{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "# Tutorial-IllinoisGRMHD: `convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C`\n", "\n", "## Authors: Leo Werneck & Zach Etienne\n", "\n", "**This module is currently under development**\n", "\n", "## This tutorial module explains the algorithm used to get the BSSN variables from the ADM variables. Further, it outlines how to impose the constraint that the conformal metric has a unit determinant.\n", "\n", "### Required and recommended citations:\n", "\n", "* **(Required)** Etienne, Z. B., Paschalidis, V., Haas R., Mösta P., and Shapiro, S. L. IllinoisGRMHD: an open-source, user-friendly GRMHD code for dynamical spacetimes. Class. Quantum Grav. 32 (2015) 175009. ([arxiv:1501.07276](http://arxiv.org/abs/1501.07276)).\n", "* **(Required)** Noble, S. C., Gammie, C. F., McKinney, J. C., Del Zanna, L. Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics. Astrophysical Journal, 641, 626 (2006) ([astro-ph/0512420](https://arxiv.org/abs/astro-ph/0512420)).\n", "* **(Recommended)** Del Zanna, L., Bucciantini N., Londrillo, P. An efficient shock-capturing central-type scheme for multidimensional relativistic flows - II. Magnetohydrodynamics. A&A 400 (2) 397-413 (2003). DOI: 10.1051/0004-6361:20021641 ([astro-ph/0210618](https://arxiv.org/abs/astro-ph/0210618))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Table of Contents\n", "$$\\label{toc}$$\n", "\n", "This module is organized as follows\n", "\n", "0. [Step 0](#src_dir): **Source directory creation**\n", "1. [Step 1](#introduction): **Introduction**\n", "1. [Step 2](#convert_adm_to_bssn__det_gammabar_eq_1): **`convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C`**\n", " 1. [Step 2.a](#physical_metric_and_its_determinant): *Loading the physical metric $\\gamma_{ij}$ and computing $\\gamma = \\det\\left(\\gamma_{ij}\\right)$*\n", " 1. [Step 2.b](#phi_and_psi): *Computing $\\phi$ and $\\psi$*\n", " 1. [Step 2.c](#enforce_det_gammabar_eq_1): *Enforcing the constraint $\\bar\\gamma = 1$*\n", " 1. [Step 2.d](#update_gfs): *Updating the gridfunctions*\n", "1. [Step 3](#code_validation): **Code validation**\n", "1. [Step 4](#latex_pdf_output): **Output this notebook to $\\LaTeX$-formatted PDF file**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step 0: Source directory creation \\[Back to [top](#toc)\\]\n", "$$\\label{src_dir}$$\n", "\n", "We will now use the [cmdline_helper.py NRPy+ module](Tutorial-Tutorial-cmdline_helper.ipynb) to create the source directory within the `IllinoisGRMHD` NRPy+ directory if it does not exist yet." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Step 0: Creation of the IllinoisGRMHD source directory\n", "# Step 0a: Add NRPy's directory to the path\n", "# https://stackoverflow.com/questions/16780014/import-file-from-parent-directory\n", "import os,sys\n", "nrpy_dir_path = os.path.join(\"..\",\"..\")\n", "if nrpy_dir_path not in sys.path:\n", " sys.path.append(nrpy_dir_path)\n", "\n", "# Step 0b: Load up cmdline_helper and create the directory\n", "import cmdline_helper as cmd\n", "IGM_src_dir_path = os.path.join(\"..\",\"src\")\n", "cmd.mkdir(IGM_src_dir_path)\n", "\n", "# Step 0c: Create the output file path\n", "outfile_path__ADM_to_BSSN__det_gammabar_eq_1__C = os.path.join(IGM_src_dir_path,\"convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step 1: Introduction \\[Back to [top](#toc)\\]\n", "$$\\label{introduction}$$\n", "\n", "In this module, we will explain the procedure used within `IllinoisGRMHD` to compute the conformal metric, $\\bar\\gamma_{ij}$, and its inverse, $\\bar\\gamma^{ij}$, from the physical metric $\\gamma_{ij}$. We will also describe how to compute $\\phi$, the conformal factor, and $\\psi\\equiv e^{\\phi}$. Finally, we also explain the procedure used to enforce the constraint $\\bar\\gamma = \\det\\left(\\bar\\gamma_{ij}\\right) = 1$.\n", "\n", "**A note on notation**: The notation used throughout the NRPy tutorial notebooks for the conformal metric is $\\bar\\gamma_{ij}$. However, in the literature, the notation $\\tilde\\gamma_{ij}$ is also used to represent the conformal metric. It is important to note that in `IllinoisGRMHD` we refer to the conformal metric using the *latter* notation, i.e. ${\\rm gtij} := \\tilde\\gamma_{ij}$ and ${\\rm gtupij} := \\tilde\\gamma^{ij}$. To keep the discussion consistent with the other notebooks, however, we will still present the discussion using the notation $\\tilde\\gamma_{ij} \\to \\bar\\gamma_{ij}$. Bottom line, here $\\tilde\\gamma_{ij}$ and $\\bar\\gamma_{ij}$ represent exactly the same quantity, the conformal metric." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step 2: `convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C` \\[Back to [top](#toc)\\]\n", "$$\\label{convert_adm_to_bssn__det_gammabar_eq_1}$$\n", "\n", "\n", "\n", "## Step 2.a: Loading the physical metric $\\gamma_{ij}$ and computing $\\gamma = \\det\\left(\\gamma_{ij}\\right)$ \\[Back to [top](#toc)\\]\n", "$$\\label{physical_metric_and_its_determinant}$$\n", "\n", "We start by reading in the physical metric ${\\rm gij\\_physL} := \\gamma_{ij}$ and computing its determinant\n", "\n", "$$\n", "\\boxed{\n", "\\begin{align}\n", "\\gamma = \\det\\left(\\gamma_{ij}\\right)\n", "&= \\gamma_{xx}\\gamma_{yy}\\gamma_{zz} + \\gamma_{xy}\\gamma_{yz}\\gamma_{xz} + \\gamma_{xz}\\gamma_{xy}\\gamma_{yz}\\\\\n", "&- \\gamma_{xz}\\gamma_{yy}\\gamma_{xz} - \\gamma_{xy}\\gamma_{xy}\\gamma_{zz} - \\gamma_{xx}\\gamma_{yz}\\gamma_{yz}\n", "\\end{align}\n", "}\\ .\n", "$$\n", "\n", "Notice that we have used the fact that $\\gamma_{ij}$ is symmetric above, i.e. $\\gamma_{ij}=\\gamma_{ji}$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Writing ../src/convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C\n" ] } ], "source": [ "%%writefile $outfile_path__ADM_to_BSSN__det_gammabar_eq_1__C\n", "#include \n", "#include \n", "#include \n", "#ifndef ENABLE_STANDALONE_IGM_C2P_SOLVER\n", "#include \"cctk.h\"\n", "#include \"cctk_Parameters.h\"\n", "#endif\n", "\n", "void IllinoisGRMHD_convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij\n", "(const cGH *cctkGH,const int *cctk_lsh,\n", " CCTK_REAL *gxx,CCTK_REAL *gxy,CCTK_REAL *gxz,CCTK_REAL *gyy,CCTK_REAL *gyz,CCTK_REAL *gzz,CCTK_REAL *alp,\n", " CCTK_REAL *gtxx,CCTK_REAL *gtxy,CCTK_REAL *gtxz,CCTK_REAL *gtyy,CCTK_REAL *gtyz,CCTK_REAL *gtzz,\n", " CCTK_REAL *gtupxx,CCTK_REAL *gtupxy,CCTK_REAL *gtupxz,CCTK_REAL *gtupyy,CCTK_REAL *gtupyz,CCTK_REAL *gtupzz,\n", " CCTK_REAL *phi,CCTK_REAL *psi,CCTK_REAL *lapm1) {\n", "\n", "#ifndef ENABLE_STANDALONE_IGM_C2P_SOLVER\n", " DECLARE_CCTK_PARAMETERS;\n", "#endif\n", "\n", "\n", "#pragma omp parallel for\n", " for(int k=0;k\n", "\n", "## Step 2.b: Computing $\\phi$ and $\\psi$ \\[Back to [top](#toc)\\]\n", "$$\\label{phi_and_psi}$$\n", "\n", "The BSSN formalism relates the physical metric, $\\gamma_{ij}$, to a conformal metric, $\\bar\\gamma{ij}$, via the relation\n", "\n", "$$\n", "\\boxed{\\bar\\gamma_{ij} = e^{-4\\phi}\\gamma_{ij}}\\ ,\n", "$$\n", "\n", "with the constraint that $\\bar\\gamma \\equiv \\det\\left(\\bar\\gamma_{ij}\\right) = 1$. This immediately implies that\n", "\n", "$$\n", "e^{-12\\phi} \\gamma = \\bar\\gamma = 1 \\implies -12\\phi = \\log\\left(\\frac{1}{\\gamma}\\right) = - \\log\\gamma\n", "\\implies \\boxed{\\phi = \\frac{1}{12}\\log\\gamma}\\ .\n", "$$\n", "\n", "Useful quantities to compute are\n", "\n", "$$\n", "\\boxed{\n", "\\begin{align}\n", "\\psi &\\equiv e^{\\phi}\\\\\n", "\\psi^{-4} &\\equiv e^{-4\\phi}\n", "\\end{align}\n", "}\\ .\n", "$$\n", "\n", "All the boxed quantities above are evaluated below." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to ../src/convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C\n" ] } ], "source": [ "%%writefile -a $outfile_path__ADM_to_BSSN__det_gammabar_eq_1__C\n", "\n", "\n", " CCTK_REAL phiL = (1.0/12.0) * log(gijdet);\n", " CCTK_REAL psiL = exp(phiL);\n", "\n", " CCTK_REAL Psim4 = 1.0/(psiL*psiL*psiL*psiL);\n", " CCTK_REAL gtxxL = gxx_physL*Psim4;\n", " CCTK_REAL gtxyL = gxy_physL*Psim4;\n", " CCTK_REAL gtxzL = gxz_physL*Psim4;\n", " CCTK_REAL gtyyL = gyy_physL*Psim4;\n", " CCTK_REAL gtyzL = gyz_physL*Psim4;\n", " CCTK_REAL gtzzL = gzz_physL*Psim4;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## Step 2.c: Enforcing the constraint $\\bar\\gamma = 1$ \\[Back to [top](#toc)\\]\n", "$$\\label{enforce_det_gammabar_eq_1}$$\n", "\n", "The BSSN formalism evolves the determinant of the conformal metric through $\\partial_{t}\\bar\\gamma = 0$. Since initially $\\bar\\gamma=1$, one would expect that $\\bar\\gamma=1$ at all times. However, numerical errors can cause the value of the determinant of the conformal metric to drift away from unity. To remedy this, we enforce the constraint $\\bar\\gamma=1$ by transforming the conformal metric according to the algebraic condition (cf. eq. 53 of [Ruchlin, Etienne, and Baumgarte (2018)](https://arxiv.org/pdf/1712.07658.pdf) with $\\hat\\gamma = 1$).\n", "\n", "$$\n", "\\boxed{\\bar{\\gamma}_{ij} \\to \\left(\\frac{1}{\\bar{\\gamma}}\\right)^{1/3} \\bar{\\gamma}_{ij}}\\ .\n", "$$\n", "\n", "We then start by evaluating\n", "\n", "$$\n", "\\boxed{\n", "\\begin{align}\n", "\\bar\\gamma = \\det\\left(\\bar\\gamma_{ij}\\right)\n", "&= \\bar\\gamma_{xx}\\bar\\gamma_{yy}\\bar\\gamma_{zz} + \\bar\\gamma_{xy}\\bar\\gamma_{yz}\\bar\\gamma_{xz} + \\bar\\gamma_{xz}\\bar\\gamma_{xy}\\bar\\gamma_{yz}\\\\\n", "&- \\bar\\gamma_{xz}\\bar\\gamma_{yy}\\bar\\gamma_{xz} - \\bar\\gamma_{xy}\\bar\\gamma_{xy}\\bar\\gamma_{zz} - \\bar\\gamma_{xx}\\bar\\gamma_{yz}\\bar\\gamma_{yz}\n", "\\end{align}\n", "}\\ .\n", "$$\n", "\n", "In the code below we also define\n", "\n", "$$\n", "\\boxed{{\\rm gtijdet\\_Fm1o3} = \\left(\\frac{1}{\\bar{\\gamma}}\\right)^{1/3}}\\ .\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to ../src/convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C\n" ] } ], "source": [ "%%writefile -a $outfile_path__ADM_to_BSSN__det_gammabar_eq_1__C\n", "\n", "\n", " /*********************************\n", " * Apply det gtij = 1 constraint *\n", " *********************************/\n", " CCTK_REAL gtijdet = gtxxL * gtyyL * gtzzL + gtxyL * gtyzL * gtxzL + gtxzL * gtxyL * gtyzL -\n", " gtxzL * gtyyL * gtxzL - gtxyL * gtxyL * gtzzL - gtxxL * gtyzL * gtyzL;\n", "\n", " CCTK_REAL gtijdet_Fm1o3 = fabs(1.0/cbrt(gtijdet));\n", "\n", " gtxxL = gtxxL * gtijdet_Fm1o3;\n", " gtxyL = gtxyL * gtijdet_Fm1o3;\n", " gtxzL = gtxzL * gtijdet_Fm1o3;\n", " gtyyL = gtyyL * gtijdet_Fm1o3;\n", " gtyzL = gtyzL * gtijdet_Fm1o3;\n", " gtzzL = gtzzL * gtijdet_Fm1o3;\n", "\n", " if(gtijdet<0.0) {\n", "#ifndef ENABLE_STANDALONE_IGM_C2P_SOLVER\n", " CCTK_VWarn(CCTK_WARN_ALERT,__LINE__, __FILE__, CCTK_THORNSTRING,\n", "#else\n", " fprintf(stderr,\n", "#endif\n", "\"WARNING: det[3-metric]<0.0 at point %d %d %d | cctk_lsh: %d %d %d. Hopefully this is occurring in gz's! gtij_phys = %.2e %.2e %.2e %.2e %.2e %.2e gtij_new = %.2e %.2e %.2e %.2e %.2e %.2e | gijdet = %.2e | gtijdet = %.2e\\n\",\n", "i,j,k,cctk_lsh[0],cctk_lsh[1],cctk_lsh[2],gxx_physL,gxy_physL,gxz_physL,gyy_physL,gyz_physL,gzz_physL,gtxxL,gtxyL,gtxzL,gtyyL,gtyzL,gtzzL,-gijdet,gtijdet);\n", "}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "## Step 2.d: Updating the gridfunctions \\[Back to [top](#toc)\\]\n", "$$\\label{update_gfs}$$\n", "\n", "Finally, we update the gridfunctions for $\\phi$, $\\psi$, $\\bar\\gamma_{ij}$, $\\gamma_{ij}$, and $\\bar\\gamma^{ij}$, respectively, in the code below.\n", "\n", "If $\\mathcal{M}$ is a $3\\times3$ symmetric matrix and $\\det(\\mathcal{M})\\neq0$, [recall that we have](https://en.wikipedia.org/wiki/Invertible_matrix#Inversion_of_3_%C3%97_3_matrices)\n", "\n", "$$\n", "\\mathcal{M}^{-1} = \n", "\\begin{pmatrix}\n", "a & b & c\\\\\n", "b & d & e\\\\\n", "c & e & f\n", "\\end{pmatrix}^{-1}\n", "=\n", "\\frac{1}{\\det(\\mathcal{M})}\n", "\\begin{pmatrix}\n", "A & B & C\\\\\n", "B & D & E\\\\\n", "C & E & F\n", "\\end{pmatrix}\\ ,\n", "$$\n", "\n", "where\n", "\n", "$$\n", "\\boxed{\n", "\\begin{align}\n", "A &= \\ \\ \\left(df - ee\\right)\\\\\n", "B &= -\\left(bf - ce\\right)\\\\\n", "C &= \\ \\ \\left(be - cd\\right)\\\\\n", "D &= \\ \\ \\left(af - cc\\right)\\\\\n", "E &= -\\left(ae - bc\\right)\\\\\n", "F &= \\ \\ \\left(ad - bb\\right)\n", "\\end{align}\n", "}\\ .\n", "$$\n", "\n", "Notice that if we replace $\\mathcal{M}\\to\\bar\\gamma_{ij}$, then we have also $\\det(\\mathcal{M})\\to1$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Appending to ../src/convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C\n" ] } ], "source": [ "%%writefile -a $outfile_path__ADM_to_BSSN__det_gammabar_eq_1__C\n", "\n", "\n", " CCTK_REAL Psi4 = psiL*psiL*psiL*psiL;\n", " /*****************************************\n", " * Set all the needed BSSN gridfunctions *\n", " *****************************************/\n", " phi[index] = phiL;\n", " psi[index] = psiL;\n", "\n", " lapm1[index] = alp[index] - 1.0;\n", "\n", " gtxx[index] = gtxxL;\n", " gtxy[index] = gtxyL;\n", " gtxz[index] = gtxzL;\n", " gtyy[index] = gtyyL;\n", " gtyz[index] = gtyzL;\n", " gtzz[index] = gtzzL;\n", "\n", " gxx[index] = gtxxL*Psi4;\n", " gxy[index] = gtxyL*Psi4;\n", " gxz[index] = gtxzL*Psi4;\n", " gyy[index] = gtyyL*Psi4;\n", " gyz[index] = gtyzL*Psi4;\n", " gzz[index] = gtzzL*Psi4;\n", "\n", " gtupxx[index] = ( gtyyL * gtzzL - gtyzL * gtyzL );\n", " gtupxy[index] = - ( gtxyL * gtzzL - gtyzL * gtxzL );\n", " gtupxz[index] = ( gtxyL * gtyzL - gtyyL * gtxzL );\n", " gtupyy[index] = ( gtxxL * gtzzL - gtxzL * gtxzL );\n", " gtupyz[index] = - ( gtxxL * gtyzL - gtxyL * gtxzL );\n", " gtupzz[index] = ( gtxxL * gtyyL - gtxyL * gtxyL );\n", " }\n", "}\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step 3: Code validation \\[Back to [top](#toc)\\]\n", "$$\\label{code_validation}$$\n", "\n", "First, we download the original `IllinoisGRMHD` source code and then compare it to the source code generated by this tutorial notebook." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Validation test for convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C: FAILED!\n", "Diff:\n", "1d0\n", "< #include \"cctk.h\"\n", "4a4,5\n", "> #ifndef ENABLE_STANDALONE_IGM_C2P_SOLVER\n", "> #include \"cctk.h\"\n", "5a7\n", "> #endif\n", "13c15,20\n", "< DECLARE_CCTK_PARAMETERS; \n", "---\n", "> \n", "> #ifndef ENABLE_STANDALONE_IGM_C2P_SOLVER\n", "> DECLARE_CCTK_PARAMETERS;\n", "> #endif\n", "> \n", "> \n", "31a39\n", "> \n", "42c50,51\n", "< \n", "---\n", "> \n", "> \n", "46c55\n", "< CCTK_REAL gtijdet = gtxxL * gtyyL * gtzzL + gtxyL * gtyzL * gtxzL + gtxzL * gtxyL * gtyzL - \n", "---\n", "> CCTK_REAL gtijdet = gtxxL * gtyyL * gtzzL + gtxyL * gtyzL * gtxzL + gtxzL * gtxyL * gtyzL -\n", "52,55c61,64\n", "< gtxyL = gtxyL * gtijdet_Fm1o3; \n", "< gtxzL = gtxzL * gtijdet_Fm1o3; \n", "< gtyyL = gtyyL * gtijdet_Fm1o3; \n", "< gtyzL = gtyzL * gtijdet_Fm1o3; \n", "---\n", "> gtxyL = gtxyL * gtijdet_Fm1o3;\n", "> gtxzL = gtxzL * gtijdet_Fm1o3;\n", "> gtyyL = gtyyL * gtijdet_Fm1o3;\n", "> gtyzL = gtyzL * gtijdet_Fm1o3;\n", "58,60c67,76\n", "< if(gtijdet<0.0) { CCTK_VWarn(CCTK_WARN_ALERT,__LINE__, __FILE__, CCTK_THORNSTRING,\n", "< \"WARNING: det[3-metric]<0.0 at point %d %d %d | cctk_lsh: %d %d %d. Hopefully this is occurring in gz's! gtij_phys = %.2e %.2e %.2e %.2e %.2e %.2e gtij_new = %.2e %.2e %.2e %.2e %.2e %.2e | gijdet = %.2e | gtijdet = %.2e\",\n", "< \t\t\t\t i,j,k,cctk_lsh[0],cctk_lsh[1],cctk_lsh[2],gxx_physL,gxy_physL,gxz_physL,gyy_physL,gyz_physL,gzz_physL,gtxxL,gtxyL,gtxzL,gtyyL,gtyzL,gtzzL,-gijdet,gtijdet); }\n", "---\n", "> if(gtijdet<0.0) {\n", "> #ifndef ENABLE_STANDALONE_IGM_C2P_SOLVER\n", "> CCTK_VWarn(CCTK_WARN_ALERT,__LINE__, __FILE__, CCTK_THORNSTRING,\n", "> #else\n", "> fprintf(stderr,\n", "> #endif\n", "> \"WARNING: det[3-metric]<0.0 at point %d %d %d | cctk_lsh: %d %d %d. Hopefully this is occurring in gz's! gtij_phys = %.2e %.2e %.2e %.2e %.2e %.2e gtij_new = %.2e %.2e %.2e %.2e %.2e %.2e | gijdet = %.2e | gtijdet = %.2e\\n\",\n", "> i,j,k,cctk_lsh[0],cctk_lsh[1],cctk_lsh[2],gxx_physL,gxy_physL,gxz_physL,gyy_physL,gyz_physL,gzz_physL,gtxxL,gtxyL,gtxzL,gtyyL,gtyzL,gtzzL,-gijdet,gtijdet);\n", "> }\n", "> \n", "92a109\n", "> \n" ] } ], "source": [ "# Verify if the code generated by this tutorial module\n", "# matches the original IllinoisGRMHD source code\n", "\n", "# First download the original IllinoisGRMHD source code\n", "import urllib\n", "from os import path\n", "\n", "original_IGM_file_url = \"https://bitbucket.org/zach_etienne/wvuthorns/raw/5611b2f0b17135538c9d9d17c7da062abe0401b6/IllinoisGRMHD/src/convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C\"\n", "original_IGM_file_name = \"convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij-original.C\"\n", "original_IGM_file_path = os.path.join(IGM_src_dir_path,original_IGM_file_name)\n", "\n", "# Then download the original IllinoisGRMHD source code\n", "# We try it here in a couple of ways in an attempt to keep\n", "# the code more portable\n", "try:\n", " original_IGM_file_code = urllib.request.urlopen(original_IGM_file_url).read().decode(\"utf-8\")\n", " # Write down the file the original IllinoisGRMHD source code\n", " with open(original_IGM_file_path,\"w\") as file:\n", " file.write(original_IGM_file_code)\n", "except:\n", " try:\n", " original_IGM_file_code = urllib.urlopen(original_IGM_file_url).read().decode(\"utf-8\")\n", " # Write down the file the original IllinoisGRMHD source code\n", " with open(original_IGM_file_path,\"w\") as file:\n", " file.write(original_IGM_file_code)\n", " except:\n", " # If all else fails, hope wget does the job\n", " !wget -O $original_IGM_file_path $original_IGM_file_url\n", "\n", "# Perform validation\n", "Validation__ADM_to_BSSN__det_gammabar_eq_1__C = !diff $original_IGM_file_path $outfile_path__ADM_to_BSSN__det_gammabar_eq_1__C\n", "\n", "if Validation__ADM_to_BSSN__det_gammabar_eq_1__C == []:\n", " # If the validation passes, we do not need to store the original IGM source code file\n", " !rm $original_IGM_file_path\n", " print(\"Validation test for convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C: PASSED!\")\n", "else:\n", " # If the validation fails, we keep the original IGM source code file\n", " print(\"Validation test for convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.C: FAILED!\")\n", " # We also print out the difference between the code generated\n", " # in this tutorial module and the original IGM source code\n", " print(\"Diff:\")\n", " for diff_line in Validation__ADM_to_BSSN__det_gammabar_eq_1__C:\n", " print(diff_line)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step 4: Output this notebook to $\\LaTeX$-formatted PDF file \\[Back to [top](#toc)\\]\n", "$$\\label{latex_pdf_output}$$\n", "\n", "The following code cell converts this Jupyter notebook into a proper, clickable $\\LaTeX$-formatted PDF file. After the cell is successfully run, the generated PDF may be found in the root NRPy+ tutorial directory, with filename\n", "[Tutorial-IllinoisGRMHD__convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.pdf](Tutorial-IllinoisGRMHD__convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.pdf) (Note that clicking on this link may not work; you may need to open the PDF file through another means)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "latex_nrpy_style_path = os.path.join(nrpy_dir_path,\"latex_nrpy_style.tplx\")\n", "#!jupyter nbconvert --to latex --template $latex_nrpy_style_path --log-level='WARN' Tutorial-IllinoisGRMHD__convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.ipynb\n", "#!pdflatex -interaction=batchmode Tutorial-IllinoisGRMHD__convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.tex\n", "#!pdflatex -interaction=batchmode Tutorial-IllinoisGRMHD__convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.tex\n", "#!pdflatex -interaction=batchmode Tutorial-IllinoisGRMHD__convert_ADM_to_BSSN__enforce_detgtij_eq_1__and_compute_gtupij.tex\n", "!rm -f Tut*.out Tut*.aux Tut*.log" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.1" } }, "nbformat": 4, "nbformat_minor": 4 }