integer_0, _CMP_GT_OQ), upwind_Integer_0 ,upwind_Integer_1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339450"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339451"}},{"Add":{"text":"// If compiled with AVX SIMD instructions enabled:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339502"}},{"Add":{"text":"#elif __AVX__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339516"}},{"Add":{"text":"#include ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339539"}},{"Add":{"text":"#define REAL_SIMD_ARRAY __m256d","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339571"}},{"Add":{"text":"#define SIMD_width 4 // 4 doubles per loop iteration","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339624"}},{"Add":{"text":"// Upwind algorithm notes, in the case of 256-bit SIMD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339680"}},{"Add":{"text":"// Sources: https://software.intel.com/sites/landingpage/IntrinsicsGuide/#text=_mm256_cmp_pd&expand=736","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339784"}},{"Add":{"text":"// ...and: https://stackoverflow.com/questions/37099874/is-avx-intrinsic-mm256-cmp-ps-supposed-to-return-nan-when-true","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339904"}},{"Add":{"text":"// The result from _mm256_cmp_pd is 0 if a>0 and NaN otherwise.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:339972"}},{"Add":{"text":"// Thus if OP is >, then: if a > b then the result is NaN, and if a <= b then the result is 0.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340071"}},{"Add":{"text":"// We want the result to be 1 if a>b and 0 otherwise, so we simply perform a logical AND operation","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340174"}},{"Add":{"text":"// on the result, against the number 1, because AND(NaN,1)=1, and AND(0,1)=0,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340256"}},{"Add":{"text":"// where NaN=0xffffff... in double precision.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340306"}},{"Add":{"text":"#define UPWIND_ALG(a) _mm256_and_pd(_mm256_cmp_pd( (a), upwind_Integer_0, _CMP_GT_OQ ), upwind_Integer_1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340412"}},{"Add":{"text":"#define ReadSIMD(a) _mm256_loadu_pd(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340451"}},{"Add":{"text":"#define WriteSIMD(a,b) _mm256_storeu_pd(a,(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340498"}},{"Add":{"text":"#define ConstSIMD(a) _mm256_set1_pd(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340537"}},{"Add":{"text":"#define AddSIMD(a,b) _mm256_add_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340581"}},{"Add":{"text":"#define SubSIMD(a,b) _mm256_sub_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340625"}},{"Add":{"text":"#define MulSIMD(a,b) _mm256_mul_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340669"}},{"Add":{"text":"#define DivSIMD(a,b) _mm256_div_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340713"}},{"Add":{"text":"#define ExpSIMD(a) _mm256_exp_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340751"}},{"Add":{"text":"#define SinSIMD(a) _mm256_sin_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340789"}},{"Add":{"text":"#define CosSIMD(a) _mm256_cos_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340827"}},{"Add":{"text":"#ifdef __FMA__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340842"}},{"Add":{"text":"#define FusedMulAddSIMD(a,b,c) _mm256_fmadd_pd((a),(b),(c))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340902"}},{"Add":{"text":"#define FusedMulSubSIMD(a,b,c) _mm256_fmsub_pd((a),(b),(c))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340962"}},{"Add":{"text":"#else","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:340968"}},{"Add":{"text":"#define FusedMulAddSIMD(a,b,c) _mm256_add_pd(_mm256_mul_pd((a),(b)), (c)) // a*b+c","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341051"}},{"Add":{"text":"#define FusedMulSubSIMD(a,b,c) _mm256_sub_pd(_mm256_mul_pd((a),(b)), (c)) // a*b-c","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341134"}},{"Add":{"text":"#endif","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341141"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341142"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341143"}},{"Add":{"text":"// If compiled with SSE2 SIMD instructions enabled:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341195"}},{"Add":{"text":"#elif __SSE2__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341210"}},{"Add":{"text":"#include ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341233"}},{"Add":{"text":"#define REAL_SIMD_ARRAY __m128d","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341265"}},{"Add":{"text":"#define SIMD_width 2 // 2 doubles per loop iteration","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341318"}},{"Add":{"text":"#define ReadSIMD(a) _mm_loadu_pd(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341354"}},{"Add":{"text":"#define WriteSIMD(a,b) _mm_storeu_pd(a,(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341398"}},{"Add":{"text":"#define ConstSIMD(a) _mm_set1_pd(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341434"}},{"Add":{"text":"#define AddSIMD(a,b) _mm_add_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341475"}},{"Add":{"text":"#define SubSIMD(a,b) _mm_sub_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341516"}},{"Add":{"text":"#define MulSIMD(a,b) _mm_mul_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341557"}},{"Add":{"text":"#define DivSIMD(a,b) _mm_div_pd((a),(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341598"}},{"Add":{"text":"#define ExpSIMD(a) _mm_exp_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341633"}},{"Add":{"text":"#define SinSIMD(a) _mm_sin_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341668"}},{"Add":{"text":"#define CosSIMD(a) _mm_cos_pd((a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341703"}},{"Add":{"text":"// See description above UPWIND_ALG for __AVX__:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341752"}},{"Add":{"text":"#define UPWIND_ALG(a) _mm_and_pd(_mm_cmpgt_pd( (a), upwind_Integer_0 ), upwind_Integer_1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341842"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341843"}},{"Add":{"text":"#ifdef __FMA__ // Unlikely that any SSE2 chip has FMA, but this will work fine.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341923"}},{"Add":{"text":"#define FusedMulAddSIMD(a,b,c) _mm_fmadd_pd((a),(b),(c))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:341980"}},{"Add":{"text":"#define FusedMulSubSIMD(a,b,c) _mm_fmsub_pd((a),(b),(c))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342037"}},{"Add":{"text":"#else","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342043"}},{"Add":{"text":"#define FusedMulAddSIMD(a,b,c) _mm_add_pd(_mm_mul_pd((a),(b)), (c)) // a*b+c","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342120"}},{"Add":{"text":"#define FusedMulSubSIMD(a,b,c) _mm_sub_pd(_mm_mul_pd((a),(b)), (c)) // a*b-c","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342197"}},{"Add":{"text":"#endif","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342204"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342205"}},{"Add":{"text":"#else","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342211"}},{"Add":{"text":"// If SIMD instructions unavailable:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342248"}},{"Add":{"text":"#define REAL_SIMD_ARRAY REAL","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342277"}},{"Add":{"text":"#define SIMD_width 1 // 1 double per loop iteration","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342329"}},{"Add":{"text":"#define ConstSIMD(a) (a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342354"}},{"Add":{"text":"#define AddSIMD(a,b) ((a)+(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342385"}},{"Add":{"text":"#define SubSIMD(a,b) ((a)-(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342416"}},{"Add":{"text":"#define MulSIMD(a,b) ((a)*(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342447"}},{"Add":{"text":"#define DivSIMD(a,b) ((a)/(b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342478"}},{"Add":{"text":"#define FusedMulAddSIMD(a,b,c) ((a)*(b) + (c))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342525"}},{"Add":{"text":"#define FusedMulSubSIMD(a,b,c) ((a)*(b) - (c))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342572"}},{"Add":{"text":"#define SqrtSIMD(a) (sqrt(a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342602"}},{"Add":{"text":"#define ExpSIMD(a) (exp(a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342630"}},{"Add":{"text":"#define SinSIMD(a) (sin(a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342658"}},{"Add":{"text":"#define CosSIMD(a) (cos(a))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342686"}},{"Add":{"text":"#define WriteSIMD(a,b) *(a)=(b)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342718"}},{"Add":{"text":"#define ReadSIMD(a) *(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342743"}},{"Add":{"text":"// Algorithm for upwinding.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342771"}},{"Add":{"text":"// *NOTE*: This upwinding is backwards from","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342815"}},{"Add":{"text":"// usual upwinding algorithms, because the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342859"}},{"Add":{"text":"// upwinding control vector in BSSN (the shift)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342908"}},{"Add":{"text":"// acts like a *negative* velocity.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:342945"}},{"Add":{"text":"#define UPWIND_ALG(UpwindVecU) UpwindVecU > 0.0 ? 1.0 : 0.0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343005"}},{"Add":{"text":"#endif","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343012"}}]}},{"FileAdd":{"meta":{"basename":"SIMD.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/SIMD.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"from sympy import Integer,Symbol,symbols,simplify,Rational,sign,Function,srepr,sin,cos,exp,log,Abs,Add,Mul,Pow,preorder_traversal,N,Float,S,var,sympify","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343176"}},{"Add":{"text":"import re, sys","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343191"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343192"}},{"Add":{"text":"# For debugging purposes, Part 1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343226"}},{"Add":{"text":"# Basic arithmetic operations","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343256"}},{"Add":{"text":"def ConstSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343280"}},{"Add":{"text":" return Float(a,34)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343303"}},{"Add":{"text":"def AbsSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343325"}},{"Add":{"text":" return Abs(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343343"}},{"Add":{"text":"def nrpyAbsSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343369"}},{"Add":{"text":" return Abs(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343387"}},{"Add":{"text":"def AddSIMD_check(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343411"}},{"Add":{"text":" return a+b","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343426"}},{"Add":{"text":"def SubSIMD_check(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343450"}},{"Add":{"text":" return a-b","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343465"}},{"Add":{"text":"def MulSIMD_check(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343489"}},{"Add":{"text":" return a*b","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343504"}},{"Add":{"text":"def FusedMulAddSIMD_check(a,b,c):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343538"}},{"Add":{"text":" return a*b + c","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343557"}},{"Add":{"text":"def FusedMulSubSIMD_check(a,b,c):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343591"}},{"Add":{"text":" return a*b - c","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343610"}},{"Add":{"text":"def DivSIMD_check(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343634"}},{"Add":{"text":" return a/b","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343649"}},{"Add":{"text":"def signSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343672"}},{"Add":{"text":" return sign(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343691"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343692"}},{"Add":{"text":"# For debugging purposes, Part 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343726"}},{"Add":{"text":"# Transcendental operations","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343754"}},{"Add":{"text":"def PowSIMD_check(a, b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343779"}},{"Add":{"text":" return a**b","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343795"}},{"Add":{"text":"def SqrtSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343818"}},{"Add":{"text":" return a**(Rational(1,2))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343848"}},{"Add":{"text":"def CbrtSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343871"}},{"Add":{"text":" return a**(Rational(1,3))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343901"}},{"Add":{"text":"def ExpSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343923"}},{"Add":{"text":" return exp(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343941"}},{"Add":{"text":"def LogSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343963"}},{"Add":{"text":" return log(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:343981"}},{"Add":{"text":"def SinSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344003"}},{"Add":{"text":" return sin(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344021"}},{"Add":{"text":"def CosSIMD_check(a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344043"}},{"Add":{"text":" return cos(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344061"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344062"}},{"Add":{"text":"# Input: SymPy expression.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344089"}},{"Add":{"text":"# Return value: SymPy expression containing all needed SIMD compiler intrinsics","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344169"}},{"Add":{"text":"# Complication: SIMD functions require numerical constants to be stored in SIMD arrays","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344256"}},{"Add":{"text":"# Resolution: This function extends lists \"SIMD_const_varnms\" and \"SIMD_const_values\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344343"}},{"Add":{"text":"# which store the name of each constant SIMD array (e.g., _Integer_1) and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344429"}},{"Add":{"text":"# the value of each variable (e.g., 1.0).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344483"}},{"Add":{"text":"def expr_convert_to_SIMD_intrins(expr, SIMD_const_varnms,SIMD_const_values,SIMD_const_suffix=\"\",debug=\"False\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344596"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344597"}},{"Add":{"text":" # Declare all variables, so we can eval them in the next (AddSIMD & MulSIMD) step","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344683"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344725"}},{"Add":{"text":" for i in range(len(item.args)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344765"}},{"Add":{"text":" if isinstance(item.args[i],Symbol):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344813"}},{"Add":{"text":" var(str(item.args[i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344852"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344853"}},{"Add":{"text":" expr_orig = expr","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344874"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344875"}},{"Add":{"text":" AbsSIMD = Function(\"AbsSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344909"}},{"Add":{"text":" AddSIMD = Function(\"AddSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344943"}},{"Add":{"text":" SubSIMD = Function(\"SubSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:344977"}},{"Add":{"text":" MulSIMD = Function(\"MulSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345011"}},{"Add":{"text":" FusedMulAddSIMD = Function(\"FusedMulAddSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345061"}},{"Add":{"text":" FusedMulSubSIMD = Function(\"FusedMulSubSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345111"}},{"Add":{"text":" DivSIMD = Function(\"DivSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345145"}},{"Add":{"text":" SignSIMD = Function(\"SignSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345181"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345182"}},{"Add":{"text":" PowSIMD = Function(\"PowSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345216"}},{"Add":{"text":" SqrtSIMD = Function(\"SqrtSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345252"}},{"Add":{"text":" CbrtSIMD = Function(\"CbrtSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345288"}},{"Add":{"text":" ExpSIMD = Function(\"ExpSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345322"}},{"Add":{"text":" LogSIMD = Function(\"LogSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345356"}},{"Add":{"text":" SinSIMD = Function(\"SinSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345390"}},{"Add":{"text":" CosSIMD = Function(\"CosSIMD\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345424"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345425"}},{"Add":{"text":" # Step 1: Replace transcendental, power, and division functions with SIMD equivalents","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345515"}},{"Add":{"text":" # Note that due to how SymPy expresses rational numbers, the following does not","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345607"}},{"Add":{"text":" # affect fractional expressions of integers","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345663"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345705"}},{"Add":{"text":" if item.func == Abs:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345734"}},{"Add":{"text":" expr = expr.xreplace({item: AbsSIMD(item.args[0])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345798"}},{"Add":{"text":" elif item.func == exp:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345829"}},{"Add":{"text":" expr = expr.xreplace({item: ExpSIMD(item.args[0])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345893"}},{"Add":{"text":" elif item.func == log:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345924"}},{"Add":{"text":" expr = expr.xreplace({item: LogSIMD(item.args[0])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:345988"}},{"Add":{"text":" elif item.func == sin:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346019"}},{"Add":{"text":" expr = expr.xreplace({item: SinSIMD(item.args[0])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346083"}},{"Add":{"text":" elif item.func == cos:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346114"}},{"Add":{"text":" expr = expr.xreplace({item: CosSIMD(item.args[0])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346178"}},{"Add":{"text":" elif item.func == sign:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346210"}},{"Add":{"text":" expr = expr.xreplace({item: SignSIMD(item.args[0])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346275"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346276"}},{"Add":{"text":" # Fun little recursive function for constructing integer powers:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346345"}},{"Add":{"text":" def IntegerPowSIMD(a, n):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346375"}},{"Add":{"text":" if n == 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346394"}},{"Add":{"text":" return MulSIMD(a, a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346427"}},{"Add":{"text":" elif n > 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346447"}},{"Add":{"text":" return MulSIMD(IntegerPowSIMD(a, n - 1), a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346503"}},{"Add":{"text":" elif n <= -2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346525"}},{"Add":{"text":" return DivSIMD(1, IntegerPowSIMD(a, -n))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346578"}},{"Add":{"text":" elif n == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346600"}},{"Add":{"text":" return DivSIMD(1, a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346633"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346634"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346676"}},{"Add":{"text":" if item.func == Pow:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346705"}},{"Add":{"text":" if item.args[1] == 0.5:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346741"}},{"Add":{"text":" expr = expr.xreplace({item: SqrtSIMD(item.args[0])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346810"}},{"Add":{"text":" elif item.args[1] == -0.5:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346849"}},{"Add":{"text":" expr = expr.xreplace({item: DivSIMD(1,SqrtSIMD(item.args[0]))})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346929"}},{"Add":{"text":" elif item.args[1] == Rational(1,3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:346977"}},{"Add":{"text":" expr = expr.xreplace({item: CbrtSIMD(item.args[0])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347046"}},{"Add":{"text":" elif item.args[1] == int(item.args[1]):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347098"}},{"Add":{"text":" expr = expr.xreplace({item: IntegerPowSIMD(item.args[0], item.args[1])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347187"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347205"}},{"Add":{"text":" expr = expr.xreplace({item: PowSIMD(item.args[0], item.args[1])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347294"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347295"}},{"Add":{"text":" # Step 2: Replace all rational numbers (expressed as Rational(a,b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347367"}},{"Add":{"text":" # and integers with the new functions RationalTMP and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347433"}},{"Add":{"text":" # IntegerTMP, where Rational(a,b) -> RationalTMP(a,b)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347499"}},{"Add":{"text":" # and Integer(a) -> IntegerTMP(a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347545"}},{"Add":{"text":" RationalTMP = Function(\"RationalTMP\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347587"}},{"Add":{"text":" IntegerTMP = Function(\"IntegerTMP\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347627"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347628"}},{"Add":{"text":" string = str(srepr(expr))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347658"}},{"Add":{"text":" string2 = re.sub(r'Integer\$([+\\-0-9]+)\$',","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347706"}},{"Add":{"text":" \"(Function('IntegerTMP')('\\\\1'))\", string)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347770"}},{"Add":{"text":" expr = eval(string2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347795"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347796"}},{"Add":{"text":" string = str(srepr(expr))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347826"}},{"Add":{"text":" string2 = re.sub(r'Rational\$([-0-9]+), ([0-9]+)\$',","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347883"}},{"Add":{"text":" \"(Function('RationalTMP')(('\\\\1'),('\\\\2')))\", string)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347958"}},{"Add":{"text":" expr = eval(string2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347983"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:347984"}},{"Add":{"text":" # Step 3: The pattern Mul(-1,Rational(a,b)) is often seen. Replace with Rational(-a,b).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348076"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348118"}},{"Add":{"text":" if item.func == Mul:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348147"}},{"Add":{"text":" idx_has_Negative1 = -10","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348183"}},{"Add":{"text":" for i in range(len(item.args)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348227"}},{"Add":{"text":" if item.args[i].func == IntegerTMP and item.args[i].args[0] == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348310"}},{"Add":{"text":" idx_has_Negative1 = i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348352"}},{"Add":{"text":" if idx_has_Negative1 >= 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348391"}},{"Add":{"text":" for i in range(len(item.args)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348439"}},{"Add":{"text":" if item.args[i].func==RationalTMP:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348494"}},{"Add":{"text":" tempitem_orig = Mul(IntegerTMP(-1),RationalTMP(item.args[i].args[0], item.args[i].args[1]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348610"}},{"Add":{"text":" tempitem_new = RationalTMP(-item.args[i].args[0], item.args[i].args[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348707"}},{"Add":{"text":" expr = expr.subs(tempitem_orig, tempitem_new )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348778"}},{"Add":{"text":" break","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348808"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348809"}},{"Add":{"text":" # Step 4: SIMD multiplication and addition compiler intrinsics read in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348884"}},{"Add":{"text":" # only two arguments at once, where SymPy's Mul() and Add()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:348956"}},{"Add":{"text":" # operators can read an arbitrary number of arguments.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349023"}},{"Add":{"text":" # Here, we split e.g., Mul(a,b,c,d) into","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349076"}},{"Add":{"text":" # MulSIMD(a,MulSIMD(b,MulSIMD(c,d))),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349126"}},{"Add":{"text":" # To accomplish this easily, we construct a string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349189"}},{"Add":{"text":" # 'MulSIMD(A,MulSIMD(B,...', where MulSIMD(a,b) is some user-","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349263"}},{"Add":{"text":" # defined function that takes in only two arguments, and then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349337"}},{"Add":{"text":" # evaluate the string using the eval() function.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349398"}},{"Add":{"text":" # Implementation detail: If we did not perform Step 2 above, the eval","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349472"}},{"Add":{"text":" # function would automatically evaluate all Rational expressions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349549"}},{"Add":{"text":" # as though they were input as integers: e.g., 1/2 evaluates to 0.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349628"}},{"Add":{"text":" # This is undesirable, so we instead define new, temporary","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349699"}},{"Add":{"text":" # functions IntegerTMP and RationalTMP that are undisturbed by","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349774"}},{"Add":{"text":" # the eval()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349799"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349841"}},{"Add":{"text":" if item.func == Mul:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349870"}},{"Add":{"text":" blahtmp = symbols('blahtmp')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349911"}},{"Add":{"text":" tempitem = blahtmp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349942"}},{"Add":{"text":" for i in range(len(item.args)-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:349988"}},{"Add":{"text":" tempitem = MulSIMD(item.args[i],tempitem)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350046"}},{"Add":{"text":" tempitem = tempitem.xreplace({blahtmp: item.args[len(item.args)-1]})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350127"}},{"Add":{"text":" expr = expr.xreplace({item: tempitem})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350178"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350220"}},{"Add":{"text":" if item.func == Add:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350249"}},{"Add":{"text":" blahtmp = symbols('blahtmp')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350290"}},{"Add":{"text":" tempitem = blahtmp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350321"}},{"Add":{"text":" for i in range(len(item.args)-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350367"}},{"Add":{"text":" tempitem = AddSIMD(item.args[i],tempitem)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350425"}},{"Add":{"text":" tempitem = tempitem.xreplace({blahtmp: item.args[len(item.args)-1]})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350506"}},{"Add":{"text":" expr = expr.xreplace({item: tempitem})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350557"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350558"}},{"Add":{"text":" # Step 5: Simplification patterns:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350597"}},{"Add":{"text":" # Step 5a: Replace the pattern Mul(Div(1,b),a) or Mul(a,Div(1,b)) with Div(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350682"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350724"}},{"Add":{"text":" if item.func == MulSIMD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350757"}},{"Add":{"text":" if item.func == MulSIMD and (item.args[0].func == DivSIMD and item.args[0].args[0].func == IntegerTMP and item.args[0].args[0].args[0] == 1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:350911"}},{"Add":{"text":" expr = expr.xreplace({item: DivSIMD(item.args[1],item.args[0].args[1])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351000"}},{"Add":{"text":" if item.func == MulSIMD and (item.args[1].func == DivSIMD and item.args[1].args[0].func == IntegerTMP and item.args[1].args[0].args[0] == 1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351154"}},{"Add":{"text":" expr = expr.xreplace({item: DivSIMD(item.args[0],item.args[1].args[1])})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351243"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351244"}},{"Add":{"text":" # Step 5: Subtraction intrinsics. SymPy replaces all a-b with a + (-b) = Add(a,Mul(-1,b))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351338"}},{"Add":{"text":" # Here, we replace","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351369"}},{"Add":{"text":" # a) AddSIMD(a,MulSIMD(-1,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351412"}},{"Add":{"text":" # b) AddSIMD(a,MulSIMD(b,-1)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351455"}},{"Add":{"text":" # c) AddSIMD(MulSIMD(-1,b),a), and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351502"}},{"Add":{"text":" # d) AddSIMD(MulSIMD(b,-1),a)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351544"}},{"Add":{"text":" # with SubSIMD(a,b)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351576"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351618"}},{"Add":{"text":" tempitem = item","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351642"}},{"Add":{"text":" # First match patterns a) and b): AddSIMD(a,MULSIMD(.,.)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351709"}},{"Add":{"text":" if item.func == AddSIMD and item.args[1].func == MulSIMD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351775"}},{"Add":{"text":" # Pattern a) AddSIMD(a,MulSIMD(-1,b)) --> SubSIMD(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351843"}},{"Add":{"text":" if item.args[1].args[0].func == IntegerTMP and item.args[1].args[0].args[0] == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:351938"}},{"Add":{"text":" tempitem = SubSIMD(item.args[0],item.args[1].args[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352008"}},{"Add":{"text":" # Pattern b) AddSIMD(a,MulSIMD(b,-1)) --> SubSIMD(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352076"}},{"Add":{"text":" elif item.args[1].args[1].func == IntegerTMP and item.args[1].args[1].args[0] == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352173"}},{"Add":{"text":" tempitem = SubSIMD(item.args[0],item.args[1].args[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352243"}},{"Add":{"text":" # Next match patterns c) and d): AddSIMD(MulSIMD(.,.),a):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352309"}},{"Add":{"text":" elif item.func == AddSIMD and item.args[0].func == MulSIMD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352377"}},{"Add":{"text":" # Pattern c) AddSIMD(MulSIMD(-1,b),a) --> SubSIMD(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352445"}},{"Add":{"text":" if item.args[0].args[0].func == IntegerTMP and item.args[0].args[0].args[0] == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352540"}},{"Add":{"text":" tempitem = SubSIMD(item.args[1],item.args[0].args[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352610"}},{"Add":{"text":" # Pattern d) AddSIMD(MulSIMD(b,-1,a)) --> SubSIMD(a,b):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352678"}},{"Add":{"text":" elif item.args[0].args[1].func == IntegerTMP and item.args[0].args[1].args[0] == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352775"}},{"Add":{"text":" tempitem = SubSIMD(item.args[1],item.args[0].args[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352845"}},{"Add":{"text":" expr = expr.subs(item,tempitem)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352885"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352886"}},{"Add":{"text":" # Step 6: Now that all multiplication and addition functions only take two","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:352965"}},{"Add":{"text":" # arguments, we can now easily define fused-multiply-add functions,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353045"}},{"Add":{"text":" # where AddSIMD(a,MulSIMD(b,c)) = b*c + a = FusedMulAddSIMD(b,c,a),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353125"}},{"Add":{"text":" # or AddSIMD(MulSIMD(b,c),a) = b*c + a = FusedMulAddSIMD(b,c,a).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353205"}},{"Add":{"text":" # Fused multiply add (FMA3) is standard on Intel CPUs with the AVX2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353277"}},{"Add":{"text":" # instruction set, starting with Haswell processors in 2013:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353350"}},{"Add":{"text":" # https://en.wikipedia.org/wiki/Haswell_(microarchitecture)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353422"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353464"}},{"Add":{"text":" tempitem = item","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353488"}},{"Add":{"text":" # If the pattern is a*b + c, replace with FMA(a,b,c)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353549"}},{"Add":{"text":" if item.func == AddSIMD and item.args[0].func == MulSIMD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353615"}},{"Add":{"text":" tempitem = FusedMulAddSIMD(item.args[0].args[0],item.args[0].args[1],item.args[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353710"}},{"Add":{"text":" # If the pattern is c + a*b, replace with FMA(a,b,c)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353771"}},{"Add":{"text":" if item.func == AddSIMD and item.args[1].func == MulSIMD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353837"}},{"Add":{"text":" tempitem = FusedMulAddSIMD(item.args[1].args[0],item.args[1].args[1],item.args[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353932"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353933"}},{"Add":{"text":" # If the pattern is a*b - c, replace with FMS(a,b,c)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:353994"}},{"Add":{"text":" if item.func == SubSIMD and item.args[0].func == MulSIMD:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354060"}},{"Add":{"text":" tempitem = FusedMulSubSIMD(item.args[0].args[0],item.args[0].args[1],item.args[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354155"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354156"}},{"Add":{"text":" if item != tempitem: expr = expr.subs(item, tempitem)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354218"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354219"}},{"Add":{"text":" # Step 7: SIMD intrinsics cannot take integers or rational numbers as arguments.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354304"}},{"Add":{"text":" # Therefore we must declare all integers & rational numbers as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354379"}},{"Add":{"text":" # const vector doubles (e.g., const _m256d ...). To make the code","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354457"}},{"Add":{"text":" # more human readable, we adopt the convention","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354516"}},{"Add":{"text":" # RationalTMP(1,3) = 1/3 = \"Rational_1_3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354569"}},{"Add":{"text":" # RationalTMP(-1,3) = -1/3 = \"Rational_m1_3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354625"}},{"Add":{"text":" # TODO: Keep track of all integers and rationals, so repeats are not computed?","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354708"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354709"}},{"Add":{"text":" # Step 7a: Set all variable names and corresponding values.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354773"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354815"}},{"Add":{"text":" if item.func == RationalTMP:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354852"}},{"Add":{"text":" # Set variable name","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354884"}},{"Add":{"text":" if item.args[0]*item.args[1] < 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:354930"}},{"Add":{"text":" SIMD_const_varnms.extend([\"_Rational_m\"+str(abs(item.args[0]))+\"_\"+str(abs(item.args[1]))+SIMD_const_suffix])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355056"}},{"Add":{"text":" elif item.args[0] > 0 and item.args[1] > 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355112"}},{"Add":{"text":" SIMD_const_varnms.extend([\"_Rational_\"+str(item.args[0])+\"_\"+str(item.args[1])+SIMD_const_suffix])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355227"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355245"}},{"Add":{"text":" # E.g., doesn't make sense to have -1/-3. SymPy should have simplified this.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355338"}},{"Add":{"text":" print(\"Found a weird Rational(a,b) expression, where a<0 and b<0. Report to SymPy devels\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355445"}},{"Add":{"text":" print(\"Specifically, found that a=\"+str(item.args[0])+\" and b=\"+str(item.args[1]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355544"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355572"}},{"Add":{"text":" # Set variable value, to 34 digits of precision","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355632"}},{"Add":{"text":" SIMD_const_values.extend([str(N(Float(item.args[0],34)/Float(item.args[1],34),34))])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355729"}},{"Add":{"text":" elif item.func == IntegerTMP:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355767"}},{"Add":{"text":" # Set variable name","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355799"}},{"Add":{"text":" if item.args[0] < 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355832"}},{"Add":{"text":" SIMD_const_varnms.extend([\"_Integer_m\"+str(-item.args[0])+SIMD_const_suffix])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355926"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:355944"}},{"Add":{"text":" SIMD_const_varnms.extend([\"_Integer_\" + str(item.args[0])+SIMD_const_suffix])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356038"}},{"Add":{"text":" # Set variable value, to 34 digits of precision","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356098"}},{"Add":{"text":" SIMD_const_values.extend([str((Float(item.args[0],34)))])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356168"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356169"}},{"Add":{"text":" # Step 7b: Replace all integers and rationals with the appropriate variable names:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356256"}},{"Add":{"text":" for item in preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356298"}},{"Add":{"text":" tempitem = item","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356322"}},{"Add":{"text":" if item.func == RationalTMP:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356359"}},{"Add":{"text":" if item.args[0]*item.args[1] < 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356405"}},{"Add":{"text":" tempitem = var(\"_Rational_m\" + str(abs(item.args[0])) + \"_\" + str(abs(item.args[1]))+SIMD_const_suffix)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356525"}},{"Add":{"text":" elif item.args[0] > 0 and item.args[1] > 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356581"}},{"Add":{"text":" tempitem = var(\"_Rational_\" + str(item.args[0]) + \"_\" + str(item.args[1])+SIMD_const_suffix)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356690"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356708"}},{"Add":{"text":" # E.g., doesn't make sense to have -1/-3. SymPy should have simplified this.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356801"}},{"Add":{"text":" print(\"Found a weird Rational(a,b) expression, where a<0 and b<0. Report to SymPy devels\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:356908"}},{"Add":{"text":" print(\"Specifically, found that a=\" + str(item.args[0]) + \" and b=\" + str(item.args[1]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357013"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357041"}},{"Add":{"text":" elif item.func == IntegerTMP:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357079"}},{"Add":{"text":" if item.args[0] < 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357112"}},{"Add":{"text":" tempitem = var(\"_Integer_m\" + str(-item.args[0])+SIMD_const_suffix)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357196"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357214"}},{"Add":{"text":" tempitem = var(\"_Integer_\" + str(item.args[0])+SIMD_const_suffix)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357296"}},{"Add":{"text":" if item != tempitem: expr = expr.subs(item, tempitem)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357358"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357359"}},{"Add":{"text":" def lookup_name_output_idx(name, list_of_names):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357412"}},{"Add":{"text":" for i in range(len(list_of_names)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357456"}},{"Add":{"text":" if list_of_names[i] == name:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357497"}},{"Add":{"text":" return i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357522"}},{"Add":{"text":" print(\"I SHOULDN'T BE HERE!\",name,list_of_names)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357579"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357599"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357600"}},{"Add":{"text":" if debug==\"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357622"}},{"Add":{"text":" expr_check = expr","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357648"}},{"Add":{"text":" if \"SIMD\" in str(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357680"}},{"Add":{"text":" expr_check = eval(str(expr).replace(\"SIMD\",\"SIMD_check\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357750"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357751"}},{"Add":{"text":" for item in preorder_traversal(expr_check):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357803"}},{"Add":{"text":" tempitem = item","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357831"}},{"Add":{"text":" if item.is_Symbol and str(item)[0]==\"_\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357884"}},{"Add":{"text":" if str(item)[:9]==\"_Integer_\" or str(item)[:10]==\"_Rational_\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:357963"}},{"Add":{"text":" tempitem = SIMD_const_values[lookup_name_output_idx(str(item), SIMD_const_varnms)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358066"}},{"Add":{"text":" if item != tempitem: expr_check = expr_check.subs(item, tempitem)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358144"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358145"}},{"Add":{"text":" expr_diff = expr_check - expr_orig","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358188"}},{"Add":{"text":" # Some variables do not want to cancel in SymPy ~0.7.4. The eval(str(srepr())) below normalizes the expression.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358308"}},{"Add":{"text":" expr_diff = eval(str(srepr(expr_diff)))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358356"}},{"Add":{"text":" for item in preorder_traversal(expr_diff):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358407"}},{"Add":{"text":" if item.func == Float:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358442"}},{"Add":{"text":" if abs(item - Integer(item)) < 1.0e-14:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358498"}},{"Add":{"text":" expr_diff = expr_diff.xreplace({item:Integer(item)})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358571"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358572"}},{"Add":{"text":" # Only simplify if expr_diff != 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358615"}},{"Add":{"text":" if expr_diff != 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358642"}},{"Add":{"text":" simp_expr_diff = simplify(expr_diff)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358691"}},{"Add":{"text":" if simp_expr_diff != 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358727"}},{"Add":{"text":" print(\"Warning: found possible diff\",(simp_expr_diff))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358798"}},{"Add":{"text":" return(expr)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358815"}}]}},{"FileAdd":{"meta":{"basename":"__init__.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/__init__.py","context":[{"change":0,"pos":15}],"contents":[]}},{"FileAdd":{"meta":{"basename":"cmdline_helper.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/cmdline_helper.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial notebook","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358900"}},{"Add":{"text":"# Tutorial-cmdline_helper.ipynb, this Python script ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:358953"}},{"Add":{"text":"# provides a multi-platform means to run executables,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359007"}},{"Add":{"text":"# remove files, and compile code.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359041"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359042"}},{"Add":{"text":"# Basic functions:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359061"}},{"Add":{"text":"# check_executable_exists(): Check to see whether an executable exists. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359134"}},{"Add":{"text":"# Error out or return False if not exists;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359204"}},{"Add":{"text":"# return True if executable exists in PATH.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359275"}},{"Add":{"text":"# C_compile(): Compile C code using gcc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359316"}},{"Add":{"text":"# Execute(): Execute generated executable file, using taskset ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359379"}},{"Add":{"text":"# if available. Calls Execute_input_string() to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359438"}},{"Add":{"text":"# redirect output from stdout & stderr to desired","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359499"}},{"Add":{"text":"# destinations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359526"}},{"Add":{"text":"# Execute_input_string(): Executes an input string and redirects ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359592"}},{"Add":{"text":"# output from stdout & stderr to desired destinations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359658"}},{"Add":{"text":"# delete_existing_files(file_or_wildcard): ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359702"}},{"Add":{"text":"# Runs del file_or_wildcard in Windows, or","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359754"}},{"Add":{"text":"# rm file_or_wildcard in Linux/MacOS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359806"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359807"}},{"Add":{"text":"# Authors: Brandon Clark","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359832"}},{"Add":{"text":"# Zach Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359856"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359900"}},{"Add":{"text":"# Kevin Lituchy","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359925"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:359926"}},{"Add":{"text":"import io, os, shlex, subprocess, sys, time, multiprocessing, getpass, platform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360006"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360007"}},{"Add":{"text":"# check_executable_exists(): Check to see whether an executable exists. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360080"}},{"Add":{"text":"# Error out or return False if not exists;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360150"}},{"Add":{"text":"# return True if executable exists in PATH.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360221"}},{"Add":{"text":"def check_executable_exists(exec_name,error_if_not_found=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360285"}},{"Add":{"text":" cmd = \"where\" if os.name == \"nt\" else \"which\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360335"}},{"Add":{"text":" try: ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360345"}},{"Add":{"text":" subprocess.check_output([cmd, exec_name])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360395"}},{"Add":{"text":" except subprocess.CalledProcessError:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360437"}},{"Add":{"text":" if error_if_not_found:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360468"}},{"Add":{"text":" print(\"Sorry, cannot execute the command: \" + exec_name)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360537"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360561"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360575"}},{"Add":{"text":" return False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360600"}},{"Add":{"text":" return True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360616"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360617"}},{"Add":{"text":"# C_compile(): Write a function to compile the Main C code into an executable file","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360700"}},{"Add":{"text":"def C_compile(main_C_output_path, main_C_output_file, compile_mode=\"optimized\", custom_compile_string=\"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360807"}},{"Add":{"text":" print(\"Compiling executable...\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360844"}},{"Add":{"text":" # Step 1: Check for gcc compiler","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360881"}},{"Add":{"text":" check_executable_exists(\"gcc\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360916"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360917"}},{"Add":{"text":" # Step 2: Delete existing version of executable","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360969"}},{"Add":{"text":" delete_string = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:360992"}},{"Add":{"text":" if os.name == \"nt\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361016"}},{"Add":{"text":" main_C_output_file += \".exe\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361053"}},{"Add":{"text":" delete_existing_files(main_C_output_file)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361099"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361104"}},{"Add":{"text":" # Step 3: Compile the executable","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361141"}},{"Add":{"text":" if compile_mode==\"safe\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361170"}},{"Add":{"text":" compile_string = \"gcc -O2 -g -fopenmp \"+str(main_C_output_path)+\" -o \"+str(main_C_output_file)+\" -lm\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361280"}},{"Add":{"text":" Execute_input_string(compile_string, os.devnull)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361337"}},{"Add":{"text":" # Check if executable exists (i.e., compile was successful), if not, try with more conservative compile flags.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361456"}},{"Add":{"text":" if not os.path.isfile(main_C_output_file):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361507"}},{"Add":{"text":" print(\"Sorry, compilation failed\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361554"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361578"}},{"Add":{"text":" elif compile_mode==\"icc\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361608"}},{"Add":{"text":" check_executable_exists(\"icc\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361647"}},{"Add":{"text":" compile_string = \"icc -O2 -xHost -qopenmp -unroll \"+str(main_C_output_path)+\" -o \"+str(main_C_output_file)+\" -lm\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361769"}},{"Add":{"text":" Execute_input_string(compile_string, os.devnull)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361826"}},{"Add":{"text":" # Check if executable exists (i.e., compile was successful), if not, try with more conservative compile flags.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361945"}},{"Add":{"text":" if not os.path.isfile(main_C_output_file):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:361996"}},{"Add":{"text":" print(\"Sorry, compilation failed\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362043"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362067"}},{"Add":{"text":" elif compile_mode==\"custom\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362100"}},{"Add":{"text":" Execute_input_string(custom_compile_string, os.devnull)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362164"}},{"Add":{"text":" # Check if executable exists (i.e., compile was successful), if not, try with more conservative compile flags.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362283"}},{"Add":{"text":" if not os.path.isfile(main_C_output_file):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362334"}},{"Add":{"text":" print(\"Sorry, compilation failed\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362381"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362405"}},{"Add":{"text":" elif compile_mode==\"optimized\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362441"}},{"Add":{"text":" compile_string = \"gcc -Ofast -fopenmp -march=native -funroll-loops \"+str(main_C_output_path)+\" -o \"+str(main_C_output_file)+\" -lm\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362580"}},{"Add":{"text":" Execute_input_string(compile_string, os.devnull)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362637"}},{"Add":{"text":" # Check if executable exists (i.e., compile was successful), if not, try with more conservative compile flags.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362756"}},{"Add":{"text":" if not os.path.isfile(main_C_output_file):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362807"}},{"Add":{"text":" # Step 3.A: Revert to more compatible gcc compile option","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362876"}},{"Add":{"text":" print(\"Most optimized compilation failed. Removing -march=native:\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:362956"}},{"Add":{"text":" compile_string = \"gcc -Ofast -fopenmp -funroll-loops \"+str(main_C_output_path)+\" -o \"+str(main_C_output_file)+\" -lm\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363085"}},{"Add":{"text":" Execute_input_string(compile_string, os.devnull)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363146"}},{"Add":{"text":" if not os.path.isfile(main_C_output_file):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363197"}},{"Add":{"text":" # Step 3.B: Revert to maximally compatible gcc compile option","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363271"}},{"Add":{"text":" print(\"Next-to-most optimized compilation failed. Moving to maximally-compatible gcc compile option:\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363386"}},{"Add":{"text":" compile_string = \"gcc -O2 \"+str(main_C_output_path)+\" -o \"+str(main_C_output_file)+\" -lm\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363488"}},{"Add":{"text":" Execute_input_string(compile_string, os.devnull)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363549"}},{"Add":{"text":" # Step 3.C: If there are still missing components within the compiler, say compilation failed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363651"}},{"Add":{"text":" if not os.path.isfile(main_C_output_file):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363702"}},{"Add":{"text":" print(\"Sorry, compilation failed\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363749"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363773"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363783"}},{"Add":{"text":" print(\"Sorry, compile_mode = \\\"\"+compile_mode+\"\\\" unsupported.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363856"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363876"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363885"}},{"Add":{"text":" print(\"Finished compilation.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363920"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363921"}},{"Add":{"text":"# Execute(): Execute generated executable file, using taskset ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:363984"}},{"Add":{"text":"# if available. Calls Execute_input_string() to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364043"}},{"Add":{"text":"# redirect output from stdout & stderr to desired","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364104"}},{"Add":{"text":"# destinations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364131"}},{"Add":{"text":"def Execute(executable, executable_output_arguments=\"\", file_to_redirect_stdout=os.devnull,verbose=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364237"}},{"Add":{"text":" # Step 1: Delete old version of executable file","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364289"}},{"Add":{"text":" if file_to_redirect_stdout != os.devnull:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364335"}},{"Add":{"text":" delete_existing_files(file_to_redirect_stdout)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364390"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364395"}},{"Add":{"text":" # Step 2: Build the script for executing the desired executable","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364463"}},{"Add":{"text":" execute_string = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364487"}},{"Add":{"text":" # When in Windows...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364512"}},{"Add":{"text":" # https://stackoverflow.com/questions/1325581/how-do-i-check-if-im-running-on-windows-in-python","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364612"}},{"Add":{"text":" if os.name == \"nt\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364636"}},{"Add":{"text":" # ... do as the Windows do","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364671"}},{"Add":{"text":" # https://stackoverflow.com/questions/49018413/filenotfounderror-subprocess-popendir-windows-7","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364774"}},{"Add":{"text":" execute_prefix = \"cmd /c \" # Run with cmd /c executable [options] on Windows","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364859"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364869"}},{"Add":{"text":" execute_prefix = \"./\" # Run with ./executable [options] on Linux & Mac","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:364953"}},{"Add":{"text":" taskset_exists = check_executable_exists(\"taskset\", error_if_not_found=False)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365035"}},{"Add":{"text":" if taskset_exists:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365058"}},{"Add":{"text":" execute_string += \"taskset -c 0\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365099"}},{"Add":{"text":" if getpass.getuser() != \"jovyan\": # on mybinder, username is jovyan, and taskset -c 0 is the fastest option.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365216"}},{"Add":{"text":" # If not on mybinder and taskset exists:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365269"}},{"Add":{"text":" has_HT_cores = False # Does CPU have hyperthreading cores?","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365340"}},{"Add":{"text":" if platform.processor() != '': # If processor string returns null, then assume CPU does not support hyperthreading.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365468"}},{"Add":{"text":" # This will yield correct behavior on ARM (e.g., cell phone) CPUs.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365578"}},{"Add":{"text":" has_HT_cores=True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365612"}},{"Add":{"text":" if has_HT_cores == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365649"}},{"Add":{"text":" # NOTE: You will observe a speed-up by using only *PHYSICAL* (as opposed to logical/hyperthreading) cores:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365772"}},{"Add":{"text":" N_cores_to_use = int(multiprocessing.cpu_count()/2) # To account for hyperthreading cores","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365878"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:365896"}},{"Add":{"text":" N_cores_to_use = int(multiprocessing.cpu_count()) # Use all cores if none are hyperthreading cores.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366012"}},{"Add":{"text":" # This will happen on ARM (e.g., cellphone) CPUs ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366128"}},{"Add":{"text":" for i in range(N_cores_to_use-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366174"}},{"Add":{"text":" execute_string += \",\"+str(i+1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366221"}},{"Add":{"text":" execute_string += \" \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366251"}},{"Add":{"text":" execute_string += execute_prefix+executable+\" \"+executable_output_arguments","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366331"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366332"}},{"Add":{"text":" # Step 3: Execute the desired executable","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366377"}},{"Add":{"text":" Execute_input_string(execute_string, file_to_redirect_stdout,verbose)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366451"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366452"}},{"Add":{"text":"# Execute_input_string(): Executes an input string and redirects ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366518"}},{"Add":{"text":"# output from stdout & stderr to desired destinations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366584"}},{"Add":{"text":"def Execute_input_string(input_string, file_to_redirect_stdout=os.devnull, verbose=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366674"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366675"}},{"Add":{"text":" if verbose:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366691"}},{"Add":{"text":" print(\"Executing `\"+input_string+\"`...\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366740"}},{"Add":{"text":" start = time.time()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366764"}},{"Add":{"text":" # https://docs.python.org/3/library/subprocess.html","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366820"}},{"Add":{"text":" if os.name != 'nt':","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366844"}},{"Add":{"text":" args = shlex.split(input_string)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366885"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366895"}},{"Add":{"text":" args = input_string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366923"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:366924"}},{"Add":{"text":" # https://stackoverflow.com/questions/18421757/live-output-from-subprocess-command","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367011"}},{"Add":{"text":" filename = \"tmp.txt\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367036"}},{"Add":{"text":" with io.open(filename, 'w') as writer, io.open(filename, 'rb', buffering=-1) as reader, io.open(file_to_redirect_stdout, 'wb') as rdirect:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367179"}},{"Add":{"text":" process = subprocess.Popen(args, stdout=rdirect, stderr=writer)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367251"}},{"Add":{"text":" while process.poll() is None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367289"}},{"Add":{"text":" # https://stackoverflow.com/questions/21689365/python-3-typeerror-must-be-str-not-bytes-with-sys-stdout-write/21689447","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367420"}},{"Add":{"text":" sys.stdout.write(reader.read().decode('utf-8'))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367480"}},{"Add":{"text":" time.sleep(0.2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367508"}},{"Add":{"text":" # Read the remaining","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367537"}},{"Add":{"text":" sys.stdout.write(reader.read().decode('utf-8'))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367593"}},{"Add":{"text":" delete_existing_files(filename)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367629"}},{"Add":{"text":" end = time.time()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367651"}},{"Add":{"text":" if verbose:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367667"}},{"Add":{"text":" print(\"Finished executing in \"+str(end-start)+\" seconds.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367734"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367735"}},{"Add":{"text":"# delete_existing_files(file_or_wildcard): ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367779"}},{"Add":{"text":"# Runs del file_or_wildcard in Windows, or","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367831"}},{"Add":{"text":"# rm file_or_wildcard in Linux/MacOS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367883"}},{"Add":{"text":"def delete_existing_files(file_or_wildcard):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367928"}},{"Add":{"text":" delete_string = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367951"}},{"Add":{"text":" if os.name == \"nt\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:367975"}},{"Add":{"text":" delete_string += \"del \" + file_or_wildcard","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368026"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368036"}},{"Add":{"text":" delete_string += \"rm -f \" + file_or_wildcard","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368089"}},{"Add":{"text":" os.system(delete_string)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368118"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368119"}},{"Add":{"text":"# https://stackoverflow.com/questions/1274405/how-to-create-new-folder","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368190"}},{"Add":{"text":"def mkdir(newpath):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368210"}},{"Add":{"text":" if not os.path.exists(os.path.join(newpath)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368260"}},{"Add":{"text":" os.makedirs(os.path.join(newpath))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368303"}}]}},{"FileAdd":{"meta":{"basename":"finite_difference.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/finite_difference.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# finite_difference.py:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368352"}},{"Add":{"text":"# As documented in the NRPy+ tutorial notebook:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368401"}},{"Add":{"text":"# Tutorial-Finite_Difference_Derivatives.ipynb ,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368453"}},{"Add":{"text":"# This module generates C kernels for numerically","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368504"}},{"Add":{"text":"# solving PDEs with finite differences.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368546"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368548"}},{"Add":{"text":"# Depends on: outputC.py and grid.py.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368586"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368587"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368618"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368661"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368662"}},{"Add":{"text":"from outputC import * # NRPy+: Core C code output module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368730"}},{"Add":{"text":"import grid as gri # NRPy+: Functions having to do with numerical grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368816"}},{"Add":{"text":"import sys # Standard Python module for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368911"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368912"}},{"Add":{"text":"from operator import itemgetter","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368944"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368945"}},{"Add":{"text":"# Step 1: Initialize free parameters for this module:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:368999"}},{"Add":{"text":"import NRPy_param_funcs as par","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369030"}},{"Add":{"text":"modulename = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369052"}},{"Add":{"text":"# Centered finite difference accuracy order","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369096"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"int\", modulename, \"FD_CENTDERIVS_ORDER\", 4))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369178"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"int\", modulename, \"FD_KO_ORDER__CENTDERIVS_PLUS\", 2))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369268"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369269"}},{"Add":{"text":"def FD_outputC(filename,sympyexpr_list, params=\"\", upwindcontrolvec=\"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369342"}},{"Add":{"text":" outCparams = parse_outCparams_string(params)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369391"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369392"}},{"Add":{"text":" # Step 0.a:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369408"}},{"Add":{"text":" # In case sympyexpr_list is a single sympy expression,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369467"}},{"Add":{"text":" # convert it to a list with just one element:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369521"}},{"Add":{"text":" if type(sympyexpr_list) is not list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369562"}},{"Add":{"text":" sympyexpr_list = [sympyexpr_list]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369604"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369605"}},{"Add":{"text":" # Step 0.b:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369621"}},{"Add":{"text":" # finite_difference.py takes control over outCparams.includebraces here,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369698"}},{"Add":{"text":" # which is necessary because outputC() is called twice:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369762"}},{"Add":{"text":" # first for the reads from main memory and finite difference ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369832"}},{"Add":{"text":" # stencil expressions, and second for the SymPy expressions and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369904"}},{"Add":{"text":" # writes to main memory. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:369938"}},{"Add":{"text":" # If outCparams.includebraces==True, then it will close off the braces ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370014"}},{"Add":{"text":" # after the finite difference stencil expressions and start new ones","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370091"}},{"Add":{"text":" # for the SymPy expressions and writes to main memory, resulting","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370164"}},{"Add":{"text":" # in a non-functioning C code. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370204"}},{"Add":{"text":" # To get around this issue, we create braces around the entire","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370271"}},{"Add":{"text":" # string of C output from this function, only if ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370329"}},{"Add":{"text":" # outCparams.includebraces==True.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370371"}},{"Add":{"text":" # See Step 6 for corresponding end brace.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370417"}},{"Add":{"text":" if outCparams.includebraces == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370460"}},{"Add":{"text":" Coutput = outCparams.preindent+\"{\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370505"}},{"Add":{"text":" indent = \" \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370528"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370538"}},{"Add":{"text":" Coutput = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370559"}},{"Add":{"text":" indent = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370579"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370584"}},{"Add":{"text":" # Step 1a:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370599"}},{"Add":{"text":" # Create a list of free symbols in the sympy expr list","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370658"}},{"Add":{"text":" # that are registered neither as gridfunctions nor","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370717"}},{"Add":{"text":" # as C parameters. These *must* be derivatives,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370773"}},{"Add":{"text":" # so we call the list \"list_of_deriv_vars\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370824"}},{"Add":{"text":" list_of_deriv_vars_with_duplicates = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370868"}},{"Add":{"text":" for expr in sympyexpr_list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370900"}},{"Add":{"text":" for var in expr.rhs.free_symbols:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370942"}},{"Add":{"text":" vartype = gri.variable_type(var)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:370987"}},{"Add":{"text":" if vartype == \"other\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371022"}},{"Add":{"text":" # vartype==\"other\" should ONLY refer to derivatives, so","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371094"}},{"Add":{"text":" # if \"_dD\" or variants do not appear in a variable classified","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371175"}},{"Add":{"text":" # neither as a gridfunction nor a Cparameter, then error out.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371256"}},{"Add":{"text":" if (\"_dD\" in str(var)) or \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371302"}},{"Add":{"text":" (\"_dKOD\" in str(var)) or \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371348"}},{"Add":{"text":" (\"_dupD\" in str(var)) or \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371394"}},{"Add":{"text":" (\"_ddnD\" in str(var)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371436"}},{"Add":{"text":" pass","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371461"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371483"}},{"Add":{"text":" print(\"Error: Unregistered variable \\\"\"+str(var)+\"\\\" in SymPy expression for \"+expr.lhs)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371592"}},{"Add":{"text":" print(\"All variables in SymPy expressions passed to FD_outputC() must be registered\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371698"}},{"Add":{"text":" print(\"in NRPy+ as either a gridfunction or Cparameter, by calling\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371787"}},{"Add":{"text":" print(str(var)+\" = register_gridfunctions...() (in ixp/grid) if \\\"\"+str(var)+\"\\\" is a gridfunction, or\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:371912"}},{"Add":{"text":" print(str(var)+\" = Cparameters() (in par) otherwise (e.g., if it is a free parameter set at C runtime).\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372038"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372070"}},{"Add":{"text":" list_of_deriv_vars_with_duplicates.append(var)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372133"}},{"Add":{"text":"# elif vartype == \"gridfunction\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372178"}},{"Add":{"text":"# list_of_deriv_vars_with_duplicates.append(var)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372242"}},{"Add":{"text":" list_of_deriv_vars = superfast_uniq(list_of_deriv_vars_with_duplicates)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372318"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372319"}},{"Add":{"text":" # Upwinding with respect to a control vector: algorithm description.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372392"}},{"Add":{"text":" # To enable, set the FD_outputC()'s fourth function argument to the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372466"}},{"Add":{"text":" # desired control vector. In BSSN, the betaU vector controls the upwinding.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372548"}},{"Add":{"text":" # See https://arxiv.org/pdf/gr-qc/0206072.pdf for motivation and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372619"}},{"Add":{"text":" # https://arxiv.org/pdf/gr-qc/0109032.pdf for implementation details,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372695"}},{"Add":{"text":" # at second order. Note that the BSSN shift vector behaves like a *negative*","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372778"}},{"Add":{"text":" # velocity. See http://www.damtp.cam.ac.uk/user/naweb/ii/advection/advection.php","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372865"}},{"Add":{"text":" # for a very basic example motivating this choice.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372922"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372923"}},{"Add":{"text":" # Step 1b: For each variable with suffix _dupD, append to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:372985"}},{"Add":{"text":" # the list_of_deriv_vars the corresponding _ddnD.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373048"}},{"Add":{"text":" # Both are required for control-vector upwinding. See","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373115"}},{"Add":{"text":" # the above print() block for further documentation","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373180"}},{"Add":{"text":" # on upwinding--both motivation and implementation","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373244"}},{"Add":{"text":" # details.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373268"}},{"Add":{"text":" if upwindcontrolvec != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373299"}},{"Add":{"text":" for var in list_of_deriv_vars:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373338"}},{"Add":{"text":" if \"_dupD\" in str(var):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373374"}},{"Add":{"text":" list_of_deriv_vars.append(sp.sympify(str(var).replace(\"_dupD\",\"_ddnD\")))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373463"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373464"}},{"Add":{"text":" # Finally, sort the list_of_deriv_vars. This ensures","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373521"}},{"Add":{"text":" # consistency in the C code output, and might even be","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373583"}},{"Add":{"text":" # tuned to reduce cache misses.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373623"}},{"Add":{"text":" # Thanks to Aaron Meurer for this nice one-liner!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373681"}},{"Add":{"text":" list_of_deriv_vars = sorted(list_of_deriv_vars,key=sp.default_sort_key)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373757"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373762"}},{"Add":{"text":" # Step 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373776"}},{"Add":{"text":" # Process list_of_deriv_vars into a list of base gridfunctions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373843"}},{"Add":{"text":" # and a list of derivative operators.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373888"}},{"Add":{"text":" # Step 2a:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373903"}},{"Add":{"text":" # First determine the base gridfunction name from","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373957"}},{"Add":{"text":" # \"list_of_deriv_vars\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:373988"}},{"Add":{"text":" deriv__base_gridfunction_name = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374027"}},{"Add":{"text":" deriv__operator = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374052"}},{"Add":{"text":" for var in list_of_deriv_vars:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374087"}},{"Add":{"text":" # Step 2a.1: Check that the number of juxtaposed integers","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374153"}},{"Add":{"text":" # at the end of a variable name matches the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374216"}},{"Add":{"text":" # number of U's + D's in the variable name:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374279"}},{"Add":{"text":" varstr = str(var)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374305"}},{"Add":{"text":" num_UDs = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374325"}},{"Add":{"text":" for i in range(len(varstr)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374362"}},{"Add":{"text":" if varstr[i] == 'D' or varstr[i] == 'U':","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374415"}},{"Add":{"text":" num_UDs += 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374444"}},{"Add":{"text":" num_digits = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374467"}},{"Add":{"text":" i = len(varstr) - 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374495"}},{"Add":{"text":" while varstr[i].isdigit():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374530"}},{"Add":{"text":" num_digits += 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374558"}},{"Add":{"text":" i-=1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374575"}},{"Add":{"text":" if num_UDs != num_digits:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374609"}},{"Add":{"text":" print(\"Error: \"+varstr+\" has \"+str(num_UDs)+\" U's and D's, but \")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374687"}},{"Add":{"text":" print(str(num_digits)+\" integers at the end. These must be equal.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374767"}},{"Add":{"text":" print(\"Please rename your gridfunction.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374821"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374845"}},{"Add":{"text":" # Step 2a.2: Based on the variable name, find the rank of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374911"}},{"Add":{"text":" # the underlying gridfunction of which we're","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:374975"}},{"Add":{"text":" # trying to take the derivative.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375027"}},{"Add":{"text":" rank = 0 # rank = \"number of juxtaposed U's and D's before the underscore in a derivative expression\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375137"}},{"Add":{"text":" underscore_position = -1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375170"}},{"Add":{"text":" for i in range(len(varstr)-1,-1,-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375215"}},{"Add":{"text":" if underscore_position > 0 and (varstr[i] == \"U\" or varstr[i] == \"D\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375298"}},{"Add":{"text":" rank += 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375324"}},{"Add":{"text":" if varstr[i] == \"_\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375357"}},{"Add":{"text":" underscore_position = i","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375397"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375398"}},{"Add":{"text":" # Step 2a.3: Based on the variable name, find the order","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375462"}},{"Add":{"text":" # of the derivative we're trying to take.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375523"}},{"Add":{"text":" deriv_order = 0 # deriv_order = \"number of D's after the underscore in a derivative expression\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375627"}},{"Add":{"text":" for i in range(underscore_position+1,len(varstr)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375686"}},{"Add":{"text":" if (varstr[i] == \"D\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375721"}},{"Add":{"text":" deriv_order += 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375754"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375755"}},{"Add":{"text":" # Step 2a.4: Based on derivative order and rank,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375812"}},{"Add":{"text":" # store the base gridfunction name in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375869"}},{"Add":{"text":" # deriv__base_gridfunction_name[]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375922"}},{"Add":{"text":" deriv__base_gridfunction_name.append(varstr[0:underscore_position]+","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:375998"}},{"Add":{"text":" varstr[len(varstr)-deriv_order-rank:len(varstr)-deriv_order])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376105"}},{"Add":{"text":" deriv__operator.append(varstr[underscore_position+1:len(varstr)-deriv_order-rank]+","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376196"}},{"Add":{"text":" varstr[len(varstr)-deriv_order:len(varstr)])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376272"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376273"}},{"Add":{"text":" # Step 2b:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376288"}},{"Add":{"text":" # Then check each base gridfunction to determine whether","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376349"}},{"Add":{"text":" # it is indeed registered as a gridfunction.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376402"}},{"Add":{"text":" # If not, exit with error.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376437"}},{"Add":{"text":" for basegf in deriv__base_gridfunction_name:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376486"}},{"Add":{"text":" is_gf = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376508"}},{"Add":{"text":" for gf in gri.glb_gridfcs_list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376548"}},{"Add":{"text":" if basegf == str(gf.name):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376587"}},{"Add":{"text":" is_gf = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376616"}},{"Add":{"text":" pass","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376637"}},{"Add":{"text":" if not is_gf:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376659"}},{"Add":{"text":" print(\"Error: Attempting to take the derivative of \"+basegf+\", which is not a registered gridfunction.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376776"}},{"Add":{"text":" print(\" Make sure your gridfunction name does not have any underscores in it!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376874"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376898"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376899"}},{"Add":{"text":" # Step 2c:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376914"}},{"Add":{"text":" # Check each derivative operator to make sure it is","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:376970"}},{"Add":{"text":" # supported. If not, error out.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377010"}},{"Add":{"text":" for i in range(len(deriv__operator)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377052"}},{"Add":{"text":" found_derivID = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377082"}},{"Add":{"text":" for derivID in [\"dD\",\"dupD\",\"ddnD\",\"dKOD\"]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377134"}},{"Add":{"text":" if derivID in deriv__operator[i]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377180"}},{"Add":{"text":" found_derivID = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377217"}},{"Add":{"text":" if not found_derivID:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377247"}},{"Add":{"text":" print(\"Error: Valid derivative operator in \"+deriv__operator[i]+\" not found.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377338"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377362"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377363"}},{"Add":{"text":" # Step 2d (Upwinded derivatives algorithm, part 1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377419"}},{"Add":{"text":" # If an upwinding control vector is specified, determine","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377480"}},{"Add":{"text":" # which of the elements of the vector will be required.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377543"}},{"Add":{"text":" # This ensures that those elements are read from memory.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377607"}},{"Add":{"text":" # For example, if a symmetry axis is specified,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377659"}},{"Add":{"text":" # upwind derivatives with respect to only","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377709"}},{"Add":{"text":" # two of the three dimensions are used. Here","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377762"}},{"Add":{"text":" # we find all directions used for upwinding.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377815"}},{"Add":{"text":" if upwindcontrolvec != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377846"}},{"Add":{"text":" upwind_directions_unsorted_withdups = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377895"}},{"Add":{"text":" for deriv_op in deriv__operator:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377936"}},{"Add":{"text":" if \"dupD\" in deriv_op:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:377971"}},{"Add":{"text":" if deriv_op[len(deriv_op)-1].isdigit():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378027"}},{"Add":{"text":" dirn = int(deriv_op[len(deriv_op)-1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378085"}},{"Add":{"text":" upwind_directions_unsorted_withdups.append(dirn)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378154"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378176"}},{"Add":{"text":" print(\"Error: Derivative operator \"+deriv_op+\" does not contain a direction\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378274"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378306"}},{"Add":{"text":" upwind_directions = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378337"}},{"Add":{"text":" if len(upwind_directions_unsorted_withdups)>0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378392"}},{"Add":{"text":" upwind_directions = superfast_uniq(upwind_directions_unsorted_withdups)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378476"}},{"Add":{"text":" upwind_directions = sorted(upwind_directions,key=sp.default_sort_key)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378558"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378559"}},{"Add":{"text":" # Step 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378573"}},{"Add":{"text":" # Evaluate the finite difference stencil for each","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378627"}},{"Add":{"text":" # derivative operator,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378658"}},{"Add":{"text":" # TODO: being careful not to needlessly recompute.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378713"}},{"Add":{"text":" # Note: Each finite difference stencil consists","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378765"}},{"Add":{"text":" # of two parts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378789"}},{"Add":{"text":" # 1) The coefficient, and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378823"}},{"Add":{"text":" # 2) The index corresponding to the coefficient.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378880"}},{"Add":{"text":" # The former is stored as a rational number, and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378937"}},{"Add":{"text":" # the latter as a simple string, such that e.g.,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:378994"}},{"Add":{"text":" # in 3D, the empty string corresponds to (i,j,k),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379052"}},{"Add":{"text":" # the string \"ip1\" corresponds to (i+1,j,k),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379105"}},{"Add":{"text":" # the string \"ip1kp1\" corresponds to (i+1,j,k+1),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379163"}},{"Add":{"text":" # etc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379178"}},{"Add":{"text":" fdcoeffs = [[] for i in range(len(deriv__operator))]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379235"}},{"Add":{"text":" fdstencl = [[[] for i in range(4)] for j in range(len(deriv__operator))]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379312"}},{"Add":{"text":" for i in range(len(deriv__operator)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379354"}},{"Add":{"text":" fdcoeffs[i], fdstencl[i] = compute_fdcoeffs_fdstencl(deriv__operator[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379435"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379436"}},{"Add":{"text":" # Step 4:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379450"}},{"Add":{"text":" # Create C code to read gridfunctions from memory","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379504"}},{"Add":{"text":" # Step 4a: Compile list of points to read from memory","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379562"}},{"Add":{"text":" # for each gridfunction i, based on list","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379616"}},{"Add":{"text":" # provided in fdstencil[i][].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379659"}},{"Add":{"text":" list_of_points_read_from_memory_with_duplicates = [[] for i in range(len(gri.glb_gridfcs_list))]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379760"}},{"Add":{"text":" for j in range(len(deriv__base_gridfunction_name)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379816"}},{"Add":{"text":" derivgfname = deriv__base_gridfunction_name[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379871"}},{"Add":{"text":" # Next find the corresponding gridfunction index:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379929"}},{"Add":{"text":" for i in range(len(gri.glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:379980"}},{"Add":{"text":" gfname = gri.glb_gridfcs_list[i].name","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380030"}},{"Add":{"text":" # If the gridfunction for the derivative matches, then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380097"}},{"Add":{"text":" # add to the list of points read from memory:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380158"}},{"Add":{"text":" if derivgfname == gfname:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380196"}},{"Add":{"text":" for k in range(len(fdstencl[j])):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380246"}},{"Add":{"text":" list_of_points_read_from_memory_with_duplicates[i].append(str(fdstencl[j][k][0]) + \",\" + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380357"}},{"Add":{"text":" str(fdstencl[j][k][1]) + \",\" + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380468"}},{"Add":{"text":" str(fdstencl[j][k][2]) + \",\" + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380579"}},{"Add":{"text":" str(fdstencl[j][k][3]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380681"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380682"}},{"Add":{"text":" # Step 4b: \"Zeroth derivative\" case:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380723"}},{"Add":{"text":" # If gridfunction appears in expression not","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380775"}},{"Add":{"text":" # as derivative (i.e., by itself), it must","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380826"}},{"Add":{"text":" # be read from memory as well.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380865"}},{"Add":{"text":" for expr in range(len(sympyexpr_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380909"}},{"Add":{"text":" for var in sympyexpr_list[expr].rhs.free_symbols:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:380967"}},{"Add":{"text":" vartype = gri.variable_type(var)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381012"}},{"Add":{"text":" if vartype == \"gridfunction\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381054"}},{"Add":{"text":" for i in range(len(gri.glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381113"}},{"Add":{"text":" gfname = gri.glb_gridfcs_list[i].name","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381171"}},{"Add":{"text":" if gfname == str(var):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381214"}},{"Add":{"text":" list_of_points_read_from_memory_with_duplicates[i].append(\"0,0,0,0\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381307"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381308"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381309"}},{"Add":{"text":" # Step 4c: Remove duplicates when reading from memory;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381368"}},{"Add":{"text":" # do not needlessly read the same variable","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381419"}},{"Add":{"text":" # from memory twice.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381448"}},{"Add":{"text":" list_of_points_read_from_memory = [[] for i in range(len(gri.glb_gridfcs_list))]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381533"}},{"Add":{"text":" for i in range(len(gri.glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381580"}},{"Add":{"text":" list_of_points_read_from_memory[i] = superfast_uniq(list_of_points_read_from_memory_with_duplicates[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381692"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381693"}},{"Add":{"text":" # Step 4d: Minimize cache misses:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381731"}},{"Add":{"text":" # Sort the list of points read from","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381776"}},{"Add":{"text":" # main memory by how they are stored","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381822"}},{"Add":{"text":" # in memory.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381844"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381845"}},{"Add":{"text":" # Step 4d.i: Define a function that maps a gridpoint","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381902"}},{"Add":{"text":" # index (i,j,k,l) to a unique memory \"address\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:381958"}},{"Add":{"text":" # which will correspond to the correct ordering","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382014"}},{"Add":{"text":" # of actual memory addresses.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382052"}},{"Add":{"text":" #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382058"}},{"Add":{"text":" # Input: a list of 4 indices, e.g., (i,j,k,l)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382112"}},{"Add":{"text":" # corresponding to a gridpoint's *spatial*","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382170"}},{"Add":{"text":" # index in memory (thus we support up to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382226"}},{"Add":{"text":" # 4D in space). If spatial dimension is","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382281"}},{"Add":{"text":" # less than 4D, then just set latter","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382333"}},{"Add":{"text":" # index/indices to zero. E.g., for 2D","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382386"}},{"Add":{"text":" # spatial indexing, set (i,j,0,0).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382436"}},{"Add":{"text":" # Output: a single number, which when sorted","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382489"}},{"Add":{"text":" # will yield a unique \"address\" in memory","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382546"}},{"Add":{"text":" # such that consecutive addresses are","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382599"}},{"Add":{"text":" # consecutive in memory.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382639"}},{"Add":{"text":" def unique_idx(idx4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382665"}},{"Add":{"text":" # os and sz are set *just for the purposes of ensuring indices are ordered in memory*","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382759"}},{"Add":{"text":" # Do not modify the values of os and sz.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382811"}},{"Add":{"text":" os = 50 # offset","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382837"}},{"Add":{"text":" sz = 100 # assumed size in each direction","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382887"}},{"Add":{"text":" if par.parval_from_str(\"MemAllocStyle\") == \"210\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:382945"}},{"Add":{"text":" return str(int(idx4[0])+os + sz*( (int(idx4[1])+os) + sz*( (int(idx4[2])+os) + sz*( int(idx4[3])+os ) ) ))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383064"}},{"Add":{"text":" elif par.parval_from_str(\"MemAllocStyle\") == \"012\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383124"}},{"Add":{"text":" return str(int(idx4[3])+os + sz*( (int(idx4[2])+os) + sz*( (int(idx4[1])+os) + sz*( int(idx4[0])+os ) ) ))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383243"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383257"}},{"Add":{"text":" print(\"Error: MemAllocStyle = \"+par.parval_from_str(\"MemAllocStyle\")+\" unsupported.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383355"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383379"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383380"}},{"Add":{"text":" # Step 4d.ii: For each gridfunction and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383424"}},{"Add":{"text":" # point read from memory, call unique_idx,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383476"}},{"Add":{"text":" # then sort according to memory \"address\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383527"}},{"Add":{"text":" # Input: list_of_points_read_from_memory[gridfunction][point],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383594"}},{"Add":{"text":" # gri.glb_gridfcs_list[gridfunction]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383642"}},{"Add":{"text":" # Output: 1) A list of points to be read from","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383692"}},{"Add":{"text":" # memory, sorted according to memory","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383744"}},{"Add":{"text":" # \"address\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383772"}},{"Add":{"text":" # sorted_list_of_points_read_from_memory[gridfunction][point]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383849"}},{"Add":{"text":" # 2) A list containing the gridfunction","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383900"}},{"Add":{"text":" # read at each point, with the number","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:383952"}},{"Add":{"text":" # of elements corresponding exactly","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384002"}},{"Add":{"text":" # to the total number of points read","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384053"}},{"Add":{"text":" # from memory for all gridfunctions:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384104"}},{"Add":{"text":" # read_from_memory_gf[]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384142"}},{"Add":{"text":" read_from_memory_gf = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384174"}},{"Add":{"text":" sorted_list_of_points_read_from_memory = [[] for i in range(len(gri.glb_gridfcs_list))]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384266"}},{"Add":{"text":" for gfidx in range(len(gri.glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384317"}},{"Add":{"text":" # Continue only if reading at least one point of gfidx from memory.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384393"}},{"Add":{"text":" # The sorting algorithm at the end of this code block is not","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384466"}},{"Add":{"text":" # well-defined (will throw an error) if no points of gfidx are","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384541"}},{"Add":{"text":" # read from memory.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384573"}},{"Add":{"text":" if len(list_of_points_read_from_memory[gfidx]) > 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384633"}},{"Add":{"text":" read_from_memory_index = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384673"}},{"Add":{"text":" for idx in list_of_points_read_from_memory[gfidx]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384736"}},{"Add":{"text":" read_from_memory_gf.append(gri.glb_gridfcs_list[gfidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384808"}},{"Add":{"text":" idxsplit = idx.split(',')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384850"}},{"Add":{"text":" idx4 = [int(idxsplit[0]),int(idxsplit[1]),int(idxsplit[2]),int(idxsplit[3])]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:384943"}},{"Add":{"text":" read_from_memory_index.append(unique_idx(idx4))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385007"}},{"Add":{"text":" # https://stackoverflow.com/questions/13668393/python-sorting-two-lists","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385095"}},{"Add":{"text":" UNUSEDlist, sorted_list_of_points_read_from_memory[gfidx] = \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385173"}},{"Add":{"text":" [list(x) for x in zip(*sorted(zip(read_from_memory_index, list_of_points_read_from_memory[gfidx]),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385292"}},{"Add":{"text":" key=itemgetter(0)))]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385363"}},{"Add":{"text":" # Step 4e: Create the full C code string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385408"}},{"Add":{"text":" # for reading from memory:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385444"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385445"}},{"Add":{"text":" # if DIM==4:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385462"}},{"Add":{"text":" # input: [i,j,k,l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385489"}},{"Add":{"text":" # output: \"i0+i,i1+j,i2+k,i3+l\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385529"}},{"Add":{"text":" # if DIM==3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385546"}},{"Add":{"text":" # input: [i,j,k,l]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385573"}},{"Add":{"text":" # output: \"i0+i,i1+j,i2+k\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385608"}},{"Add":{"text":" # etc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385619"}},{"Add":{"text":" def ijkl_string(idx4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385646"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385687"}},{"Add":{"text":" retstring = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385710"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385739"}},{"Add":{"text":" if i>0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385759"}},{"Add":{"text":" # Add a comma","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385789"}},{"Add":{"text":" retstring += \",\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385822"}},{"Add":{"text":" retstring += \"i\"+str(i)+\"+\"+str(idx4[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385875"}},{"Add":{"text":" return retstring.replace(\"+-\", \"-\").replace(\"+0\", \"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385937"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:385938"}},{"Add":{"text":" def out__type_var(in_var,AddPrefix_for_UpDownWindVars=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386003"}},{"Add":{"text":" varname = str(in_var)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386033"}},{"Add":{"text":" # Disable prefixing upwinded and downwinded variables","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386095"}},{"Add":{"text":" # if the upwind control vector algorithm is disabled.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386157"}},{"Add":{"text":" if upwindcontrolvec == \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386192"}},{"Add":{"text":" AddPrefix_for_UpDownWindVars = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386241"}},{"Add":{"text":" if AddPrefix_for_UpDownWindVars:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386282"}},{"Add":{"text":" if \"_dupD\" in varname: # Variables suffixed with \"_dupD\" are set","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386360"}},{"Add":{"text":" # to be the \"pure\" upwinded derivative,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386435"}},{"Add":{"text":" # before the upwinding algorithm has been","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386512"}},{"Add":{"text":" # applied. However, when they are used","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386586"}},{"Add":{"text":" # in the RHS expressions, it is assumed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386661"}},{"Add":{"text":" # that the up. algorithm has been applied.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386739"}},{"Add":{"text":" # To ensure consistency we rename all","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386812"}},{"Add":{"text":" # _dupD suffixed variables as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386877"}},{"Add":{"text":" # _dupDPUREUPWIND, and use them as input","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:386953"}},{"Add":{"text":" # into the upwinding algorithm. The output","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387031"}},{"Add":{"text":" # will be the original _dupD variable.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387105"}},{"Add":{"text":" varname = \"UpwindAlgInput\"+varname","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387156"}},{"Add":{"text":" if \"_ddnD\" in varname: # For consistency with _dupD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387220"}},{"Add":{"text":" varname = \"UpwindAlgInput\"+varname","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387271"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387316"}},{"Add":{"text":" return \"const REAL_SIMD_ARRAY \" + varname","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387370"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387384"}},{"Add":{"text":" TYPE = par.parval_from_str(\"PRECISION\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387436"}},{"Add":{"text":" return \"const \"+ TYPE + \" \" + varname","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387486"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387487"}},{"Add":{"text":" def varsuffix(idx4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387512"}},{"Add":{"text":" if idx4 == [0,0,0,0]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387542"}},{"Add":{"text":" return \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387564"}},{"Add":{"text":" return \"_\"+ijkl_string(idx4).replace(\",\",\"_\").replace(\"+\",\"p\").replace(\"-\",\"m\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387652"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387653"}},{"Add":{"text":" def read_from_memory_Ccode_onept(gfname,idx):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387703"}},{"Add":{"text":" idxsplit = idx.split(',')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387737"}},{"Add":{"text":" idx4 = [int(idxsplit[0]),int(idxsplit[1]),int(idxsplit[2]),int(idxsplit[3])]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387822"}},{"Add":{"text":" gf_array_name = \"in_gfs\" # Default array name.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387877"}},{"Add":{"text":" gfaccess_str = gri.gfaccess(gf_array_name,gfname,ijkl_string(idx4))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387953"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:387998"}},{"Add":{"text":" retstring = out__type_var(gfname) + varsuffix(idx4) +\" = ReadSIMD(&\" + gfaccess_str + \");\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388101"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388115"}},{"Add":{"text":" retstring = out__type_var(gfname) + varsuffix(idx4) +\" = \" + gfaccess_str + \";\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388207"}},{"Add":{"text":" return retstring+\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388237"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388238"}},{"Add":{"text":" read_from_memory_Ccode = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388270"}},{"Add":{"text":" count = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388284"}},{"Add":{"text":" for gfidx in range(len(gri.glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388335"}},{"Add":{"text":" for pt in range(len(sorted_list_of_points_read_from_memory[gfidx])):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388412"}},{"Add":{"text":" read_from_memory_Ccode += read_from_memory_Ccode_onept(read_from_memory_gf[count].name,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388512"}},{"Add":{"text":" sorted_list_of_points_read_from_memory[gfidx][pt])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388630"}},{"Add":{"text":" count += 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388653"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388654"}},{"Add":{"text":" # Step 5: Output C code. C code consists of three parts","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388714"}},{"Add":{"text":" # a) Read gridfunctions from memory at needed pts.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388777"}},{"Add":{"text":" # b) Perform arithmetic needed for input expressions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388842"}},{"Add":{"text":" # provided in sympyexpr_list[].rhs and associated","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388907"}},{"Add":{"text":" # finite differences.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:388944"}},{"Add":{"text":" # c) Write output to gridfunctions specified in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389004"}},{"Add":{"text":" # sympyexpr_list[].lhs.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389043"}},{"Add":{"text":" def indent_Ccode(Ccode):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389072"}},{"Add":{"text":" Ccodesplit = Ccode.splitlines()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389112"}},{"Add":{"text":" outstring = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389135"}},{"Add":{"text":" for i in range(len(Ccodesplit)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389176"}},{"Add":{"text":" outstring += outCparams.preindent+indent+Ccodesplit[i]+'\\n'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389248"}},{"Add":{"text":" return outstring","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389273"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389278"}},{"Add":{"text":" # Step 5a: Read gridfunctions from memory at needed pts.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389339"}},{"Add":{"text":" # *** No need to do anything here; already set in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389393"}},{"Add":{"text":" # string \"read_from_memory_Ccode\". ***","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389440"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389441"}},{"Add":{"text":" # FIXME: Update these code comments:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389482"}},{"Add":{"text":" # Step 5b: Perform arithmetic needed for finite differences","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389546"}},{"Add":{"text":" # associated with input expressions provided in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389607"}},{"Add":{"text":" # sympyexpr_list[].rhs.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389644"}},{"Add":{"text":" # Note that exprs and lhsvarnames contain","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389699"}},{"Add":{"text":" # i) finite difference expressions (constructed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389761"}},{"Add":{"text":" # in steps above) and associated variable names,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389827"}},{"Add":{"text":" # and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389850"}},{"Add":{"text":" # ii) Input expressions sympyexpr_list[], which","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389911"}},{"Add":{"text":" # in general depend on finite difference","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389969"}},{"Add":{"text":" # variables.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:389999"}},{"Add":{"text":" exprs = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390020"}},{"Add":{"text":" lhsvarnames = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390041"}},{"Add":{"text":" # Step 5b.i: Output finite difference expressions to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390098"}},{"Add":{"text":" # Coutput string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390130"}},{"Add":{"text":" for i in range(len(list_of_deriv_vars)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390175"}},{"Add":{"text":" exprs.append(sp.sympify(0)) # Append a new element to the list of derivative expressions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390273"}},{"Add":{"text":" lhsvarnames.append(out__type_var(list_of_deriv_vars[i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390338"}},{"Add":{"text":" var = deriv__base_gridfunction_name[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390385"}},{"Add":{"text":" for j in range(len(fdcoeffs[i])):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390427"}},{"Add":{"text":" varname = str(var)+varsuffix(fdstencl[i][j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390484"}},{"Add":{"text":" exprs[i] += fdcoeffs[i][j]*sp.sympify(varname)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390543"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390544"}},{"Add":{"text":" # Multiply each expression by the appropriate power","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390604"}},{"Add":{"text":" # of 1/dx[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390627"}},{"Add":{"text":" invdx = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390646"}},{"Add":{"text":" for d in range(par.parval_from_str(\"DIM\")):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390698"}},{"Add":{"text":" invdx.append(sp.sympify(\"invdx\"+str(d)))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390751"}},{"Add":{"text":" # First-order or Kreiss-Oliger derivatives:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390803"}},{"Add":{"text":" if (len(deriv__operator[i]) == 5 and \"dKOD\" in deriv__operator[i]) or \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390883"}},{"Add":{"text":" (len(deriv__operator[i]) == 3 and \"dD\" in deriv__operator[i]) or \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:390961"}},{"Add":{"text":" (len(deriv__operator[i]) == 5 and (\"dupD\" in deriv__operator[i] or \"ddnD\" in deriv__operator[i])):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391071"}},{"Add":{"text":" dirn = int(deriv__operator[i][len(deriv__operator[i])-1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391145"}},{"Add":{"text":" exprs[i] *= invdx[dirn]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391185"}},{"Add":{"text":" # Second-order derivs:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391216"}},{"Add":{"text":" elif len(deriv__operator[i]) == 5 and \"dDD\" in deriv__operator[i]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391291"}},{"Add":{"text":" dirn1 = int(deriv__operator[i][len(deriv__operator[i]) - 2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391364"}},{"Add":{"text":" dirn2 = int(deriv__operator[i][len(deriv__operator[i]) - 1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391437"}},{"Add":{"text":" exprs[i] *= invdx[dirn1]*invdx[dirn2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391487"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391501"}},{"Add":{"text":" print(\"Error: was unable to parse derivative operator: \",deriv__operator[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391590"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391614"}},{"Add":{"text":" # Step 5b.ii: If upwind control vector is specified,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391671"}},{"Add":{"text":" # add upwind control vectors to the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391723"}},{"Add":{"text":" # derivative expression list, so its","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391776"}},{"Add":{"text":" # needed elements are read from memory.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391832"}},{"Add":{"text":" if upwindcontrolvec != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391863"}},{"Add":{"text":" for i in range(len(upwind_directions)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391911"}},{"Add":{"text":" exprs.append(upwindcontrolvec[upwind_directions[i]])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:391976"}},{"Add":{"text":" lhsvarnames.append(out__type_var(\"UpwindControlVectorU\"+str(upwind_directions[i])))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392072"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392073"}},{"Add":{"text":" # Step 5b.iii: Output useful code comment regarding","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392129"}},{"Add":{"text":" # which step we are on. *At most* this","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392185"}},{"Add":{"text":" # is a 3-step process:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392225"}},{"Add":{"text":" # 1. Read from memory & compute FD stencils,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392284"}},{"Add":{"text":" # 2. Perform upwinding, and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392326"}},{"Add":{"text":" # 3. Evaluate remaining expressions+write","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392382"}},{"Add":{"text":" # results to main memory.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392425"}},{"Add":{"text":" NRPy_FD_StepNumber = 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392452"}},{"Add":{"text":" NRPy_FD__Number_of_Steps = 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392485"}},{"Add":{"text":" if len(list_of_deriv_vars) > 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392521"}},{"Add":{"text":" NRPy_FD__Number_of_Steps += 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392559"}},{"Add":{"text":" if upwindcontrolvec != \"\" and len(upwind_directions) > 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392621"}},{"Add":{"text":" NRPy_FD__Number_of_Steps += 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392659"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392660"}},{"Add":{"text":" if len(read_from_memory_Ccode) > 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392700"}},{"Add":{"text":" Coutput += indent_Ccode(\"/* \\n * NRPy+ Finite Difference Code Generation, Step \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392789"}},{"Add":{"text":" + str(NRPy_FD_StepNumber) + \" of \" + str(NRPy_FD__Number_of_Steps)+","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392889"}},{"Add":{"text":" \": Read from main memory and compute finite difference stencils:\\n */\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:392995"}},{"Add":{"text":" NRPy_FD_StepNumber = NRPy_FD_StepNumber + 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393047"}},{"Add":{"text":" default_CSE_varprefix = outCparams.CSE_varprefix","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393104"}},{"Add":{"text":" # Prefix chosen CSE variables with \"FD\", for the finite difference coefficients:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393193"}},{"Add":{"text":" Coutput += indent_Ccode(outputC(exprs,lhsvarnames,\"returnstring\",params=params + \",CSE_varprefix=\"+default_CSE_varprefix+\"FD,includebraces=False,SIMD_const_suffix=_FDcoeff\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393375"}},{"Add":{"text":" prestring=read_from_memory_Ccode))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393450"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393451"}},{"Add":{"text":" # Step 5b.iv: Implement control-vector upwinding algorithm.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393515"}},{"Add":{"text":" if upwindcontrolvec != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393546"}},{"Add":{"text":" if len(upwind_directions) > 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393585"}},{"Add":{"text":" Coutput += indent_Ccode(\"/* \\n * NRPy+ Finite Difference Code Generation, Step \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393678"}},{"Add":{"text":" + str(NRPy_FD_StepNumber) + \" of \" + str(NRPy_FD__Number_of_Steps) +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393783"}},{"Add":{"text":" \": Implement upwinding algorithm:\\n */\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393862"}},{"Add":{"text":" NRPy_FD_StepNumber = NRPy_FD_StepNumber + 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393918"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393967"}},{"Add":{"text":" Coutput += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:393998"}},{"Add":{"text":"const double tmp_upwind_Integer_1 = 1.000000000000000000000000000000000;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394071"}},{"Add":{"text":"const REAL_SIMD_ARRAY upwind_Integer_1 = ConstSIMD(tmp_upwind_Integer_1);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394145"}},{"Add":{"text":"const double tmp_upwind_Integer_0 = 0.000000000000000000000000000000000;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394218"}},{"Add":{"text":"const REAL_SIMD_ARRAY upwind_Integer_0 = ConstSIMD(tmp_upwind_Integer_0);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394292"}},{"Add":{"text":"\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394296"}},{"Add":{"text":" for dirn in upwind_directions:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394339"}},{"Add":{"text":" Coutput += indent_Ccode(out__type_var(\"UpWind\" + str(dirn)) + \" = UPWIND_ALG(UpwindControlVectorU\" + str(dirn) + \");\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394476"}},{"Add":{"text":" upwindU = [sp.sympify(0) for i in range(par.parval_from_str(\"DIM\"))]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394553"}},{"Add":{"text":" for dirn in upwind_directions:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394592"}},{"Add":{"text":" upwindU[dirn] = sp.sympify(\"UpWind\"+str(dirn))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394651"}},{"Add":{"text":" for i in range(len(list_of_deriv_vars)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394700"}},{"Add":{"text":" if len(deriv__operator[i]) == 5 and (\"dupD\" in deriv__operator[i]):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394780"}},{"Add":{"text":" var_dupD = sp.sympify(\"UpwindAlgInput\"+str(list_of_deriv_vars[i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394863"}},{"Add":{"text":" var_ddnD = sp.sympify(\"UpwindAlgInput\"+str(list_of_deriv_vars[i]).replace(\"_dupD\",\"_ddnD\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:394971"}},{"Add":{"text":" upwind_dirn = int(deriv__operator[i][len(deriv__operator[i])-1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395052"}},{"Add":{"text":" upwind_expr = upwindU[upwind_dirn]*(var_dupD - var_ddnD) + var_ddnD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395136"}},{"Add":{"text":" # For convenience, we require out__type_var() above to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395207"}},{"Add":{"text":" # prefix up/downwinded variables with \"UpwindAlgInput\".","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395279"}},{"Add":{"text":" # Here we do not wish to have this prefix.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395338"}},{"Add":{"text":" Coutput += indent_Ccode(outputC(upwind_expr,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395399"}},{"Add":{"text":" out__type_var(str(list_of_deriv_vars[i]),AddPrefix_for_UpDownWindVars=False),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395525"}},{"Add":{"text":" \"returnstring\",params=params + \",includebraces=False\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395629"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395630"}},{"Add":{"text":" # Step 5b.v: Add input RHS & LHS expressions from","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395684"}},{"Add":{"text":" # sympyexpr_list[]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395719"}},{"Add":{"text":" Coutput += indent_Ccode(\"/* \\n * NRPy+ Finite Difference Code Generation, Step \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395804"}},{"Add":{"text":" + str(NRPy_FD_StepNumber) + \" of \" + str(NRPy_FD__Number_of_Steps) +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395901"}},{"Add":{"text":" \": Evaluate SymPy expressions and write to main memory:\\n */\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:395994"}},{"Add":{"text":" exprs = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396015"}},{"Add":{"text":" lhsvarnames = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396036"}},{"Add":{"text":" for i in range(len(sympyexpr_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396077"}},{"Add":{"text":" exprs.append(sympyexpr_list[i].rhs)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396121"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396166"}},{"Add":{"text":" lhsvarnames.append(\"const REAL_SIMD_ARRAY __RHS_exp_\"+str(i))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396240"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396254"}},{"Add":{"text":" lhsvarnames.append(sympyexpr_list[i].lhs)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396308"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396309"}},{"Add":{"text":" # Step 5c: Write output to gridfunctions specified in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396367"}},{"Add":{"text":" # sympyexpr_list[].lhs.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396404"}},{"Add":{"text":" write_to_mem_string = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396433"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396474"}},{"Add":{"text":" for i in range(len(sympyexpr_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396519"}},{"Add":{"text":" write_to_mem_string += \"WriteSIMD(&\"+sympyexpr_list[i].lhs+\", __RHS_exp_\"+str(i)+\");\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396619"}},{"Add":{"text":" Coutput += indent_Ccode(outputC(exprs,lhsvarnames,\"returnstring\", params = params+\",includebraces=False,preindent=0\", prestring=\"\",poststring=write_to_mem_string))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396787"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396792"}},{"Add":{"text":" # Step 6: Add consistent indentation to the output end brace. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396859"}},{"Add":{"text":" # See Step 0.b for corresponding start brace.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396917"}},{"Add":{"text":" if outCparams.includebraces == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:396960"}},{"Add":{"text":" Coutput += outCparams.preindent+\"}\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397006"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397007"}},{"Add":{"text":" # Step 7: Output the C code in desired format: stdout, string, or file.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397083"}},{"Add":{"text":" if filename == \"stdout\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397112"}},{"Add":{"text":" print(Coutput)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397135"}},{"Add":{"text":" elif filename == \"returnstring\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397172"}},{"Add":{"text":" return Coutput+'\\n'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397200"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397210"}},{"Add":{"text":" # Output to the file specified by outCfilename","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397265"}},{"Add":{"text":" with open(filename, outCparams.outCfileaccess) as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397329"}},{"Add":{"text":" file.write(Coutput)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397361"}},{"Add":{"text":" successstr = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397385"}},{"Add":{"text":" if outCparams.outCfileaccess == \"a\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397430"}},{"Add":{"text":" successstr = \"Appended \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397467"}},{"Add":{"text":" elif outCparams.outCfileaccess == \"w\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397514"}},{"Add":{"text":" successstr = \"Wrote \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397548"}},{"Add":{"text":" print(successstr + \"to file \\\"\" + filename + \"\\\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397607"}},{"Add":{"text":"# print(gri.glb_gridfcs_list[1].name,list_of_points_read_from_memory[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397683"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397684"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397685"}},{"Add":{"text":"# Define the to-be-inverted matrix, A.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397725"}},{"Add":{"text":"# We define A row-by-row, according to the prescription","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397782"}},{"Add":{"text":"# derived in notes/notes.pdf, via the following pattern","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397839"}},{"Add":{"text":"# that applies for arbitrary order.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397876"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397878"}},{"Add":{"text":"# As an example, consider a 5-point finite difference","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397933"}},{"Add":{"text":"# stencil (4th-order accurate), where we wish to compute","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:397991"}},{"Add":{"text":"# some derivative at the center point.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398031"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398033"}},{"Add":{"text":"# Then A is given by:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398056"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398058"}},{"Add":{"text":"# -2^0 -1^0 1 1^0 2^0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398086"}},{"Add":{"text":"# -2^1 -1^1 0 1^1 2^1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398114"}},{"Add":{"text":"# -2^2 -1^2 0 1^2 2^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398142"}},{"Add":{"text":"# -2^3 -1^3 0 1^3 2^3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398170"}},{"Add":{"text":"# -2^4 -1^4 0 1^4 2^4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398198"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398200"}},{"Add":{"text":"# Then right-multiplying A^{-1}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398233"}},{"Add":{"text":"# by (1 0 0 0 0)^T will yield 0th deriv. stencil","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398283"}},{"Add":{"text":"# by (0 1 0 0 0)^T will yield 1st deriv. stencil","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398333"}},{"Add":{"text":"# by (0 0 1 0 0)^T will yield 2nd deriv. stencil","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398383"}},{"Add":{"text":"# etc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398391"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398393"}},{"Add":{"text":"# Next suppose we want an upwinded, 4th-order accurate","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398449"}},{"Add":{"text":"# stencil. For this case, A is given by:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398491"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398493"}},{"Add":{"text":"# -1^0 1 1^0 2^0 3^0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398521"}},{"Add":{"text":"# -1^1 0 1^1 2^1 3^1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398549"}},{"Add":{"text":"# -1^2 0 1^2 2^2 3^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398577"}},{"Add":{"text":"# -1^3 0 1^3 2^3 3^3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398605"}},{"Add":{"text":"# -1^4 0 1^4 2^4 3^4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398633"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398635"}},{"Add":{"text":"# ... and similarly for the downwinded derivative.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398687"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398689"}},{"Add":{"text":"# Finally, let's consider a 3rd-order accurate","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398737"}},{"Add":{"text":"# stencil. This would correspond to an in-place","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398786"}},{"Add":{"text":"# upwind stencil with stencil radius of 2 gridpoints,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398841"}},{"Add":{"text":"# where other, centered derivatives are 4th-order","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398892"}},{"Add":{"text":"# accurate. For this case, A is given by:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398935"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398937"}},{"Add":{"text":"# -1^0 1 1^0 2^0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398959"}},{"Add":{"text":"# -1^1 0 1^1 2^1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:398981"}},{"Add":{"text":"# -1^2 0 1^2 2^2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399003"}},{"Add":{"text":"# -1^3 0 1^3 2^3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399025"}},{"Add":{"text":"# -1^4 0 1^4 2^4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399047"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399049"}},{"Add":{"text":"# ... and similarly for the downwinded derivative.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399101"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399103"}},{"Add":{"text":"# The general pattern is as follows:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399141"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399143"}},{"Add":{"text":"# 1) The top row is all 1's,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399173"}},{"Add":{"text":"# 2) If the second row has N elements (N must be odd),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399229"}},{"Add":{"text":"# .... then the radius of the stencil is rs = (N-1)/2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399284"}},{"Add":{"text":"# .... and the j'th row e_j = j-rs-1. For example,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399336"}},{"Add":{"text":"# .... for 4th order, we have rs = 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399374"}},{"Add":{"text":"# .... j | element","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399395"}},{"Add":{"text":"# .... 1 | -2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399411"}},{"Add":{"text":"# .... 2 | -1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399427"}},{"Add":{"text":"# .... 3 | 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399443"}},{"Add":{"text":"# .... 4 | 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399459"}},{"Add":{"text":"# .... 5 | 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399475"}},{"Add":{"text":"# 3) The L'th row, L>2 will be the same as the second","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399530"}},{"Add":{"text":"# .... row, but with each element e_j -> e_j^(L-1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399582"}},{"Add":{"text":"# A1 is used later to validate the inverted","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399627"}},{"Add":{"text":"# matrix.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399638"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399639"}},{"Add":{"text":"def compute_fdcoeffs_fdstencl(derivstring,FDORDER=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399694"}},{"Add":{"text":" # Step 0: Set finite differencing order, stencil size, and up/downwinding","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399772"}},{"Add":{"text":" if FDORDER == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399794"}},{"Add":{"text":" FDORDER = par.parval_from_str(\"FD_CENTDERIVS_ORDER\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399855"}},{"Add":{"text":" if \"dKOD\" in derivstring:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399889"}},{"Add":{"text":" FDORDER += par.parval_from_str(\"FD_KO_ORDER__CENTDERIVS_PLUS\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399964"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399965"}},{"Add":{"text":" STENCILSIZE = FDORDER+1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:399993"}},{"Add":{"text":" UPDOWNWIND = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400012"}},{"Add":{"text":" if \"dupD\" in derivstring:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400042"}},{"Add":{"text":" UPDOWNWIND = 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400066"}},{"Add":{"text":" elif \"ddnD\" in derivstring:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400098"}},{"Add":{"text":" UPDOWNWIND = -1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400122"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400123"}},{"Add":{"text":" # Step 1: Set up matrix based on the stencil size (FDORDER+1).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400190"}},{"Add":{"text":" # See documentation above for details on how this","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400252"}},{"Add":{"text":" # matrix is set up.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400284"}},{"Add":{"text":" M = sp.zeros(STENCILSIZE,STENCILSIZE)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400326"}},{"Add":{"text":" for i in range(STENCILSIZE):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400359"}},{"Add":{"text":" for j in range(STENCILSIZE):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400396"}},{"Add":{"text":" if i == 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400419"}},{"Add":{"text":" M[(i,j)] = 1 # Setting n^0 = 1 for all n, including n=0, because this matches the pattern","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400525"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400543"}},{"Add":{"text":" dist_from_xeq0_col = j - sp.Rational((STENCILSIZE - 1),2) + UPDOWNWIND","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400630"}},{"Add":{"text":" if dist_from_xeq0_col==0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400672"}},{"Add":{"text":" M[(i,j)] = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400705"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400727"}},{"Add":{"text":" M[(i, j)] = dist_from_xeq0_col**(i)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400783"}},{"Add":{"text":" Minv = sp.zeros(STENCILSIZE,STENCILSIZE)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400828"}},{"Add":{"text":" Minv = M**(-1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400847"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400848"}},{"Add":{"text":" # Step 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400862"}},{"Add":{"text":" # Based on the input derivative string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400910"}},{"Add":{"text":" # pick out the relevant row of the matrix","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:400960"}},{"Add":{"text":" # inverse, as outlined in the detailed code","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401012"}},{"Add":{"text":" # comments prior to this function definition.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401066"}},{"Add":{"text":" derivtype = \"FirstDeriv\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401095"}},{"Add":{"text":" matrixrow = 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401113"}},{"Add":{"text":" if \"DDD\" in derivstring:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401142"}},{"Add":{"text":" print(\"Error: Only derivatives up to second order currently supported.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401223"}},{"Add":{"text":" print(\" Feel free to contribute to NRPy+ to extend its functionality!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401309"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401329"}},{"Add":{"text":" elif \"DD\" in derivstring:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401359"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401360"}},{"Add":{"text":" if derivstring[len(derivstring)-1] == derivstring[len(derivstring)-2]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401439"}},{"Add":{"text":" # Assuming i==j, we call \\partial_i \\partial_j gf an \"unmixed\" second derivative,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401533"}},{"Add":{"text":" # or more simply, just \"SecondDeriv\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401587"}},{"Add":{"text":" derivtype = \"SecondDeriv\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401625"}},{"Add":{"text":" matrixrow = 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401651"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401665"}},{"Add":{"text":" # Assuming i!=j, we call \\partial_i \\partial_j gf a MIXED second derivative,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401754"}},{"Add":{"text":" # which is computed using a composite of first derivative operations.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401840"}},{"Add":{"text":" derivtype = \"MixedSecondDeriv\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401883"}},{"Add":{"text":" elif \"dKOD\" in derivstring:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401915"}},{"Add":{"text":" derivtype = \"KreissOligerDeriv\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401955"}},{"Add":{"text":" matrixrow = STENCILSIZE - 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:401991"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402001"}},{"Add":{"text":" # Up/downwinded and first derivs are all of \"FirstDeriv\" type","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402071"}},{"Add":{"text":" pass","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402084"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402085"}},{"Add":{"text":" # Step 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402099"}},{"Add":{"text":" # Set finite difference coefficients","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402144"}},{"Add":{"text":" # and stencil points corresponding to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402190"}},{"Add":{"text":" # each finite difference coefficient.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402236"}},{"Add":{"text":" fdcoeffs = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402254"}},{"Add":{"text":" fdstencl = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402272"}},{"Add":{"text":" if derivtype != \"MixedSecondDeriv\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402312"}},{"Add":{"text":" for i in range(STENCILSIZE):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402349"}},{"Add":{"text":" idx4 = [0, 0, 0, 0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402381"}},{"Add":{"text":" # First compute finite difference coefficient.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402440"}},{"Add":{"text":" fdcoeff = sp.factorial(matrixrow)*Minv[(i,matrixrow)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402506"}},{"Add":{"text":" # Do not store fdcoeff or fdstencil if","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402557"}},{"Add":{"text":" # finite difference coefficient is zero.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402610"}},{"Add":{"text":" if fdcoeff != 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402639"}},{"Add":{"text":" fdcoeffs.append(fdcoeff)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402680"}},{"Add":{"text":" if derivtype == \"KreissOligerDeriv\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402733"}},{"Add":{"text":" fdcoeffs[i] *= (-1)**(sp.Rational((STENCILSIZE+1),2))/2**matrixrow","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402820"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402821"}},{"Add":{"text":" # Next store finite difference stencil point","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402882"}},{"Add":{"text":" # corresponding to coefficient.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:402930"}},{"Add":{"text":" gridpt_posn = i - int((STENCILSIZE-1)/2) + UPDOWNWIND","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403000"}},{"Add":{"text":" if gridpt_posn != 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403037"}},{"Add":{"text":" dirn = int(derivstring[len(derivstring)-1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403101"}},{"Add":{"text":" idx4[dirn] = gridpt_posn","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403146"}},{"Add":{"text":" fdstencl.append(idx4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403184"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403194"}},{"Add":{"text":" # Mixed second derivative finite difference coeffs","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403253"}},{"Add":{"text":" # consist of products of first deriv coeffs,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403310"}},{"Add":{"text":" # defined in first Minv matrix row.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403358"}},{"Add":{"text":" for i in range(STENCILSIZE):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403395"}},{"Add":{"text":" for j in range(STENCILSIZE):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403436"}},{"Add":{"text":" idx4 = [0, 0, 0, 0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403472"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403473"}},{"Add":{"text":" # First compute finite difference coefficient.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403536"}},{"Add":{"text":" fdcoeff = (sp.factorial(matrixrow)*Minv[(i,matrixrow)]) * \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403612"}},{"Add":{"text":" (sp.factorial(matrixrow)*Minv[(j,matrixrow)])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403684"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403685"}},{"Add":{"text":" # Do not store fdcoeff or fdstencil if","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403740"}},{"Add":{"text":" # finite difference coefficient is zero.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403797"}},{"Add":{"text":" if fdcoeff != 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403830"}},{"Add":{"text":" fdcoeffs.append(fdcoeff)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403875"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403876"}},{"Add":{"text":" # Next store finite difference stencil point","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403941"}},{"Add":{"text":" # corresponding to coefficient.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:403993"}},{"Add":{"text":" gridpt_posn1 = i - int((STENCILSIZE - 1) / 2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404059"}},{"Add":{"text":" gridpt_posn2 = j - int((STENCILSIZE - 1) / 2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404125"}},{"Add":{"text":" dirn1 = int(derivstring[len(derivstring) - 1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404192"}},{"Add":{"text":" dirn2 = int(derivstring[len(derivstring) - 2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404259"}},{"Add":{"text":" idx4[dirn1] = gridpt_posn1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404306"}},{"Add":{"text":" idx4[dirn2] = gridpt_posn2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404353"}},{"Add":{"text":" fdstencl.append(idx4)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404395"}},{"Add":{"text":" return fdcoeffs,fdstencl","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404424"}}]}},{"FileAdd":{"meta":{"basename":"grid.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/grid.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# grid.py: functions & parameters related to numerical grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404497"}},{"Add":{"text":"# functions: Automatic loop output, output C code needed for gridfunction memory I/O, gridfunction registration","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404609"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404610"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404641"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404684"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404685"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404749"}},{"Add":{"text":"import sympy as sp # Import SymPy, a computer algebra system written entirely in Python","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404853"}},{"Add":{"text":"from collections import namedtuple # Standard Python `collections` module: defines named tuples data structure","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404964"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:404965"}},{"Add":{"text":"# Initialize globals related to the grid","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405006"}},{"Add":{"text":"glb_gridfcs_list = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405028"}},{"Add":{"text":"glb_gridfc = namedtuple('gridfunction', 'gftype name rank DIM')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405093"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405094"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405116"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"GridFuncMemAccess\", \"SENRlike\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405205"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"MemAllocStyle\",\"210\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405284"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"int\", thismodule, \"DIM\", 3))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405350"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405351"}},{"Add":{"text":"Nxx = par.Cparameters(\"int\", thismodule,[\"Nxx0\",\"Nxx1\",\"Nxx2\"],[64,32,64]) # Default to 64x32x64 grid","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405453"}},{"Add":{"text":"Nxx_plus_2NGHOSTS = par.Cparameters(\"int\", thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405508"}},{"Add":{"text":" [\"Nxx_plus_2NGHOSTS0\",\"Nxx_plus_2NGHOSTS1\",\"Nxx_plus_2NGHOSTS2\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405596"}},{"Add":{"text":" [ 70, 38, 70]) # Default to 64x32x64 grid w/ NGHOSTS=3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405724"}},{"Add":{"text":"xx = par.Cparameters(\"REAL\",thismodule,[ \"xx0\", \"xx1\", \"xx2\"],1e300) # These are C variables, not parameters, and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405839"}},{"Add":{"text":" # will be overwritten; best to initialize to crazy","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:405960"}},{"Add":{"text":" # number to ensure they are overwritten!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406071"}},{"Add":{"text":"dxx = par.Cparameters(\"REAL\",thismodule,[ \"dxx0\", \"dxx1\", \"dxx2\"],0.1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406150"}},{"Add":{"text":"invdx = par.Cparameters(\"REAL\",thismodule,[ \"invdx0\", \"invdx1\", \"invdx2\"],1.0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406229"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406230"}},{"Add":{"text":"def variable_type(var):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406254"}},{"Add":{"text":" var_is_gf = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406276"}},{"Add":{"text":" for gf in range(len(glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406320"}},{"Add":{"text":" if str(var) == glb_gridfcs_list[gf].name:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406370"}},{"Add":{"text":" var_is_gf = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406399"}},{"Add":{"text":" var_is_parameter = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406428"}},{"Add":{"text":"# for paramname in range(len(par.glb_params_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406484"}},{"Add":{"text":"# if str(var) == par.glb_params_list[paramname].parname:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406549"}},{"Add":{"text":"# var_is_parameter = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406587"}},{"Add":{"text":" for paramname in range(len(par.glb_Cparams_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406642"}},{"Add":{"text":" if str(var) == par.glb_Cparams_list[paramname].parname:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406706"}},{"Add":{"text":" var_is_parameter = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406742"}},{"Add":{"text":" if var_is_parameter and var_is_gf:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406781"}},{"Add":{"text":" print(\"Error: variable \"+str(var)+\" is registered both as a gridfunction and as a Cparameter.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406885"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406905"}},{"Add":{"text":" if not (var_is_parameter or var_is_gf):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406949"}},{"Add":{"text":" return \"other\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406972"}},{"Add":{"text":" if var_is_parameter:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:406997"}},{"Add":{"text":" return \"Cparameter\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407025"}},{"Add":{"text":" if var_is_gf:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407043"}},{"Add":{"text":" return \"gridfunction\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407073"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407074"}},{"Add":{"text":"def find_gftype(varname):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407100"}},{"Add":{"text":" for gf in glb_gridfcs_list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407132"}},{"Add":{"text":" if gf.name == varname:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407163"}},{"Add":{"text":" return gf.gftype","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407192"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407197"}},{"Add":{"text":"def gfaccess(gfarrayname = \"\", varname = \"\", ijklstring = \"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407260"}},{"Add":{"text":" found_registered_gf = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407292"}},{"Add":{"text":" for gf in glb_gridfcs_list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407324"}},{"Add":{"text":" if gf.name == varname:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407355"}},{"Add":{"text":" if found_registered_gf:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407391"}},{"Add":{"text":" print(\"Error: found duplicate gridfunction name: \"+gf.name)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407467"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407495"}},{"Add":{"text":" found_registered_gf = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407534"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407535"}},{"Add":{"text":" if not found_registered_gf:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407567"}},{"Add":{"text":" print(\"Error: gridfunction \\\"\"+varname+\"\\\" is not registered!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407639"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407659"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407660"}},{"Add":{"text":" gftype = find_gftype(varname)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407694"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407695"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407732"}},{"Add":{"text":" retstring = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407751"}},{"Add":{"text":" if par.parval_from_str(\"GridFuncMemAccess\") == \"SENRlike\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407814"}},{"Add":{"text":" if gfarrayname == \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407844"}},{"Add":{"text":" print(\"Error: GridFuncMemAccess = SENRlike requires gfarrayname be passed to gfaccess()\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407946"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:407970"}},{"Add":{"text":" # FIXME: if gftype == \"AUX\" then override gfarrayname to aux_gfs[].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408046"}},{"Add":{"text":" # This enables expressions containing a mixture of AUX and EVOL","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408125"}},{"Add":{"text":" # gridfunctions, though in a slightly hacky way.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408189"}},{"Add":{"text":" if gftype == \"AUX\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408217"}},{"Add":{"text":" gfarrayname = \"aux_gfs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408253"}},{"Add":{"text":" elif gftype == \"AUXEVOL\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408287"}},{"Add":{"text":" gfarrayname = \"auxevol_gfs\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408327"}},{"Add":{"text":" # Return gfarrayname[IDX3(varname,i0)] for DIM=1, gfarrayname[IDX3(varname,i0,i1)] for DIM=2, etc.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408434"}},{"Add":{"text":" retstring += gfarrayname + \"[IDX\" + str(DIM+1) + \"(\" + varname.upper()+\"GF\" + \", \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408525"}},{"Add":{"text":" elif par.parval_from_str(\"GridFuncMemAccess\") == \"ETK\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408585"}},{"Add":{"text":" # Return varname[CCTK_GFINDEX3D(i0,i1,i2)] for DIM=3. Error otherwise","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408663"}},{"Add":{"text":" if DIM != 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408684"}},{"Add":{"text":" print(\"Error: GridFuncMemAccess = ETK currently requires that gridfunctions be 3D. Can be easily extended.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408805"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408829"}},{"Add":{"text":" if gfarrayname == \"rhs_gfs\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408866"}},{"Add":{"text":" retstring += varname + \"_rhsGF\" + \"[CCTK_GFINDEX\"+str(DIM)+\"D(cctkGH, \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408950"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:408964"}},{"Add":{"text":" retstring += varname + \"GF\" + \"[CCTK_GFINDEX\"+str(DIM)+\"D(cctkGH, \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409044"}},{"Add":{"text":" elif par.parval_from_str(\"GridFuncMemAccess\") == \"CarpetX\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409108"}},{"Add":{"text":" # Return varname_.ptr[varname_.offset(i0,i1,i2,...)].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409170"}},{"Add":{"text":" if gfarrayname == \"rhs_gfs\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409207"}},{"Add":{"text":" retstring += varname + \"_rhsGF\" + \"_.ptr[\" + varname + \"_rhsGF_.offset(\";","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409293"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409307"}},{"Add":{"text":" retstring += varname + \"GF\" + \"_.ptr[\" + varname + \"GF_.offset(\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409384"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409394"}},{"Add":{"text":" print(\"grid::GridFuncMemAccess = \"+par.parval_from_str(\"GridFuncMemAccess\")+\" not supported\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409496"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409516"}},{"Add":{"text":" if ijklstring == \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409541"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409570"}},{"Add":{"text":" retstring += \"i\"+str(i)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409606"}},{"Add":{"text":" if i != DIM-1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409633"}},{"Add":{"text":" retstring += ', '","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409667"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409677"}},{"Add":{"text":" retstring += ijklstring","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409709"}},{"Add":{"text":" return retstring + \")]\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409737"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409738"}},{"Add":{"text":"# Gridfunction basenames cannot end in integers.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409787"}},{"Add":{"text":"# For example, rank-1 gridfunction vecU1 has","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409835"}},{"Add":{"text":"# basename \"vecU\". Thus this gridfunction has","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409884"}},{"Add":{"text":"# a valid basename. If we instead defined a","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409931"}},{"Add":{"text":"# scalar gridfunction \"u2\", this would have a","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:409980"}},{"Add":{"text":"# basename of \"u2\" -- not a valid basename.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410027"}},{"Add":{"text":"# Being so strict enables us to determine","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410072"}},{"Add":{"text":"# quickly what a gridfunction is by its name","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410120"}},{"Add":{"text":"# alone, which is useful, e.g., when setting","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410168"}},{"Add":{"text":"# up parity boundary conditions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410204"}},{"Add":{"text":"def verify_gridfunction_basename_is_valid(gf_basename):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410260"}},{"Add":{"text":" # First check for zero-length basenames:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410305"}},{"Add":{"text":" if len(gf_basename) == 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410335"}},{"Add":{"text":" print(\"Error: tried to register gridfunction without a name!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410406"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410426"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410431"}},{"Add":{"text":" # https://stackoverflow.com/questions/1303243/how-to-find-out-if-a-python-object-is-a-string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410528"}},{"Add":{"text":" if sys.version_info[0] < 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410560"}},{"Add":{"text":" if not isinstance(gf_basename,basestring):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410611"}},{"Add":{"text":" print(\"ERROR: gf_names must be strings\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410664"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410688"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410698"}},{"Add":{"text":" if not isinstance(gf_basename, str):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410743"}},{"Add":{"text":" print(\"ERROR: gf_names must be strings\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410796"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410820"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410821"}},{"Add":{"text":" if len(gf_basename) > 0 and gf_basename[-1].isdigit():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410880"}},{"Add":{"text":" print(\"Error: tried to register gridfunction with base name: \"+gf_basename)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:410964"}},{"Add":{"text":" print(\" Gridfunctions with base names ending in an integer is forbidden; pick a new name.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411064"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411084"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411085"}},{"Add":{"text":"import sys","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411096"}},{"Add":{"text":"def register_gridfunctions(gf_type,gf_names,rank=0,is_indexed=False,DIM=3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411172"}},{"Add":{"text":" # Step 0: Sanity check","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411199"}},{"Add":{"text":" if (rank > 0 and is_indexed == False) or (rank == 0 and is_indexed == True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411280"}},{"Add":{"text":" print(\"Error: Attempted to register *indexed* gridfunction(s) with rank 0, or *scalar* gridfunctions with rank>0.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411404"}},{"Add":{"text":" print(\" Gridfunctions = \",gf_names)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411454"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411474"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411475"}},{"Add":{"text":" # Step 1: convert gf_names to a list if it's not already a list","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411543"}},{"Add":{"text":" if type(gf_names) is not list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411578"}},{"Add":{"text":" gf_namestmp = [gf_names]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411611"}},{"Add":{"text":" gf_names = gf_namestmp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411642"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411643"}},{"Add":{"text":" # Step 2: if the gridfunction is not indexed, then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411698"}},{"Add":{"text":" # gf_names == base names. Check that the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411751"}},{"Add":{"text":" # gridfunction basenames are valid:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411799"}},{"Add":{"text":" if is_indexed==False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411825"}},{"Add":{"text":" for i in range(len(gf_names)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411864"}},{"Add":{"text":" verify_gridfunction_basename_is_valid(gf_names[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411927"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411944"}},{"Add":{"text":" # Step 3: Verify that gridfunction type is valid.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:411998"}},{"Add":{"text":" if not (gf_type == \"EVOL\" or gf_type == \"AUX\" or gf_type == \"AUXEVOL\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412074"}},{"Add":{"text":" print(\"Error in registering gridfunction(s) with unsupported type \"+gf_type+\".\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412163"}},{"Add":{"text":" print(\"Supported types include \\\"EVOL\\\" for gridfunctions related to evolved quantities or \\\"AUX\\\" for all others.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412288"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412308"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412309"}},{"Add":{"text":" # Step 4: Check for duplicate grid function registrations. If:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412376"}},{"Add":{"text":" # a) A duplicate is found, error out. Otherwise","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412436"}},{"Add":{"text":" # b) Append to list of gridfunctions, stored in glb_gridfcs_list[].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412516"}},{"Add":{"text":" for i in range(len(gf_names)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412551"}},{"Add":{"text":" for j in range(len(glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412598"}},{"Add":{"text":" if gf_names[i] == glb_gridfcs_list[j].name:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412654"}},{"Add":{"text":" print(\"Error: Tried to register the gridfunction \\\"\"+gf_names[i]+\"\\\" twice (ignored type)\\n\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412766"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412794"}},{"Add":{"text":" # If no duplicate found, append to \"gridfunctions\" list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412859"}},{"Add":{"text":" glb_gridfcs_list.append(glb_gridfc(gf_type,gf_names[i],rank,DIM))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412933"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412934"}},{"Add":{"text":" # Step 5: Return SymPy object corresponding to symbol or","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:412995"}},{"Add":{"text":" # list of symbols representing gridfunction in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413054"}},{"Add":{"text":" # SymPy expression","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413085"}},{"Add":{"text":" OBJ_TMPS = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413103"}},{"Add":{"text":" for i in range(len(gf_names)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413138"}},{"Add":{"text":" OBJ_TMPS.append(sp.symbols(gf_names[i], real=True))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413198"}},{"Add":{"text":"# OBJ_TMPS.append(sp.sympify(gf_names[i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413248"}},{"Add":{"text":" if len(gf_names)==1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413273"}},{"Add":{"text":" return OBJ_TMPS[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413300"}},{"Add":{"text":" return OBJ_TMPS","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413320"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413321"}},{"Add":{"text":"# Given output directory \"outdir\" as input, the ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413370"}},{"Add":{"text":"# following function outputs a file called","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413415"}},{"Add":{"text":"# \"outdir/gridfunction_defines.h\", which","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413458"}},{"Add":{"text":"# #define's all the gridfunction aliases, and ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413507"}},{"Add":{"text":"# returns two lists, corresponding to the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413551"}},{"Add":{"text":"# names (strings) of the evolved and auxiliary ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413601"}},{"Add":{"text":"# gridfunction names respectively.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413638"}},{"Add":{"text":"# ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413643"}},{"Add":{"text":"# For example, if we define only two gridfunctions uu and vv,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413705"}},{"Add":{"text":"# which are evolved quantities (i.e., represent","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413755"}},{"Add":{"text":"# the solution of the PDEs we are solving and are","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413807"}},{"Add":{"text":"# registered with gftype == \"EVOL\"), then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413851"}},{"Add":{"text":"# this function will create a file with the following ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413908"}},{"Add":{"text":"# content:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413921"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413923"}},{"Add":{"text":"# | /* This file is automatically generated by NRPy+. Do not edit. */","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:413993"}},{"Add":{"text":"# | /* EVOLVED VARIABLES: */","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414022"}},{"Add":{"text":"# | #define NUM_EVOL_GFS 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414049"}},{"Add":{"text":"# | #define UUGF 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414068"}},{"Add":{"text":"# | #define VVGF 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414087"}},{"Add":{"text":"# |","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414091"}},{"Add":{"text":"# | /* AUXILIARY VARIABLES: */","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414122"}},{"Add":{"text":"# | #define NUM_AUX_GFS 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414148"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414150"}},{"Add":{"text":"# The function will return two lists: the lists of ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414202"}},{"Add":{"text":"# EVOL and AUX gridfunction names, respectively. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414255"}},{"Add":{"text":"# For this example, the first list (all gridfunctions ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414313"}},{"Add":{"text":"# registered as EVOL) will be [\"uu\",\"vv\"], and the ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414368"}},{"Add":{"text":"# second (all gridfunctions registered as AUX) will","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414423"}},{"Add":{"text":"# be the empty list: []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414450"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414451"}},{"Add":{"text":"def gridfunction_lists():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414477"}},{"Add":{"text":" evolved_variables_list = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414511"}},{"Add":{"text":" auxiliary_variables_list = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414545"}},{"Add":{"text":" auxevol_variables_list = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414577"}},{"Add":{"text":" for i in range(len(glb_gridfcs_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414620"}},{"Add":{"text":" if glb_gridfcs_list[i].gftype == \"EVOL\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414669"}},{"Add":{"text":" evolved_variables_list.append(glb_gridfcs_list[i].name)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414737"}},{"Add":{"text":" if glb_gridfcs_list[i].gftype == \"AUX\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414785"}},{"Add":{"text":" auxiliary_variables_list.append(glb_gridfcs_list[i].name)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414855"}},{"Add":{"text":" if glb_gridfcs_list[i].gftype == \"AUXEVOL\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414907"}},{"Add":{"text":" auxevol_variables_list.append(glb_gridfcs_list[i].name)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414975"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:414976"}},{"Add":{"text":" # Next we alphabetize the lists","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415012"}},{"Add":{"text":" evolved_variables_list.sort()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415046"}},{"Add":{"text":" auxiliary_variables_list.sort()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415082"}},{"Add":{"text":" auxevol_variables_list.sort()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415116"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415117"}},{"Add":{"text":" return evolved_variables_list,auxiliary_variables_list,auxevol_variables_list","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415199"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415200"}},{"Add":{"text":"def output__gridfunction_defines_h__return_gf_lists(outdir):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415261"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415262"}},{"Add":{"text":" evolved_variables_list, auxiliary_variables_list, auxevol_variables_list = gridfunction_lists()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415362"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415363"}},{"Add":{"text":" # Finally we set up the #define statements:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415411"}},{"Add":{"text":" with open(outdir+\"/gridfunction_defines.h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415473"}},{"Add":{"text":" file.write(\"/* This file is automatically generated by NRPy+. Do not edit. */\\n\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415565"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415566"}},{"Add":{"text":" file.write(\"/* EVOLVED VARIABLES: */\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415615"}},{"Add":{"text":" file.write(\"#define NUM_EVOL_GFS \"+str(len(evolved_variables_list))+\"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415697"}},{"Add":{"text":" for i in range(len(evolved_variables_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415750"}},{"Add":{"text":" file.write(\"#define \"+evolved_variables_list[i].upper()+\"GF\\t\"+str(i)+\"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415838"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415839"}},{"Add":{"text":" file.write(\"\\n\\n /* AUXILIARY VARIABLES: */\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415895"}},{"Add":{"text":" file.write(\"#define NUM_AUX_GFS \" + str(len(auxiliary_variables_list)) + \"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:415982"}},{"Add":{"text":" for i in range(len(auxiliary_variables_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416037"}},{"Add":{"text":" file.write(\"#define \" + auxiliary_variables_list[i].upper() + \"GF\\t\" + str(i) + \"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416135"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416136"}},{"Add":{"text":" file.write(\"\\n\\n /* AUXEVOL VARIABLES: */\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416190"}},{"Add":{"text":" file.write(\"#define NUM_AUXEVOL_GFS \"+str(len(auxevol_variables_list))+\"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416275"}},{"Add":{"text":" for i in range(len(auxevol_variables_list)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416328"}},{"Add":{"text":" file.write(\"#define \"+auxevol_variables_list[i].upper()+\"GF\\t\"+str(i)+\"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416416"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416417"}},{"Add":{"text":" return evolved_variables_list,auxiliary_variables_list,auxevol_variables_list","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416499"}}]}},{"FileAdd":{"meta":{"basename":"indexedexp.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/indexedexp.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# indexedexp.py: functions related to indexed expressions, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416577"}},{"Add":{"text":"# including e.g., tensors and pseudotensors:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416622"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416623"}},{"Add":{"text":"# Step 1: Load needed modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416653"}},{"Add":{"text":"import NRPy_param_funcs as par","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416684"}},{"Add":{"text":"import grid as gri","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416703"}},{"Add":{"text":"import sympy as sp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416722"}},{"Add":{"text":"import sys","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416733"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416734"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416756"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"symmetry_axes\", \"\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416834"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416835"}},{"Add":{"text":"def zerorank1(DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416858"}},{"Add":{"text":" if DIM == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416876"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416917"}},{"Add":{"text":" return [sp.sympify(0) for i in range(DIM)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416964"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416965"}},{"Add":{"text":"def zerorank2(DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:416988"}},{"Add":{"text":" if DIM == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417006"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417047"}},{"Add":{"text":" return [[sp.sympify(0) for i in range(DIM)] for j in range(DIM)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417116"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417117"}},{"Add":{"text":"def zerorank3(DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417140"}},{"Add":{"text":" if DIM == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417158"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417199"}},{"Add":{"text":" return [[[sp.sympify(0) for i in range(DIM)] for j in range(DIM)] for k in range(DIM)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417290"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417291"}},{"Add":{"text":"def zerorank4(DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417314"}},{"Add":{"text":" if DIM == -1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417332"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417373"}},{"Add":{"text":" return [[[[sp.sympify(0) for i in range(DIM)] for j in range(DIM)] for k in range(DIM)] for l in range(DIM)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417486"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417487"}},{"Add":{"text":"def apply_symmetry_condition_to_derivatives(IDX_OBJ):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417541"}},{"Add":{"text":" symmetry_axes = par.parval_from_str(\"indexedexp::symmetry_axes\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417610"}},{"Add":{"text":" if symmetry_axes == \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417638"}},{"Add":{"text":" return IDX_OBJ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417661"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417662"}},{"Add":{"text":" rank = 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417675"}},{"Add":{"text":" if isinstance(IDX_OBJ[0], list):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417712"}},{"Add":{"text":" if not isinstance(IDX_OBJ[0][0], list):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417760"}},{"Add":{"text":" rank = 2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417781"}},{"Add":{"text":" elif not isinstance(IDX_OBJ[0][0][0], list):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417834"}},{"Add":{"text":" rank = 3","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417855"}},{"Add":{"text":" elif not isinstance(IDX_OBJ[0][0][0][0], list):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417911"}},{"Add":{"text":" rank = 4","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417932"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:417946"}},{"Add":{"text":" print(\"Error: could not figure out rank for \",IDX_OBJ)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418013"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418037"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418038"}},{"Add":{"text":" def does_IDXOBJ_perform_derivative_across_symmetry_axis(idxobj_str):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418111"}},{"Add":{"text":" returnval = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418137"}},{"Add":{"text":" if \"_d\" in idxobj_str:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418168"}},{"Add":{"text":" # First we find the order of the derivative:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418225"}},{"Add":{"text":" deriv_order = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418253"}},{"Add":{"text":" underscore_position = -1000","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418293"}},{"Add":{"text":" for i in range(len(idxobj_str)-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418340"}},{"Add":{"text":" if idxobj_str[i] == \"_\" and idxobj_str[i+1]==\"d\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418406"}},{"Add":{"text":" # The order of the derivative is given by the number of D's in a row after the _d:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418509"}},{"Add":{"text":" for k in range(i+2,len(idxobj_str)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418566"}},{"Add":{"text":" if idxobj_str[k] == \"D\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418615"}},{"Add":{"text":" deriv_order = deriv_order + 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418673"}},{"Add":{"text":" if deriv_order > 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418705"}},{"Add":{"text":" print(\"Error. Derivative order > 2 not supported. Found derivative order = \"+str(deriv_order))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418816"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418844"}},{"Add":{"text":" end_idx_of_idxobj_str = len(idxobj_str)-1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418898"}},{"Add":{"text":" for j in range(end_idx_of_idxobj_str,end_idx_of_idxobj_str-deriv_order,-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:418986"}},{"Add":{"text":" if idxobj_str[j] in symmetry_axes:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419037"}},{"Add":{"text":" return True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419069"}},{"Add":{"text":" return False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419090"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419091"}},{"Add":{"text":" if rank == 1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419109"}},{"Add":{"text":" DIM = len(IDX_OBJ)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419136"}},{"Add":{"text":" for i0 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419166"}},{"Add":{"text":" if does_IDXOBJ_perform_derivative_across_symmetry_axis(str(IDX_OBJ[i0])) == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419260"}},{"Add":{"text":" IDX_OBJ[i0] = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419304"}},{"Add":{"text":" if rank == 2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419322"}},{"Add":{"text":" DIM = len(IDX_OBJ[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419352"}},{"Add":{"text":" for i0 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419382"}},{"Add":{"text":" for i1 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419416"}},{"Add":{"text":" if does_IDXOBJ_perform_derivative_across_symmetry_axis(str(IDX_OBJ[i0][i1])) == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419518"}},{"Add":{"text":" IDX_OBJ[i0][i1] = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419570"}},{"Add":{"text":" if rank == 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419588"}},{"Add":{"text":" DIM = len(IDX_OBJ[0][0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419621"}},{"Add":{"text":" for i0 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419651"}},{"Add":{"text":" for i1 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419685"}},{"Add":{"text":" for i2 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419723"}},{"Add":{"text":" if does_IDXOBJ_perform_derivative_across_symmetry_axis(str(IDX_OBJ[i0][i1][i2])) == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419833"}},{"Add":{"text":" IDX_OBJ[i0][i1][i2] = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419893"}},{"Add":{"text":" if rank == 4:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419911"}},{"Add":{"text":" DIM = len(IDX_OBJ[0][0][0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419947"}},{"Add":{"text":" for i0 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:419977"}},{"Add":{"text":" for i1 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420011"}},{"Add":{"text":" for i2 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420049"}},{"Add":{"text":" for i3 in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420091"}},{"Add":{"text":" if does_IDXOBJ_perform_derivative_across_symmetry_axis(str(IDX_OBJ[i0][i1][i2][i3])) == True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420209"}},{"Add":{"text":" IDX_OBJ[i0][i1][i2][i3] = sp.sympify(0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420277"}},{"Add":{"text":" return IDX_OBJ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420296"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420297"}},{"Add":{"text":"def declarerank1(objname, DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420332"}},{"Add":{"text":" if DIM==-1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420348"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420389"}},{"Add":{"text":" IDX_OBJ_TMP = [sp.sympify(objname + str(i)) for i in range(DIM)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420458"}},{"Add":{"text":" return apply_symmetry_condition_to_derivatives(IDX_OBJ_TMP)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420522"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420523"}},{"Add":{"text":"def register_gridfunctions_for_single_rank1(gf_type,gf_basename, DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420597"}},{"Add":{"text":" # Step 0: Verify the gridfunction basename is valid:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420654"}},{"Add":{"text":" gri.verify_gridfunction_basename_is_valid(gf_basename)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420713"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420718"}},{"Add":{"text":" # Step 1: Declare a list of SymPy variables, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420768"}},{"Add":{"text":" # where IDX_OBJ_TMP[i] = gf_basename+str(i)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420824"}},{"Add":{"text":" IDX_OBJ_TMP = declarerank1(gf_basename, DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420873"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420874"}},{"Add":{"text":" # Step 2: Register each gridfunction","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420915"}},{"Add":{"text":" if DIM==-1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420931"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420972"}},{"Add":{"text":" gf_list = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:420989"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421014"}},{"Add":{"text":" gf_list.append(str(IDX_OBJ_TMP[i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421058"}},{"Add":{"text":" gri.register_gridfunctions(gf_type, gf_list, rank=1, is_indexed=True, DIM=DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421141"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421142"}},{"Add":{"text":" # Step 3: Return array of SymPy variables","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421188"}},{"Add":{"text":" return IDX_OBJ_TMP","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421211"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421212"}},{"Add":{"text":"def declarerank2(objname, symmetry_option, DIM=-1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421264"}},{"Add":{"text":" if DIM==-1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421280"}},{"Add":{"text":" DIM = par.parval_from_str(\"DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421321"}},{"Add":{"text":" IDX_OBJ_TMP = [[sp.sympify(objname + str(i) + str(j)) for j in range(DIM)] for i in range(DIM)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421421"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421446"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421475"}},{"Add":{"text":" if symmetry_option == \"sym01\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421518"}},{"Add":{"text":" if (j < i):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:421546"}},{"Add":{"text":" # j>> t2.txt","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431036"}},{"Add":{"text":" # cat t2.txt | sed \"s/ //g\" |sed \"s/ //g;s/\$[0-3]\$/[\\1]/g\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431101"}},{"Add":{"text":" outDET = a[0][1]*a[1][3]*a[2][2]*a[3][0]-a[0][1]*a[1][2]*a[2][3]*a[3][0]-a[0][0]*a[1][3]*a[2][2]*a[3][1]+ \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431213"}},{"Add":{"text":" a[0][0]*a[1][2]*a[2][3]*a[3][1]-a[0][1]*a[1][3]*a[2][0]*a[3][2]+a[0][0]*a[1][3]*a[2][1]*a[3][2]+ \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431325"}},{"Add":{"text":" a[0][1]*a[1][0]*a[2][3]*a[3][2]-a[0][0]*a[1][1]*a[2][3]*a[3][2]+ \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431405"}},{"Add":{"text":" a[0][3]*(a[1][2]*a[2][1]*a[3][0]-a[1][1]*a[2][2]*a[3][0]-a[1][2]*a[2][0]*a[3][1]+a[1][0]*a[2][2]*a[3][1]+","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431519"}},{"Add":{"text":" a[1][1]*a[2][0]*a[3][2]-a[1][0]*a[2][1]*a[3][2])+ \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431588"}},{"Add":{"text":" (a[0][1]*a[1][2]*a[2][0]-a[0][0]*a[1][2]*a[2][1]-a[0][1]*a[1][0]*a[2][2]+a[0][0]*a[1][1]*a[2][2])*a[3][3]+\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431709"}},{"Add":{"text":" a[0][2]*(-(a[1][3]*a[2][1]*a[3][0])+a[1][1]*a[2][3]*a[3][0]+a[1][3]*a[2][0]*a[3][1]-a[1][0]*a[2][3]*a[3][1]-","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431826"}},{"Add":{"text":" a[1][1]*a[2][0]*a[3][3]+a[1][0]*a[2][1]*a[3][3])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431892"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431893"}},{"Add":{"text":" outINV = [[sp.sympify(0) for i in range(4)] for j in range(4)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431960"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:431961"}},{"Add":{"text":" # CForm[FullSimplify[Inverse[A]*Det[A]]] >>> t.txt","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:432016"}},{"Add":{"text":" # cat t.txt | sed \"s/,/\\n/g;s/List(//g;s/))/)/g;s/)//g;s/(//g\"|grep -v ^$|sed \"s/ //g;s/\$[0-3]\$/[\\1]/g\"| awk '{line[NR]=$0}END{count=1;for(i=0;i<4;i++) { for(j=0;j<4;j++) { printf \"outINV[%d][%d] = %s\\n\", i,j,line[count];count++; }}}'","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:432257"}},{"Add":{"text":" outINV[0][0] = -a[1][3]*a[2][2]*a[3][1]+a[1][2]*a[2][3]*a[3][1]+a[1][3]*a[2][1]*a[3][2]-a[1][1]*a[2][3]*a[3][2]-a[1][2]*a[2][1]*a[3][3]+a[1][1]*a[2][2]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:432421"}},{"Add":{"text":" outINV[0][1] = a[0][3]*a[2][2]*a[3][1]-a[0][2]*a[2][3]*a[3][1]-a[0][3]*a[2][1]*a[3][2]+a[0][1]*a[2][3]*a[3][2]+a[0][2]*a[2][1]*a[3][3]-a[0][1]*a[2][2]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:432585"}},{"Add":{"text":" outINV[0][2] = -a[0][3]*a[1][2]*a[3][1]+a[0][2]*a[1][3]*a[3][1]+a[0][3]*a[1][1]*a[3][2]-a[0][1]*a[1][3]*a[3][2]-a[0][2]*a[1][1]*a[3][3]+a[0][1]*a[1][2]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:432749"}},{"Add":{"text":" outINV[0][3] = a[0][3]*a[1][2]*a[2][1]-a[0][2]*a[1][3]*a[2][1]-a[0][3]*a[1][1]*a[2][2]+a[0][1]*a[1][3]*a[2][2]+a[0][2]*a[1][1]*a[2][3]-a[0][1]*a[1][2]*a[2][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:432913"}},{"Add":{"text":" outINV[1][0] = a[1][3]*a[2][2]*a[3][0]-a[1][2]*a[2][3]*a[3][0]-a[1][3]*a[2][0]*a[3][2]+a[1][0]*a[2][3]*a[3][2]+a[1][2]*a[2][0]*a[3][3]-a[1][0]*a[2][2]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:433077"}},{"Add":{"text":" outINV[1][1] = -a[0][3]*a[2][2]*a[3][0]+a[0][2]*a[2][3]*a[3][0]+a[0][3]*a[2][0]*a[3][2]-a[0][0]*a[2][3]*a[3][2]-a[0][2]*a[2][0]*a[3][3]+a[0][0]*a[2][2]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:433241"}},{"Add":{"text":" outINV[1][2] = a[0][3]*a[1][2]*a[3][0]-a[0][2]*a[1][3]*a[3][0]-a[0][3]*a[1][0]*a[3][2]+a[0][0]*a[1][3]*a[3][2]+a[0][2]*a[1][0]*a[3][3]-a[0][0]*a[1][2]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:433405"}},{"Add":{"text":" outINV[1][3] = -a[0][3]*a[1][2]*a[2][0]+a[0][2]*a[1][3]*a[2][0]+a[0][3]*a[1][0]*a[2][2]-a[0][0]*a[1][3]*a[2][2]-a[0][2]*a[1][0]*a[2][3]+a[0][0]*a[1][2]*a[2][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:433569"}},{"Add":{"text":" outINV[2][0] = -a[1][3]*a[2][1]*a[3][0]+a[1][1]*a[2][3]*a[3][0]+a[1][3]*a[2][0]*a[3][1]-a[1][0]*a[2][3]*a[3][1]-a[1][1]*a[2][0]*a[3][3]+a[1][0]*a[2][1]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:433733"}},{"Add":{"text":" outINV[2][1] = a[0][3]*a[2][1]*a[3][0]-a[0][1]*a[2][3]*a[3][0]-a[0][3]*a[2][0]*a[3][1]+a[0][0]*a[2][3]*a[3][1]+a[0][1]*a[2][0]*a[3][3]-a[0][0]*a[2][1]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:433897"}},{"Add":{"text":" outINV[2][2] = -a[0][3]*a[1][1]*a[3][0]+a[0][1]*a[1][3]*a[3][0]+a[0][3]*a[1][0]*a[3][1]-a[0][0]*a[1][3]*a[3][1]-a[0][1]*a[1][0]*a[3][3]+a[0][0]*a[1][1]*a[3][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434061"}},{"Add":{"text":" outINV[2][3] = a[0][3]*a[1][1]*a[2][0]-a[0][1]*a[1][3]*a[2][0]-a[0][3]*a[1][0]*a[2][1]+a[0][0]*a[1][3]*a[2][1]+a[0][1]*a[1][0]*a[2][3]-a[0][0]*a[1][1]*a[2][3]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434225"}},{"Add":{"text":" outINV[3][0] = a[1][2]*a[2][1]*a[3][0]-a[1][1]*a[2][2]*a[3][0]-a[1][2]*a[2][0]*a[3][1]+a[1][0]*a[2][2]*a[3][1]+a[1][1]*a[2][0]*a[3][2]-a[1][0]*a[2][1]*a[3][2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434389"}},{"Add":{"text":" outINV[3][1] = -a[0][2]*a[2][1]*a[3][0]+a[0][1]*a[2][2]*a[3][0]+a[0][2]*a[2][0]*a[3][1]-a[0][0]*a[2][2]*a[3][1]-a[0][1]*a[2][0]*a[3][2]+a[0][0]*a[2][1]*a[3][2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434553"}},{"Add":{"text":" outINV[3][2] = a[0][2]*a[1][1]*a[3][0]-a[0][1]*a[1][2]*a[3][0]-a[0][2]*a[1][0]*a[3][1]+a[0][0]*a[1][2]*a[3][1]+a[0][1]*a[1][0]*a[3][2]-a[0][0]*a[1][1]*a[3][2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434717"}},{"Add":{"text":" outINV[3][3] = -a[0][2]*a[1][1]*a[2][0]+a[0][1]*a[1][2]*a[2][0]+a[0][2]*a[1][0]*a[2][1]-a[0][0]*a[1][2]*a[2][1]-a[0][1]*a[1][0]*a[2][2]+a[0][0]*a[1][1]*a[2][2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434881"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434882"}},{"Add":{"text":" for mu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434906"}},{"Add":{"text":" for nu in range(4):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434934"}},{"Add":{"text":" outINV[mu][nu] /= outDET","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434971"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434972"}},{"Add":{"text":" return outINV, outDET","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:434998"}}]}},{"FileAdd":{"meta":{"basename":"latex_nrpy_style.tplx","metadata":420},"path":"BaikalX/doc/nrpytutorial/latex_nrpy_style.tplx","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"% Based on http://nbviewer.jupyter.org/github/ipython/nbconvert-examples/blob/master/citations/Tutorial.ipynb , authored by Brian E. Granger","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435164"}},{"Add":{"text":"((*- extends 'article.tplx' -*))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435197"}},{"Add":{"text":"((* block docclass *))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435220"}},{"Add":{"text":" % Declare the document class","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435253"}},{"Add":{"text":" \\documentclass[landscape,letterpaper,10pt,english]{article}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435317"}},{"Add":{"text":"((* endblock docclass *))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435343"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435344"}},{"Add":{"text":"% ((* block Xauthor *))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435368"}},{"Add":{"text":"% \\author{Zachariah Etienne}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435397"}},{"Add":{"text":"% ((* endblock Xauthor *))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435424"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435425"}},{"Add":{"text":"% ((* block Xbibliography *))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435455"}},{"Add":{"text":"% \\bibliographystyle{unsrt}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435483"}},{"Add":{"text":"% \\bibliography{ipython}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435508"}},{"Add":{"text":"% ((* endblock Xbibliography *))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435541"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435542"}},{"Add":{"text":"((* block commands *))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435565"}},{"Add":{"text":"% Start the section counter at -1, so the Table of Contents is Section 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435638"}},{"Add":{"text":" \\setcounter{section}{-2}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435666"}},{"Add":{"text":"% Prevent overflowing lines due to hard-to-break entities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435724"}},{"Add":{"text":" \\sloppy ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435737"}},{"Add":{"text":" % Setup hyperref package","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435766"}},{"Add":{"text":" \\hypersetup{","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435783"}},{"Add":{"text":" breaklinks=true, % so long urls are correctly broken across lines","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435856"}},{"Add":{"text":" colorlinks=true,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435879"}},{"Add":{"text":" urlcolor=urlcolor,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435904"}},{"Add":{"text":" linkcolor=linkcolor,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435931"}},{"Add":{"text":" citecolor=citecolor,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435958"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435966"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:435973"}},{"Add":{"text":" % Slightly bigger margins than the latex defaults","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436027"}},{"Add":{"text":" \\geometry{verbose,tmargin=0.5in,bmargin=0.5in,lmargin=0.5in,rmargin=0.5in}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436106"}},{"Add":{"text":"((* endblock commands *))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436132"}}]}},{"FileAdd":{"meta":{"basename":"loop.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/loop.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# This module contains infrastructure for generating","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436197"}},{"Add":{"text":"# C-code loops of arbitrary dimension","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436237"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436238"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436269"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436312"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436313"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436411"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436412"}},{"Add":{"text":"# loop1D() is just a special case of loop(), and in fact is called by loop().","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436490"}},{"Add":{"text":"# For documentation on the inputs, see loop()'s documentation below.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436561"}},{"Add":{"text":"def loop1D(idxvar=\"i0\",lower=\"0\",upper=\"Nx0\",incr=\"1\",OpenMPpragma=\"#pragma omp parallel for\",tabprefix=\"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436670"}},{"Add":{"text":" if not (isinstance(idxvar, str) and isinstance(lower, str) and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436737"}},{"Add":{"text":" isinstance(upper, str) and isinstance(incr, str) and isinstance(OpenMPpragma, str)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436834"}},{"Add":{"text":" print(\"Error: all inputs to loop1D() must be STRINGS, and to loop() must be LISTS OF STRINGS\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436937"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436957"}},{"Add":{"text":" OMPheader = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:436976"}},{"Add":{"text":" if OpenMPpragma != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437003"}},{"Add":{"text":" OMPheader = OpenMPpragma + \"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437043"}},{"Add":{"text":" incrstr = \"++\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437062"}},{"Add":{"text":" if incr != \"1\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437082"}},{"Add":{"text":" incrstr = \"+=\"+incr","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437110"}},{"Add":{"text":" loopbody = tabprefix+\"for(int \"+idxvar+\"=\"+lower+\"; \"+idxvar+\"<\"+upper+\"; \"+idxvar+incrstr+\")\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437209"}},{"Add":{"text":" return OMPheader+loopbody+\" {\\n\", tabprefix+\"} // END LOOP: \"+loopbody.replace(tabprefix,\"\")+\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437311"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437312"}},{"Add":{"text":"# loop() creates a C code loop, taking as input:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437361"}},{"Add":{"text":"# idxvar (string or list of strings): the index variable name or list of names.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437444"}},{"Add":{"text":"# In the case that idxvar is a list of N strings, we adopt the formulation:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437527"}},{"Add":{"text":"# idxvar[0]=outermost loop variable","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437574"}},{"Add":{"text":"# idxvar[N-1]=innermost loop variable","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437623"}},{"Add":{"text":"# lower (string or list of strings): lower loop index of idxvar or idxvar[i].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437704"}},{"Add":{"text":"# See definition of \"idxvar\" if lower is a list of strings. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437773"}},{"Add":{"text":"# idxvar[] must have the same length as idxvar.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437829"}},{"Add":{"text":"# upper (string or list of strings): Defined similarly to \"lower\", except","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437906"}},{"Add":{"text":"# this refers to the *upper* loop index of idxvar or idxvar[i].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:437978"}},{"Add":{"text":"# incr (string or list of strings): Defined similarly to \"lower\", except","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438055"}},{"Add":{"text":"# this refers to the loop increment of idxvar or idxvar[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438122"}},{"Add":{"text":"# (incr[i] = 1 -> idxvar++)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438158"}},{"Add":{"text":"# OpenMPpragma (string or list of strings): Defined similarly to \"lower\", except","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438242"}},{"Add":{"text":"# this refers to the OpenMP pragma corresponding to idxvar or idxvar[i].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438323"}},{"Add":{"text":"# tabprefix (optional; string): Sets the tab stop for the C code.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438392"}},{"Add":{"text":"# loopguts (optional; string): The loop interior.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438445"}},{"Add":{"text":"#","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438447"}},{"Add":{"text":"# Example: loop([\"i0\",\"i1\"],[\"0\",\"5\"],[\"N\",\"N-5\"],[\"1\",\"5\"],[\"#pragma omp parallel for\",\"\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438540"}},{"Add":{"text":"# \"double a=-2;\\n gf[IDX3(GF,i0,i1)]=-2*a;\\n\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438602"}},{"Add":{"text":"# Output:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438612"}},{"Add":{"text":"# #pragma omp parallel for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:438639"}},{"Add":{"text":"# for(int i0=0;i0= 2):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:446692"}},{"Add":{"text":" # When not in an interactive mode, the NRPy::MainModule parameter must be set,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:446775"}},{"Add":{"text":" # either in the param file (preferred!) or as a command line argument.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:446852"}},{"Add":{"text":" with open(sys.argv[1], \"r\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:446893"}},{"Add":{"text":" for line in file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:446919"}},{"Add":{"text":" par.set_paramsvals_value(line, sys.argv[1], FindMainModuleMode=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447000"}},{"Add":{"text":" # Search for NRPy::MainModule in the command line arguments","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447064"}},{"Add":{"text":" for i in range(2,len(sys.argv)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447101"}},{"Add":{"text":" par.set_paramsvals_value(sys.argv[i], \"\", FindMainModuleMode=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447176"}},{"Add":{"text":" # The NRPy::MainModule parameter has already been set,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447235"}},{"Add":{"text":" # and parse_param_string__set__params_and_paramsvars()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447296"}},{"Add":{"text":" # will error out with a \"Critical Error\" if it has not been set.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447367"}},{"Add":{"text":" idx = par.get_params_idx(par.glb_param(\"ignoretype\", \"NRPy\", \"MainModule\", \"ignoredefval\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447463"}},{"Add":{"text":" MainModule = par.glb_paramsvals_list[idx]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447509"}},{"Add":{"text":" if MainModule == \"NODEFAULT\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447543"}},{"Add":{"text":" print(\"Error: Could not find NRPy::MainModule defined in the parameter file \\\"\"+sys.argv[1]+\"\\\" or on the command line!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447673"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447693"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447694"}},{"Add":{"text":" # Next initialize all of MainModule's parameters.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447748"}},{"Add":{"text":" # Note that MainModule must also initialize parameters for modules","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447819"}},{"Add":{"text":" # on which it depends, except outputC (which NRPy+ loads by default).","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:447893"}},{"Add":{"text":" # https://stackoverflow.com/questions/10675054/how-to-import-a-module-in-python-with-importlib-import-module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448006"}},{"Add":{"text":" importlib.import_module(MainModule+\".\"+MainModule)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448061"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448062"}},{"Add":{"text":" # Next overwrite default parameters with values specified in the parameter file.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448147"}},{"Add":{"text":" with open(sys.argv[1], \"r\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448188"}},{"Add":{"text":" for line in file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448214"}},{"Add":{"text":" par.set_paramsvals_value(line, sys.argv[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448270"}},{"Add":{"text":" # Next overwrite default parameters and values specified in the parameter file with command-line parameter assignments.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448394"}},{"Add":{"text":" for i in range(2,len(sys.argv)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448431"}},{"Add":{"text":" par.set_paramsvals_value(sys.argv[i], \"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448481"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448482"}},{"Add":{"text":"# Next load the MainModule, if it hasn't been loaded already.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448544"}},{"Add":{"text":"#importlib.import_module(MainModule+\".\"+MainModule)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448596"}},{"Add":{"text":"getattr(importlib.import_module(MainModule+\".\"+MainModule), MainModule)()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448670"}},{"Add":{"text":"# Initialize parameters for the core outputC module,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448723"}},{"Add":{"text":"# which is the default MainModule.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448758"}},{"Add":{"text":"# Call function initparams() from outputC module (in outputC.py):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448824"}},{"Add":{"text":"# getattr(importlib.import_module(MainModule), 'initparams')()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448887"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448888"}},{"Add":{"text":"# Step 3b (temporary): Set a SymPy expression to test processing","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448953"}},{"Add":{"text":"import sympy as sp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448972"}},{"Add":{"text":"#from outputC import *","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:448995"}},{"Add":{"text":"#getattr(importlib.import_module(\"outputC\"),'outputC')([sympify(\"3*a*b**4+c*sin(a*b**4)\"),sympify(\"6*a*b**4\")],[\"output1\",\"output2\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449129"}},{"Add":{"text":"#getattr(importlib.import_module(\"outputC\"),'outputC')(sp.sympify(\"3*a*b**4+2*c*sin(a*b**4)\"),\"output1\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449234"}}]}},{"FileAdd":{"meta":{"basename":"outputC.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/outputC.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# As documented in the NRPy+ tutorial module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449294"}},{"Add":{"text":"# Tutorial-Coutput__Parameter_Interface.ipynb","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449342"}},{"Add":{"text":"# this core NRPy+ module is used for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449381"}},{"Add":{"text":"# generating C code and functions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449418"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449419"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449450"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449493"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449494"}},{"Add":{"text":"import loop as lp # NRPy+: C code loop interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449571"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449646"}},{"Add":{"text":"from SIMD import expr_convert_to_SIMD_intrins # NRPy+: SymPy expression => SIMD intrinsics interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449747"}},{"Add":{"text":"import sympy as sp # Import SymPy","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449808"}},{"Add":{"text":"import re, sys # Standard Python: regular expressions & OS-independent system functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:449927"}},{"Add":{"text":"from collections import namedtuple # Standard Python: Enable namedtuple data type","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450020"}},{"Add":{"text":"lhrh = namedtuple('lhrh', 'lhs rhs')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450057"}},{"Add":{"text":"outCparams = namedtuple('outCparams', 'preindent includebraces declareoutputvars outCfileaccess outCverbose CSE_enable CSE_varprefix SIMD_enable SIMD_const_suffix SIMD_debug enable_TYPE')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450245"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450246"}},{"Add":{"text":"# Sometimes SymPy has problems evaluating complicated expressions involving absolute","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450331"}},{"Add":{"text":"# values, resulting in hangs. So instead of using sp.Abs(), if we instead use","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450412"}},{"Add":{"text":"# nrpyAbs, we can sidestep the internal SymPy evaluation and force the C","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450488"}},{"Add":{"text":"# codegen to output our desired fabs().","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450531"}},{"Add":{"text":"nrpyAbs = sp.Function('nrpyAbs')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450564"}},{"Add":{"text":"custom_functions_for_SymPy_ccode = {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450601"}},{"Add":{"text":" \"nrpyAbs\": \"fabs\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450624"}},{"Add":{"text":" 'Pow': [(lambda b, e: e == 0.5, lambda b, e: 'sqrt(%s)' % (b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450696"}},{"Add":{"text":" (lambda b, e: e ==-0.5, lambda b, e: '(1.0/sqrt(%s))' % (b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450774"}},{"Add":{"text":" (lambda b, e: e == sp.S.One/3, lambda b, e: 'cbrt(%s)' % (b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450849"}},{"Add":{"text":" (lambda b, e: e ==-sp.S.One/3, lambda b, e: '(1.0/cbrt(%s))' % (b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:450930"}},{"Add":{"text":" (lambda b, e: e == 2, lambda b, e: '((%s)*(%s))' % (b,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451016"}},{"Add":{"text":" (lambda b, e: e == 3, lambda b, e: '((%s)*(%s)*(%s))' % (b,b,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451104"}},{"Add":{"text":" (lambda b, e: e == 4, lambda b, e: '((%s)*(%s)*(%s)*(%s))' % (b,b,b,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451194"}},{"Add":{"text":" (lambda b, e: e == 5, lambda b, e: '((%s)*(%s)*(%s)*(%s)*(%s))' % (b,b,b,b,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451286"}},{"Add":{"text":" (lambda b, e: e ==-1, lambda b, e: '(1.0/(%s))' % (b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451376"}},{"Add":{"text":" (lambda b, e: e ==-2, lambda b, e: '(1.0/((%s)*(%s)))' % (b,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451468"}},{"Add":{"text":" (lambda b, e: e ==-3, lambda b, e: '(1.0/((%s)*(%s)*(%s)))' % (b,b,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451562"}},{"Add":{"text":" (lambda b, e: e ==-4, lambda b, e: '(1.0/((%s)*(%s)*(%s)*(%s)))' % (b,b,b,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451658"}},{"Add":{"text":" (lambda b, e: e ==-5, lambda b, e: '(1.0/((%s)*(%s)*(%s)*(%s)*(%s)))' % (b,b,b,b,b)),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451756"}},{"Add":{"text":" (lambda b, e: e !=-5, 'pow')]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451798"}},{"Add":{"text":"## (lambda b, e: e != 2, 'pow')]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451834"}},{"Add":{"text":"}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451836"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451837"}},{"Add":{"text":"# Parameter initialization is called once, within nrpy.py.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:451896"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", __name__, \"PRECISION\", \"double\")) # __name__ = \"outputC\", this module's name.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452017"}},{"Add":{"text":"# par.initialize_param(par.glb_param(\"bool\", thismodule, \"SIMD_enable\", False))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452097"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452098"}},{"Add":{"text":"# super fast 'uniq' function:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452128"}},{"Add":{"text":"# f8() function from https://www.peterbe.com/plog/uniqifiers-benchmark","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452199"}},{"Add":{"text":"def superfast_uniq(seq): # Author: Dave Kirby","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452245"}},{"Add":{"text":" # Order preserving","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452268"}},{"Add":{"text":" seen = set()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452285"}},{"Add":{"text":" return [x for x in seq if x not in seen and not seen.add(x)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452350"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452351"}},{"Add":{"text":"def check_if_string__error_if_not(allegedstring,stringdesc):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452412"}},{"Add":{"text":" import sys","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452427"}},{"Add":{"text":" if sys.version_info[0] == 3:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452460"}},{"Add":{"text":" string_types = str","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452487"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452497"}},{"Add":{"text":" string_types = basestring","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452531"}},{"Add":{"text":" if not isinstance(allegedstring, string_types):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452583"}},{"Add":{"text":" print(\"ERROR: \"+str(stringdesc)+\" ==\"+str(allegedstring)+\" not a string!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452666"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452686"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452687"}},{"Add":{"text":"def ccode_postproc(string):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452715"}},{"Add":{"text":" PRECISION = par.parval_from_str(\"PRECISION\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452764"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452765"}},{"Add":{"text":" # In the C math library, e.g., pow(x,y) assumes x and y are doubles, and returns a double.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452860"}},{"Add":{"text":" # If x and y are floats, then for consistency should use powf(x,y) instead.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:452941"}},{"Add":{"text":" # Similarly, in the case of x and y being long doubles, should use powl(x,y) for consistency.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453040"}},{"Add":{"text":" # First we find the appropriate suffix depending on the desired precision:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453119"}},{"Add":{"text":" cmathsuffix = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453140"}},{"Add":{"text":" if PRECISION == \"double\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453170"}},{"Add":{"text":" pass","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453183"}},{"Add":{"text":" elif PRECISION == \"long double\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453220"}},{"Add":{"text":" cmathsuffix = \"l\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453246"}},{"Add":{"text":" elif PRECISION == \"float\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453277"}},{"Add":{"text":" cmathsuffix = \"f\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453303"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453313"}},{"Add":{"text":" print(\"Error: \"+__name__+\"::PRECISION = \\\"\"+ PRECISION +\"\\\" not supported\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453397"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453417"}},{"Add":{"text":" # ... then we append the above suffix to standard C math library functions:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453497"}},{"Add":{"text":" for func in ['pow', 'sqrt', 'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'exp', 'log', 'fabs']:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453597"}},{"Add":{"text":" string2 = re.sub(func+r'\\(', func + cmathsuffix+\"(\", string); string = string2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453684"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453685"}},{"Add":{"text":" # Finally, SymPy prefers to output Rationals as long-double fractions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453760"}},{"Add":{"text":" # E.g., Rational(1,3) is output as 1.0L/3.0L.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453811"}},{"Add":{"text":" # The Intel compiler vectorizer complains miserably about this,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453880"}},{"Add":{"text":" # and strictly speaking it is useless when we're in double precision.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:453955"}},{"Add":{"text":" # So here we get rid of the \"L\" suffix on floating point numbers:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454025"}},{"Add":{"text":" if PRECISION!=\"long double\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454058"}},{"Add":{"text":" string2 = re.sub(r'([0-9.]+)L/([0-9.]+)L', '(\\\\1 / \\\\2)', string); string = string2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454150"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454151"}},{"Add":{"text":" return string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454169"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454170"}},{"Add":{"text":"def parse_outCparams_string(params):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454207"}},{"Add":{"text":" # Default values:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454229"}},{"Add":{"text":" preindent = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454248"}},{"Add":{"text":" includebraces = \"True\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454275"}},{"Add":{"text":" declareoutputvars = \"False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454307"}},{"Add":{"text":" outCfileaccess = \"w\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454332"}},{"Add":{"text":" outCverbose = \"True\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454357"}},{"Add":{"text":" CSE_enable = \"True\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454381"}},{"Add":{"text":" CSE_varprefix = \"tmp\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454407"}},{"Add":{"text":" SIMD_enable = \"False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454433"}},{"Add":{"text":" SIMD_const_suffix = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454460"}},{"Add":{"text":" SIMD_debug = \"False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454485"}},{"Add":{"text":" enable_TYPE = \"True\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454510"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454511"}},{"Add":{"text":" if params != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454532"}},{"Add":{"text":" params2 = re.sub(\"^,\",\"\",params)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454573"}},{"Add":{"text":" params = params2.strip()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454606"}},{"Add":{"text":" splitstring = re.split(\"=|,\", params)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454652"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454653"}},{"Add":{"text":" if len(splitstring) % 2 != 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454691"}},{"Add":{"text":" print(\"outputC: Invalid params string: \"+params)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454752"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454776"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454777"}},{"Add":{"text":" parnm = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454796"}},{"Add":{"text":" value = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454815"}},{"Add":{"text":" for i in range(int(len(splitstring)/2)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454864"}},{"Add":{"text":" parnm.append(splitstring[2*i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454907"}},{"Add":{"text":" value.append(splitstring[2*i+1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454952"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454953"}},{"Add":{"text":" for i in range(len(parnm)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:454989"}},{"Add":{"text":" # Clean the string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455020"}},{"Add":{"text":" if value[i] == \"true\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455055"}},{"Add":{"text":" value[i] = \"True\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455089"}},{"Add":{"text":" if value[i] == \"false\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455125"}},{"Add":{"text":" value[i] = \"False\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455160"}},{"Add":{"text":" if parnm[i] == \"preindent\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455200"}},{"Add":{"text":" if not value[i].isdigit():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455243"}},{"Add":{"text":" print(\"Error: preindent must be set to an integer (corresponding to the number of tab stops). \")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455360"}},{"Add":{"text":" print(value[i]+\" is not an integer.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455418"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455450"}},{"Add":{"text":" preindent = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455481"}},{"Add":{"text":" for i in range(int(value[i])):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455528"}},{"Add":{"text":" preindent += \" \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455567"}},{"Add":{"text":" elif parnm[i] == \"includebraces\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455613"}},{"Add":{"text":" includebraces = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455654"}},{"Add":{"text":" elif parnm[i] == \"declareoutputvars\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455704"}},{"Add":{"text":" declareoutputvars = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455749"}},{"Add":{"text":" elif parnm[i] == \"outCfileaccess\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455796"}},{"Add":{"text":" outCfileaccess = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455838"}},{"Add":{"text":" elif parnm[i] == \"outCverbose\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455882"}},{"Add":{"text":" outCverbose = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455921"}},{"Add":{"text":" elif parnm[i] == \"CSE_enable\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:455964"}},{"Add":{"text":" CSE_enable = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456002"}},{"Add":{"text":" elif parnm[i] == \"CSE_varprefix\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456048"}},{"Add":{"text":" CSE_varprefix = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456089"}},{"Add":{"text":" elif parnm[i] == \"SIMD_enable\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456133"}},{"Add":{"text":" SIMD_enable = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456172"}},{"Add":{"text":" elif parnm[i] == \"SIMD_const_suffix\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456222"}},{"Add":{"text":" SIMD_const_suffix = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456267"}},{"Add":{"text":" elif parnm[i] == \"SIMD_debug\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456310"}},{"Add":{"text":" SIMD_debug = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456348"}},{"Add":{"text":" elif parnm[i] == \"enable_TYPE\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456392"}},{"Add":{"text":" enable_TYPE = value[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456431"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456449"}},{"Add":{"text":" print(\"Error: outputC parameter name \\\"\"+parnm[i]+\"\\\" unrecognized.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456535"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456563"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456564"}},{"Add":{"text":" return outCparams(preindent,includebraces,declareoutputvars,outCfileaccess,outCverbose,CSE_enable,CSE_varprefix,SIMD_enable,SIMD_const_suffix,SIMD_debug,enable_TYPE)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456734"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456735"}},{"Add":{"text":"import sympy as sp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456754"}},{"Add":{"text":"# Input: sympyexpr = a single SymPy expression *or* a list of SymPy expressions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456834"}},{"Add":{"text":"# output_varname_str = a single output variable name *or* a list of output","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456916"}},{"Add":{"text":"# variable names, one per sympyexpr.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:456981"}},{"Add":{"text":"# Output: C code, as a string.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457012"}},{"Add":{"text":"def outputC(sympyexpr, output_varname_str, filename = \"stdout\", params = \"\", prestring = \"\", poststring = \"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457123"}},{"Add":{"text":" outCparams = parse_outCparams_string(params)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457172"}},{"Add":{"text":" preindent = outCparams.preindent","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457209"}},{"Add":{"text":" TYPE = par.parval_from_str(\"PRECISION\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457253"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457254"}},{"Add":{"text":" if outCparams.enable_TYPE == \"False\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457296"}},{"Add":{"text":" TYPE = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457314"}},{"Add":{"text":" ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457319"}},{"Add":{"text":" # Step 0: Initialize","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457344"}},{"Add":{"text":" # commentblock: comment block containing the input SymPy string,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457414"}},{"Add":{"text":" # set only if outCverbose==True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457465"}},{"Add":{"text":" # outstring: the output C code string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457511"}},{"Add":{"text":" commentblock = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457533"}},{"Add":{"text":" outstring = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457552"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457553"}},{"Add":{"text":" # Step 1: If SIMD_enable==True, then check if TYPE==\"double\". If not, error out.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457638"}},{"Add":{"text":" # Otherwise set TYPE=\"REAL_SIMD_ARRAY\", which should be #define'd","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457716"}},{"Add":{"text":" # within the C code. For example for AVX-256, the C code should have","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457797"}},{"Add":{"text":" # #define REAL_SIMD_ARRAY __m256d","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457843"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457884"}},{"Add":{"text":" if not (TYPE == \"double\" or TYPE == \"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:457933"}},{"Add":{"text":" print(\"SIMD output currently only supports double precision or typeless. Sorry!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458027"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458051"}},{"Add":{"text":" if TYPE == \"double\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458080"}},{"Add":{"text":" TYPE = \"REAL_SIMD_ARRAY\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458117"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458131"}},{"Add":{"text":" TYPE = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458153"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458154"}},{"Add":{"text":" # Step 2a: Apply sanity checks when either sympyexpr or","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458214"}},{"Add":{"text":" # output_varname_str is a list.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458259"}},{"Add":{"text":" if type(output_varname_str) is list and type(sympyexpr) is not list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458332"}},{"Add":{"text":" print(\"Error: Provided a list of output variable names, but only one SymPy expression.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458429"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458449"}},{"Add":{"text":" if type(sympyexpr) is list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458481"}},{"Add":{"text":" if type(output_varname_str) is not list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458530"}},{"Add":{"text":" print(\"Error: Provided a list of SymPy expressions, but no corresponding list of output variable names\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458647"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458671"}},{"Add":{"text":" elif len(output_varname_str) != len(sympyexpr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458727"}},{"Add":{"text":" print(\"Error: Length of SymPy expressions list (\"+str(len(sympyexpr))+","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458810"}},{"Add":{"text":" \") != Length of corresponding output variable name list (\"+str(len(output_varname_str))+\")\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458921"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:458945"}},{"Add":{"text":" # Step 2b: If sympyexpr and output_varname_str are not lists,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459011"}},{"Add":{"text":" # convert them to lists of one element each, to","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459072"}},{"Add":{"text":" # simplify proceeding code.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459113"}},{"Add":{"text":" if type(output_varname_str) is not list and type(sympyexpr) is not list:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459190"}},{"Add":{"text":" output_varname_strtmp = [output_varname_str]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459243"}},{"Add":{"text":" output_varname_str = output_varname_strtmp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459294"}},{"Add":{"text":" sympyexprtmp = [sympyexpr]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459329"}},{"Add":{"text":" sympyexpr = sympyexprtmp","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459362"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459363"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459364"}},{"Add":{"text":" # Step 3: If outCparams.verbose = True, then output the original SymPy","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459439"}},{"Add":{"text":" # expression(s) in code comments prior to actual C code","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459507"}},{"Add":{"text":" if outCparams.outCverbose == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459548"}},{"Add":{"text":" commentblock += preindent+\"/*\\n\"+preindent+\" * Original SymPy expression\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459631"}},{"Add":{"text":" if len(output_varname_str)>1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459669"}},{"Add":{"text":" commentblock += \"s\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459701"}},{"Add":{"text":" commentblock += \":\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459731"}},{"Add":{"text":" for i in range(len(output_varname_str)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459780"}},{"Add":{"text":" if i==0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459801"}},{"Add":{"text":" if len(output_varname_str)!=1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459848"}},{"Add":{"text":" commentblock += preindent+\" * \\\"[\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459904"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459926"}},{"Add":{"text":" commentblock += preindent+\" * \\\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459981"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:459999"}},{"Add":{"text":" commentblock += preindent+\" * \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460050"}},{"Add":{"text":" commentblock += output_varname_str[i] + \" = \" + str(sympyexpr[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460128"}},{"Add":{"text":" if i==len(output_varname_str)-1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460173"}},{"Add":{"text":" if len(output_varname_str)!=1:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460220"}},{"Add":{"text":" commentblock += \"]\\\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460264"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460286"}},{"Add":{"text":" commentblock += \"\\\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460329"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460347"}},{"Add":{"text":" commentblock += \",\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460385"}},{"Add":{"text":" commentblock += preindent+\" */\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460427"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460428"}},{"Add":{"text":" # Step 4: Add proper indentation of C code:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460476"}},{"Add":{"text":" if outCparams.includebraces == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460519"}},{"Add":{"text":" indent = outCparams.preindent+\" \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460563"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460573"}},{"Add":{"text":" indent = outCparams.preindent+\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460614"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460615"}},{"Add":{"text":" # Step 5: Should the output variable, e.g., outvar, be declared?","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460684"}},{"Add":{"text":" # If so, start output line with e.g., \"double outvar \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460751"}},{"Add":{"text":" outtypestring = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460774"}},{"Add":{"text":" if outCparams.declareoutputvars == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460821"}},{"Add":{"text":" outtypestring = outCparams.preindent+indent+TYPE + \" \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460884"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460894"}},{"Add":{"text":" outtypestring = outCparams.preindent+indent","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460946"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:460947"}},{"Add":{"text":" # Step 6a: If common subexpression elimination (CSE) disabled, then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461019"}},{"Add":{"text":" # just output the SymPy string in the most boring way,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461086"}},{"Add":{"text":" # nearly consistent with SymPy's ccode() function,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461149"}},{"Add":{"text":" # though with support for float & long double types","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461213"}},{"Add":{"text":" # as well.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461236"}},{"Add":{"text":" SIMD_decls = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461256"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461257"}},{"Add":{"text":" if outCparams.CSE_enable == \"False\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461298"}},{"Add":{"text":" # If CSE is disabled:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461328"}},{"Add":{"text":" for i in range(len(sympyexpr)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461368"}},{"Add":{"text":" outstring += outtypestring + ccode_postproc(sp.ccode(sympyexpr[i], output_varname_str[i],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461470"}},{"Add":{"text":" user_functions=custom_functions_for_SymPy_ccode))+\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461590"}},{"Add":{"text":" # Step 6b: If CSE enabled, then perform CSE using SymPy and then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461659"}},{"Add":{"text":" # resulting C code.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461692"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461702"}},{"Add":{"text":" # If CSE is enabled:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461731"}},{"Add":{"text":" SIMD_const_varnms = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461762"}},{"Add":{"text":" SIMD_const_values = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461793"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461794"}},{"Add":{"text":" CSE_results = sp.cse(sympyexpr, sp.numbered_symbols(outCparams.CSE_varprefix), order='canonical')","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461900"}},{"Add":{"text":" for commonsubexpression in CSE_results[0]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:461951"}},{"Add":{"text":" FULLTYPESTRING = \"const \" + TYPE + \" \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462002"}},{"Add":{"text":" if outCparams.enable_TYPE == \"False\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462052"}},{"Add":{"text":" FULLTYPESTRING = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462088"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462089"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462138"}},{"Add":{"text":" outstring += outCparams.preindent + indent + FULLTYPESTRING + str(commonsubexpression[0]) + \" = \" + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462256"}},{"Add":{"text":" str(expr_convert_to_SIMD_intrins(commonsubexpression[1],SIMD_const_varnms,SIMD_const_values,outCparams.SIMD_const_suffix,outCparams.SIMD_debug)) + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462438"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462456"}},{"Add":{"text":" outstring += outCparams.preindent+indent+FULLTYPESTRING+ccode_postproc(sp.ccode(commonsubexpression[1],commonsubexpression[0],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462599"}},{"Add":{"text":" user_functions=custom_functions_for_SymPy_ccode))+\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462750"}},{"Add":{"text":" for i,result in enumerate(CSE_results[1]):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462801"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462850"}},{"Add":{"text":" outstring += outtypestring + output_varname_str[i] + \" = \" + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:462929"}},{"Add":{"text":" str(expr_convert_to_SIMD_intrins(result,SIMD_const_varnms,SIMD_const_values,outCparams.SIMD_const_suffix,outCparams.SIMD_debug)) + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463095"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463113"}},{"Add":{"text":" outstring += outtypestring+ccode_postproc(sp.ccode(result,output_varname_str[i],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463210"}},{"Add":{"text":" user_functions=custom_functions_for_SymPy_ccode))+\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463332"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463333"}},{"Add":{"text":" # Step 6b.i: If SIMD_enable == True , and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463383"}},{"Add":{"text":" # there is at least one SIMD const variable, ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463448"}},{"Add":{"text":" # then declare the SIMD_const_varnms and SIMD_const_values arrays","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463533"}},{"Add":{"text":" if outCparams.SIMD_enable == \"True\" and len(SIMD_const_varnms) != 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463610"}},{"Add":{"text":" # Step 6a) Sort the list of definitions. Idea from:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463674"}},{"Add":{"text":" # https://stackoverflow.com/questions/9764298/is-it-possible-to-sort-two-listswhich-reference-each-other-in-the-exact-same-w","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463811"}},{"Add":{"text":" SIMD_const_varnms, SIMD_const_values = \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463864"}},{"Add":{"text":" (list(t) for t in zip(*sorted(zip(SIMD_const_varnms, SIMD_const_values))))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463955"}},{"Add":{"text":" # Step 6b) Remove duplicates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:463996"}},{"Add":{"text":" uniq_varnms = superfast_uniq(SIMD_const_varnms)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464056"}},{"Add":{"text":" uniq_values = superfast_uniq(SIMD_const_values)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464116"}},{"Add":{"text":" SIMD_const_varnms = uniq_varnms","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464160"}},{"Add":{"text":" SIMD_const_values = uniq_values","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464204"}},{"Add":{"text":" if len(SIMD_const_varnms) != len(SIMD_const_values):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464269"}},{"Add":{"text":" print(\"Error: SIMD constant declaration arrays SIMD_const_varnms[] and SIMD_const_values[] have inconsistent sizes!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464403"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464431"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464432"}},{"Add":{"text":" for i in range(len(SIMD_const_varnms)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464484"}},{"Add":{"text":" if outCparams.enable_TYPE == \"False\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464538"}},{"Add":{"text":" SIMD_decls += outCparams.preindent + indent + SIMD_const_varnms[i] + \" = \" + SIMD_const_values[i]+\";\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464660"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464682"}},{"Add":{"text":" SIMD_decls += outCparams.preindent + indent + \"const double \" + outCparams.CSE_varprefix + SIMD_const_varnms[i] + \" = \" + SIMD_const_values[i] + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:464853"}},{"Add":{"text":" SIMD_decls += outCparams.preindent+indent+ \"const REAL_SIMD_ARRAY \" + SIMD_const_varnms[i] + \" = ConstSIMD(\"+ outCparams.CSE_varprefix + SIMD_const_varnms[i] + \");\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465040"}},{"Add":{"text":" SIMD_decls += \"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465075"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465076"}},{"Add":{"text":" # Step 7: Construct final output string","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465120"}},{"Add":{"text":" final_Ccode_output_str = commentblock","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465162"}},{"Add":{"text":" # Step 7a: Output C code in indented curly brackets if","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465221"}},{"Add":{"text":" # outCparams.includebraces = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465268"}},{"Add":{"text":" if outCparams.includebraces == \"True\": final_Ccode_output_str += outCparams.preindent+\"{\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465364"}},{"Add":{"text":" final_Ccode_output_str += prestring + SIMD_decls + outstring + poststring","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465442"}},{"Add":{"text":" if outCparams.includebraces == \"True\": final_Ccode_output_str += outCparams.preindent+\"}\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465538"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465539"}},{"Add":{"text":" # Step 8: If filename == \"stdout\", then output","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465590"}},{"Add":{"text":" # C code to standard out (useful for copy-paste or interactive","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465665"}},{"Add":{"text":" # mode). Otherwise output to file specified in variable name.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465739"}},{"Add":{"text":" if filename == \"stdout\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465768"}},{"Add":{"text":" # Output to standard out (stdout; \"the screen\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465824"}},{"Add":{"text":" print(final_Ccode_output_str)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465862"}},{"Add":{"text":" elif filename == \"returnstring\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465899"}},{"Add":{"text":" return final_Ccode_output_str","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465937"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:465947"}},{"Add":{"text":" # Output to the file specified by the function input parameter string 'filename':","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466037"}},{"Add":{"text":" with open(filename, outCparams.outCfileaccess) as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466101"}},{"Add":{"text":" file.write(final_Ccode_output_str)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466148"}},{"Add":{"text":" successstr = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466172"}},{"Add":{"text":" if outCparams.outCfileaccess == \"a\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466217"}},{"Add":{"text":" successstr = \"Appended \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466254"}},{"Add":{"text":" elif outCparams.outCfileaccess == \"w\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466301"}},{"Add":{"text":" successstr = \"Wrote \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466335"}},{"Add":{"text":" print(successstr + \"to file \\\"\" + filename + \"\\\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466394"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466395"}},{"Add":{"text":"outC_function_prototype_dict = {}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466429"}},{"Add":{"text":"outC_function_dict = {}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466463"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466464"}},{"Add":{"text":"def Cfunction(desc=\"\",type=\"void\",name=None,params=None,preloop=\"\",body=None,loopopts=\"\",postloop=\"\",opts=\"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466575"}},{"Add":{"text":" if name == None or params == None or body == None:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466630"}},{"Add":{"text":" print(\"Cfunction() error: strings must be provided for function name, parameters, and body\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466731"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466751"}},{"Add":{"text":" func_prototype = type+\" \"+name+\"(\"+params+\")\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466801"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466802"}},{"Add":{"text":" include_Cparams_str = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466831"}},{"Add":{"text":" if not \"DisableCparameters\" in opts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466872"}},{"Add":{"text":" if \"EnableSIMD\" in loopopts:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466909"}},{"Add":{"text":" include_Cparams_str = \"#include \\\"set_Cparameters-SIMD.h\\\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466983"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:466997"}},{"Add":{"text":" include_Cparams_str = \"#include \\\"set_Cparameters.h\\\"\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467066"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467067"}},{"Add":{"text":" complete_func = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467091"}},{"Add":{"text":" if desc != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467110"}},{"Add":{"text":" complete_func = \"/*\\n\" + desc + \"\\n */\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467160"}},{"Add":{"text":" complete_func += func_prototype + \" {\\n\"+include_Cparams_str+preloop+\"\\n\"+lp.simple_loop(loopopts,body)+postloop+\"}\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467283"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467284"}},{"Add":{"text":" return func_prototype+\";\",complete_func","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467328"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467329"}},{"Add":{"text":"def add_to_Cfunction_dict(desc=\"\",type=\"void\",name=None,params=None,preloop=\"\",body=None,loopopts=\"\",postloop=\"\",opts=\"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467452"}},{"Add":{"text":" outC_function_prototype_dict[name],outC_function_dict[name] = Cfunction(desc,type,name,params,preloop,body,loopopts,postloop,opts)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467587"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467588"}},{"Add":{"text":"def outCfunction(outfile=\"\",desc=\"\",type=\"void\",name=None,params=None,preloop=\"\",body=None,loopopts=\"\",postloop=\"\",opts=\"\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467713"}},{"Add":{"text":" ignoreprototype,Cfunc = Cfunction(desc,type,name,params,preloop,body,loopopts,postloop,opts)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467810"}},{"Add":{"text":" if outfile == \"returnstring\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467844"}},{"Add":{"text":" return Cfunc","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467865"}},{"Add":{"text":" with open(outfile,\"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467901"}},{"Add":{"text":" file.write(Cfunc)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467927"}},{"Add":{"text":" print(\"Output C function \"+name+\"() to file \"+outfile)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:467990"}}]}},{"FileAdd":{"meta":{"basename":"reference_metric.py","metadata":420},"path":"BaikalX/doc/nrpytutorial/reference_metric.py","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"# reference_metric.py: Define all needed quantities","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468065"}},{"Add":{"text":"# for a reference metric. ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468096"}},{"Add":{"text":"# Given uniform (reference metric) coordinate ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468143"}},{"Add":{"text":"# (xx[0],xx[1],xx[2]), you must define:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468186"}},{"Add":{"text":"# 1) xxmin[3],xxmax[3]: Valid ranges for each","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468236"}},{"Add":{"text":"# uniform coordinate xx0,xx1,xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468275"}},{"Add":{"text":"# 2) xxSph[3]: Spherical coordinate (r,theta,phi),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468330"}},{"Add":{"text":"# in terms of uniform coordinate xx0,xx1,xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468381"}},{"Add":{"text":"# 3) xxCart[3]: Cartesian coordinate (x,y,z),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468431"}},{"Add":{"text":"# in terms of uniform coordinate xx0,xx1,xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468482"}},{"Add":{"text":"# 4) scalefactor_orthog:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468511"}},{"Add":{"text":"# orthogonal coordinate scale factor","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468554"}},{"Add":{"text":"# (positive root of diagonal reference metric ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468607"}},{"Add":{"text":"# components)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468627"}},{"Add":{"text":"# 5) Cart_to_xx[3]: Inverse of xxCart:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468670"}},{"Add":{"text":"# xx0,xx1,xx2 as functions of (x,y,z). ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468716"}},{"Add":{"text":"# In the case that there exists no closed-form","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468769"}},{"Add":{"text":"# expression, then a root finder might be needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468824"}},{"Add":{"text":"# 6) UnitVectors[3][3]: Unit vectors of reference ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468879"}},{"Add":{"text":"# metric.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468895"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468896"}},{"Add":{"text":"# Author: Zachariah B. Etienne","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468927"}},{"Add":{"text":"# zachetie **at** gmail **dot* com","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468970"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:468971"}},{"Add":{"text":"import sympy as sp # Import SymPy","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469029"}},{"Add":{"text":"from outputC import outputC,superfast_uniq,outC_function_dict,add_to_Cfunction_dict # NRPy+: Core C code output module","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469148"}},{"Add":{"text":"import NRPy_param_funcs as par # NRPy+: Parameter interface","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469220"}},{"Add":{"text":"import grid as gri # NRPy+: Functions having to do with numerical grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469316"}},{"Add":{"text":"import indexedexp as ixp # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469435"}},{"Add":{"text":"import sys # Standard Python modules for multiplatform OS-level functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469541"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469542"}},{"Add":{"text":"# Step 0a: Initialize parameters","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469575"}},{"Add":{"text":"thismodule = __name__","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469597"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"CoordSystem\", \"Spherical\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469681"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"enable_rfm_precompute\", \"False\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469771"}},{"Add":{"text":"par.initialize_param(par.glb_param(\"char\", thismodule, \"rfm_precompute_Ccode_outdir\", \"Ccode\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469867"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469868"}},{"Add":{"text":"# Step 0b: Declare global variables","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469904"}},{"Add":{"text":"xx = gri.xx","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469916"}},{"Add":{"text":"xxCart = ixp.zerorank1(DIM=4) # Must be set in terms of xx[]s","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:469978"}},{"Add":{"text":"Cart_to_xx = ixp.zerorank1(DIM=4) # Must be set in terms of xx[]s","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470044"}},{"Add":{"text":"Cartx,Carty,Cartz = sp.symbols(\"Cartx Carty Cartz\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470107"}},{"Add":{"text":"Cart = [Cartx,Carty,Cartz]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470134"}},{"Add":{"text":"xxSph = ixp.zerorank1(DIM=4) # Must be set in terms of xx[]s","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470196"}},{"Add":{"text":"scalefactor_orthog = ixp.zerorank1(DIM=4) # Must be set in terms of xx[]s","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470270"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470271"}},{"Add":{"text":"scalefactor_orthog_funcform = ixp.zerorank1(DIM=4) # Must be set in terms of generic functions of xx[]s","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470375"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470376"}},{"Add":{"text":"have_already_called_reference_metric_function = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470430"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470431"}},{"Add":{"text":"def reference_metric(SymPySimplifyExpressions=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470484"}},{"Add":{"text":" global f0_of_xx0_funcform, f1_of_xx1_funcform, f2_of_xx0_xx1_funcform, f3_of_xx0_funcform, f4_of_xx2_funcform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470598"}},{"Add":{"text":" global f0_of_xx0, f1_of_xx1, f2_of_xx0_xx1, f3_of_xx0, f4_of_xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470667"}},{"Add":{"text":" f0_of_xx0_funcform = sp.Function('f0_of_xx0_funcform')(xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470737"}},{"Add":{"text":" f1_of_xx1_funcform = sp.Function('f1_of_xx1_funcform')(xx[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470807"}},{"Add":{"text":" f2_of_xx0_xx1_funcform = sp.Function('f2_of_xx0_xx1_funcform')(xx[0], xx[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470888"}},{"Add":{"text":" f3_of_xx0_funcform = sp.Function('f3_of_xx0_funcform')(xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:470958"}},{"Add":{"text":" f4_of_xx2_funcform = sp.Function('f4_of_xx2_funcform')(xx[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471028"}},{"Add":{"text":" f0_of_xx0, f1_of_xx1, f2_of_xx0_xx1, f3_of_xx0, f4_of_xx2 = par.Cparameters(\"REAL\", thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471128"}},{"Add":{"text":" [\"f0_of_xx0\", \"f1_of_xx1\", \"f2_of_xx0_xx1\", \"f3_of_xx0\", \"f4_of_xx2\"], 1e300)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471240"}},{"Add":{"text":" # FIXME: Hack","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471258"}},{"Add":{"text":" f0_of_xx0__D0, f0_of_xx0__DD00, f0_of_xx0__DDD000 = par.Cparameters(\"REAL\", thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471350"}},{"Add":{"text":" [\"f0_of_xx0__D0\", \"f0_of_xx0__DD00\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471459"}},{"Add":{"text":" \"f0_of_xx0__DDD000\"], 1e300)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471561"}},{"Add":{"text":" f1_of_xx1__D1, f1_of_xx1__DD11, f1_of_xx1__DDD111 = par.Cparameters(\"REAL\", thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471653"}},{"Add":{"text":" [\"f1_of_xx1__D1\", \"f1_of_xx1__DD11\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471762"}},{"Add":{"text":" \"f1_of_xx1__DDD111\"], 1e300)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471864"}},{"Add":{"text":" f2_of_xx0_xx1__D0,f2_of_xx0_xx1__D1,f2_of_xx0_xx1__DD00,f2_of_xx0_xx1__DD11 = \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471948"}},{"Add":{"text":" par.Cparameters(\"REAL\", thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:471992"}},{"Add":{"text":" [\"f2_of_xx0_xx1__D0\",\"f2_of_xx0_xx1__D1\",\"f2_of_xx0_xx1__DD00\",\"f2_of_xx0_xx1__DD11\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472103"}},{"Add":{"text":" 1e300)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472134"}},{"Add":{"text":" f3_of_xx0__D0,f3_of_xx0__DD00 = par.Cparameters(\"REAL\", thismodule,[\"f3_of_xx0__D0\",\"f3_of_xx0__DD00\"], 1e300)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472253"}},{"Add":{"text":" f4_of_xx2__D2,f4_of_xx2__DD22 = par.Cparameters(\"REAL\", thismodule,[\"f4_of_xx2__D2\",\"f4_of_xx2__DD22\"], 1e300)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472372"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472373"}},{"Add":{"text":" global have_already_called_reference_metric_function # setting to global enables other modules to see updated value.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472494"}},{"Add":{"text":" have_already_called_reference_metric_function = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472551"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472552"}},{"Add":{"text":" CoordSystem = par.parval_from_str(\"reference_metric::CoordSystem\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472623"}},{"Add":{"text":" M_PI,M_SQRT1_2 = par.Cparameters(\"#define\",thismodule,[\"M_PI\",\"M_SQRT1_2\"],\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472706"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472707"}},{"Add":{"text":" global xxmin","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472724"}},{"Add":{"text":" global xxmax","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472741"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472742"}},{"Add":{"text":" global UnitVectors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472765"}},{"Add":{"text":" UnitVectors = ixp.zerorank2(DIM=3)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472804"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472805"}},{"Add":{"text":" # Set up hatted metric tensor, rescaling matrix, and rescaling vector","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472879"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472880"}},{"Add":{"text":" #####################################################################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:472954"}},{"Add":{"text":" # SPHERICAL-LIKE COORDINATE SYSTEMS WITH & WITHOUT RADIAL RESCALING #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473028"}},{"Add":{"text":" #####################################################################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473102"}},{"Add":{"text":" if CoordSystem == \"Spherical\" or CoordSystem == \"SinhSpherical\" or CoordSystem == \"SinhSphericalv2\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473207"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473208"}},{"Add":{"text":" # Adding assumption real=True can help simplify expressions involving xx[0] & xx[1] below.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473307"}},{"Add":{"text":" xx[0] = sp.symbols(\"xx0\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473352"}},{"Add":{"text":" xx[1] = sp.symbols(\"xx1\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473397"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473398"}},{"Add":{"text":" if CoordSystem == \"Spherical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473437"}},{"Add":{"text":" RMAX = par.Cparameters(\"REAL\", thismodule, [\"RMAX\"],10.0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473507"}},{"Add":{"text":" xxmin = [sp.sympify(0), sp.sympify(0), -M_PI]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473565"}},{"Add":{"text":" xxmax = [ RMAX, M_PI, M_PI]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473623"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473624"}},{"Add":{"text":" r = xx[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473647"}},{"Add":{"text":" th = xx[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473670"}},{"Add":{"text":" ph = xx[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473693"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473694"}},{"Add":{"text":" Cart_to_xx[0] = sp.sqrt(Cartx ** 2 + Carty ** 2 + Cartz ** 2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473768"}},{"Add":{"text":" Cart_to_xx[1] = sp.acos(Cartz / Cart_to_xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473827"}},{"Add":{"text":" Cart_to_xx[2] = sp.atan2(Carty, Cartx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473878"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473879"}},{"Add":{"text":" elif CoordSystem == \"SinhSpherical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473924"}},{"Add":{"text":" xxmin = [sp.sympify(0), sp.sympify(0), -M_PI]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:473982"}},{"Add":{"text":" xxmax = [sp.sympify(1), M_PI, M_PI]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474040"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474041"}},{"Add":{"text":" AMPL, SINHW = par.Cparameters(\"REAL\",thismodule,[\"AMPL\",\"SINHW\"],[10.0,0.2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474130"}},{"Add":{"text":" # Set SinhSpherical radial coordinate by default; overwrite later if CoordSystem == \"SinhSphericalv2\".","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474245"}},{"Add":{"text":" r = AMPL * (sp.exp(xx[0] / SINHW) - sp.exp(-xx[0] / SINHW)) / \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474321"}},{"Add":{"text":" (sp.exp(1 / SINHW) - sp.exp(-1 / SINHW))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474385"}},{"Add":{"text":" th = xx[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474408"}},{"Add":{"text":" ph = xx[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474431"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474432"}},{"Add":{"text":" Cart_to_xx[0] = SINHW*sp.asinh(sp.sqrt(Cartx ** 2 + Carty ** 2 + Cartz ** 2)*sp.sinh(1/SINHW)/AMPL)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474544"}},{"Add":{"text":" Cart_to_xx[1] = sp.acos(Cartz / sp.sqrt(Cartx ** 2 + Carty ** 2 + Cartz ** 2))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474635"}},{"Add":{"text":" Cart_to_xx[2] = sp.atan2(Carty, Cartx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474686"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474687"}},{"Add":{"text":" # SinhSphericalv2 adds the parameter \"const_dr\", which allows for a region near xx[0]=0 to have","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474791"}},{"Add":{"text":" # constant radial resolution of const_dr, provided the sinh() term does not dominate near xx[0]=0.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474898"}},{"Add":{"text":" elif CoordSystem == \"SinhSphericalv2\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:474945"}},{"Add":{"text":" xxmin = [sp.sympify(0), sp.sympify(0), -M_PI]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475003"}},{"Add":{"text":" xxmax = [sp.sympify(1), M_PI, M_PI]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475061"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475062"}},{"Add":{"text":" AMPL, SINHW = par.Cparameters(\"REAL\",thismodule,[\"AMPL\",\"SINHW\"],[10.0,0.2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475151"}},{"Add":{"text":" const_dr = par.Cparameters(\"REAL\",thismodule,[\"const_dr\"],0.0625)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475229"}},{"Add":{"text":" r = AMPL*( const_dr*xx[0] + (sp.exp(xx[0] / SINHW) - sp.exp(-xx[0] / SINHW)) /","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475320"}},{"Add":{"text":" (sp.exp(1 / SINHW) - sp.exp(-1 / SINHW)) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475386"}},{"Add":{"text":" th = xx[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475409"}},{"Add":{"text":" ph = xx[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475432"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475433"}},{"Add":{"text":" # NO CLOSED-FORM EXPRESSION FOR RADIAL INVERSION.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475495"}},{"Add":{"text":" # Cart_to_xx[0] = \"NewtonRaphson\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475541"}},{"Add":{"text":" # Cart_to_xx[1] = sp.acos(Cartz / sp.sqrt(Cartx ** 2 + Carty ** 2 + Cartz ** 2))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475634"}},{"Add":{"text":" # Cart_to_xx[2] = sp.atan2(Carty, Cartx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475687"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475688"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475689"}},{"Add":{"text":" xxSph[0] = r","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475710"}},{"Add":{"text":" xxSph[1] = th","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475732"}},{"Add":{"text":" xxSph[2] = ph","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475754"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475755"}},{"Add":{"text":" # Now define xCart, yCart, and zCart in terms of x0,xx[1],xx[2].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475828"}},{"Add":{"text":" # Note that the relation between r and x0 is not necessarily trivial in SinhSpherical coordinates. See above.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:475948"}},{"Add":{"text":" xxCart[0] = xxSph[0]*sp.sin(xxSph[1])*sp.cos(xxSph[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476011"}},{"Add":{"text":" xxCart[1] = xxSph[0]*sp.sin(xxSph[1])*sp.sin(xxSph[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476074"}},{"Add":{"text":" xxCart[2] = xxSph[0]*sp.cos(xxSph[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476120"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476121"}},{"Add":{"text":" scalefactor_orthog[0] = sp.diff(xxSph[0],xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476177"}},{"Add":{"text":" scalefactor_orthog[1] = xxSph[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476218"}},{"Add":{"text":" scalefactor_orthog[2] = xxSph[0]*sp.sin(xxSph[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476276"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476277"}},{"Add":{"text":" f0_of_xx0 = xxSph[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476306"}},{"Add":{"text":" f1_of_xx1 = sp.sin(xxSph[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476343"}},{"Add":{"text":" scalefactor_orthog_funcform[0] = sp.diff(f0_of_xx0_funcform,xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476418"}},{"Add":{"text":" scalefactor_orthog_funcform[1] = f0_of_xx0_funcform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476478"}},{"Add":{"text":" scalefactor_orthog_funcform[2] = f0_of_xx0_funcform*f1_of_xx1_funcform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476557"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476558"}},{"Add":{"text":" # Set the unit vectors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476589"}},{"Add":{"text":" UnitVectors = [[ sp.sin(xxSph[1])*sp.cos(xxSph[2]), sp.sin(xxSph[1])*sp.sin(xxSph[2]), sp.cos(xxSph[1])],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476704"}},{"Add":{"text":" [ sp.cos(xxSph[1])*sp.cos(xxSph[2]), sp.cos(xxSph[1])*sp.sin(xxSph[2]), -sp.sin(xxSph[1])],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476819"}},{"Add":{"text":" [ -sp.sin(xxSph[2]), sp.cos(xxSph[2]), sp.sympify(0) ]]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476934"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:476935"}},{"Add":{"text":" ######################################################################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477010"}},{"Add":{"text":" # SPHERICAL-LIKE COORDINATE SYSTEMS WITH RADIAL AND THETA RESCALINGS #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477085"}},{"Add":{"text":" ######################################################################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477160"}},{"Add":{"text":" elif CoordSystem == \"NobleSphericalThetaOptionOne\" or CoordSystem == \"NobleSphericalThetaOptionTwo\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477265"}},{"Add":{"text":" # WARNING: CANNOT BE USED FOR SENR RUNS;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477314"}},{"Add":{"text":" # THESE DO NOT DEFINE xxmin, xxmax, Cart_to_xx","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477370"}},{"Add":{"text":" # ALSO THE RADIAL RESCALINGS ARE NOT ODD FUNCTIONS OF xx0,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477438"}},{"Add":{"text":" # MEANING THAT CURVI. BOUNDARY CONDITIONS WILL NOT WORK.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477504"}},{"Add":{"text":" Rin,R0 = par.Cparameters(\"REAL\", thismodule, [\"Rin\",\"R0\"],[1.08986052555408,0.0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477594"}},{"Add":{"text":" x0beg = sp.log(Rin-R0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477625"}},{"Add":{"text":" xx[0] = sp.symbols(\"xx0\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477670"}},{"Add":{"text":" r = R0 + sp.exp(x0beg + xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477710"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477711"}},{"Add":{"text":" # 0.053407075111026485 == 0.017*pi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477754"}},{"Add":{"text":" th_c,xi,x1beg = par.Cparameters(\"REAL\", thismodule, [\"th_c\",\"xi\",\"x1beg\"],[0.053407075111026485,0.25,0.0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477869"}},{"Add":{"text":" xx[1] = sp.symbols(\"xx1\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477914"}},{"Add":{"text":" x1j = x1beg + xx[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:477942"}},{"Add":{"text":" if CoordSystem == \"NobleSphericalThetaOptionOne\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478000"}},{"Add":{"text":" th = th_c + (M_PI - 2*th_c)*x1j + xi*sp.sin(2*M_PI*x1j)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478068"}},{"Add":{"text":" elif CoordSystem == \"NobleSphericalThetaOptionTwo\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478128"}},{"Add":{"text":" x1_n_exponent = par.Cparameters(\"REAL\", thismodule, [\"x1_n_exponent\"],9.0)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478215"}},{"Add":{"text":" th = M_PI/2 * ( 1 + (1 - xi)*(2*x1j - 1) + (xi - 2*th_c/M_PI)*(2*x1j - 1)**x1_n_exponent )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478318"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478319"}},{"Add":{"text":" xx[2] = sp.symbols(\"xx2\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478364"}},{"Add":{"text":" ph = xx[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478383"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478384"}},{"Add":{"text":" xxSph[0] = r","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478405"}},{"Add":{"text":" xxSph[1] = th","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478427"}},{"Add":{"text":" xxSph[2] = ph","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478449"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478450"}},{"Add":{"text":" # Now define xCart, yCart, and zCart in terms of x0,xx[1],xx[2].","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478523"}},{"Add":{"text":" # Note that the relation between r and x0 is not necessarily trivial in SinhSpherical coordinates. See above.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478643"}},{"Add":{"text":" xxCart[0] = xxSph[0]*sp.sin(xxSph[1])*sp.cos(xxSph[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478706"}},{"Add":{"text":" xxCart[1] = xxSph[0]*sp.sin(xxSph[1])*sp.sin(xxSph[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478769"}},{"Add":{"text":" xxCart[2] = xxSph[0]*sp.cos(xxSph[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478815"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478816"}},{"Add":{"text":" scalefactor_orthog[0] = sp.diff(xxSph[0],xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478872"}},{"Add":{"text":" scalefactor_orthog[1] = xxSph[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478913"}},{"Add":{"text":" scalefactor_orthog[2] = xxSph[0]*sp.sin(xxSph[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478971"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:478972"}},{"Add":{"text":" # Set the unit vectors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479003"}},{"Add":{"text":" UnitVectors = [[ sp.sin(xxSph[1])*sp.cos(xxSph[2]), sp.sin(xxSph[1])*sp.sin(xxSph[2]), sp.cos(xxSph[1])],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479118"}},{"Add":{"text":" [ sp.cos(xxSph[1])*sp.cos(xxSph[2]), sp.cos(xxSph[1])*sp.sin(xxSph[2]), -sp.sin(xxSph[1])],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479233"}},{"Add":{"text":" [ -sp.sin(xxSph[2]), sp.cos(xxSph[2]), sp.sympify(0) ]]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479348"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479349"}},{"Add":{"text":" ##########################################################################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479428"}},{"Add":{"text":" # CYLINDRICAL-LIKE COORDINATE SYSTEMS WITH & WITHOUT RADIAL/Z RESCALINGS #","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479507"}},{"Add":{"text":" ##########################################################################","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479586"}},{"Add":{"text":" elif CoordSystem == \"Cylindrical\" or CoordSystem == \"SinhCylindrical\" or CoordSystem == \"SinhCylindricalv2\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479699"}},{"Add":{"text":" # Assuming the cylindrical radial coordinate","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479752"}},{"Add":{"text":" # is positive makes nice simplifications of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479806"}},{"Add":{"text":" # unit vectors possible.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479841"}},{"Add":{"text":" xx[0] = sp.symbols(\"xx0\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479886"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479887"}},{"Add":{"text":" if CoordSystem == \"Cylindrical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:479928"}},{"Add":{"text":" RHOMAX,ZMIN,ZMAX = par.Cparameters(\"REAL\",thismodule,[\"RHOMAX\",\"ZMIN\",\"ZMAX\"],[10.0,-10.0,10.0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480037"}},{"Add":{"text":" xxmin = [sp.sympify(0), -M_PI, ZMIN]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480086"}},{"Add":{"text":" xxmax = [ RHOMAX, M_PI, ZMAX]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480135"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480136"}},{"Add":{"text":" RHOCYL = xx[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480163"}},{"Add":{"text":" PHICYL = xx[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480190"}},{"Add":{"text":" ZCYL = xx[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480217"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480218"}},{"Add":{"text":" Cart_to_xx[0] = sp.sqrt(Cartx ** 2 + Carty ** 2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480279"}},{"Add":{"text":" Cart_to_xx[1] = sp.atan2(Carty, Cartx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480330"}},{"Add":{"text":" Cart_to_xx[2] = Cartz","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480364"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480365"}},{"Add":{"text":" elif CoordSystem == \"SinhCylindrical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480412"}},{"Add":{"text":" xxmin = [sp.sympify(0), -M_PI, sp.sympify(-1)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480471"}},{"Add":{"text":" xxmax = [sp.sympify(1), M_PI, sp.sympify(+1)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480530"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480531"}},{"Add":{"text":" AMPLRHO, SINHWRHO, AMPLZ, SINHWZ = par.Cparameters(\"REAL\",thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480613"}},{"Add":{"text":" [\"AMPLRHO\",\"SINHWRHO\",\"AMPLZ\",\"SINHWZ\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480717"}},{"Add":{"text":" [ 10.0, 0.2, 10.0, 0.2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480820"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480821"}},{"Add":{"text":" # Set SinhCylindrical radial & z coordinates by default; overwrite later if CoordSystem == \"SinhCylindricalv2\".","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:480945"}},{"Add":{"text":" RHOCYL = AMPLRHO * (sp.exp(xx[0] / SINHWRHO) - sp.exp(-xx[0] / SINHWRHO)) / (sp.exp(1 / SINHWRHO) - sp.exp(-1 / SINHWRHO))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481080"}},{"Add":{"text":" # phi coordinate remains unchanged.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481128"}},{"Add":{"text":" PHICYL = xx[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481155"}},{"Add":{"text":" ZCYL = AMPLZ * (sp.exp(xx[2] / SINHWZ) - sp.exp(-xx[2] / SINHWZ)) / (sp.exp(1 / SINHWZ) - sp.exp(-1 / SINHWZ))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481288"}},{"Add":{"text":" Cart_to_xx[0] = SINHWRHO*sp.asinh(sp.sqrt(Cartx ** 2 + Carty ** 2)*sp.sinh(1/SINHWRHO)/AMPLRHO)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481396"}},{"Add":{"text":" Cart_to_xx[1] = sp.atan2(Carty, Cartx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481447"}},{"Add":{"text":" Cart_to_xx[2] = SINHWZ*sp.asinh(Cartz*sp.sinh(1/SINHWZ)/AMPLZ)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481522"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481523"}},{"Add":{"text":" # SinhCylindricalv2 adds the parameters \"const_drho\", \"const_dz\", which allows for regions near xx[0]=0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481635"}},{"Add":{"text":" # and xx[2]=0 to have constant rho and z resolution of const_drho and const_dz, provided the sinh() terms","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481749"}},{"Add":{"text":" # do not dominate near xx[0]=0 and xx[2]=0.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481801"}},{"Add":{"text":" elif CoordSystem == \"SinhCylindricalv2\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481850"}},{"Add":{"text":" xxmin = [sp.sympify(0), -M_PI, sp.sympify(-1)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481909"}},{"Add":{"text":" xxmax = [sp.sympify(1), M_PI, sp.sympify(+1)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:481968"}},{"Add":{"text":" AMPLRHO, SINHWRHO, AMPLZ, SINHWZ = par.Cparameters(\"REAL\",thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482050"}},{"Add":{"text":" [\"AMPLRHO\",\"SINHWRHO\",\"AMPLZ\",\"SINHWZ\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482154"}},{"Add":{"text":" [ 10.0, 0.2, 10.0, 0.2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482257"}},{"Add":{"text":" const_drho, const_dz = par.Cparameters(\"REAL\",thismodule,[\"const_drho\",\"const_dz\"],[0.0625,0.0625])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482369"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482370"}},{"Add":{"text":" RHOCYL = AMPLRHO * ( const_drho*xx[0] + (sp.exp(xx[0] / SINHWRHO) - sp.exp(-xx[0] / SINHWRHO)) / (sp.exp(1 / SINHWRHO) - sp.exp(-1 / SINHWRHO)) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482528"}},{"Add":{"text":" PHICYL = xx[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482555"}},{"Add":{"text":" ZCYL = AMPLZ * ( const_dz *xx[2] + (sp.exp(xx[2] / SINHWZ ) - sp.exp(-xx[2] / SINHWZ )) / (sp.exp(1 / SINHWZ ) - sp.exp(-1 / SINHWZ )) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482713"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482714"}},{"Add":{"text":" # NO CLOSED-FORM EXPRESSION FOR RADIAL OR Z INVERSION.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482781"}},{"Add":{"text":" # Cart_to_xx[0] = \"NewtonRaphson\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482827"}},{"Add":{"text":" # Cart_to_xx[1] = sp.atan2(Carty, Cartx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482880"}},{"Add":{"text":" # Cart_to_xx[2] = \"NewtonRaphson\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482926"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482927"}},{"Add":{"text":" xxCart[0] = RHOCYL*sp.cos(PHICYL)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:482969"}},{"Add":{"text":" xxCart[1] = RHOCYL*sp.sin(PHICYL)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483011"}},{"Add":{"text":" xxCart[2] = ZCYL","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483036"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483037"}},{"Add":{"text":" xxSph[0] = sp.sqrt(RHOCYL**2 + ZCYL**2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483085"}},{"Add":{"text":" xxSph[1] = sp.acos(ZCYL / xxSph[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483129"}},{"Add":{"text":" xxSph[2] = PHICYL","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483155"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483156"}},{"Add":{"text":" scalefactor_orthog[0] = sp.diff(RHOCYL,xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483210"}},{"Add":{"text":" scalefactor_orthog[1] = RHOCYL","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483249"}},{"Add":{"text":" scalefactor_orthog[2] = sp.diff(ZCYL,xx[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483301"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483302"}},{"Add":{"text":" f0_of_xx0 = RHOCYL","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483342"}},{"Add":{"text":" f4_of_xx2 = sp.diff(ZCYL,xx[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483395"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483396"}},{"Add":{"text":" scalefactor_orthog_funcform[0] = sp.diff(f0_of_xx0_funcform,xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483471"}},{"Add":{"text":" scalefactor_orthog_funcform[1] = f0_of_xx0_funcform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483531"}},{"Add":{"text":" scalefactor_orthog_funcform[2] = f4_of_xx2_funcform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483591"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483592"}},{"Add":{"text":" # Set the unit vectors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483623"}},{"Add":{"text":" UnitVectors = [[ sp.cos(PHICYL), sp.sin(PHICYL), sp.sympify(0)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483696"}},{"Add":{"text":" [-sp.sin(PHICYL), sp.cos(PHICYL), sp.sympify(0)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483769"}},{"Add":{"text":" [ sp.sympify(0), sp.sympify(0), sp.sympify(1)]]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483842"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483843"}},{"Add":{"text":" elif CoordSystem == \"SymTP\" or CoordSystem == \"SinhSymTP\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483906"}},{"Add":{"text":" # var1, var2= sp.symbols('var1 var2',real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:483962"}},{"Add":{"text":" bScale, SINHWAA, AMAX = par.Cparameters(\"REAL\",thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484029"}},{"Add":{"text":" [\"bScale\",\"SINHWAA\",\"AMAX\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484106"}},{"Add":{"text":" [0.5, 0.2, 10.0 ])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484183"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484184"}},{"Add":{"text":" # Assuming xx0, xx1, and bScale","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484224"}},{"Add":{"text":" # are positive makes nice simplifications of","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484279"}},{"Add":{"text":" # unit vectors possible.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484314"}},{"Add":{"text":" xx[0],xx[1] = sp.symbols(\"xx0 xx1\", real=True)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484369"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484370"}},{"Add":{"text":" xxmin = [sp.sympify(0), sp.sympify(0),-M_PI]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484423"}},{"Add":{"text":" xxmax = [ AMAX, M_PI, M_PI]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484476"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484477"}},{"Add":{"text":" AA = xx[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484496"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484497"}},{"Add":{"text":" if CoordSystem == \"SinhSymTP\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484536"}},{"Add":{"text":" # With xxmax[0] == AMAX, sinh(xx0/AMAX) will evaluate to a number between 0 and 1.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484631"}},{"Add":{"text":" # Similarly, sinh(xx0/(AMAX*SINHWAA)) / sinh(1/SINHWAA) will also evaluate to a number between 0 and 1.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484749"}},{"Add":{"text":" # Then AA = AMAX*sinh(xx0/(AMAX*SINHWAA)) / sinh(1/SINHWAA) will evaluate to a number between 0 and AMAX.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:484869"}},{"Add":{"text":" AA = AMAX * (sp.exp(xx[0] / (AMAX*SINHWAA)) - sp.exp(-xx[0] / (AMAX*SINHWAA))) / (sp.exp(1 / SINHWAA) - sp.exp(-1 / AMAX))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485004"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485005"}},{"Add":{"text":" var1 = sp.sqrt(AA**2 + (bScale * sp.sin(xx[1]))**2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485065"}},{"Add":{"text":" var2 = sp.sqrt(AA**2 + bScale**2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485107"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485108"}},{"Add":{"text":" RHOSYMTP = AA*sp.sin(xx[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485144"}},{"Add":{"text":" PHSYMTP = xx[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485168"}},{"Add":{"text":" ZSYMTP = var2*sp.cos(xx[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485204"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485205"}},{"Add":{"text":" xxCart[0] = AA *sp.sin(xx[1])*sp.cos(xx[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485258"}},{"Add":{"text":" xxCart[1] = AA *sp.sin(xx[1])*sp.sin(xx[2])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485311"}},{"Add":{"text":" xxCart[2] = ZSYMTP","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485338"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485339"}},{"Add":{"text":" xxSph[0] = sp.sqrt(RHOSYMTP**2 + ZSYMTP**2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485391"}},{"Add":{"text":" xxSph[1] = sp.acos(ZSYMTP / xxSph[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485437"}},{"Add":{"text":" xxSph[2] = PHSYMTP","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485464"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485465"}},{"Add":{"text":" if CoordSystem == \"SymTP\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485500"}},{"Add":{"text":" rSph = sp.sqrt(Cartx ** 2 + Carty ** 2 + Cartz ** 2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485566"}},{"Add":{"text":" thSph = sp.acos(Cartz / rSph)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485608"}},{"Add":{"text":" phSph = sp.atan2(Carty, Cartx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485651"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485652"}},{"Add":{"text":" # Mathematica script to compute Cart_to_xx[]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485709"}},{"Add":{"text":"# AA = x1;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485732"}},{"Add":{"text":"# var2 = Sqrt[AA^2 + bScale^2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485776"}},{"Add":{"text":"# RHOSYMTP = AA*Sin[x2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485813"}},{"Add":{"text":"# ZSYMTP = var2*Cos[x2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485850"}},{"Add":{"text":"# Solve[{rSph == Sqrt[RHOSYMTP^2 + ZSYMTP^2],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485908"}},{"Add":{"text":"# thSph == ArcCos[ZSYMTP/Sqrt[RHOSYMTP^2 + ZSYMTP^2]],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:485982"}},{"Add":{"text":"# phSph == x3},","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486017"}},{"Add":{"text":"# {x1, x2, x3}]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486051"}},{"Add":{"text":" Cart_to_xx[0] = sp.sqrt(-bScale**2 + rSph**2 +","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486110"}},{"Add":{"text":" sp.sqrt(bScale**4 + 2*bScale**2*rSph**2 + rSph**4 -","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486198"}},{"Add":{"text":" 4*bScale**2*rSph**2*sp.cos(thSph)**2))*M_SQRT1_2 # M_SQRT1_2 = 1/sqrt(2); define this way for UnitTesting","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486348"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486349"}},{"Add":{"text":" # The sign() function in the following expression ensures the correct root is taken.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486446"}},{"Add":{"text":" Cart_to_xx[1] = sp.acos(sp.sign(Cartz)*(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486499"}},{"Add":{"text":" sp.sqrt(1 + rSph**2/bScale**2 -","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486569"}},{"Add":{"text":" sp.sqrt(bScale**4 + 2*bScale**2*rSph**2 + rSph**4 -","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486667"}},{"Add":{"text":" 4*bScale**2*rSph**2*sp.cos(thSph)**2)/bScale**2)*M_SQRT1_2)) # M_SQRT1_2 = 1/sqrt(2); define this way for UnitTesting","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486839"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486840"}},{"Add":{"text":" Cart_to_xx[2] = phSph","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486874"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486875"}},{"Add":{"text":" elif CoordSystem == \"SinhSymTP\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486916"}},{"Add":{"text":" pass","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:486933"}},{"Add":{"text":" # Closed form expression for Cart_to_xx in SinhSymTP may exist, but has not yet been found","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487036"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487037"}},{"Add":{"text":" scalefactor_orthog[0] = sp.diff(AA,xx[0]) * var1 / var2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487101"}},{"Add":{"text":" scalefactor_orthog[1] = var1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487138"}},{"Add":{"text":" scalefactor_orthog[2] = AA * sp.sin(xx[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487189"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487190"}},{"Add":{"text":" f0_of_xx0 = AA","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487226"}},{"Add":{"text":" f1_of_xx1 = sp.sin(xx[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487273"}},{"Add":{"text":" f2_of_xx0_xx1 = var1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487311"}},{"Add":{"text":" f3_of_xx0 = var2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487349"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487350"}},{"Add":{"text":" scalefactor_orthog_funcform[0] = sp.diff(f0_of_xx0_funcform,xx[0]) * f2_of_xx0_xx1_funcform/f3_of_xx0_funcform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487469"}},{"Add":{"text":" scalefactor_orthog_funcform[1] = f2_of_xx0_xx1_funcform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487533"}},{"Add":{"text":" scalefactor_orthog_funcform[2] = f0_of_xx0_funcform*f1_of_xx1_funcform","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487612"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487613"}},{"Add":{"text":" # Set the transpose of the matrix of unit vectors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487671"}},{"Add":{"text":" UnitVectors = [[sp.sin(xx[1]) * sp.cos(xx[2]) * var2 / var1,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487740"}},{"Add":{"text":" sp.sin(xx[1]) * sp.sin(xx[2]) * var2 / var1,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487809"}},{"Add":{"text":" AA * sp.cos(xx[1]) / var1],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487861"}},{"Add":{"text":" [AA * sp.cos(xx[1]) * sp.cos(xx[2]) / var1,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487928"}},{"Add":{"text":" AA * sp.cos(xx[1]) * sp.sin(xx[2]) / var1,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:487995"}},{"Add":{"text":" -sp.sin(xx[1]) * var2 / var1],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488054"}},{"Add":{"text":" [-sp.sin(xx[2]), sp.cos(xx[2]), sp.sympify(0)]]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488125"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488126"}},{"Add":{"text":" elif CoordSystem == \"Cartesian\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488163"}},{"Add":{"text":" xmin, xmax, ymin, ymax, zmin, zmax = par.Cparameters(\"REAL\",thismodule,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488243"}},{"Add":{"text":" [\"xmin\",\"xmax\",\"ymin\",\"ymax\",\"zmin\",\"zmax\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488349"}},{"Add":{"text":" [ -10.0, 10.0, -10.0, 10.0, -10.0, 10.0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488455"}},{"Add":{"text":" xxmin = [\"xmin\", \"ymin\", \"zmin\"]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488496"}},{"Add":{"text":" xxmax = [\"xmax\", \"ymax\", \"zmax\"]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488537"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488538"}},{"Add":{"text":" xxCart[0] = xx[0]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488564"}},{"Add":{"text":" xxCart[1] = xx[1]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488590"}},{"Add":{"text":" xxCart[2] = xx[2]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488616"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488617"}},{"Add":{"text":" xxSph[0] = sp.sqrt(xx[0] ** 2 + xx[1] ** 2 + xx[2] ** 2)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488682"}},{"Add":{"text":" xxSph[1] = sp.acos(xx[2] / xxSph[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488727"}},{"Add":{"text":" xxSph[2] = sp.atan2(xx[1], xx[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488769"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488770"}},{"Add":{"text":" Cart_to_xx[0] = Cartx","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488800"}},{"Add":{"text":" Cart_to_xx[1] = Carty","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488830"}},{"Add":{"text":" Cart_to_xx[2] = Cartz","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488860"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488861"}},{"Add":{"text":" scalefactor_orthog[0] = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488907"}},{"Add":{"text":" scalefactor_orthog[1] = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488953"}},{"Add":{"text":" scalefactor_orthog[2] = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:488999"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489000"}},{"Add":{"text":" scalefactor_orthog_funcform[0] = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489055"}},{"Add":{"text":" scalefactor_orthog_funcform[1] = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489110"}},{"Add":{"text":" scalefactor_orthog_funcform[2] = sp.sympify(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489165"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489166"}},{"Add":{"text":" # Set the transpose of the matrix of unit vectors","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489224"}},{"Add":{"text":" UnitVectors = [[sp.sympify(1), sp.sympify(0), sp.sympify(0)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489294"}},{"Add":{"text":" [sp.sympify(0), sp.sympify(1), sp.sympify(0)],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489364"}},{"Add":{"text":" [sp.sympify(0), sp.sympify(0), sp.sympify(1)]]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489434"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489435"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489445"}},{"Add":{"text":" print(\"CoordSystem == \" + CoordSystem + \" is not supported.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489515"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489535"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489536"}},{"Add":{"text":" # Finally, call ref_metric__hatted_quantities()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489588"}},{"Add":{"text":" # to construct hatted metric, derivs of hatted","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489640"}},{"Add":{"text":" # metric, and Christoffel symbols","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489679"}},{"Add":{"text":" ref_metric__hatted_quantities(SymPySimplifyExpressions)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489739"}},{"Add":{"text":" # ref_metric__hatted_quantities(scalefactor_orthog_funcform,SymPySimplifyExpressions)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489829"}},{"Add":{"text":" # ref_metric__hatted_quantities(scalefactor_orthog,SymPySimplifyExpressions)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489910"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489911"}},{"Add":{"text":"def ref_metric__hatted_quantities(SymPySimplifyExpressions=True):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489977"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:489978"}},{"Add":{"text":" enable_rfm_precompute = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490012"}},{"Add":{"text":" if par.parval_from_str(thismodule+\"::enable_rfm_precompute\") == \"True\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490088"}},{"Add":{"text":" enable_rfm_precompute = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490125"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490126"}},{"Add":{"text":" # Step 0: Set dimension DIM","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490158"}},{"Add":{"text":" DIM = par.parval_from_str(\"grid::DIM\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490201"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490202"}},{"Add":{"text":" global ReU,ReDD,ghatDD,ghatUU,detgammahat","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490248"}},{"Add":{"text":" ReU = ixp.zerorank1()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490277"}},{"Add":{"text":" ReDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490306"}},{"Add":{"text":" ghatDD = ixp.zerorank2()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490335"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490336"}},{"Add":{"text":" # Step 1: Compute ghatDD (reference metric), ghatUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490392"}},{"Add":{"text":" # (inverse reference metric), as well as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490445"}},{"Add":{"text":" # rescaling vector ReU & rescaling matrix ReDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490504"}},{"Add":{"text":" if enable_rfm_precompute == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490543"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490572"}},{"Add":{"text":" scalefactor_orthog[i] = sp.sympify(scalefactor_orthog[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490642"}},{"Add":{"text":" ghatDD[i][i] = scalefactor_orthog[i]**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490694"}},{"Add":{"text":" ReU[i] = 1/scalefactor_orthog[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490739"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490772"}},{"Add":{"text":" ReDD[i][j] = scalefactor_orthog[i]*scalefactor_orthog[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490845"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490855"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490884"}},{"Add":{"text":" scalefactor_orthog_funcform[i] = sp.sympify(scalefactor_orthog_funcform[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:490972"}},{"Add":{"text":" ghatDD[i][i] = scalefactor_orthog_funcform[i]**2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491033"}},{"Add":{"text":" ReU[i] = 1/scalefactor_orthog_funcform[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491087"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491120"}},{"Add":{"text":" ReDD[i][j] = scalefactor_orthog_funcform[i]*scalefactor_orthog_funcform[j]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491211"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491212"}},{"Add":{"text":" # Step 1b: Compute ghatUU","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491242"}},{"Add":{"text":" ghatUU, detgammahat = ixp.symm_matrix_inverter3x3(ghatDD)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491304"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491305"}},{"Add":{"text":" # Step 1c: Sanity check: verify that ReDD, ghatDD,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491360"}},{"Add":{"text":" # and ghatUU are all symmetric rank-2:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491412"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491437"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491466"}},{"Add":{"text":" if ReDD[i][j] != ReDD[j][i]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491507"}},{"Add":{"text":" print(\"Error: ReDD[\"+ str(i) + \"][\" + str(j) + \"] != ReDD[\"+ str(j) + \"][\" + str(i) + \": \" + str(ReDD[i][j]) + \"!=\" + str(ReDD[j][i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491658"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491686"}},{"Add":{"text":" if ghatDD[i][j] != ghatDD[j][i]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491731"}},{"Add":{"text":" print(\"Error: ghatDD[\"+ str(i) + \"][\" + str(j) + \"] != ghatDD[\"+ str(j) + \"][\" + str(i) + \": \" + str(ghatDD[i][j]) + \"!=\" + str(ghatDD[j][i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491890"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491918"}},{"Add":{"text":" if ghatUU[i][j] != ghatUU[j][i]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:491963"}},{"Add":{"text":" print(\"Error: ghatUU[\"+ str(i) + \"][\" + str(j) + \"] != ghatUU[\"+ str(j) + \"][\" + str(i) + \": \" + str(ghatUU[i][j]) + \"!=\" + str(ghatUU[j][i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492122"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492150"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492151"}},{"Add":{"text":" # Step 2: Compute det(ghat) and its 1st & 2nd derivatives","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492213"}},{"Add":{"text":" global detgammahatdD,detgammahatdDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492253"}},{"Add":{"text":" detgammahatdD = ixp.zerorank1(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492293"}},{"Add":{"text":" detgammahatdDD = ixp.zerorank2(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492333"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492358"}},{"Add":{"text":" detgammahatdD[i] = (sp.diff(detgammahat, xx[i]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492415"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492444"}},{"Add":{"text":" detgammahatdDD[i][j] = sp.diff(detgammahatdD[i], xx[j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492512"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492513"}},{"Add":{"text":" # Step 3a: Compute 1st & 2nd derivatives of rescaling vector.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492579"}},{"Add":{"text":" # (E.g., needed in BSSN for betaUdDD computation)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492642"}},{"Add":{"text":" global ReUdD,ReUdDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492666"}},{"Add":{"text":" ReUdD = ixp.zerorank2(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492698"}},{"Add":{"text":" ReUdDD = ixp.zerorank3(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492730"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492755"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492784"}},{"Add":{"text":" ReUdD[i][j] = sp.diff(ReU[i], xx[j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492833"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492866"}},{"Add":{"text":" ReUdDD[i][j][k] = sp.diff(ReUdD[i][j], xx[k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492928"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492929"}},{"Add":{"text":" # Step 3b: Compute 1st & 2nd derivatives of rescaling matrix.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:492995"}},{"Add":{"text":" global ReDDdD,ReDDdDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493021"}},{"Add":{"text":" ReDDdD = ixp.zerorank3(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493053"}},{"Add":{"text":" ReDDdDD = ixp.zerorank4(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493086"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493111"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493140"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493173"}},{"Add":{"text":" ReDDdD[i][j][k] = (sp.diff(ReDD[i][j],xx[k]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493235"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493272"}},{"Add":{"text":" # Simplifying this doesn't appear to help overall NRPy run time.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493357"}},{"Add":{"text":" ReDDdDD[i][j][k][l] = sp.diff(ReDDdD[i][j][k],xx[l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493430"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493431"}},{"Add":{"text":" # Step 3c: Compute 1st & 2nd derivatives of reference metric.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493497"}},{"Add":{"text":" global ghatDDdD,ghatDDdDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493527"}},{"Add":{"text":" ghatDDdD = ixp.zerorank3(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493561"}},{"Add":{"text":" ghatDDdDD = ixp.zerorank4(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493596"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493621"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493650"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493683"}},{"Add":{"text":" if SymPySimplifyExpressions==True:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493734"}},{"Add":{"text":"# ghatDDdD[i][j][k] = sp.trigsimp(sp.diff(ghatDD[i][j],xx[k])) # FIXME: BAD: MUST BE SIMPLIFIED OR ANSWER IS INCORRECT! Must be some bug in sympy...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:493902"}},{"Add":{"text":" ghatDDdD[i][j][k] = sp.simplify(sp.diff(ghatDD[i][j],xx[k])) # FIXME: BAD: MUST BE SIMPLIFIED OR ANSWER IS INCORRECT! Must be some bug in sympy...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494069"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494091"}},{"Add":{"text":" ghatDDdD[i][j][k] = (sp.diff(ghatDD[i][j],xx[k])) # FIXME: BAD: MUST BE SIMPLIFIED OR ANSWER IS INCORRECT! Must be some bug in sympy...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494247"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494284"}},{"Add":{"text":" ghatDDdDD[i][j][k][l] = (sp.diff(ghatDDdD[i][j][k],xx[l]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494363"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494364"}},{"Add":{"text":" # Step 4a: Compute Christoffel symbols of reference metric.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494428"}},{"Add":{"text":" global GammahatUDD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494451"}},{"Add":{"text":" GammahatUDD = ixp.zerorank3(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494488"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494513"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494542"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494575"}},{"Add":{"text":" for m in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494612"}},{"Add":{"text":"# GammahatUDD[i][k][l] += sp.trigsimp((sp.Rational(1,2))*ghatUU[i][m]*\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494703"}},{"Add":{"text":" GammahatUDD[i][k][l] += (sp.Rational(1,2))*ghatUU[i][m]*\\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494781"}},{"Add":{"text":" (ghatDDdD[m][k][l] + ghatDDdD[m][l][k] - ghatDDdD[k][l][m])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494885"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494886"}},{"Add":{"text":" # Step 4b: Compute derivs of Christoffel symbols of reference metric.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494960"}},{"Add":{"text":" global GammahatUDDdD","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:494985"}},{"Add":{"text":" GammahatUDDdD = ixp.zerorank4(DIM)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495024"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495049"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495078"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495111"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495148"}},{"Add":{"text":" GammahatUDDdD[i][j][k][l] = (sp.diff(GammahatUDD[i][j][k],xx[l]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495234"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495235"}},{"Add":{"text":" # Step 4c: If rfm_precompute is disabled, then we are finished with this function.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495322"}},{"Add":{"text":" # Otherwise continue to Step 5.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495367"}},{"Add":{"text":" if enable_rfm_precompute == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495406"}},{"Add":{"text":" return","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495421"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495431"}},{"Add":{"text":" CoordSystem = par.parval_from_str(\"reference_metric::CoordSystem\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495506"}},{"Add":{"text":" # if not ((\"Spherical\" in CoordSystem) or (\"SymTP\" in CoordSystem)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495583"}},{"Add":{"text":" # if not (( \"Spherical\" in CoordSystem)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495633"}},{"Add":{"text":" # print(\"Error: CoordSystem == \"+CoordSystem+\" does not yet support rfm precompute infrastructure.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495746"}},{"Add":{"text":" # sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495772"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495773"}},{"Add":{"text":" # enable_rfm_precompute: precompute and store in memory complicated","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495849"}},{"Add":{"text":" # expressions related to the reference metric (a.k.a., \"hatted","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495924"}},{"Add":{"text":" # quantities\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495951"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:495952"}},{"Add":{"text":" # The precomputed \"hatted quantity\" expressions will be stored in","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496026"}},{"Add":{"text":" # a C struct called rfmstruct. As these expressions generally","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496099"}},{"Add":{"text":" # involve computationally expensive transcendental functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496171"}},{"Add":{"text":" # of xx0,xx1,or xx2, and xx0,xx1, and xx2 remain fixed across","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496244"}},{"Add":{"text":" # most (if not all) of a given simulation, setting up the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496313"}},{"Add":{"text":" # rfmstruct can greatly improve performance.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496369"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496370"}},{"Add":{"text":" # The core challenge in setting up the rfmstruct is collecting","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496441"}},{"Add":{"text":" # all the information needed to automatically generate it.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496511"}},{"Add":{"text":" # Step 5 and onwards implements this algorithm, using the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496577"}},{"Add":{"text":" # *generic functional form* of the hatted quantities (as","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496645"}},{"Add":{"text":" # opposed to the exact closed-form expressions of the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496710"}},{"Add":{"text":" # hatted quantities) computed above.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496758"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496759"}},{"Add":{"text":" # Step 5: Now that all hatted quantities are written in terms of generic SymPy functions,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496857"}},{"Add":{"text":" # we will now replace SymPy functions with simple variables using rigid NRPy+ syntax,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:496959"}},{"Add":{"text":" # and store these variables to globals defined above.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497029"}},{"Add":{"text":" def make_replacements(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497066"}},{"Add":{"text":" sympy_version = sp.__version__.replace(\"rc\",\"...\").replace(\"b\",\"...\") # Ignore the rc's and b's for release candidates & betas.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497206"}},{"Add":{"text":" sympy_major_version = int(sympy_version.split(\".\")[0])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497273"}},{"Add":{"text":" sympy_minor_version = int(sympy_version.split(\".\")[1])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497340"}},{"Add":{"text":" if sympy_major_version < 1 or (sympy_major_version >= 1 and sympy_minor_version < 2):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497438"}},{"Add":{"text":" print(\"Detected SymPy version \"+sympy_version)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497501"}},{"Add":{"text":" print(\"Sorry, reference metric precomputation unsupported in SymPy < 1.2!\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497593"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497621"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497622"}},{"Add":{"text":" for item in sp.preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497675"}},{"Add":{"text":" if item.func == sp.Derivative:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497722"}},{"Add":{"text":" stringfunc = str(item.args[0]).split(\"_funcform(\", 1)[0] # store everything before _funcform(...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497840"}},{"Add":{"text":" stringderv = str(item.args[1]).replace(\" \", \"\") # Ignore whitespace","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:497929"}},{"Add":{"text":" deriv_wrt = stringderv.split(\",\")[0].replace(\"(xx\", \"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498005"}},{"Add":{"text":" derivorder = int(stringderv.split(\",\")[1].replace(\")\", \"\"))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498085"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498086"}},{"Add":{"text":" derivop = \"__D\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498122"}},{"Add":{"text":" for i in range(derivorder - 1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498174"}},{"Add":{"text":" derivop += \"D\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498213"}},{"Add":{"text":" derivop += deriv_wrt","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498254"}},{"Add":{"text":" for i in range(derivorder - 1):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498306"}},{"Add":{"text":" derivop += deriv_wrt","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498351"}},{"Add":{"text":" expr = expr.xreplace(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498393"}},{"Add":{"text":" {item: sp.sympify(stringfunc + derivop)})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498459"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498460"}},{"Add":{"text":" for item in sp.preorder_traversal(expr):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498513"}},{"Add":{"text":" if \"_funcform\" in str(item.func):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498563"}},{"Add":{"text":" stringfunc = str(item.func).split(\"_funcform\", 1)[0] # store everything before _funcform(...","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498677"}},{"Add":{"text":" expr = expr.xreplace({item: sp.sympify(stringfunc)})","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498750"}},{"Add":{"text":" return expr","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498774"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498775"}},{"Add":{"text":" detgammahat = make_replacements(detgammahat)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498828"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498857"}},{"Add":{"text":" ReU[i] = make_replacements(ReU[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498904"}},{"Add":{"text":" detgammahatdD[i] = make_replacements(detgammahatdD[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:498971"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499004"}},{"Add":{"text":" ReDD[i][j] = make_replacements(ReDD[i][j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499063"}},{"Add":{"text":" ReUdD[i][j] = make_replacements(ReUdD[i][j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499124"}},{"Add":{"text":" ghatDD[i][j] = make_replacements(ghatDD[i][j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499187"}},{"Add":{"text":" ghatUU[i][j] = make_replacements(ghatUU[i][j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499250"}},{"Add":{"text":" detgammahatdDD[i][j] = make_replacements(detgammahatdDD[i][j])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499329"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499366"}},{"Add":{"text":" ReDDdD[i][j][k] = make_replacements(ReDDdD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499439"}},{"Add":{"text":" ReUdDD[i][j][k] = make_replacements(ReUdDD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499512"}},{"Add":{"text":" ghatDDdD[i][j][k] = make_replacements(ghatDDdD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499589"}},{"Add":{"text":" GammahatUDD[i][j][k] = make_replacements(GammahatUDD[i][j][k])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499672"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499713"}},{"Add":{"text":" ReDDdDD[i][j][k][l] = make_replacements(ReDDdDD[i][j][k][l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499798"}},{"Add":{"text":" ghatDDdDD[i][j][k][l] = make_replacements(ghatDDdDD[i][j][k][l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499887"}},{"Add":{"text":" GammahatUDDdD[i][j][k][l] = make_replacements(GammahatUDDdD[i][j][k][l])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499984"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:499985"}},{"Add":{"text":" # Step 6: At this point, each expression is written in terms of the generic functions","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500079"}},{"Add":{"text":" # of xx0, xx1, and/or xx2 and their derivatives. Depending on the functions, some","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500177"}},{"Add":{"text":" # of these derivatives may be zero. In Step 5 we'll evaluate the function","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500267"}},{"Add":{"text":" # derivatives exactly and set the expressions to zero. Otherwise in the C code","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500362"}},{"Add":{"text":" # we'd be storing performing arithmetic with zeros -- wasteful!","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500442"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500443"}},{"Add":{"text":" # Step 6.a: Construct the full list of *unique* NRPy+ variables representing the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500532"}},{"Add":{"text":" # SymPy functions and derivatives, so that all zero derivatives can be","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500621"}},{"Add":{"text":" # computed.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500651"}},{"Add":{"text":" freevars = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500673"}},{"Add":{"text":" freevars.extend(detgammahat.free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500723"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500752"}},{"Add":{"text":" freevars.extend(ReU[i].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500801"}},{"Add":{"text":" freevars.extend(detgammahatdD[i].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500860"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500893"}},{"Add":{"text":" freevars.extend(ReDD[i][j].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:500950"}},{"Add":{"text":" freevars.extend(ReUdD[i][j].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501008"}},{"Add":{"text":" freevars.extend(ghatDD[i][j].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501067"}},{"Add":{"text":" freevars.extend(ghatUU[i][j].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501126"}},{"Add":{"text":" freevars.extend(detgammahatdDD[i][j].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501193"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501230"}},{"Add":{"text":" freevars.extend(ReDDdD[i][j][k].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501296"}},{"Add":{"text":" freevars.extend(ReUdDD[i][j][k].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501362"}},{"Add":{"text":" freevars.extend(ghatDDdD[i][j][k].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501430"}},{"Add":{"text":" freevars.extend(GammahatUDD[i][j][k].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501501"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501542"}},{"Add":{"text":" freevars.extend(ReDDdDD[i][j][k][l].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501616"}},{"Add":{"text":" freevars.extend(ghatDDdDD[i][j][k][l].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501692"}},{"Add":{"text":" freevars.extend(GammahatUDDdD[i][j][k][l].free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501772"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501773"}},{"Add":{"text":" freevars_uniq = superfast_uniq(freevars)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501822"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501823"}},{"Add":{"text":" freevars_uniq_xx_indep = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501859"}},{"Add":{"text":" for i in range(len(freevars_uniq)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501903"}},{"Add":{"text":" freevars_uniq_xx_indep.append(freevars_uniq[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501963"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:501964"}},{"Add":{"text":" # Step 6.b: Using the expressions f?_of_xx? set in reference_metric(),","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502043"}},{"Add":{"text":" # evaluate each needed derivative and, in the case it is zero,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502124"}},{"Add":{"text":" # set the corresponding \"freevar\" variable to zero.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502194"}},{"Add":{"text":" freevars_uniq_vals = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502226"}},{"Add":{"text":" for i in range(len(freevars_uniq)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502270"}},{"Add":{"text":" var = freevars_uniq[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502305"}},{"Add":{"text":" basename = str(var).split(\"__\")[0].replace(\"_funcform\", \"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502377"}},{"Add":{"text":" derivatv = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502403"}},{"Add":{"text":" if \"__\" in str(var):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502436"}},{"Add":{"text":" derivatv = str(var).split(\"__\")[1].replace(\"_funcform\", \"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502512"}},{"Add":{"text":" if basename == \"f0_of_xx0\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502552"}},{"Add":{"text":" basefunc = f0_of_xx0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502589"}},{"Add":{"text":" elif basename == \"f1_of_xx1\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502631"}},{"Add":{"text":" basefunc = f1_of_xx1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502668"}},{"Add":{"text":" elif basename == \"f2_of_xx0_xx1\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502714"}},{"Add":{"text":" basefunc = f2_of_xx0_xx1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502755"}},{"Add":{"text":" elif basename == \"f3_of_xx0\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502797"}},{"Add":{"text":" basefunc = f3_of_xx0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502834"}},{"Add":{"text":" elif basename == \"f4_of_xx2\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502876"}},{"Add":{"text":" basefunc = f4_of_xx2","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502913"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:502931"}},{"Add":{"text":" print(\"Error: function inside \" + str(var) + \" undefined.\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503007"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503035"}},{"Add":{"text":" diff_result = basefunc","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503070"}},{"Add":{"text":" if derivatv == \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503101"}},{"Add":{"text":" pass","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503122"}},{"Add":{"text":" else:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503140"}},{"Add":{"text":" derivorder = derivatv.replace(\"d\", \"\").replace(\"D\", \"\").replace(\"0\", \"0 \").replace(\"1\", \"1 \").replace(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503259"}},{"Add":{"text":" \"2\", \"2 \").split(\" \")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503301"}},{"Add":{"text":" for derivdirn in derivorder:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503346"}},{"Add":{"text":" if derivdirn != \"\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503386"}},{"Add":{"text":" derivwrt = xx[int(derivdirn)]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503440"}},{"Add":{"text":" diff_result = sp.diff(diff_result, derivwrt)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503509"}},{"Add":{"text":" freevars_uniq_vals.append(diff_result)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503560"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503561"}},{"Add":{"text":" frees_uniq = superfast_uniq(diff_result.free_symbols)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503627"}},{"Add":{"text":" xx_dep = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503654"}},{"Add":{"text":" for dirn in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503688"}},{"Add":{"text":" if gri.xx[dirn] in frees_uniq:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503735"}},{"Add":{"text":" xx_dep = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503769"}},{"Add":{"text":" if xx_dep == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503801"}},{"Add":{"text":" freevars_uniq_xx_indep[i] = diff_result","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503857"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503858"}},{"Add":{"text":" # Step 6.c: Finally, substitute integers for all functions & derivatives that evaluate to integers","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:503965"}},{"Add":{"text":" for varidx in range(len(freevars_uniq)):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504014"}},{"Add":{"text":" detgammahat = detgammahat.subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504112"}},{"Add":{"text":" for i in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504145"}},{"Add":{"text":" ReU[i] = ReU[i].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504237"}},{"Add":{"text":" detgammahatdD[i] = detgammahatdD[i].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504349"}},{"Add":{"text":" for j in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504386"}},{"Add":{"text":" ReDD[i][j] = ReDD[i][j].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504490"}},{"Add":{"text":" ReUdD[i][j] = ReUdD[i][j].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504596"}},{"Add":{"text":" ghatDD[i][j] = ghatDD[i][j].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504704"}},{"Add":{"text":" ghatUU[i][j] = ghatUU[i][j].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504812"}},{"Add":{"text":" detgammahatdDD[i][j] = detgammahatdDD[i][j].subs(freevars_uniq[varidx],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:504904"}},{"Add":{"text":" freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505005"}},{"Add":{"text":" for k in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505046"}},{"Add":{"text":" ReDDdD[i][j][k] = ReDDdD[i][j][k].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505164"}},{"Add":{"text":" ReUdDD[i][j][k] = ReUdDD[i][j][k].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505282"}},{"Add":{"text":" ghatDDdD[i][j][k] = ghatDDdD[i][j][k].subs(freevars_uniq[varidx], freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505404"}},{"Add":{"text":" GammahatUDD[i][j][k] = GammahatUDD[i][j][k].subs(freevars_uniq[varidx],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505500"}},{"Add":{"text":" freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505605"}},{"Add":{"text":" for l in range(DIM):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505650"}},{"Add":{"text":" ReDDdDD[i][j][k][l] = ReDDdDD[i][j][k][l].subs(freevars_uniq[varidx],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505748"}},{"Add":{"text":" freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505855"}},{"Add":{"text":" ghatDDdDD[i][j][k][l] = ghatDDdDD[i][j][k][l].subs(freevars_uniq[varidx],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:505957"}},{"Add":{"text":" freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506068"}},{"Add":{"text":" GammahatUDDdD[i][j][k][l] = GammahatUDDdD[i][j][k][l].subs(freevars_uniq[varidx],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506178"}},{"Add":{"text":" freevars_uniq_xx_indep[varidx])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506297"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506298"}},{"Add":{"text":" # Step 7: Construct needed C code for declaring rfmstruct, allocating storage for","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506388"}},{"Add":{"text":" # rfmstruct arrays, defining each element in each array, reading the","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506473"}},{"Add":{"text":" # rfmstruct data from memory (both with and without SIMD enabled), and","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506560"}},{"Add":{"text":" # freeing allocated memory for the rfmstrcut arrays.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506629"}},{"Add":{"text":" # struct_str: String that declares the rfmstruct struct.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506694"}},{"Add":{"text":" struct_str = \"typedef struct __rfmstruct__ {\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506750"}},{"Add":{"text":" define_str = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506774"}},{"Add":{"text":" # rfmstruct stores pointers to (so far) 1D arrays. The malloc_str string allocates space for the arrays.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506887"}},{"Add":{"text":" malloc_str = \"rfm_struct rfmstruct;\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506934"}},{"Add":{"text":" freemm_str = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506958"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:506959"}},{"Add":{"text":" # readvr_str reads the arrays from memory as needed","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507019"}},{"Add":{"text":" readvr_str = [\"\", \"\", \"\"]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507053"}},{"Add":{"text":" readvr_SIMD_outer_str = [\"\", \"\", \"\"]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507098"}},{"Add":{"text":" readvr_SIMD_inner_str = [\"\", \"\", \"\"]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507143"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507144"}},{"Add":{"text":" # Sort freevars_uniq_vals and freevars_uniq_xx_indep, according to alphabetized freevars_uniq_xx_indep.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507256"}},{"Add":{"text":" # Without this step, the ordering of elements in rfmstruct would be random, and would change each time","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507370"}},{"Add":{"text":" # this function was called.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507409"}},{"Add":{"text":" if len(freevars_uniq_xx_indep) > 0:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507453"}},{"Add":{"text":" freevars_uniq_xx_indep, freevars_uniq_vals = (list(x) for x in zip(*sorted(zip(freevars_uniq_xx_indep, freevars_uniq_vals),key=str)))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507599"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507600"}},{"Add":{"text":" # Tease out how many variables each function in freevars_uniq_vals","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507675"}},{"Add":{"text":" which_freevar = 0","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507701"}},{"Add":{"text":" for expr in freevars_uniq_vals:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507741"}},{"Add":{"text":" if \"_of_xx\" in str(freevars_uniq_xx_indep[which_freevar]):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507812"}},{"Add":{"text":" frees = expr.free_symbols","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507854"}},{"Add":{"text":" frees_uniq = superfast_uniq(frees)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507905"}},{"Add":{"text":" xx_list = []","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507934"}},{"Add":{"text":" malloc_size = 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:507966"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508001"}},{"Add":{"text":" if gri.xx[i] in frees_uniq:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508049"}},{"Add":{"text":" xx_list.append(gri.xx[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508099"}},{"Add":{"text":" malloc_size *= gri.Nxx_plus_2NGHOSTS[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508163"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508164"}},{"Add":{"text":" struct_str += \"\\tREAL *restrict \" + str(freevars_uniq_xx_indep[which_freevar]) + \";\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508267"}},{"Add":{"text":" malloc_str += \"rfmstruct.\" + str(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508317"}},{"Add":{"text":" freevars_uniq_xx_indep[which_freevar]) + \" = (REAL *)malloc(sizeof(REAL)*\" + str(malloc_size) + \");\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508440"}},{"Add":{"text":" freemm_str += \"free(rfmstruct.\" + str(freevars_uniq_xx_indep[which_freevar]) + \");\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508542"}},{"Add":{"text":" output_define_and_readvr = False","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508591"}},{"Add":{"text":" for dirn in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508629"}},{"Add":{"text":" if (gri.xx[dirn] in frees_uniq) and not (gri.xx[(dirn+1)%3] in frees_uniq) and not (gri.xx[(dirn+2)%3] in frees_uniq):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:508768"}},{"Add":{"text":" define_str += \"for(int i\"+str(dirn)+\"=0;i\"+str(dirn)+\"\" + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:509366"}},{"Add":{"text":" str(freevars_uniq_xx_indep[which_freevar]) + \"[i\"+str(dirn)+\"];\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:509474"}},{"Add":{"text":" readvr_SIMD_outer_str[dirn] += \"const double NOSIMD\" + str(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:509558"}},{"Add":{"text":" freevars_uniq_xx_indep[which_freevar]) + \" = rfmstruct->\" + str(freevars_uniq_xx_indep[which_freevar]) + \"[i\"+str(dirn)+\"]; \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:509712"}},{"Add":{"text":" readvr_SIMD_outer_str[dirn] += \"const REAL_SIMD_ARRAY \" + str(freevars_uniq_xx_indep[which_freevar]) + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:509841"}},{"Add":{"text":" \" = ConstSIMD(NOSIMD\" + str(freevars_uniq_xx_indep[which_freevar]) + \");\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:509969"}},{"Add":{"text":" readvr_SIMD_inner_str[dirn] += \"const REAL_SIMD_ARRAY \" + str(freevars_uniq_xx_indep[which_freevar]) + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:510098"}},{"Add":{"text":" \" = ReadSIMD(&rfmstruct->\" + str(freevars_uniq_xx_indep[which_freevar]) + \"[i\"+str(dirn)+\"]);\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:510247"}},{"Add":{"text":" output_define_and_readvr = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:510303"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:510304"}},{"Add":{"text":" if (output_define_and_readvr == False) and (gri.xx[0] in frees_uniq) and (gri.xx[1] in frees_uniq):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:510420"}},{"Add":{"text":" define_str += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:510458"}},{"Add":{"text":"for(int i1=0;i1\" + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:510895"}},{"Add":{"text":" str(freevars_uniq_xx_indep[which_freevar]) + \"[i0 + Nxx_plus_2NGHOSTS0*i1];\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511011"}},{"Add":{"text":" readvr_SIMD_outer_str[0] += \"const double NOSIMD\" + str(freevars_uniq_xx_indep[which_freevar]) + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511130"}},{"Add":{"text":" \" = rfmstruct->\" + str(freevars_uniq_xx_indep[which_freevar]) + \"[i0 + Nxx_plus_2NGHOSTS0*i1]; \"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511275"}},{"Add":{"text":" readvr_SIMD_outer_str[0] += \"const REAL_SIMD_ARRAY \" + str(freevars_uniq_xx_indep[which_freevar]) + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511397"}},{"Add":{"text":" \" = ConstSIMD(NOSIMD\" + str(freevars_uniq_xx_indep[which_freevar]) + \");\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511521"}},{"Add":{"text":" readvr_SIMD_inner_str[0] += \"const REAL_SIMD_ARRAY \" + str(freevars_uniq_xx_indep[which_freevar]) + \\","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511643"}},{"Add":{"text":" \" = ReadSIMD(&rfmstruct->\" + str(freevars_uniq_xx_indep[which_freevar]) + \"[i0 + Nxx_plus_2NGHOSTS0*i1]);\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511800"}},{"Add":{"text":" output_define_and_readvr = True","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511852"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511853"}},{"Add":{"text":" if output_define_and_readvr == False:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:511907"}},{"Add":{"text":" print(\"ERROR: Could not figure out the (xx0,xx1,xx2) dependency within the expression for \"+str(freevars_uniq_xx_indep[which_freevar])+\":\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512067"}},{"Add":{"text":" print(str(freevars_uniq_vals[which_freevar]))","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512133"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512165"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512166"}},{"Add":{"text":" which_freevar += 1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512197"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512198"}},{"Add":{"text":" struct_str += \"} rfm_struct;\\n\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512240"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512241"}},{"Add":{"text":" # Step 8: Output needed C code to files","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512289"}},{"Add":{"text":" outdir = par.parval_from_str(thismodule+\"::rfm_precompute_Ccode_outdir\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512370"}},{"Add":{"text":" with open(outdir + \"/rfm_struct__declare.h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512437"}},{"Add":{"text":" file.write(struct_str)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512472"}},{"Add":{"text":" with open(outdir + \"/rfm_struct__malloc.h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512538"}},{"Add":{"text":" file.write(malloc_str)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512573"}},{"Add":{"text":" with open(outdir + \"/rfm_struct__define.h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512639"}},{"Add":{"text":" file.write(define_str)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512674"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512701"}},{"Add":{"text":" with open(outdir + \"/rfm_struct__read\" + str(i) + \".h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512783"}},{"Add":{"text":" file.write(readvr_str[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512825"}},{"Add":{"text":" with open(outdir + \"/rfm_struct__SIMD_outer_read\" + str(i) + \".h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512918"}},{"Add":{"text":" file.write(readvr_SIMD_outer_str[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:512971"}},{"Add":{"text":" with open(outdir + \"/rfm_struct__SIMD_inner_read\" + str(i) + \".h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513064"}},{"Add":{"text":" file.write(readvr_SIMD_inner_str[i])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513117"}},{"Add":{"text":" with open(outdir + \"/rfm_struct__freemem.h\", \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513184"}},{"Add":{"text":" file.write(freemm_str)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513219"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513220"}},{"Add":{"text":"def get_EigenCoord():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513242"}},{"Add":{"text":" CoordSystem_orig = par.parval_from_str(\"reference_metric::CoordSystem\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513318"}},{"Add":{"text":" for EigenCoordstr in [\"Spherical\",\"Cylindrical\",\"SymTP\",\"Cartesian\"]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513392"}},{"Add":{"text":" if EigenCoordstr in CoordSystem_orig:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513438"}},{"Add":{"text":" return EigenCoordstr","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513471"}},{"Add":{"text":" print(\"Error: Could not find EigenCoord for reference_metric::CoordSystem == \"+CoordSystem_orig)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513572"}},{"Add":{"text":" sys.exit(1)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513588"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513589"}},{"Add":{"text":"def set_Nxx_dxx_invdx_params__and__xx_h(outdir=\".\"):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513642"}},{"Add":{"text":" import os","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513656"}},{"Add":{"text":" with open(os.path.join(outdir,\"set_Nxx_dxx_invdx_params__and__xx.h\"),\"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513743"}},{"Add":{"text":" file.write(\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513766"}},{"Add":{"text":"void set_Nxx_dxx_invdx_params__and__xx(const int EigenCoord, const int Nxx[3], ","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513846"}},{"Add":{"text":" paramstruct *restrict params, REAL *restrict xx[3]) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:513939"}},{"Add":{"text":" // Override parameter defaults with values based on command line arguments and NGHOSTS.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514031"}},{"Add":{"text":" params->Nxx0 = Nxx[0];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514058"}},{"Add":{"text":" params->Nxx1 = Nxx[1];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514085"}},{"Add":{"text":" params->Nxx2 = Nxx[2];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514112"}},{"Add":{"text":" params->Nxx_plus_2NGHOSTS0 = Nxx[0] + 2*NGHOSTS;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514165"}},{"Add":{"text":" params->Nxx_plus_2NGHOSTS1 = Nxx[1] + 2*NGHOSTS;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514218"}},{"Add":{"text":" params->Nxx_plus_2NGHOSTS2 = Nxx[2] + 2*NGHOSTS;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514271"}},{"Add":{"text":" // Step 0d: Set up space and time coordinates","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514321"}},{"Add":{"text":" // Step 0d.i: Declare \\Delta x^i=dxx{0,1,2} and invdxx{0,1,2}, as well as xxmin[3] and xxmax[3]:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514422"}},{"Add":{"text":"#include \"set_Cparameters.h\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514451"}},{"Add":{"text":" REAL xxmin[3],xxmax[3];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514479"}},{"Add":{"text":" if(EigenCoord == 0) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514505"}},{"Add":{"text":"\"\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514510"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514537"}},{"Add":{"text":" file.write(\" xxmin[\"+str(i)+\"] = \"+str(xxmin[i])+\";\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514612"}},{"Add":{"text":" file.write(\" xxmax[\"+str(i)+\"] = \"+str(xxmax[i])+\";\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514687"}},{"Add":{"text":" file.write(\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514710"}},{"Add":{"text":" } else if (EigenCoord == 1) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514744"}},{"Add":{"text":"\"\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514749"}},{"Add":{"text":" CoordSystem_orig = par.parval_from_str(\"reference_metric::CoordSystem\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514829"}},{"Add":{"text":" par.set_parval_from_str(\"reference_metric::CoordSystem\",get_EigenCoord())","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514911"}},{"Add":{"text":" reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514938"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:514965"}},{"Add":{"text":" file.write(\" xxmin[\"+str(i)+\"] = \"+str(xxmin[i])+\";\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515040"}},{"Add":{"text":" file.write(\" xxmax[\"+str(i)+\"] = \"+str(xxmax[i])+\";\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515115"}},{"Add":{"text":" par.set_parval_from_str(\"reference_metric::CoordSystem\",CoordSystem_orig)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515197"}},{"Add":{"text":" reference_metric()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515224"}},{"Add":{"text":" file.write(\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515247"}},{"Add":{"text":" }","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515253"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515254"}},{"Add":{"text":" params->dxx0 = (xxmax[0] - xxmin[0]) / ((REAL)Nxx[0]);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515313"}},{"Add":{"text":" params->dxx1 = (xxmax[1] - xxmin[1]) / ((REAL)Nxx[1]);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515372"}},{"Add":{"text":" params->dxx2 = (xxmax[2] - xxmin[2]) / ((REAL)Nxx[2]);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515431"}},{"Add":{"text":" params->invdx0 = 1.0/params->dxx0;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515470"}},{"Add":{"text":" params->invdx1 = 1.0/params->dxx1;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515509"}},{"Add":{"text":" params->invdx2 = 1.0/params->dxx2;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515548"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515549"}},{"Add":{"text":" // Now that params.dxx{0,1,2} and params.invdxx{0,1,2} have been set,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515623"}},{"Add":{"text":" // Step 0d.iii: Set up uniform coordinate grids","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515675"}},{"Add":{"text":" xx[0] = (REAL *)malloc(sizeof(REAL)*Nxx_plus_2NGHOSTS0);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515736"}},{"Add":{"text":" for(int j=0;jdxx0; // Cell-centered grid.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515878"}},{"Add":{"text":" xx[1] = (REAL *)malloc(sizeof(REAL)*Nxx_plus_2NGHOSTS1);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:515939"}},{"Add":{"text":" for(int j=0;jdxx1; // Cell-centered grid.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516081"}},{"Add":{"text":" xx[2] = (REAL *)malloc(sizeof(REAL)*Nxx_plus_2NGHOSTS2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516142"}},{"Add":{"text":" for(int j=0;jdxx2; // Cell-centered grid.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516284"}},{"Add":{"text":" //fprintf(stderr,\"hey inside setxx: %e %e %e | %e %e\\\\n\",xxmin[0],xxmin[1],xxmin[2],xx[0][0],params->dxx0);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516396"}},{"Add":{"text":"}","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516398"}},{"Add":{"text":"\"\"\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516403"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516404"}},{"Add":{"text":"def xxCart_h(funcname,cparamsloc,outfile):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516447"}},{"Add":{"text":" import outputC","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516466"}},{"Add":{"text":" # Arbitrary-coordinate NRPy+ file output, Part 1: output the conversion from (x0,x1,x2) to Cartesian (x,y,z)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516579"}},{"Add":{"text":" Cout = outputC.outputC([xxCart[0],xxCart[1],xxCart[2]],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516639"}},{"Add":{"text":" [\"xCart[0]\",\"xCart[1]\",\"xCart[2]\"],","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516702"}},{"Add":{"text":" \"returnstring\",params=\"preindent=1\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516766"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516767"}},{"Add":{"text":" with open(outfile, \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516804"}},{"Add":{"text":" file.write(\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516827"}},{"Add":{"text":"inline void \"\"\"+funcname+\"\"\"(const paramstruct *restrict params, REAL *restrict xx[3],const int i0,const int i1,const int i2, REAL xCart[3]) {","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:516970"}},{"Add":{"text":"#include \"\"\"+\"\\\"\"+cparamsloc+\"\\\"\"+\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517008"}},{"Add":{"text":" REAL xx0 = xx[0][i0];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517034"}},{"Add":{"text":" REAL xx1 = xx[1][i1];","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517060"}},{"Add":{"text":" REAL xx2 = xx[2][i2];\\n\"\"\"+Cout+\"}\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517103"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517104"}},{"Add":{"text":"# Compute proper distance in all 3 directions. Used to find the appropriate timestep for the CFL condition.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517212"}},{"Add":{"text":"def ds_dirn(delxx):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517232"}},{"Add":{"text":" ds_dirn = ixp.zerorank1(3)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517263"}},{"Add":{"text":" for i in range(3):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517286"}},{"Add":{"text":" ds_dirn[i] = delxx[i]*scalefactor_orthog[i]","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517338"}},{"Add":{"text":" return ds_dirn","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517357"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517358"}},{"Add":{"text":"# Find the appropriate timestep for the CFL condition.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517413"}},{"Add":{"text":"def add_find_timestep_func_to_dict():","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517451"}},{"Add":{"text":" # Compute proper distance in all 3 directions.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517502"}},{"Add":{"text":" delxx = ixp.declarerank1(\"dxx\", DIM=3)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517545"}},{"Add":{"text":" ds_drn = ds_dirn(delxx)","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517573"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517574"}},{"Add":{"text":" ds_dirn_h = outputC([ds_drn[0], ds_drn[1], ds_drn[2]], [\"ds_dirn0\", \"ds_dirn1\", \"ds_dirn2\"],\"returnstring\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517686"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517687"}},{"Add":{"text":" desc=\"Find the CFL-constrained timestep\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517732"}},{"Add":{"text":" add_to_Cfunction_dict(","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517759"}},{"Add":{"text":" desc =desc,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517783"}},{"Add":{"text":" type =\"REAL\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517809"}},{"Add":{"text":" name =\"find_timestep\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517844"}},{"Add":{"text":" params =\"const paramstruct *restrict params, REAL *restrict xx[3]\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:517922"}},{"Add":{"text":" preloop =\"REAL dsmin = 1e38; // Start with a crazy high value... close to the largest number in single precision.\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518047"}},{"Add":{"text":" body =\"REAL ds_dirn0, ds_dirn1, ds_dirn2;\\n\"+ds_dirn_h+\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518118"}},{"Add":{"text":"#ifndef MIN","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518130"}},{"Add":{"text":"#define MIN(A, B) ( ((A) < (B)) ? (A) : (B) )","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518176"}},{"Add":{"text":"#endif","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518183"}},{"Add":{"text":" // Set dsmin = MIN(dsmin, ds_dirn0, ds_dirn1, ds_dirn2);","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518248"}},{"Add":{"text":" dsmin = MIN(dsmin,MIN(ds_dirn0,MIN(ds_dirn1,ds_dirn2)));","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518313"}},{"Add":{"text":"\"\"\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518318"}},{"Add":{"text":" loopopts =\"InteriorPoints,Read_xxs,DisableOpenMP\",","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518377"}},{"Add":{"text":" postloop =\"return dsmin*CFL_FACTOR/wavespeed;\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518435"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518436"}},{"Add":{"text":"def out_timestep_func_to_file(outfile):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518476"}},{"Add":{"text":" add_find_timestep_func_to_dict()","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518513"}},{"Add":{"text":" with open(outfile, \"w\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518550"}},{"Add":{"text":" file.write(outC_function_dict[\"find_timestep\"])","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518606"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518607"}},{"Add":{"text":"def out_default_free_parameters_for_rfm(free_parameters_file,","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518669"}},{"Add":{"text":" domain_size=1.0,sinh_width=0.4,sinhv2_const_dr=0.05,SymTP_bScale=0.5):","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518780"}},{"Add":{"text":" CoordSystem = par.parval_from_str(\"reference_metric::CoordSystem\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518851"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518852"}},{"Add":{"text":" with open(free_parameters_file, \"a\") as file:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518902"}},{"Add":{"text":" file.write(\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518925"}},{"Add":{"text":"// Set free-parameter values.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518955"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:518956"}},{"Add":{"text":"const REAL domain_size = \"\"\" + str(domain_size) + \"\"\";","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519014"}},{"Add":{"text":"const REAL sinh_width = \"\"\" + str(sinh_width) + \"\"\";","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519071"}},{"Add":{"text":"const REAL sinhv2_const_dr= \"\"\" + str(sinhv2_const_dr) + \"\"\";","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519133"}},{"Add":{"text":"const REAL SymTP_bScale = \"\"\" + str(SymTP_bScale) + \";\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519194"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519195"}},{"Add":{"text":" coordparams = \"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519220"}},{"Add":{"text":" if CoordSystem == \"Spherical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519259"}},{"Add":{"text":" coordparams += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519290"}},{"Add":{"text":"params.RMAX = domain_size;\\n\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519322"}},{"Add":{"text":" elif \"SinhSpherical\" in CoordSystem:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519367"}},{"Add":{"text":" coordparams += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519398"}},{"Add":{"text":"params.AMPL = domain_size;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519425"}},{"Add":{"text":"params.SINHW= sinh_width;\\n\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519457"}},{"Add":{"text":" if CoordSystem == \"SinhSphericalv2\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519506"}},{"Add":{"text":" coordparams += \" params.const_dr = sinhv2_const_dr;\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519584"}},{"Add":{"text":" elif \"SymTP\" in CoordSystem:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519621"}},{"Add":{"text":" coordparams += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519652"}},{"Add":{"text":"params.bScale = SymTP_bScale;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519683"}},{"Add":{"text":"params.AMAX = domain_size;\\n\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519718"}},{"Add":{"text":" if CoordSystem == \"SinhSymTP\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519761"}},{"Add":{"text":" coordparams += \" params.SINHWAA = sinh_width;\\n\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519833"}},{"Add":{"text":" elif CoordSystem == \"Cartesian\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519874"}},{"Add":{"text":" coordparams += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519905"}},{"Add":{"text":"params.xmin = -domain_size, params.xmax = domain_size;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:519960"}},{"Add":{"text":"params.ymin = -domain_size, params.ymax = domain_size;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520015"}},{"Add":{"text":"params.zmin = -domain_size, params.zmax = domain_size;\\n\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520075"}},{"Add":{"text":" elif CoordSystem == \"Cylindrical\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520118"}},{"Add":{"text":" coordparams += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520149"}},{"Add":{"text":"params.ZMIN = -domain_size;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520179"}},{"Add":{"text":"params.ZMAX = domain_size;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520209"}},{"Add":{"text":"params.RHOMAX = domain_size;\\n\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520244"}},{"Add":{"text":" elif \"SinhCylindrical\" in CoordSystem:","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520291"}},{"Add":{"text":" coordparams += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520322"}},{"Add":{"text":"params.AMPLRHO = domain_size;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520352"}},{"Add":{"text":"params.SINHWRHO= sinh_width;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520381"}},{"Add":{"text":"params.AMPLZ = domain_size;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520411"}},{"Add":{"text":"params.SINHWZ = sinh_width;\\n\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520445"}},{"Add":{"text":" if CoordSystem == \"SinhCylindricalv2\":","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520496"}},{"Add":{"text":" coordparams += \"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520531"}},{"Add":{"text":"params.const_drho = sinhv2_const_dr;","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520568"}},{"Add":{"text":"params.const_dz = sinhv2_const_dr;\\n\"\"\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520610"}},{"Add":{"text":" file.write(coordparams + \"\\n\")","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520649"}}]}},{"FileAdd":{"meta":{"basename":"requirements.txt","metadata":420},"path":"BaikalX/doc/nrpytutorial/requirements.txt","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"sympy","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520676"}},{"Add":{"text":"matplotlib","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520687"}}]}},{"FileAdd":{"meta":{"basename":"run_Jupyter_notebook.sh","metadata":493},"path":"BaikalX/doc/nrpytutorial/run_Jupyter_notebook.sh","context":[{"change":0,"pos":15}],"contents":[{"Add":{"text":"#!/bin/bash","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520727"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520728"}},{"Add":{"text":"if [ -z \"$1\" ]; then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520749"}},{"Add":{"text":" echo \"Correct usage of this script:\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520790"}},{"Add":{"text":" echo \"./run_Jupyter_notebook.sh [Jupyter notebook (a file with .ipynb extension)]\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520877"}},{"Add":{"text":" exit","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520886"}},{"Add":{"text":"fi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520889"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520890"}},{"Add":{"text":"if [ ! -f $1 ]; then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520911"}},{"Add":{"text":" echo \"You input: ./run_Jupyter_notebook.sh\" $1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:520962"}},{"Add":{"text":" echo \"Jupyter notebook\" \\\"$1\\\" \"not found!\"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521010"}},{"Add":{"text":" exit","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521019"}},{"Add":{"text":"fi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521022"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521023"}},{"Add":{"text":"# NRPy+ Jupyter notebooks are completely Python 2/3 cross-compatible.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521093"}},{"Add":{"text":"# However `jupyter nbconvert` will refuse to run if the notebook","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521160"}},{"Add":{"text":"# was generated using a different kernel. Here we fool Jupyter","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521225"}},{"Add":{"text":"# to think the notebook was written using the native python kernel.","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521295"}},{"Add":{"text":"PYTHONMAJORVERSION=`python -c \"import sys;print(sys.version_info[0])\"`","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521366"}},{"Add":{"text":"if (( $PYTHONMAJORVERSION == 3 )); then","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521406"}},{"Add":{"text":" cat $1 | sed \"s/ \\\"name\\\": \\\"python2\\\"/ \\\"name\\\": \\\"python3\\\"/g\" > $1-tmp ; mv $1-tmp $1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521503"}},{"Add":{"text":"else","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521508"}},{"Add":{"text":" cat $1 | sed \"s/ \\\"name\\\": \\\"python3\\\"/ \\\"name\\\": \\\"python2\\\"/g\" > $1-tmp ; mv $1-tmp $1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521605"}},{"Add":{"text":"fi","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521608"}},{"Add":{"text":"","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521609"}},{"Add":{"text":"time jupyter nbconvert --to notebook --inplace --execute --ExecutePreprocessor.timeout=-1 $1","pos":"5MZ436MULWYB6UYDJ26MWB7SUPJEN4NOXW5B5HEDIINWN32HINDAC:521702"}}]}}],"owner":"eschnett","repo":"cactusamrex","login":null}

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