MRST_inside_colab.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "MRST-inside-colab.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "VB7Hj7QdkHUi"
      ],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/yohanesnuwara/MRST-simulations/blob/master/MRST_inside_colab.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dtn5FdUPgSHe"
      },
      "source": [
        "Install octave in Google Colab. Takes ~2 mins"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_dca6992Zfrg",
        "outputId": "0f53a040-6dbb-4606-975b-83405f3b8567",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!apt install octave"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Reading package lists... Done\n",
            "Building dependency tree       \n",
            "Reading state information... Done\n",
            "The following additional packages will be installed:\n",
            "  aglfn epstool fonts-droid-fallback fonts-noto-mono ghostscript gnuplot-data\n",
            "  gnuplot-qt gsfonts imagemagick-6-common info install-info libamd2\n",
            "  libauthen-sasl-perl libcamd2 libccolamd2 libcholmod3 libcolamd2\n",
            "  libcupsfilters1 libcupsimage2 libcxsparse3 libdata-dump-perl libemf1\n",
            "  libencode-locale-perl libfftw3-single3 libfile-listing-perl libfltk-gl1.3\n",
            "  libfltk1.3 libfont-afm-perl libgail-common libgail18 libglpk40\n",
            "  libgraphicsmagick++-q16-12 libgraphicsmagick-q16-3 libgs9 libgs9-common\n",
            "  libgtk2.0-0 libgtk2.0-bin libgtk2.0-common libhtml-form-perl\n",
            "  libhtml-format-perl libhtml-parser-perl libhtml-tagset-perl\n",
            "  libhtml-tree-perl libhttp-cookies-perl libhttp-daemon-perl libhttp-date-perl\n",
            "  libhttp-message-perl libhttp-negotiate-perl libijs-0.35 libio-html-perl\n",
            "  libio-socket-ssl-perl libjbig2dec0 liblqr-1-0 liblua5.3-0\n",
            "  liblwp-mediatypes-perl liblwp-protocol-https-perl libmagick++-6.q16-7\n",
            "  libmagickcore-6.q16-3 libmagickwand-6.q16-3 libmailtools-perl libmetis5\n",
            "  libnet-http-perl libnet-smtp-ssl-perl libnet-ssleay-perl libnotify4\n",
            "  liboctave4 libosmesa6 libplot2c2 libportaudio2 libpstoedit0c2a libqrupdate1\n",
            "  libqscintilla2-qt5-13 libqscintilla2-qt5-l10n libqt5opengl5 libqt5svg5\n",
            "  libsuitesparseconfig5 libtext-unidecode-perl libtimedate-perl\n",
            "  libtry-tiny-perl libumfpack5 liburi-perl libwmf0.2-7 libwww-perl\n",
            "  libwww-robotrules-perl libwxbase3.0-0v5 libwxgtk3.0-0v5 libxml-libxml-perl\n",
            "  libxml-namespacesupport-perl libxml-parser-perl libxml-sax-base-perl\n",
            "  libxml-sax-expat-perl libxml-sax-perl libzip4 netbase notification-daemon\n",
            "  octave-common octave-doc perl-openssl-defaults poppler-data pstoedit\n",
            "  tex-common texinfo\n",
            "Suggested packages:\n",
            "  fonts-noto ghostscript-x gnuplot-doc texinfo-doc-nonfree libdigest-hmac-perl\n",
            "  libgssapi-perl libfftw3-bin libfftw3-dev libiodbc2-dev\n",
            "  default-libmysqlclient-dev graphicsmagick-dbg gvfs libcrypt-ssleay-perl\n",
            "  libmagickcore-6.q16-3-extra libqscintilla2-doc libwmf0.2-7-gtk\n",
            "  libauthen-ntlm-perl liboctave-dev www-browser | pdf-viewer poppler-utils\n",
            "  fonts-japanese-mincho | fonts-ipafont-mincho fonts-japanese-gothic\n",
            "  | fonts-ipafont-gothic fonts-arphic-ukai fonts-arphic-uming fonts-nanum xfig\n",
            "  | ivtools-bin | tgif | transfig debhelper texlive-base texlive-latex-base\n",
            "  texlive-generic-recommended texlive-fonts-recommended\n",
            "The following NEW packages will be installed:\n",
            "  aglfn epstool fonts-droid-fallback fonts-noto-mono ghostscript gnuplot-data\n",
            "  gnuplot-qt gsfonts imagemagick-6-common info install-info libamd2\n",
            "  libauthen-sasl-perl libcamd2 libccolamd2 libcholmod3 libcolamd2\n",
            "  libcupsfilters1 libcupsimage2 libcxsparse3 libdata-dump-perl libemf1\n",
            "  libencode-locale-perl libfftw3-single3 libfile-listing-perl libfltk-gl1.3\n",
            "  libfltk1.3 libfont-afm-perl libgail-common libgail18 libglpk40\n",
            "  libgraphicsmagick++-q16-12 libgraphicsmagick-q16-3 libgs9 libgs9-common\n",
            "  libgtk2.0-0 libgtk2.0-bin libgtk2.0-common libhtml-form-perl\n",
            "  libhtml-format-perl libhtml-parser-perl libhtml-tagset-perl\n",
            "  libhtml-tree-perl libhttp-cookies-perl libhttp-daemon-perl libhttp-date-perl\n",
            "  libhttp-message-perl libhttp-negotiate-perl libijs-0.35 libio-html-perl\n",
            "  libio-socket-ssl-perl libjbig2dec0 liblqr-1-0 liblua5.3-0\n",
            "  liblwp-mediatypes-perl liblwp-protocol-https-perl libmagick++-6.q16-7\n",
            "  libmagickcore-6.q16-3 libmagickwand-6.q16-3 libmailtools-perl libmetis5\n",
            "  libnet-http-perl libnet-smtp-ssl-perl libnet-ssleay-perl libnotify4\n",
            "  liboctave4 libosmesa6 libplot2c2 libportaudio2 libpstoedit0c2a libqrupdate1\n",
            "  libqscintilla2-qt5-13 libqscintilla2-qt5-l10n libqt5opengl5 libqt5svg5\n",
            "  libsuitesparseconfig5 libtext-unidecode-perl libtimedate-perl\n",
            "  libtry-tiny-perl libumfpack5 liburi-perl libwmf0.2-7 libwww-perl\n",
            "  libwww-robotrules-perl libwxbase3.0-0v5 libwxgtk3.0-0v5 libxml-libxml-perl\n",
            "  libxml-namespacesupport-perl libxml-parser-perl libxml-sax-base-perl\n",
            "  libxml-sax-expat-perl libxml-sax-perl libzip4 netbase notification-daemon\n",
            "  octave octave-common octave-doc perl-openssl-defaults poppler-data pstoedit\n",
            "  tex-common texinfo\n",
            "0 upgraded, 103 newly installed, 0 to remove and 12 not upgraded.\n",
            "Need to get 53.6 MB of archives.\n",
            "After this operation, 210 MB of additional disk space will be used.\n",
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            "Selecting previously unselected package libemf1:amd64.\n",
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            "Selecting previously unselected package libfltk1.3:amd64.\n",
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            "Selecting previously unselected package libwmf0.2-7:amd64.\n",
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            "Selecting previously unselected package libgraphicsmagick++-q16-12.\n",
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            "Selecting previously unselected package libhtml-tagset-perl.\n",
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            "Selecting previously unselected package liblwp-protocol-https-perl.\n",
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            "Selecting previously unselected package libmagick++-6.q16-7:amd64.\n",
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            "Selecting previously unselected package libnet-smtp-ssl-perl.\n",
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            "Selecting previously unselected package libmailtools-perl.\n",
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            "Selecting previously unselected package libqrupdate1:amd64.\n",
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            "Selecting previously unselected package libpstoedit0c2a.\n",
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            "Selecting previously unselected package libqscintilla2-qt5-l10n.\n",
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            "Selecting previously unselected package libqscintilla2-qt5-13.\n",
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            "Selecting previously unselected package libtext-unidecode-perl.\n",
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            "Selecting previously unselected package libxml-sax-base-perl.\n",
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            "Selecting previously unselected package notification-daemon.\n",
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VB7Hj7QdkHUi"
      },
      "source": [
        "## Running Optimization of a Matlab Function using Optimizers in Python"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fmPAUkwbr8Cn",
        "outputId": "735ce43b-e0f6-470d-aafd-473584f6af2a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "!pip install bayesian-optimization\n",
        "from bayes_opt import BayesianOptimization"
      ],
      "execution_count": 146,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: bayesian-optimization in /usr/local/lib/python3.6/dist-packages (1.2.0)\n",
            "Requirement already satisfied: scipy>=0.14.0 in /usr/local/lib/python3.6/dist-packages (from bayesian-optimization) (1.4.1)\n",
            "Requirement already satisfied: numpy>=1.9.0 in /usr/local/lib/python3.6/dist-packages (from bayesian-optimization) (1.18.5)\n",
            "Requirement already satisfied: scikit-learn>=0.18.0 in /usr/local/lib/python3.6/dist-packages (from bayesian-optimization) (0.22.2.post1)\n",
            "Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.6/dist-packages (from scikit-learn>=0.18.0->bayesian-optimization) (0.17.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7DY_U_ADwHjs",
        "outputId": "69619497-c20f-48cf-e6f3-0767233e2208",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile obj.m\n",
        "function z = obj(x,y)\n",
        "z = 0.9 * exp(-((x - 0.5) / 0.5)^2 - ((y - 0.5) / 0.5)^2);\n",
        "z = z + exp(-((x + 0.2) / 0.5)^2 - ((y + 0.2) / 0.5)^2); \n",
        "z = z + log1p(x*y*x*y);\n",
        "end"
      ],
      "execution_count": 138,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Overwriting obj.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j32wUpV25xtg",
        "outputId": "4d722677-661d-4f9c-f040-3d8d7ffe5c79",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile implement_obj.m\n",
        "addpath '/content' % to obtain objective function\n",
        "\n",
        "# read input from input.txt\n",
        "fileID = fopen('input.txt','r');\n",
        "formatSpec = '%f';\n",
        "P = fscanf(fileID,formatSpec);\n",
        "x = P(1); \n",
        "y = P(2);\n",
        "\n",
        "display(obj(x,y))"
      ],
      "execution_count": 139,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Overwriting implement_obj.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ECiDqVFKrSPz"
      },
      "source": [
        "def shadow_objective(x, y):\n",
        "  \"\"\"\n",
        "  Shadowing an objective function in Matlab to be called with Python\n",
        "  \n",
        "  Works by converting (x,y) input into input.txt file, then\n",
        "  run the Matlab file \"implement.m\" to extract the input.txt\n",
        "  and internally compute with the Matlab objective function \"obj\" \n",
        "  \"\"\"\n",
        "\n",
        "  # convert (x,y) input into input text file\n",
        "  input = [x, y]\n",
        "  np.savetxt('input.txt', input)\n",
        "\n",
        "  # execute matlab based on inputs given \n",
        "  z = !octave -W implement_obj.m\n",
        "\n",
        "  # output is a string. Convert output to numpy float\n",
        "  z = np.float64(z)[0]\n",
        "\n",
        "  return z"
      ],
      "execution_count": 141,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qAIHvbHF4kMU",
        "outputId": "e130b29e-7970-465d-9b02-1523b6444844",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# execute the objective function\n",
        "shadow_objective(0.2022, 0.4161)"
      ],
      "execution_count": 143,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.73546"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 143
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ht31ihjYuSnJ",
        "outputId": "8b11a219-c036-4c78-8bbb-bc2bbc5b246f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Bounded region of parameter space\n",
        "pbounds = {\"x\": (-1, 1), \"y\": (-1, 1)}\n",
        "\n",
        "optimizer = BayesianOptimization(\n",
        "    f=shadow_objective, # it is a Python obj. func. that carries a Matlab obj. func.\n",
        "    pbounds=pbounds,\n",
        "    verbose=2,  # verbose = 1 prints only when a maximum is observed, verbose = 0 is silent\n",
        "    random_state=42,\n",
        ")\n",
        "\n",
        "optimizer.maximize(init_points=5, n_iter=20)"
      ],
      "execution_count": 144,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "|   iter    |  target   |     x     |     y     |\n",
            "-------------------------------------------------\n",
            "| \u001b[0m 1       \u001b[0m | \u001b[0m 0.1071  \u001b[0m | \u001b[0m-0.2509  \u001b[0m | \u001b[0m 0.9014  \u001b[0m |\n",
            "| \u001b[95m 2       \u001b[0m | \u001b[95m 0.7202  \u001b[0m | \u001b[95m 0.464   \u001b[0m | \u001b[95m 0.1973  \u001b[0m |\n",
            "| \u001b[0m 3       \u001b[0m | \u001b[0m 0.351   \u001b[0m | \u001b[0m-0.688   \u001b[0m | \u001b[0m-0.688   \u001b[0m |\n",
            "| \u001b[0m 4       \u001b[0m | \u001b[0m 0.355   \u001b[0m | \u001b[0m-0.8838  \u001b[0m | \u001b[0m 0.7324  \u001b[0m |\n",
            "| \u001b[95m 5       \u001b[0m | \u001b[95m 0.7355  \u001b[0m | \u001b[95m 0.2022  \u001b[0m | \u001b[95m 0.4161  \u001b[0m |\n",
            "| \u001b[0m 6       \u001b[0m | \u001b[0m 0.6934  \u001b[0m | \u001b[0m 1.0     \u001b[0m | \u001b[0m-1.0     \u001b[0m |\n",
            "| \u001b[95m 7       \u001b[0m | \u001b[95m 0.815   \u001b[0m | \u001b[95m 1.0     \u001b[0m | \u001b[95m 1.0     \u001b[0m |\n",
            "| \u001b[0m 8       \u001b[0m | \u001b[0m 0.07783 \u001b[0m | \u001b[0m 0.1909  \u001b[0m | \u001b[0m-1.0     \u001b[0m |\n",
            "| \u001b[0m 9       \u001b[0m | \u001b[0m 0.06808 \u001b[0m | \u001b[0m-1.0     \u001b[0m | \u001b[0m-0.01803 \u001b[0m |\n",
            "| \u001b[0m 10      \u001b[0m | \u001b[0m 0.382   \u001b[0m | \u001b[0m 1.0     \u001b[0m | \u001b[0m 0.3126  \u001b[0m |\n",
            "| \u001b[0m 11      \u001b[0m | \u001b[0m 0.6991  \u001b[0m | \u001b[0m-1.0     \u001b[0m | \u001b[0m-1.0     \u001b[0m |\n",
            "| \u001b[0m 12      \u001b[0m | \u001b[0m 0.5812  \u001b[0m | \u001b[0m 0.5346  \u001b[0m | \u001b[0m 1.0     \u001b[0m |\n",
            "| \u001b[0m 13      \u001b[0m | \u001b[0m 0.2218  \u001b[0m | \u001b[0m 1.0     \u001b[0m | \u001b[0m-0.487   \u001b[0m |\n",
            "| \u001b[95m 14      \u001b[0m | \u001b[95m 0.8894  \u001b[0m | \u001b[95m-0.03191 \u001b[0m | \u001b[95m-0.0291  \u001b[0m |\n",
            "| \u001b[0m 15      \u001b[0m | \u001b[0m 0.6062  \u001b[0m | \u001b[0m-0.2889  \u001b[0m | \u001b[0m 0.1732  \u001b[0m |\n",
            "| \u001b[0m 16      \u001b[0m | \u001b[0m 0.5793  \u001b[0m | \u001b[0m 0.2203  \u001b[0m | \u001b[0m-0.2169  \u001b[0m |\n",
            "| \u001b[0m 17      \u001b[0m | \u001b[0m 0.6736  \u001b[0m | \u001b[0m-0.9859  \u001b[0m | \u001b[0m 0.9942  \u001b[0m |\n",
            "| \u001b[0m 18      \u001b[0m | \u001b[0m 0.7268  \u001b[0m | \u001b[0m 0.1022  \u001b[0m | \u001b[0m 0.1264  \u001b[0m |\n",
            "| \u001b[95m 19      \u001b[0m | \u001b[95m 0.9133  \u001b[0m | \u001b[95m 0.6736  \u001b[0m | \u001b[95m 0.6331  \u001b[0m |\n",
            "| \u001b[95m 20      \u001b[0m | \u001b[95m 0.9729  \u001b[0m | \u001b[95m-0.247   \u001b[0m | \u001b[95m-0.2897  \u001b[0m |\n",
            "| \u001b[0m 21      \u001b[0m | \u001b[0m 0.9641  \u001b[0m | \u001b[0m-0.3017  \u001b[0m | \u001b[0m-0.1485  \u001b[0m |\n",
            "| \u001b[95m 22      \u001b[0m | \u001b[95m 1.017   \u001b[0m | \u001b[95m-0.1564  \u001b[0m | \u001b[95m-0.1911  \u001b[0m |\n",
            "| \u001b[0m 23      \u001b[0m | \u001b[0m 0.7075  \u001b[0m | \u001b[0m 1.0     \u001b[0m | \u001b[0m 0.7575  \u001b[0m |\n",
            "| \u001b[0m 24      \u001b[0m | \u001b[0m 0.9794  \u001b[0m | \u001b[0m 0.4926  \u001b[0m | \u001b[0m 0.5352  \u001b[0m |\n",
            "| \u001b[0m 25      \u001b[0m | \u001b[0m 1.016   \u001b[0m | \u001b[0m-0.1976  \u001b[0m | \u001b[0m-0.1574  \u001b[0m |\n",
            "=================================================\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B1Jw3Dlz7Xmi",
        "outputId": "04ad03bf-caec-4151-a3f7-73409bd9f714",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        }
      },
      "source": [
        "# -------------------------\n",
        "# Plot the function\n",
        "# -------------------------\n",
        "N = 32\n",
        "n = 2 ** 7\n",
        "x = np.linspace(-1, 1, n)\n",
        "y = np.linspace(-1, 1, n)\n",
        "x, y = np.meshgrid(x, y)\n",
        "z = black_box_function(x, y)\n",
        "\n",
        "# z = []\n",
        "# for i in range(len(x)):\n",
        "#   _ = shadow_objective(x[i], y[i])\n",
        "#   z.append(_)\n",
        "\n",
        "fig = plt.figure(figsize=(4, 4))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "ax.set_title(\"Bayesian Optimization\", fontsize=15)\n",
        "# ax.contour(x, y, z, N, linewidths=0.8, colors='k')\n",
        "ax.contourf(x, y, z, N, cmap=\"RdBu_r\", vmin=-0.2, vmax=1.2)\n",
        "plt.xticks([])\n",
        "plt.yticks([])\n",
        "\n",
        "# -------------------------\n",
        "# Plot points\n",
        "# -------------------------\n",
        "# https://github.com/fmfn/BayesianOptimization/blob/master/examples/basic-tour.ipynb\n",
        "\n",
        "for i, res in enumerate(optimizer.res):\n",
        "    plt.scatter(res[\"params\"][\"x\"], res[\"params\"][\"y\"], color=\"k\", s=10)\n",
        "    plt.text(\n",
        "        res[\"params\"][\"x\"] + 0.03 + 0.03 * len(str(i)),\n",
        "        res[\"params\"][\"y\"] + 0.01,\n",
        "        str(i + 1),\n",
        "        size=10,\n",
        "        rotation=0.0,\n",
        "        ha=\"center\",\n",
        "        va=\"center\",\n",
        "    )\n",
        "\n",
        "ax.axis(\"off\")\n",
        "plt.tight_layout()\n",
        "#plt.savefig(\"bayes_opt.pdf\")\n",
        "plt.show()"
      ],
      "execution_count": 152,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2LfNk8N0kEId"
      },
      "source": [
        "## MRST"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "axdabnci5WCV",
        "outputId": "e19f1696-3509-4ad1-803c-6b8ad38f44ed",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!git clone https://github.com/yohanesnuwara/MRST-simulations"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'MRST-simulations'...\n",
            "remote: Enumerating objects: 20, done.\u001b[K\n",
            "remote: Counting objects: 100% (20/20), done.\u001b[K\n",
            "remote: Compressing objects: 100% (18/18), done.\u001b[K\n",
            "remote: Total 173 (delta 6), reused 0 (delta 0), pack-reused 153\n",
            "Receiving objects: 100% (173/173), 27.72 MiB | 23.40 MiB/s, done.\n",
            "Resolving deltas: 100% (70/70), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EL81aobrJbYa",
        "outputId": "14cbbc6f-c234-4e66-8f8f-d1e8db987eab",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!git clone https://github.com/yohanesnuwara/reservoir_datasets"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'reservoir_datasets'...\n",
            "remote: Enumerating objects: 69, done.\u001b[K\n",
            "remote: Counting objects: 100% (69/69), done.\u001b[K\n",
            "remote: Compressing objects: 100% (47/47), done.\u001b[K\n",
            "remote: Total 189 (delta 22), reused 67 (delta 20), pack-reused 120\u001b[K\n",
            "Receiving objects: 100% (189/189), 97.03 MiB | 22.15 MiB/s, done.\n",
            "Resolving deltas: 100% (44/44), done.\n",
            "Checking out files: 100% (138/138), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JhdQzMnsKwVW",
        "outputId": "60728190-2c00-4ceb-eca4-e6563f62485b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!git clone https://bitbucket.org/mrst/mrst-core.git"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'mrst-core'...\n",
            "remote: Counting objects: 8934, done.\u001b[K\n",
            "remote: Compressing objects: 100% (4594/4594), done.\u001b[K\n",
            "remote: Total 8934 (delta 6763), reused 6247 (delta 4254)\u001b[K\n",
            "Receiving objects: 100% (8934/8934), 5.71 MiB | 16.37 MiB/s, done.\n",
            "Resolving deltas: 100% (6763/6763), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MiT3dGFZQuHL",
        "outputId": "2299d905-9865-4de5-96b3-c2e447a672b5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!git clone https://yohanesnuwara@bitbucket.org/mrst/mrst-autodiff.git"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Cloning into 'mrst-autodiff'...\n",
            "remote: Counting objects: 40863, done.\u001b[K\n",
            "remote: Compressing objects: 100% (12732/12732), done.\u001b[K\n",
            "remote: Total 40863 (delta 29923), reused 37400 (delta 27804)\u001b[K\n",
            "Receiving objects: 100% (40863/40863), 15.26 MiB | 25.70 MiB/s, done.\n",
            "Resolving deltas: 100% (29923/29923), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uLl_qo3U6vfQ"
      },
      "source": [
        "## Compute Lorenz SPE10"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6y8xgx1RvAnd"
      },
      "source": [
        "### Overwriting, writing files, and modifying directories"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cYgKlIHpzbqe"
      },
      "source": [
        "#### Main program"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4FHec9XFlWvs",
        "outputId": "d41cde78-8fb5-414b-9ec4-2a979334662f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/MRST-simulations/simulations/computeLorenzSPE10.m\n",
        "%% Lorenz coefficient for layers of SPE 10, Model 2\n",
        "% In this example, we first compute the Lorenz coefficient for all layers\n",
        "% of the SPE10 model subject to a five-spot well pattern. We then pick one\n",
        "% of the layers and show how we can balance the well allocation and improve\n",
        "% the Lorenz coefficient and the areal sweep by moving some of the wells to\n",
        "% regions with better sand quality.\n",
        "%mrstModule add diagnostics spe10 incomp\n",
        "\n",
        "addpath '/content/mrst-core/utils/units'\n",
        "addpath '/content/mrst-core/gridprocessing'\n",
        "addpath '/content/mrst-core/modules'\n",
        "addpath '/content/mrst-core/params/wells_and_bc'\n",
        "addpath '/content/mrst-core/solvers'\n",
        "\n",
        "%% Base model\n",
        "% We set up a grid. Later, we will assign petrophysical properties from one\n",
        "% single layer at the time to compute Lorenz coefficients inside the main\n",
        "% loop\n",
        "cartDims = [  60,  220,  1];\n",
        "physDims = [1200, 2200, 2*cartDims(end)] .* ft();\n",
        "G  = cartGrid(cartDims, physDims);\n",
        "G  = computeGeometry(G);\n",
        "\n",
        "% Set parameters describing the \n",
        "wtype    = {'bhp', 'bhp', 'bhp', 'bhp', 'bhp'};\n",
        "wtarget  = [200,   200,   200,   200,   500] .* barsa();\n",
        "wrad     = [0.125, 0.125, 0.125, 0.125, 0.125] .* meter;\n",
        "wloc     = [  1,   60,     1,   60,  30;\n",
        "              1,    1,   220,  220, 111];\n",
        "wname    = {'P1', 'P2', 'P3', 'P4', 'I'};\n",
        "\n",
        "% Set fluid model: Here, we use a simple fluid model with properties that\n",
        "% are typical for water. Replace this by a multiphase fluid object if you\n",
        "% also want to include fluid effects in the calculation\n",
        "fluid = initSingleFluid('mu', 1*centi*poise, ...\n",
        "                        'rho', 1014*kilogram/meter^3);\n",
        "\n",
        "%% Compute Lorenz coefficient for each layer\n",
        "Lc = zeros(85,1);\n",
        "\n",
        "for n=1:85\n",
        "    \n",
        "    % --- Set petrophysical data for this particular layer\n",
        "    % To avoid problems with very small porosity values, we explicitly\n",
        "    % impose a lower threshold of 1e-4\n",
        "    rock = getSPE10rock(1:cartDims(1),1:cartDims(2),n);\n",
        "    rock.poro = max(rock.poro, 1e-4);\n",
        "    \n",
        "    % --- Set up well model\n",
        "    % To ensure that we get the correct well index when updating the\n",
        "    % petrophysical data, we simply regenerate the well objects.\n",
        "    W = [];\n",
        "    for w = 1 : numel(wtype)\n",
        "        W = verticalWell(W, G, rock, wloc(1,w), wloc(2,w), 1, ...\n",
        "            'Type', wtype{w}, 'Val', wtarget(w), ...\n",
        "            'Radius', wrad(w), 'Name', wname{w}, ...\n",
        "            'InnerProduct', 'ip_tpf', 'Comp_i', 1);\n",
        "    end\n",
        "    \n",
        "    % --- Initiate and solve flow problem \n",
        "    rS = initState(G, W, 0, 0.0);\n",
        "    T  = computeTrans(G, rock);\n",
        "    rS = incompTPFA(rS, G, T, fluid, 'wells', W);\n",
        "    \n",
        "    % --- Compute flow diagnostics\n",
        "    D       = computeTOFandTracer(rS, G, rock, 'wells', W, 'maxTOF', inf);\n",
        "    [F,Phi] = computeFandPhi(poreVolume(G,rock), D.tof);\n",
        "    Lc(n)   = computeLorenz(F,Phi);\n",
        "    [Ev,tD] = computeSweep(F, Phi);\n",
        "\n",
        "end\n",
        "\n",
        "%% Produce the results\n",
        "display(Lc) % Lorenz coefficient each layer\n",
        "display(F)  % F and Phi are Lorenz parameters\n",
        "display(Phi)\n",
        "display(Ev) % Ev and tD are sweep parameters\n",
        "display(tD)\n",
        "\n",
        "\n",
        "%{\n",
        "%% Improve Lorenz/sweep by moving wells\n",
        "% Here, we have first computed Lorenz coefficient, sweep and well-pair\n",
        "% connections for the layer with lowest/highest Lorenz coefficient and then\n",
        "% tried to move the wells having small allocation factors to the nearest\n",
        "% high-poro region that seems reasonably well connected with the injector. \n",
        "minCase = false;  %#ok<*UNRCH>\n",
        "if minCase\n",
        "    [~,n]=min(Lc);\n",
        "else\n",
        "    [~,n]=max(Lc);                                                         \n",
        "end\n",
        "rock = getSPE10rock(1:cartDims(1),1:cartDims(2),n);\n",
        "rock.poro = max(rock.poro, 1e-4);\n",
        "pv = poreVolume(G, rock);\n",
        "\n",
        "nwloc = wloc;\n",
        "fig1=figure('Position',[250 490 750 300]); col = {'b','g'};\n",
        "for nstep=1:2\n",
        "    % Set well conditions\n",
        "    W = [];\n",
        "    for w = 1 : numel(wtype)\n",
        "        W = verticalWell(W, G, rock, nwloc(1,w), nwloc(2,w), 1, ...\n",
        "            'Type', wtype{w}, 'Val', wtarget(w), ...\n",
        "            'Radius', wrad(w), 'Name', wname{w}, ...\n",
        "            'InnerProduct', 'ip_tpf');\n",
        "    end\n",
        "\n",
        "    % Compute flow field and diagnostics\n",
        "    rS = initState(G, W, 0);\n",
        "    T  = computeTrans(G, rock);\n",
        "    rS = incompTPFA(rS, G, T, fluid, 'wells', W);\n",
        "    D  = computeTOFandTracer(rS, G, rock, 'wells', W, 'maxTOF', inf);\n",
        "    WP = computeWellPairs(rS, G, rock, W, D);\n",
        "    [F,Phi] = computeFandPhi(pv, D.tof);\n",
        "    computeLorenz(F,Phi)\n",
        "    [Ev,tD] = computeSweep(F, Phi);\n",
        "\n",
        "    % Plot F-Phi and sweep diagram\n",
        "    % To reduce the number of points, we resample the data\n",
        "    figure(fig1);\n",
        "    subplot(1,2,1); hold on; \n",
        "    xq = linspace(0,1,100);\n",
        "    vq = interp1(Phi,F,xq);\n",
        "    plot(xq,vq,['-',col{nstep}],'LineWidth',2); hold off;\n",
        "    \n",
        "    subplot(1,2,2); hold on;\n",
        "    [T,ia] = unique(tD);\n",
        "    E = Ev(ia);\n",
        "    xq = linspace(0,5+(1-minCase)*20,100);\n",
        "    vq = interp1(T,E,xq);\n",
        "    plot(xq,vq,['-',col{nstep}],'LineWidth',2); hold off;\n",
        "    \n",
        "    % Plot porosity map and well-pair connections\n",
        "    figure('Position',[710   420   720   400]);\n",
        "    plotCellData(G,rock.poro,'EdgeColor','none');\n",
        "    plotWell(G,W,'height',10,'LineWidth',4);\n",
        "    plotWellPairConnections(G,WP,D,W,pv,1e-4);\n",
        "    cmap=jet(128); colormap(.4*cmap + .6*ones(size(cmap))); clear cmap;\n",
        "    view(0,70); set(gca,'DataAspectRatio',[1 1 .5]); axis off\n",
        "    cax = caxis;\n",
        "\n",
        "    % Plot zoom around each producer in separate axes\n",
        "    pos = [.05 .05 .25 .35;  .725 .05 .25 .35; ...\n",
        "        .05 .6 .25 .35; .725 .6 .25 .35];\n",
        "    for i=1:4\n",
        "        axes('position', pos(i,:));\n",
        "        if nstep==1\n",
        "            rad(:,i) = sum(bsxfun(@minus,G.cells.centroids,....\n",
        "                G.cells.centroids(W(i).cells,:)).^2,2); %#ok<SAGROW>\n",
        "        end\n",
        "        plotCellData(G,rock.poro,rad(:,i)<3500,'EdgeColor','k','EdgeAlpha',.1);\n",
        "        plotWell(G,W(i),'height',10,'LineWidth',10);\n",
        "        caxis(cax);\n",
        "        view(0,70); set(gca,'DataAspectRatio',[1 1 .5]); axis off tight;\n",
        "    end\n",
        "    \n",
        "    % Impose manually improved well positions for next pass\n",
        "    if minCase\n",
        "        nwloc     = [  1,   53,     1,   59,  30;\n",
        "                       1,    2,   218,  220, 111];\n",
        "    else\n",
        "        nwloc     = [  1,   60,     7,   60,  30;\n",
        "                       6,   11,   220,  219, 111];\n",
        "    end\n",
        "    vertcat(rS.wellSol.flux)\n",
        "end\n",
        "figure(fig1);\n",
        "subplot(1,2,1); hold on; plot([0 1],[0 1],'k'); hold off; title('Lorenz');\n",
        "subplot(1,2,2); set(gca,'XLim',[0 5+(1-minCase)*20]); title('Sweep');\n",
        "%}"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Overwriting /content/MRST-simulations/simulations/computeLorenzSPE10.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mMWhJtdOzVp2"
      },
      "source": [
        "#### Functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tkRkqMmqWpNn",
        "outputId": "9c3cd682-9456-4790-b99e-9276fded513f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/gridprocessing/tensorGrid.m\n",
        "function G = tensorGrid(x, varargin)\n",
        "%Construct Cartesian grid with variable physical cell sizes.\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   G = tensorGrid(x)\n",
        "%   G = tensorGrid(x, y)\n",
        "%   G = tensorGrid(x, y, 'depthz', dz)\n",
        "%   G = tensorGrid(x, y, z)\n",
        "%   G = tensorGrid(x, y, z, 'depthz', dz)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   x,y,z    - Vectors giving cell vertices, in units of meters, of individual\n",
        "%              coordinate directions.  Specifically, the grid cell at\n",
        "%              logical location (I,J,K) will have a physical dimension of\n",
        "%              [x(I+1)-x(I), y(J+1)-y(J), z(K+1)-z(K)] (meters).\n",
        "%\n",
        "%   dz       - Depth, in units of meters, at which upper reservoir nodes\n",
        "%              are encountered.  Assumed to be a\n",
        "%              NUMEL(x)-by-NUMEL(y) array of nodal depths.\n",
        "%\n",
        "%              OPTIONAL.\n",
        "%              Default value: depthz = ZEROS([numel(x), numel(y)])\n",
        "%                             (i.e., top of reservoir at zero depth).\n",
        "%\n",
        "%   cellnodes- OPTIONAL.\n",
        "%              Default value FALSE.  If TRUE, the corner points of each\n",
        "%              cell is added as field G.cellNodes.  The field has one row\n",
        "%              per cell, the sequence of nodes on each is (imin,\n",
        "%              jmin,kmin), (imax,jmin,kmin), (imin,jmax,kmin), ...\n",
        "%\n",
        "% RETURNS:\n",
        "%   G - Grid structure with a subset of the fields `grid_structure`.\n",
        "%       Specifically, the geometry fields are missing:\n",
        "%         - G.cells.volumes\n",
        "%         - G.cells.centroids\n",
        "%\n",
        "%         - G.faces.areas\n",
        "%         - G.faces.normals\n",
        "%         - G.faces.centroids\n",
        "%\n",
        "%       These fields may be computed using the function `computeGeometry`.\n",
        "%\n",
        "%       There is, however, an additional field not described in\n",
        "%       `grid_structure:\n",
        "%\n",
        "%           `cartDims` is a length 1, 2 or 3 vector giving number of cells\n",
        "%           in each coordinate direction.  In other words \n",
        "%\n",
        "%                      `all(G.cartDims == celldim)`.\n",
        "%\n",
        "%       `G.cells.faces(:,2)` contains integers 1-6 corresponding to\n",
        "%       directions W, E, S, N, T, B respectively.\n",
        "%\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `grid_structure`, `computeGeometry`\n",
        "\n",
        "%{\n",
        "Copyright 2009-2020 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "   % Find first char option\n",
        "   firstOpt = find(cellfun(@ischar, varargin), 1, 'first');\n",
        "   dim = nargin();\n",
        "   if ~isempty(firstOpt)\n",
        "       % If option N is char, then the dimension is N-1 since the first N-1\n",
        "       % entries correspond to coordinates. Note that there is an\n",
        "       % off-by-one offset here since we always assume at least one\n",
        "       % coordinate is given.\n",
        "       dim = firstOpt;\n",
        "   end\n",
        "\n",
        "   switch dim\n",
        "       case 1\n",
        "           G = tensorGrid1D(x, varargin{:});\n",
        "       case 2\n",
        "           G = tensorGrid2D(x, varargin{:});\n",
        "       case 3\n",
        "           G = tensorGrid3D(x, varargin{:});\n",
        "       otherwise\n",
        "           error('Invalid grid dimension \"%d\"', dim);\n",
        "   end\n",
        "\n",
        "   % Record grid constructor in grid.\n",
        "   G.type    = { mfilename };\n",
        "   G.griddim = numel(G.cartDims);\n",
        "end\n",
        "\n",
        "function G = tensorGrid3D(x, y, z, varargin)\n",
        "   addpath '/content/mrst-core/utils'\n",
        "   mrstNargInCheck(3, 5, nargin);\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Check input data -----------------------------------------------------\n",
        "   x = x(:); dx=diff(x);\n",
        "   if ~all(dx > 0)\n",
        "      warning('tensorGrid:xData', 'Nonmonotone x-data, truncating..');\n",
        "      while ~all(dx>0)\n",
        "         i = find(dx>0); x = x([1; i+1]); dx = diff(x);\n",
        "      end\n",
        "   end\n",
        "   y=y(:); dy = diff(y);\n",
        "   if ~all(dy > 0)\n",
        "      warning('tensorGrid:yData', 'Nonmonotone y-data, truncating..');\n",
        "      while ~all(dy>0)\n",
        "         i = find(dy>0); y = y([1; i+1]); dy = diff(y);\n",
        "      end\n",
        "   end\n",
        "   z=z(:); dz = diff(z);\n",
        "   if ~all(dz > 0)\n",
        "      warning('tensorGrid:yData', 'Nonmonotone z-data, truncating..');\n",
        "      while ~all(dz>0)\n",
        "         i = find(dz>0); z = z([1; i+1]); dz = diff(z);\n",
        "      end\n",
        "   end\n",
        "\n",
        "   sx = numel(x)-1; sy = numel(y)-1; sz = numel(z)-1;\n",
        "   celldim = [sx, sy, sz];\n",
        "\n",
        "   opt = struct('depthz', zeros(sx+1, sy+1), 'cellnodes', false);\n",
        "   opt = merge_options(opt, varargin{:});\n",
        "   if numel(opt.depthz) ~= (sx+1) * (sy+1)\n",
        "      error(msgid('DepthZ:WrongSize'), ...\n",
        "         'Input argument ''depthz'' is wrongly sized.')\n",
        "   end\n",
        "\n",
        "   numC = sx * sy * sz;             % Number of cells.\n",
        "   numN = (sx+1) * (sy+1) * (sz+1); % Number of nodes.\n",
        "\n",
        "   numFX = (sx+1) * sy * sz;        % Number of faces parallel to yz-plane.\n",
        "   numFY = sx * (sy+1) * sz;        % Number of faces parallel to xz-plane.\n",
        "   numFZ = sx * sy * (sz+1);        % Number of faces parallel to xy-plane.\n",
        "   numF  = numFX + numFY + numFZ;\n",
        "\n",
        "   %--------------------------------------------------------------------------\n",
        "   % Nodes/Coordinates -------------------------------------------------------\n",
        "\n",
        "   [xCoord, yCoord, zCoord] = ndgrid(x, y, z);\n",
        "\n",
        "   zCoord = bsxfun(@plus, zCoord, reshape(opt.depthz, [sx, sy] + 1));\n",
        "\n",
        "   coords = [xCoord(:), yCoord(:), zCoord(:)];\n",
        "\n",
        "   %--------------------------------------------------------------------------\n",
        "   % Generate face-edges ----------------------------------------------------\n",
        "\n",
        "   % Node index matrix\n",
        "   N = reshape(1 : numN, [sx+1, sy+1, sz+1]);\n",
        "\n",
        "   %--------------------------------------------------------------------------\n",
        "   % x-faces -----------------------------------------------------------------\n",
        "   %\n",
        "   NF1 = reshape(N(1:sx+1, 1:sy  , 1:sz  ), 1, []);\n",
        "   NF2 = reshape(N(1:sx+1, 2:sy+1, 1:sz  ), 1, []);\n",
        "   NF3 = reshape(N(1:sx+1, 2:sy+1, 2:sz+1), 1, []);\n",
        "   NF4 = reshape(N(1:sx+1, 1:sy  , 2:sz+1), 1, []);\n",
        "\n",
        "   faceNodesX = reshape([NF1; NF2; NF3; NF4], [], 1);\n",
        "\n",
        "   %--------------------------------------------------------------------------\n",
        "   % y-faces -----------------------------------------------------------------\n",
        "   %\n",
        "   NF1 = reshape(N(1:sx  , 1:sy+1, 1:sz  ), 1, []);\n",
        "   NF2 = reshape(N(1:sx  , 1:sy+1, 2:sz+1), 1, []);\n",
        "   NF3 = reshape(N(2:sx+1, 1:sy+1, 2:sz+1), 1, []);\n",
        "   NF4 = reshape(N(2:sx+1, 1:sy+1, 1:sz  ), 1, []);\n",
        "\n",
        "   faceNodesY = reshape([NF1; NF2; NF3; NF4], [], 1);\n",
        "\n",
        "   %--------------------------------------------------------------------------\n",
        "   % z-faces -----------------------------------------------------------------\n",
        "   %\n",
        "   NF1 = reshape(N(1:sx  , 1:sy,   1:sz+1), 1, []);\n",
        "   NF2 = reshape(N(2:sx+1, 1:sy,   1:sz+1), 1, []);\n",
        "   NF3 = reshape(N(2:sx+1, 2:sy+1, 1:sz+1), 1, []);\n",
        "   NF4 = reshape(N(1:sx  , 2:sy+1, 1:sz+1), 1, []);\n",
        "\n",
        "   faceNodesZ = reshape([NF1; NF2; NF3; NF4], [], 1);\n",
        "\n",
        "   %--------------------------------------------------------------------------\n",
        "   % Assemble grid_structure faceNodes structure -----------------------------\n",
        "   %\n",
        "   faceNodes = [faceNodesX; ...\n",
        "      faceNodesY; ...\n",
        "      faceNodesZ];\n",
        "\n",
        "   clear -regexp ^faceNodes. ^N ^NF.\n",
        "   %--------------------------------------------------------------------------\n",
        "   % Generate cell-faces ----------------------------------------------------\n",
        "\n",
        "   foffset = 0;\n",
        "   % Face index matrices\n",
        "   FX = reshape(foffset + (1:numFX), sx+1, sy  , sz  ); foffset = foffset + numFX;\n",
        "   FY = reshape(foffset + (1:numFY), sx  , sy+1, sz  ); foffset = foffset + numFY;\n",
        "   FZ = reshape(foffset + (1:numFZ), sx  , sy  , sz+1);\n",
        "\n",
        "   F1 = reshape(FX(1:sx  , :, :), 1, []); %W == 1\n",
        "   F2 = reshape(FX(2:sx+1, :, :), 1, []); %E == 2\n",
        "\n",
        "   F3 = reshape(FY(:, 1:sy  , :), 1, []); %S == 3\n",
        "   F4 = reshape(FY(:, 2:sy+1, :), 1, []); %N == 4\n",
        "\n",
        "   F5 = reshape(FZ(:, :, 1:sz  ), 1, []); %T == 5\n",
        "   F6 = reshape(FZ(:, :, 2:sz+1), 1, []); %B == 6\n",
        "\n",
        "   cellFaces = [reshape([F1; F2; F3; F4; F5; F6], [], 1), ...\n",
        "      kron(ones([numC, 1]), [ 1, 2, 3, 4, 5, 6]')];\n",
        "\n",
        "   clear -regexp ^F.\n",
        "\n",
        "   %--------------------------------------------------------------------------\n",
        "   % Generate neighbors -----------------------------------------------------\n",
        "\n",
        "   % Cell index matrix\n",
        "   C = zeros([sx+2, sy+2, sz+2]);\n",
        "   C(2:sx+1, 2:sy+1, 2:sz+1) = reshape(1:numC, [sx, sy, sz]);\n",
        "\n",
        "   NX1 = reshape(C( 1:sx+1, 2:sy+1, 2:sz+1), [], 1);\n",
        "   NX2 = reshape(C( 2:sx+2, 2:sy+1, 2:sz+1), [], 1);\n",
        "\n",
        "   NY1 = reshape(C( 2:sx+1, 1:sy+1, 2:sz+1), [], 1);\n",
        "   NY2 = reshape(C( 2:sx+1, 2:sy+2, 2:sz+1), [], 1);\n",
        "\n",
        "   NZ1 = reshape(C( 2:sx+1, 2:sy+1, 1:sz+1), [], 1);\n",
        "   NZ2 = reshape(C( 2:sx+1, 2:sy+1, 2:sz+2), [], 1);\n",
        "\n",
        "   neighbors = [ [NX1, NX2]; ...\n",
        "      [NY1, NY2]; ...\n",
        "      [NZ1, NZ2] ];\n",
        "\n",
        "   clear -regexp ^N..\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Generate cell nodes -------------------------------------------------\n",
        "   if opt.cellnodes\n",
        "      % Index to first node in each cell\n",
        "      k  = firstnodeindex([sx+1, sy+1, sz+1], 1:sx, 1:sy, 1:sz);\n",
        "      di = 1;\n",
        "      dj = sx+1;\n",
        "      dk = (sx+1)*(sy+1);\n",
        "      cNodes = [k, k+di, k+dj, k+di+dj, k+dk, k+di+dk, k+dj+dk, k+di+dj+dk];\n",
        "   end\n",
        "   %--------------------------------------------------------------------------\n",
        "   % Assemble structure -----------------------------------------------------\n",
        "\n",
        "   G.cells = struct('num',      numC,                   ...\n",
        "                    'facePos',  (1:6:(numC+1)*6)', ...\n",
        "                    'indexMap', (1 : numC)');\n",
        "\n",
        "   G.faces = struct('num',       numF,                   ...\n",
        "                    'nodePos',   (1:4:(numF+1)*4)', ...\n",
        "                    'neighbors', (neighbors),       ...\n",
        "                    'tag',       zeros(numF, 1));\n",
        "\n",
        "   G.nodes = struct('num', numN, 'coords', coords);\n",
        "\n",
        "   G.cells.faces = cellFaces;\n",
        "   G.faces.nodes = faceNodes;\n",
        "   if opt.cellnodes\n",
        "      G.cellNodes = cNodes;\n",
        "   end\n",
        "   G.cartDims = celldim;\n",
        "end\n",
        "\n",
        "\n",
        "function G = tensorGrid2D(x, y, varargin)\n",
        "   mrstNargInCheck(2, 4, nargin);\n",
        "   opt = struct('cellnodes', false);\n",
        "   opt = merge_options(opt, varargin{:});\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Check input data -----------------------------------------------------\n",
        "   x = x(:); dx=diff(x);\n",
        "   if ~all(dx > 0)\n",
        "      warning('tensorGrid:xData', 'Nonmonotone x-data, truncating..');\n",
        "      while ~all(dx>0)\n",
        "         i = find(dx>0); x = x([1; i+1]); dx = diff(x);\n",
        "      end\n",
        "   end\n",
        "   y=y(:); dy = diff(y);\n",
        "   if ~all(dy > 0)\n",
        "      warning('tensorGrid:yData', 'Nonmonotone y-data, truncating..');\n",
        "      while ~all(dy>0)\n",
        "         i = find(dy>0); y = y([1; i+1]); dy = diff(y);\n",
        "      end\n",
        "   end\n",
        "\n",
        "   sx = numel(x)-1; sy = numel(y)-1;\n",
        "   celldim = [sx, sy];\n",
        "\n",
        "   numC = sx * sy;             % Number of cells.\n",
        "   numN = (sx+1) * (sy+1);     % Number of nodes.s\n",
        "\n",
        "   numFX = (sx+1) * sy;        % Number of faces parallel to y-axis.\n",
        "   numFY = sx * (sy+1);        % Number of faces parallel to x-axis.\n",
        "   numF  = numFX + numFY;\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Nodes/Coordinates ----------------------------------------------------\n",
        "\n",
        "   [xCoord, yCoord] = ndgrid(x, y);\n",
        "   coords = [xCoord(:), yCoord(:)];\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Generate face-edges --------------------------------------------------\n",
        "\n",
        "   % Node index matrix\n",
        "   N = reshape(1 : numN, [sx+1, sy+1]);\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % x-faces --------------------------------------------------------------\n",
        "   %\n",
        "   NF1 = reshape(N(1:sx+1, 1:sy  ), 1, []);\n",
        "   NF2 = reshape(N(1:sx+1, 2:sy+1), 1, []);\n",
        "\n",
        "   faceNodesX = reshape([NF1; NF2], [], 1);\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % y-faces --------------------------------------------------------------\n",
        "   %\n",
        "   NF1 = reshape(N(1:sx  , 1:sy+1), 1, []);\n",
        "   NF2 = reshape(N(2:sx+1, 1:sy+1), 1, []);\n",
        "\n",
        "   faceNodesY = reshape([NF2; NF1], [], 1);\n",
        "   % Note:\n",
        "   % Nodes need to be reversed to obtain normals\n",
        "   % pointing in positive i-direction in computeGeometry.\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Assemble grid_structure faceNodes structure --------------------------\n",
        "   %\n",
        "   faceNodes = [faceNodesX; ...\n",
        "                faceNodesY];\n",
        "\n",
        "   clear -regexp ^faceNodes. ^N ^NF.\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Generate cell-faces --------------------------------------------------\n",
        "\n",
        "   foffset = 0;\n",
        "   % Face index matrices\n",
        "   FX = reshape(foffset + (1:numFX), sx+1, sy  ); foffset = foffset + numFX;\n",
        "   FY = reshape(foffset + (1:numFY), sx  , sy+1);\n",
        "\n",
        "   F1 = reshape(FX(1:sx  , :), 1, []); %W == 1\n",
        "   F2 = reshape(FX(2:sx+1, :), 1, []); %E == 2\n",
        "\n",
        "   F3 = reshape(FY(:, 1:sy  ), 1, []); %S == 3\n",
        "   F4 = reshape(FY(:, 2:sy+1), 1, []); %N == 4\n",
        "\n",
        "   cellFaces = [reshape([F1; F3; F2; F4], [], 1), ...\n",
        "                kron(ones([numC, 1]), [ 1, 3, 2, 4]')];\n",
        "\n",
        "   clear -regexp ^F.\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Generate neighbors ---------------------------------------------------\n",
        "\n",
        "   % Cell index matrix\n",
        "   C = zeros([sx+2, sy+2]);\n",
        "   C(2:sx+1, 2:sy+1) = reshape(1:numC, [sx, sy]);\n",
        "\n",
        "   NX1 = reshape(C( 1:sx+1, 2:sy+1), [], 1);\n",
        "   NX2 = reshape(C( 2:sx+2, 2:sy+1), [], 1);\n",
        "\n",
        "   NY1 = reshape(C( 2:sx+1, 1:sy+1), [], 1);\n",
        "   NY2 = reshape(C( 2:sx+1, 2:sy+2), [], 1);\n",
        "\n",
        "   neighbors = [[NX1, NX2]; [NY1, NY2]];\n",
        "\n",
        "   clear -regexp ^N..\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Generate cell nodes --------------------------------------------------\n",
        "   if opt.cellnodes\n",
        "      % Index to first node in each cell\n",
        "      k  = firstnodeindex([sx+1, sy+1], 1:sx, 1:sy);\n",
        "      di = 1;\n",
        "      dj = sx+1;\n",
        "      cNodes = [k, k+di, k+dj, k+di+dj];\n",
        "   end\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Assemble structure ---------------------------------------------------\n",
        "\n",
        "   G.cells = struct('num',      numC,                   ...\n",
        "                    'facePos',  (1:4:(numC+1)*4)', ...\n",
        "                    'indexMap', (1 : numC)');\n",
        "\n",
        "   G.faces = struct('num',       numF,                   ...\n",
        "                    'nodePos',   (1:2:(numF+1)*2)', ...\n",
        "                    'neighbors', neighbors,       ...\n",
        "                    'tag',       zeros(numF, 1));\n",
        "\n",
        "   G.nodes = struct('num', numN, 'coords', coords);\n",
        "\n",
        "   G.cells.faces = cellFaces;\n",
        "   G.faces.nodes = faceNodes;\n",
        "   if opt.cellnodes\n",
        "      G.cellNodes = cNodes;\n",
        "   end\n",
        "   G.cartDims = celldim;\n",
        "end\n",
        "\n",
        "function G = tensorGrid1D(x, varargin)\n",
        "   mrstNargInCheck(1, 3, nargin);\n",
        "   opt = struct('cellnodes', false);\n",
        "   opt = merge_options(opt, varargin{:});\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Check input data -----------------------------------------------------\n",
        "   x = x(:); dx=diff(x);\n",
        "   if ~all(dx > 0)\n",
        "      warning('tensorGrid:xData', 'Nonmonotone x-data, truncating..');\n",
        "      while ~all(dx>0)\n",
        "         i = find(dx>0); x = x([1; i+1]); dx = diff(x);\n",
        "      end\n",
        "   end\n",
        "   sx = numel(x)-1;\n",
        "   celldim = sx;\n",
        "\n",
        "   numC = sx;         % Number of cells.\n",
        "   numN = (sx+1);     % Number of nodes.\n",
        "   numF = numN;       % Number of faces.\n",
        "\n",
        "   %-----------------------------------------------------------------------\n",
        "   % Nodes/Coordinates ----------------------------------------------------\n",
        "\n",
        "   coords = x;\n",
        "   v = (0:numC)';\n",
        "   neighbors = [v, circshift(v, -1)];\n",
        "\n",
        "   G.cells = struct('num',      numC,                   ...\n",
        "                    'facePos',  (1:2:(numC+1)*2)', ...\n",
        "                    'indexMap', (1 : numC)');\n",
        "\n",
        "   G.faces = struct('num',       numF,                   ...\n",
        "                    'nodePos',   (1:numF+1)', ...\n",
        "                    'neighbors', neighbors,       ...\n",
        "                    'tag',       zeros(numF, 1));\n",
        "\n",
        "   G.nodes = struct('num', numN, 'coords', coords);\n",
        "\n",
        "   cellFaces = [1; reshape(repmat(2:numC, 2, 1), [], 1); numC+1];\n",
        "   cellFaceTag = repmat([1; 2], numC, 1);\n",
        "   % Faces are equal to nodes for this type of grid\n",
        "   G.cells.faces = [cellFaces, cellFaceTag];\n",
        "   G.faces.nodes = (1:numF)';\n",
        "   if opt.cellnodes\n",
        "      G.cellNodes = (1:numC)';\n",
        "   end\n",
        "   G.cartDims = celldim;\n",
        "end\n",
        "\n",
        "\n",
        "function k = firstnodeindex(sz, varargin)\n",
        "   assert(numel(sz) == numel(varargin));\n",
        "   assert(all(cellfun(@min, varargin) > 0));\n",
        "   assert(all(cellfun(@max, varargin)<= sz));\n",
        "\n",
        "   r       = cell(size(varargin));\n",
        "   [r{:}]  = ndgrid(varargin{:});\n",
        "   k       = reshape(sub2ind(sz, r{:}), [], 1);\n",
        "end"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Overwriting /content/mrst-core/gridprocessing/tensorGrid.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l4q1wlzzZ0Ap",
        "outputId": "17c25cc5-8a05-4fe2-9825-382adf35fb2a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/incompTPFA.m\n",
        "function state = incompTPFA(state, G, T, fluid, varargin)\n",
        "%Solve incompressible flow problem (fluxes/pressures) using TPFA method.\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   state = incompTPFA(state, G, T, fluid)\n",
        "%   state = incompTPFA(state, G, T, fluid, 'pn1', pv1, ...)\n",
        "%\n",
        "% DESCRIPTION:\n",
        "%   This function assembles and solves a (block) system of linear equations\n",
        "%   defining interface fluxes and cell pressures at the next time step in a\n",
        "%   sequential splitting scheme for the reservoir simulation problem\n",
        "%   defined by Darcy's law and a given set of external influences (wells,\n",
        "%   sources, and boundary conditions).\n",
        "%\n",
        "%   This function uses a two-point flux approximation (TPFA) method with\n",
        "%   minimal memory consumption within the constraints of operating on a\n",
        "%   fully unstructured polyhedral grid structure.\n",
        "%\n",
        "% REQUIRED PARAMETERS:\n",
        "%   state  - Reservoir and well solution structure either properly\n",
        "%            initialized from functions 'initResSol' and 'initWellSol'\n",
        "%            respectively, or the results from a previous call to function\n",
        "%            'incompTPFA' and, possibly, a transport solver such as\n",
        "%            function 'implicitTransport'.\n",
        "%\n",
        "%   G, T   - Grid and half-transmissibilities as computed by the function\n",
        "%            'computeTrans'.\n",
        "%\n",
        "%   fluid  - Fluid object as defined by function 'initSimpleFluid'.\n",
        "%\n",
        "% OPTIONAL PARAMETERS:\n",
        "%   W      - Well structure as defined by function 'addWell'.  May be empty\n",
        "%            (i.e., W = []) which is interpreted as a model without\n",
        "%            any wells.\n",
        "%\n",
        "%   bc     - Boundary condition structure as defined by function 'addBC'.\n",
        "%            This structure accounts for all external boundary conditions to\n",
        "%            the reservoir flow.  May be empty (i.e., bc = struct([])) which\n",
        "%            is interpreted as all external no-flow (homogeneous Neumann)\n",
        "%            conditions.\n",
        "%\n",
        "%   src    - Explicit source contributions as defined by function\n",
        "%            'addSource'.  May be empty (i.e., src = struct([])) which is\n",
        "%            interpreted as a reservoir model without explicit sources.\n",
        "%\n",
        "%   LinSolve     - Handle to linear system solver software to which the\n",
        "%                  fully assembled system of linear equations will be\n",
        "%                  passed.  Assumed to support the syntax\n",
        "%\n",
        "%                        x = LinSolve(A, b)\n",
        "%\n",
        "%                  in order to solve a system Ax=b of linear equations.\n",
        "%                  Default value: LinSolve = @mldivide (backslash).\n",
        "%\n",
        "%   MatrixOutput - Whether or not to return the final system matrix 'A' to\n",
        "%                  the caller of function 'incompTPFA'.\n",
        "%                  Logical.  Default value: MatrixOutput = FALSE.\n",
        "%\n",
        "%   verbose - Enable output.  Default value dependent upon global verbose\n",
        "%             settings of function 'mrstVerbose'.\n",
        "%\n",
        "%   condition_number - Display estimated condition number of linear system.\n",
        "%\n",
        "%   gravity   - The current gravity in vector form. Defaults to gravity().\n",
        "%\n",
        "% RETURNS:\n",
        "%   state - Update reservoir and well solution structure with new values\n",
        "%           for the fields:\n",
        "%              - pressure -- Pressure values for all cells in the\n",
        "%                            discretised reservoir model, 'G'.\n",
        "%              - facePressure --\n",
        "%                            Pressure values for all interfaces in the\n",
        "%                            discretised reservoir model, 'G'.\n",
        "%              - flux     -- Flux across global interfaces corresponding to\n",
        "%                            the rows of 'G.faces.neighbors'.\n",
        "%              - A        -- System matrix.  Only returned if specifically\n",
        "%                            requested by setting option 'MatrixOutput'.\n",
        "%\n",
        "%              - wellSol  -- Well solution structure array, one element for\n",
        "%                            each well in the model, with new values for\n",
        "%                            the fields:\n",
        "%                              - flux     -- Perforation fluxes through all\n",
        "%                                            perforations for corresponding\n",
        "%                                            well.  The fluxes are\n",
        "%                                            interpreted as injection\n",
        "%                                            fluxes, meaning positive\n",
        "%                                            values correspond to injection\n",
        "%                                            into reservoir while negative\n",
        "%                                            values mean\n",
        "%                                            production/extraction out of\n",
        "%                                            reservoir.\n",
        "%                              - pressure -- Well bottom-hole pressure.\n",
        "%\n",
        "% NOTE:\n",
        "%   If there are no external influences, i.e., if all of the structures\n",
        "%   'W', 'bc', and 'src' are empty and there are no effects of gravity,\n",
        "%   then the input values 'xr' and 'xw' are returned unchanged and a\n",
        "%   warning is printed in the command window. This warning is printed with\n",
        "%   message ID\n",
        "%\n",
        "%           'incompTPFA:DrivingForce:Missing'\n",
        "%\n",
        "% EXAMPLE:\n",
        "%    G   = computeGeometry(cartGrid([3, 3, 5]));\n",
        "%\n",
        "%    f   = initSingleFluid('mu' , 1*centi*poise, ...\n",
        "%                          'rho', 1000*kilogram/meter^3);\n",
        "%    rock.perm = rand(G.cells.num, 1)*darcy()/100;\n",
        "%\n",
        "%    bc  = pside([], G, 'LEFT', 2*barsa);\n",
        "%    src = addSource([], 1, 1);\n",
        "%    W   = verticalWell([], G, rock, 1, G.cartDims(2), []   , ...\n",
        "%                       'Type', 'rate', 'Val', 1*meter^3/day, ...\n",
        "%                       'InnerProduct', 'ip_tpf');\n",
        "%    W   = verticalWell(W, G, rock, G.cartDims(1), G.cartDims(2), [], ...\n",
        "%                       'Type', 'bhp', 'Val', 1*barsa, ...\n",
        "%                       'InnerProduct', 'ip_tpf');\n",
        "%\n",
        "%    T   = computeTrans(G, rock);\n",
        "%\n",
        "%    state         = initResSol (G, 10);\n",
        "%    state.wellSol = initWellSol(G, 10);\n",
        "%\n",
        "%    state = incompTPFA(state, G, T, f, 'bc', bc, 'src', src, ...\n",
        "%                       'wells', W, 'MatrixOutput', true);\n",
        "%\n",
        "%    plotCellData(G, state.pressure)\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `computeTrans`, `addBC`, `addSource`, `addWell`, `initSingleFluid`, `initResSol`,\n",
        "%   `initWellSol`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "\n",
        "   opt = struct('bc', [], 'src', [], 'wells', [], ...\n",
        "                'W', [], 'bcp',[],...\n",
        "                'LinSolve',     @mldivide,        ...\n",
        "                'MatrixOutput', false, ...\n",
        "                'Verbose',      mrstVerbose,...\n",
        "                'gravity',      gravity(), ...\n",
        "                'condition_number',false,...\n",
        "                'pc_form','nonwetting',...\n",
        "                'reduce',false,...\n",
        "                'use_trans',false);\n",
        "\n",
        "   opt = merge_options(opt, varargin{:});\n",
        "   opt = treatLegacyForceOptions(opt);\n",
        "   do_solve = checkDrivingForcesIncomp(G, opt);\n",
        "   if ~do_solve\n",
        "       return\n",
        "   end\n",
        "\n",
        "   g_vec   = opt.gravity;\n",
        "   % If gravity is overriden, we cannot say anything about the effects of\n",
        "   % gravity on rhs.\n",
        "   grav = (norm(g_vec(1:G.griddim)) > 0) || isfield(G, 'grav_pressure');\n",
        "\n",
        "   if all([~opt.MatrixOutput , ...\n",
        "           isempty(opt.bc)   , ...\n",
        "           isempty(opt.src)  , ...\n",
        "           isempty(opt.bcp)  , ...\n",
        "           isempty(opt.wells), ~grav])\n",
        "      warning(msgid('DrivingForce:Missing'),                   ...\n",
        "             ['No external driving forces present in model--', ...\n",
        "              'state remains unchanged.\\n']);\n",
        "   end\n",
        "\n",
        "   % ---------------------------------------------------------------------\n",
        "   dispif(opt.Verbose, 'Setting up linear system...\\t\\t\\t');\n",
        "   t0 = ticif (opt.Verbose);\n",
        "\n",
        "   % Preliminaries\n",
        "   [neighborship, n_isnnc] = getNeighbourship(G, 'Topological', true);\n",
        "   [cellNo, cf, cn_isnnc] = getCellNoFaces(G);\n",
        "   nif    = size(neighborship, 1);\n",
        "   ncf    = size(cf, 1);\n",
        "   nc     = G.cells.num;\n",
        "   nw     = length(opt.wells);\n",
        "   n      = nc + nw;\n",
        "\n",
        "   [mob, omega, rho] = dynamic_quantities(state, fluid);\n",
        "   totmob = sum(mob, 2);\n",
        "\n",
        "   % Compute effective (mobility-weighted) transmissibilities.\n",
        "   [T, ft] = compute_trans(G, T, cellNo, cf, neighborship, totmob, opt);\n",
        "\n",
        "   % Identify internal faces\n",
        "   i  = all(neighborship ~= 0, 2);\n",
        "\n",
        "   % Boundary conditions and source terms.\n",
        "   hh = zeros(nif, 1);\n",
        "   dF = false(nif, 1);\n",
        "   [grav, ff] = deal(zeros(ncf, 1));\n",
        "\n",
        "   [ff(~cn_isnnc), gg, hh(~n_isnnc), ...\n",
        "    grav(~cn_isnnc), dF(~n_isnnc), dC] = ...\n",
        "      computePressureRHS(G, omega, opt.bc, opt.src);\n",
        "\n",
        "   % made to add capillary pressure\n",
        "   pc = getIncompCapillaryPressure(state, fluid);\n",
        "   if ~isempty(pc)\n",
        "      if any(abs(pc) > 0)\n",
        "         cc = capPressureRHS(G, mob, pc, opt.pc_form);\n",
        "         grav = grav + cc;\n",
        "      end\n",
        "   end\n",
        "\n",
        "   sgn = 2*(neighborship(cf, 1) == cellNo) - 1;\n",
        "   j   = i(cf) | dF(cf);\n",
        "   fg  = accumarray(cf(j), grav(j).*sgn(j), [nif, 1]);\n",
        "   if ~isempty(opt.bcp)\n",
        "      fg(opt.bcp.face) = fg(opt.bcp.face) + opt.bcp.value;\n",
        "      warning('mrst:periodic_bc', ...\n",
        "             ['Face pressures are not well defined for ', ...\n",
        "              'periodic boundary faces']);\n",
        "\n",
        "      if any(G.faces.neighbors(:,1) == G.faces.neighbors(:,2))\n",
        "         error(['Periodic boundary: This code do not work ', ...\n",
        "                'if a face is in and outflow']);\n",
        "      end\n",
        "   end\n",
        "\n",
        "\n",
        "   rhs = accumarray(cellNo, -ft(cf).*(sgn.*fg(cf)+ff), [n, 1]) + ...\n",
        "         [gg; zeros(nw, 1)]                                    + ...\n",
        "         accumarray(cellNo, -hh(cf), [n, 1]); clear sgn;\n",
        "\n",
        "\n",
        "   d  = zeros(G.cells.num, 1);\n",
        "\n",
        "   % Wells --------------------------\n",
        "   C    = cell (nw, 1);\n",
        "   D    = zeros(nw, 1);\n",
        "   W    = opt.wells;\n",
        "\n",
        "   for k = 1 : nw\n",
        "      wc       = W(k).cells;\n",
        "      nwc      = numel(wc);\n",
        "      w        = k + nc;\n",
        "\n",
        "      wi       = W(k).WI .* totmob(wc);\n",
        "      dp       = computeIncompWellPressureDrop(W(k), mob, rho, norm(gravity));\n",
        "      d   (wc) = d   (wc) + wi;\n",
        "      state.wellSol(k).cdp = dp;\n",
        "      if     strcmpi(W(k).type, 'bhp')\n",
        "         ww=max(wi);\n",
        "         rhs (w)  = rhs (w)  + ww*W(k).val;\n",
        "         rhs (wc) = rhs (wc) + wi.*(W(k).val + dp);\n",
        "         C{k}     = -sparse(1, nc);\n",
        "         D(k)     = ww;\n",
        "\n",
        "      elseif strcmpi(W(k).type, 'rate')\n",
        "         rhs (w)  = rhs (w)  + W(k).val;\n",
        "         rhs (wc) = rhs (wc) + wi.*dp;\n",
        "\n",
        "         C{k}     =-sparse(ones(nwc, 1), wc, wi, 1, nc);\n",
        "         D(k)     = sum(wi);\n",
        "\n",
        "         rhs (w)  = rhs (w) - wi.'*dp;\n",
        "\n",
        "      else\n",
        "         error('Unsupported well type.');\n",
        "      end\n",
        "   end\n",
        "\n",
        "   C = vertcat(C{:});\n",
        "   D = spdiags(D, 0, nw, nw);\n",
        "   %-----------------------------------------\n",
        "\n",
        "\n",
        "   % Add up internal face transmissibilities plus Dirichlet pressure\n",
        "   % faces for each cell.\n",
        "   d  = d + ...\n",
        "        accumarray(cellNo(dF(cf)), T(dF(cf)), [nc, 1]) +...\n",
        "        accumarray(reshape(neighborship(i,:), [], 1), ...\n",
        "                   repmat(ft(i), [2,1]),  [nc, 1]);\n",
        "\n",
        "   % Assemble coefficient matrix for internal faces.  Boundary conditions\n",
        "   % may introduce additional diagonal entries.  Also, wells introduce\n",
        "   % additional equations and unknowns.\n",
        "   I  = [neighborship(i,1); neighborship(i,2); (1:nc)'];\n",
        "   J  = [neighborship(i,2); neighborship(i,1); (1:nc)'];\n",
        "   V  = [-ft(i); -ft(i); d]; clear d;\n",
        "   A  = sparse(double(I), double(J), V, nc, nc);\n",
        "   A = [A, C'; C D]; \n",
        "   if(~opt.reduce)\n",
        "    clear I J V C D;\n",
        "   end\n",
        "   tocif(opt.Verbose, t0);\n",
        "   \n",
        "   % if reduce to cells\n",
        "\n",
        "\n",
        "   % ---------------------------------------------------------------------\n",
        "   dispif(opt.Verbose, 'Solving linear system...\\t\\t\\t');\n",
        "   t0 = ticif (opt.Verbose);\n",
        "\n",
        "   if ~any(dF) && (isempty(W) || ~any(strcmpi({ W.type }, 'bhp')))\n",
        "      if A(1) > 0\n",
        "         A(1) = 2*A(1);\n",
        "      else\n",
        "         [j, j] = max(diag(A));  %#ok\n",
        "         A(j,j) = 2 * A(j,j);\n",
        "      end\n",
        "   end\n",
        "\n",
        "   if opt.condition_number\n",
        "      disp('***************************************');\n",
        "      disp(['Conditon number is :   ', num2str(condest(A))]);\n",
        "      disp('***************************************');\n",
        "   end\n",
        "   if opt.MatrixOutput\n",
        "      state.A   = A;\n",
        "      state.rhs = rhs;\n",
        "   end\n",
        "   \n",
        "   if(opt.reduce)\n",
        "      rhs_r = rhs(1:nc);\n",
        "      A_r = A(1:nc,1:nc);\n",
        "      rhs_w = rhs(nc+1:end);\n",
        "      rhs_r = rhs_r - C'*(D\\ rhs_w);\n",
        "      A_r = A_r - C'*(D\\C);\n",
        "      state.A = A_r;\n",
        "      state.rhs = rhs_r;\n",
        "      p_r = opt.LinSolve(A_r, rhs_r);\n",
        "      p = nan(size(rhs));\n",
        "      p(1:nc) = p_r;\n",
        "      p(nc+1:end) = D\\(rhs_w - C*p_r);\n",
        "   else \n",
        "    p = opt.LinSolve(A, rhs);\n",
        "   end \n",
        "   tocif(opt.Verbose, t0);\n",
        "\n",
        "   clear A rhs;\n",
        "\n",
        "   % ---------------------------------------------------------------------\n",
        "   dispif(opt.Verbose, 'Computing fluxes, face pressures etc...\\t\\t');\n",
        "   t0 = ticif (opt.Verbose);\n",
        "\n",
        "   % Reconstruct face pressures and fluxes.\n",
        "   fpress     =  ...\n",
        "          accumarray(cf, (p(cellNo)+grav).*T, [nif, 1])./ ...\n",
        "          accumarray(cf(:,1), T, [nif,1]);\n",
        "\n",
        "\n",
        "   % Neumann faces\n",
        "   b         = any(G.faces.neighbors==0, 2);\n",
        "   fpress(b) = fpress(b) - hh(b)./ft(b);\n",
        "\n",
        "\n",
        "   % Contribution from gravity\n",
        "   %fg         = accumarray(cf, grav.*sgn, [nf, 1]);\n",
        "   %fpress(~i) = fpress(~i) + fg(~i);\n",
        "\n",
        "   % Dirichlet faces\n",
        "   fpress(dF) = dC;\n",
        "\n",
        "\n",
        "   % Sign for boundary faces\n",
        "   sgn  = 2*(G.faces.neighbors(~i,2)==0)-1;\n",
        "   ni   = neighborship(i,:);\n",
        "   flux = -accumarray(find(i),  ft(i) .*(p(ni(:,2))-p(ni(:,1))-fg(i)), [nif, 1]);\n",
        "   c    = sum(G.faces.neighbors(~i,:),2) ;\n",
        "   fg  = accumarray(cf, grav, [nif, 1]);\n",
        "   flux(~i) = -sgn.*ft(~i).*( fpress(~i) - p(c) - fg(~i) );\n",
        "   %flux = -sgn.*ft((fpress(~i)-p(c)-grav));\n",
        "   state.pressure(1 : nc) = p(1 : nc);\n",
        "   state.flux             = flux;\n",
        "   state.facePressure     = fpress;\n",
        "\n",
        "   for k = 1 : nw\n",
        "      wc = W(k).cells;\n",
        "      dp = state.wellSol(k).cdp;\n",
        "      state.wellSol(k).flux     = W(k).WI.*totmob(wc).*(p(nc+k) + dp - p(wc));\n",
        "      state.wellSol(k).pressure = p(nc + k);\n",
        "   end\n",
        "\n",
        "   tocif(opt.Verbose, t0);\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function [mob, omega, rho] = dynamic_quantities(state, fluid)\n",
        "   [rho, kr, mu] = getIncompProps(state, fluid);\n",
        "   mob    = bsxfun(@rdivide, kr, mu);\n",
        "   totmob = sum(mob, 2);\n",
        "   omega  = sum(bsxfun(@times, mob, rho), 2) ./ totmob;\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function [T, ft] = compute_trans(G, T, cellNo, cellFaces, neighborship, totmob, opt) %#ok\n",
        "    niface = size(neighborship, 1);\n",
        "    if opt.use_trans\n",
        "      neighborcount = sum(neighborship > 0, 2);\n",
        "      assert (numel(T) == niface, ...\n",
        "             ['Expected one transmissibility for each interface ', ...\n",
        "              '(=%d) but got %d.'], niface, numel(T));\n",
        "\n",
        "      fmob = accumarray(cellFaces, totmob(cellNo), ...\n",
        "                        [niface, 1]);\n",
        "  \n",
        "      fmob = fmob ./ neighborcount;\n",
        "      ft   = T .* fmob;\n",
        "\n",
        "      % Synthetic one-sided transmissibilities.\n",
        "      th = ft .* neighborcount;\n",
        "      T  = th(cellFaces(:,1));\n",
        "\n",
        "   else\n",
        "\n",
        "      % Define face transmissibility as harmonic average of mobility\n",
        "      % weighted one-sided transmissibilities.\n",
        "      %\n",
        "      assert (numel(T) == numel(cellNo), ...\n",
        "             ['Expected one one-sided transmissibility for each ', ...\n",
        "              'half face (=%d), but got %d.'], numel(cellNo), numel(T));\n",
        "\n",
        "      T  = T .* totmob(cellNo);\n",
        "      ft = 1 ./ accumarray(cellFaces, 1 ./ T, [niface, 1]);\n",
        "\n",
        "   end\n",
        "end"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/incompTPFA.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GrGEDM6vigu3",
        "outputId": "b826c406-5108-4cc1-a2b1-6240c67d0ff6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/computeFandPhi.m\n",
        "function [F,Phi] = computeFandPhi(arg1, varargin)\n",
        "%Compute flow-capacity/storage-capacity diagram (F,Phi)\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   [F,Phi] = computeFandPhi(pv, tof)\n",
        "%   [F,Phi] = computeFandPhi(rtd)\n",
        "%   [F,Phi] = computeFandPhi(rtd, 'sum', true/false);\n",
        "%\n",
        "% DESCRIPTION:\n",
        "%   Compute the flow-capacity/storage-capacity based upon either:\n",
        "%    1. Pore volumes and time-of-flight values per cell. In this case,\n",
        "%       Phi is defined as the cumulative pore volume and F is the\n",
        "%       cumulative flux as function of residence time. Assuming\n",
        "%       incompressible flow, the instant flux is computed as the ratio of\n",
        "%       pore volume and the residence time.\n",
        "%    2. Residence-time distribution. In this case, F is the integral of the\n",
        "%       RTD values, whereas Phi is the first-order moment (i.e., the\n",
        "%       integral of the product of time and RTD values).\n",
        "%   Making an analogue to 1D displacement theory, the F-Phi curve is the\n",
        "%   equivalent to a plot of the fractional flow versus saturation.\n",
        "%   Technical description: see Section 13.2-13.3 in the MRST book, Shavali\n",
        "%   et al. (SPE 146446), and Shook and Mitchell (SPE 124625)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   vol - pore volume, one value per cell\n",
        "%   tof - two-component vector with time-of-flight from injector and\n",
        "%         time-of-flight from producer, one value per cell\n",
        "%   rtd - structure with residence-time distribution from computeRTD\n",
        "%\n",
        "% RETURNS:\n",
        "%   F   - flow capacity = cumulative flux for increasing time-of-flight\n",
        "%         values, where the flux per cell is defined from the relation\n",
        "%                volume = flux * total_travel_time\n",
        "%   Phi - storage capacity = cumulative pore volume for increasing\n",
        "%         time-of-flight values\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `computeTOFandTracer`, `computeLorenz`, `computeSweep`\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "if isstruct(arg1)\n",
        "    [F,Phi] = computeFandPhiFromDist(arg1, varargin{:});\n",
        "    return\n",
        "else\n",
        "    pv = arg1; tof = varargin{1};\n",
        "end\n",
        "\n",
        "assert(size(tof,2) == 2, 'Tof input must have two columns.')\n",
        "\n",
        "t      = sum(tof,2);     % total travel time\n",
        "[ts,order] = sort(t);    % sort cells base on travel time\n",
        "v      = pv(order);      % put volumes in order\n",
        "Phi    = cumsum(v);      % cumulative sum\n",
        "vt     = full(Phi(end)); % total volume of region\n",
        "Phi    = [0; Phi/vt];    % normalize to units of pore volumes\n",
        "flux   = v./ts;          % back out flux based on incompressible flow\n",
        "ff     = cumsum(flux);   % cumulative sum\n",
        "ft     = full(ff(end));  % total flux computed\n",
        "F      = [0; ff/ft];     % normalize and store flux\n",
        "end"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/computeFandPhi.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bOrCw6MozjU-",
        "outputId": "eed0e376-6e2c-4669-d12f-2a4dea70e2a7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/computeSweep.m\n",
        "function [Ev,tD] = computeSweep(F,Phi)\n",
        "%Compute sweep efficiency versus dimensionless time (PVI)\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   [Ev,tD] = computeSweep(F, Phi)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   F   - flow capacity\n",
        "%   Phi - storage capacity\n",
        "%\n",
        "% RETURNS:\n",
        "%   tD  - dimensionless time (PVI)\n",
        "%   Ev  - sweep efficiency. Analogue: 1D displacement using the F-Phi curve\n",
        "%         as flux funcion\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `computeFandPhi`, `computeLorenz`\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "\n",
        "% remove any null segments (to avoid division by zero)\n",
        "hit        = true(size(F));\n",
        "hit(2:end) = F(1:end-1) <= F(2:end) - sqrt(eps);\n",
        "F          = F(hit);\n",
        "Phi        = Phi(hit);\n",
        "\n",
        "% compute dimensionless time\n",
        "tD = [0; (Phi(2:end)-Phi(1:end-1))./(F(2:end)-F(1:end-1))];\n",
        "\n",
        "% compute sweep\n",
        "Ev   = Phi + (1-F).*tD;\n",
        "\n",
        "end"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/computeSweep.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kdptT6x5gA2k",
        "outputId": "be0baac0-5f1e-4af9-c991-522dac77762c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/validateStateForDiagnostics.m\n",
        "function state = validateStateForDiagnostics(state)\n",
        "%Validate and fix state for flow diagnostics\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   state = validateStateForDiagnostics(state)\n",
        "%\n",
        "% DESCRIPTION:\n",
        "%   Routine for ensuring that states are suitable for diagnostic routines.\n",
        "%   Not all solvers produce the \"flux\" fields directly, but may instead\n",
        "%   give component fluxes that must be combined to form the flux. This\n",
        "%   routine will, if possible, ensure that flux exists in the state.\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   state - State produced by one of MRST's solvers.\n",
        "%\n",
        "% RETURNS:\n",
        "%   state - State with flux at wellSol and interfaces, if possible.\n",
        "%\n",
        "% NOTE:\n",
        "%   This routine will throw an error if there is insufficient data to\n",
        "%   produce the correct fields.\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `computeTOFandTracer`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "% Check whether the state object has total flux and if necessary construct\n",
        "% this flux from black-oil or similar type of model\n",
        "if isfield(state, 'flux')\n",
        "   state.flux = sum(state.flux,2);\n",
        "else\n",
        "   error('Reservoir state must provide total Darcy flux');\n",
        "end\n",
        "if  isfield(state, 'wellSol') \n",
        "    if isfield(state.wellSol, 'flux')\n",
        "       for i=1:numel(state.wellSol)\n",
        "          state.wellSol(i).flux = sum(state.wellSol(i).flux, 2);\n",
        "       end\n",
        "    elseif isfield(state.wellSol, 'cqs')\n",
        "       for i=1:numel(state.wellSol)\n",
        "          state.wellSol(i).flux = sum(state.wellSol(i).cqs, 2);\n",
        "       end\n",
        "   end\n",
        "end"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/validateStateForDiagnostics.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8NQJslEmgddp",
        "outputId": "aceea8ad-dae3-4d9a-b7a0-6dd0232cbe68",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/computeTimeOfFlight.m\n",
        "function [T, A, q] = computeTimeOfFlight(state, G, rock, varargin)\n",
        "%Compute time of flight using finite-volume scheme.\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%    T        = computeTimeOfFlight(state, G, rock)\n",
        "%    T        = computeTimeOfFlight(state, G, rock, 'pn1', pv1, ...)\n",
        "%   [T, A]    = computeTimeOfFlight(...)\n",
        "%   [T, A, q] = computeTimeOfFlight(...)\n",
        "%\n",
        "% DESCRIPTION:\n",
        "%   Compute time-of-flight by solving\n",
        "%\n",
        "%       v·\\nabla T = \\phi\n",
        "%\n",
        "%   using a first-order finite-volume method with upwind flux. Here, 'v' is\n",
        "%   the Darcy velocity, '\\phi' is the porosity, and T is time-of-flight.\n",
        "%   The time-of-flight T(x) is the time it takes an inert particles that is\n",
        "%   passively advected with the fluid to travel from the nearest inflow\n",
        "%   point to the point 'x' inside the reservoir. For the computation to\n",
        "%   make sense, inflow points must be specified in terms of inflow\n",
        "%   boundaries, source terms, wells, or combinations of these.\n",
        "%\n",
        "% REQUIRED PARAMETERS:\n",
        "%   G     - Grid structure.\n",
        "%\n",
        "%   rock  - Rock data structure.\n",
        "%           Must contain a valid porosity field, 'rock.poro'.\n",
        "%\n",
        "%   state - Reservoir state structure, must contain valid cell interface\n",
        "%           fluxes, 'state.flux'. Typically, 'state' will contain the\n",
        "%           solution produced by a flow solver like 'incompTPFA'.\n",
        "%\n",
        "% OPTIONAL PARAMETERS (supplied in 'key'/value pairs):\n",
        "%   wells - Well structure as defined by function 'addWell'.  May be empty\n",
        "%           (i.e., wells = []) which is interpreted as a model without any\n",
        "%           wells.\n",
        "%\n",
        "%   src   - Explicit source contributions as defined by function\n",
        "%           'addSource'.  May be empty (i.e., src = []) which is\n",
        "%           interpreted as a reservoir model without explicit sources.\n",
        "%\n",
        "%   bc    - Boundary condition structure as defined by function 'addBC'.\n",
        "%           This structure accounts for all external boundary conditions\n",
        "%           to the reservoir flow.  May be empty (i.e., bc = []) which is\n",
        "%           interpreted as all external no-flow (homogeneous Neumann)\n",
        "%           conditions.\n",
        "%\n",
        "%   reverse - Boolean variable. If true, the reverse time-of-flight will be\n",
        "%           computed, i.e., the travel time from a cell inside the\n",
        "%           reservoir to the nearest outflow point (well, source, or\n",
        "%           outflow boundary). Default: FALSE, i.e, compute forward tof.\n",
        "%\n",
        "%   tracer - Cell-array of cell-index vectors for which to solve a\n",
        "%           stationary tracer equation:\n",
        "%\n",
        "%             \\nabla·(v C) = 0,      C(inflow,t)=1\n",
        "%\n",
        "%           One equation is solved for each vector with tracer injected in\n",
        "%           the cells with the given indices. Each vector adds one\n",
        "%           additional right-hand side to the original tof-system. Output\n",
        "%           given as additional columns in T.\n",
        "%\n",
        "%   computeWellTOFs - Boolean variable. If true, time-of-flight values are\n",
        "%           computed individually for each influence region by solving\n",
        "%           equations of the form:\n",
        "%\n",
        "%              \\nabla·(v C_i T) = \\phi C_i,    T(inflow)=0\n",
        "%\n",
        "%           where C_i denotes the tracer concentration associated with each\n",
        "%           individual influence region\n",
        "%\n",
        "%   firstArrival - Boolean variable. If true, also compute the first-arrival\n",
        "%           time by a graph algorithm (requires MATLAB R2015b or newer)\n",
        "\n",
        "%   allowInf - Switch to turn off (true) or on (false) maximal TOF\n",
        "%           thresholding. Default is false.\n",
        "%\n",
        "%   maxTOF - Maximal TOF thresholding to avoid singular/ill-conditioned\n",
        "%           systems. Default (empty) is 50*PVI (pore-volumes-injected).\n",
        "%           Only takes effect if 'allowInf' is set to false.\n",
        "%\n",
        "%   solver - Function handle to solver for use in TOF/tracer equations.\n",
        "%           Default (empty) is matlab mldivide (i.e., \\)\n",
        "%\n",
        "%   processCycles - Extend TOF thresholding to strongly connected\n",
        "%           components in flux graph by considering Dulmage-Mendelsohn\n",
        "%           decomposition (dmperm). Recommended for highly cyclic flux\n",
        "%           fields. Only takes effect if 'allowInf' is set to false.\n",
        "%\n",
        "%\n",
        "%\n",
        "% RETURNS:\n",
        "%   T - Cell values of a piecewise constant approximation to time-of-flight\n",
        "%       computed as the solution of the boundary-value problem\n",
        "%\n",
        "%           (*)    v · \\nabla T = \\phi\n",
        "%\n",
        "%       using a finite-volume scheme with single-point upwind approximation\n",
        "%       to the flux.\n",
        "%\n",
        "%   A - Discrete left-hand side of (*), a G.cells.num-by-G.cells.num matrix\n",
        "%       whose entries are\n",
        "%\n",
        "%           A_ij = min(F_ij, 0), and\n",
        "%           A_ii = sum_j max(F_ij, 0) + max(2*q_i, 0),\n",
        "%\n",
        "%       where F_ij = -F_ji is the flux from cell i to cell j\n",
        "%\n",
        "%           F_ij = A_ij n_ij · v_ij.\n",
        "%\n",
        "%       and n_ij is the outward-pointing normal of cell i for grid face ij.\n",
        "%       The discretization uses a simple model for cells containing inflow.\n",
        "%       If q_i denotes the rate and V_i the volume of cell i, then T_i is\n",
        "%       set to half the time it takes to fill the cell, T_i = V_i/(2q_i).\n",
        "%\n",
        "%       OPTIONAL.  Only returned if specifically requested.\n",
        "%\n",
        "%   q - Aggregate source term contributions (per grid cell) from wells,\n",
        "%       explicit sources and boundary conditions.  These are the\n",
        "%       contributions referred to as 'q_i' in the definition of the matrix\n",
        "%       elements, 'A_ii'.  Measured in units of m^3/s.\n",
        "%\n",
        "%       OPTIONAL.  Only returned if specifically requested.\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `simpleTimeOfFlight`, `solveIncompFlow`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2018 SINTEF Digital, Applied Mathematics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "\n",
        "opt = struct('bc',              [], ...\n",
        "             'src',             [], ...\n",
        "             'wells',           [], ...\n",
        "             'reverse',         false,...\n",
        "             'allowInf',        false, ...\n",
        "             'maxTOF',          [], ...\n",
        "             'tracer',          {{}}, ...\n",
        "             'solver',          [], ...\n",
        "             'processCycles',   false, ...\n",
        "             'computeWellTOFs', false, ...\n",
        "             'firstArrival',    false);\n",
        "\n",
        "opt = merge_options(opt, varargin{:});\n",
        "\n",
        "checkInput(G, rock, opt)\n",
        "if size(state.flux, 2) > 1\n",
        "    state = validateStateForDiagnostics(state);\n",
        "end\n",
        "\n",
        "tr = opt.tracer;\n",
        "if ~iscell(tr), tr = {tr}; end\n",
        "\n",
        "% Find external sources of inflow: q contains the contribution from from\n",
        "% sources (src) and wells (W), while qb contains the cell-wise sum of\n",
        "% fluxes from boundary conditions.\n",
        "[q,qb] = computeSourceTerm(state, G, opt.wells, opt.src, opt.bc);\n",
        "\n",
        "pv = poreVolume(G, rock);\n",
        "\n",
        "if opt.reverse\n",
        "   q  = -q;\n",
        "   qb = -qb;\n",
        "   state.flux = -state.flux;\n",
        "end\n",
        "\n",
        "% Build upwind flux matrix in which we define v_ji = max(flux_ij, 0) and\n",
        "% v_ij = -min(flux_ij, 0). Then the diagonal of the discretization matrix\n",
        "% is obtained by summing rows in the upwind flux matrix. This will give the\n",
        "% correct diagonal in all cells except for those with a positive fluid\n",
        "% source. In these cells, the average time-of-flight is set to half the\n",
        "% time it takes to fill the cell, which means that the diagonal entry\n",
        "% should be equal twice the fluid rate inside these cells.\n",
        "i  = ~any(G.faces.neighbors==0, 2);\n",
        "n  = double(G.faces.neighbors(i,:));\n",
        "nc = G.cells.num;\n",
        "qp = max(q+qb, 0);\n",
        "\n",
        "out = min(state.flux(i), 0);\n",
        "in  = max(state.flux(i), 0);\n",
        "\n",
        "% Cell wise total inflow\n",
        "inflow  = accumarray([n(:, 2); n(:, 1)], [in; -out]);\n",
        "\n",
        "% The diagonal entries are equal to the sum of outfluxes minus divergence\n",
        "% which equals the influx plus the positive source terms.\n",
        "d = inflow + qp;\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "% Handling of t -> inf (if opt.allowInf == false):\n",
        "% We locate cells that have sufficiently small influx to reach maxTOF\n",
        "% locally, i.e., t-t_up >= maxTOF <=> pv/influx >= maxTOF. System is\n",
        "% modified such that these cells are set to maxTOF and upstream connections\n",
        "% are removed.\n",
        "% If no maxTOF is given, it is set to the time it takes to fill 50\n",
        "% pore volumes (subject to change)\n",
        "if ~opt.allowInf\n",
        "    if isempty(opt.maxTOF)\n",
        "        if ~opt.reverse, str = 'Forward '; else str = 'Backward'; end\n",
        "        opt.maxTOF = 50*sum(pv)/sum(qp);\n",
        "        dispif(mrstVerbose, ...\n",
        "               '%s maximal TOF set to %5.2f years.\\n', str, opt.maxTOF/year)\n",
        "    end\n",
        "\n",
        "    % Find cells that reach max TOF locally\n",
        "    maxIn = max(d);\n",
        "    aboveMax = full(pv./ (max(d, eps*maxIn)) ) > opt.maxTOF;\n",
        "\n",
        "    % Set aboveMax-cells to maxTOF\n",
        "    d(aboveMax)  = maxIn;\n",
        "    pv(aboveMax) = maxIn*opt.maxTOF;\n",
        "    % remove upstream connections\n",
        "    in(aboveMax(n(:,2)))  = 0;\n",
        "    out(aboveMax(n(:,1))) = 0;\n",
        "end\n",
        "\n",
        "% Inflow flux matrix\n",
        "A  = sparse(n(:,2), n(:,1),  in, nc, nc)...\n",
        "   + sparse(n(:,1), n(:,2), -out, nc, nc);\n",
        "if ~isempty(d)\n",
        "    A = -A + spdiags(d, 0, nc, nc);\n",
        "end\n",
        "\n",
        "if ~opt.allowInf && opt.processCycles\n",
        "    [A, pv] = thresholdConnectedComponents(A, pv, maxIn, opt);\n",
        "end\n",
        "\n",
        "% Build right-hand sides for tracer equations. Since we have doubled the\n",
        "% rate in any cells with a positive source, we need to also double the rate\n",
        "% on the right-hand side here.\n",
        "numTrRHS = numel(tr);\n",
        "TrRHS = zeros(nc,numTrRHS);\n",
        "for i=1:numTrRHS\n",
        "   TrRHS(tr{i},i) = qp(tr{i});\n",
        "end\n",
        "\n",
        "% Time of flight for velocity field.\n",
        "if isempty(opt.solver)\n",
        "   T  = A \\ [pv TrRHS];\n",
        "else % if other solver, iterate over RHSs\n",
        "   T = zeros(size(TrRHS)+[0, 1]);\n",
        "   T(:, 1) = opt.solver(A, pv);\n",
        "   for k = 2:size(T, 2)\n",
        "       T(:, k) = opt.solver(A, TrRHS(:, k-1));\n",
        "   end\n",
        "end\n",
        "\n",
        "% reset all tof > maxTOF to maxTOF\n",
        "if ~opt.allowInf\n",
        "    T(T>opt.maxTOF) = opt.maxTOF;\n",
        "end\n",
        "\n",
        "% compute individual well-tofs A*(c_i.*tau_i) = c_i.*pv\n",
        "if opt.computeWellTOFs\n",
        "    C   = T(:, 2:end);\n",
        "    pvi = bsxfun(@times, C, pv);\n",
        "    pvi(pvi<0) = 0;\n",
        "    if isempty(opt.solver)\n",
        "        X  = A \\ pvi;\n",
        "    else % if other solver, iterate over RHSs\n",
        "        X = zeros(size(pvi));\n",
        "        for k = 1:size(X, 2)\n",
        "            X(:, k) = opt.solver(A, pvi(:, k));\n",
        "        end\n",
        "    end\n",
        "    X(X<0) = 0;\n",
        "    % disregard tracer values < sqrt(eps)\n",
        "    ix     = and(pvi*opt.maxTOF > X, C > sqrt(eps));\n",
        "    X(~ix) = opt.maxTOF;\n",
        "    X(ix)  = X(ix)./C(ix);\n",
        "    %X      = min(X, opt.maxTOF);\n",
        "    T      = [T, X];\n",
        "\n",
        "    if opt.firstArrival\n",
        "      if verLessThan('matlab','8.6')\n",
        "\t    warning('Computing first arrival requires MATLAB R2015b or later');\n",
        "        T  = [T, X];  % add dummy data equal TOF  \n",
        "      else\n",
        "\t    n(out<0, [1 2]) = n(out<0, [2 1]);\n",
        "        % add edges for well-to-connection cell\n",
        "        nconn = cellfun(@numel, tr);\n",
        "        wnum  = rldecode((1:numel(tr))', nconn(:));\n",
        "        wc    = vertcat(tr{:});\n",
        "        n1    = [n(:,1); wnum+nc];\n",
        "        n2    = [n(:,2); wc];\n",
        "        fl    = [inflow(n(:,2)); qp(wc)];\n",
        "        fl    = max(fl, max(fl)*eps);\n",
        "        gr    = digraph(n1, n2, pv(n2)./fl);\n",
        "        X = T(:, 2:(numTrRHS+1));\n",
        "        for k = 1:size(X,2)\n",
        "            [~, t] = shortestpathtree(gr, nc+k, 'OutputForm', 'vector');\n",
        "            X(:,k) = t(1:nc);\n",
        "        end\n",
        "        X = min(X, opt.maxTOF);\n",
        "        T = [T, X];\n",
        "      end\n",
        "    end\n",
        "end\n",
        "\n",
        "end\n",
        "\n",
        "\n",
        "function [q, qb] = computeSourceTerm(state, G, W, src, bc)\n",
        "   qi = [];  % Cells to which sources are connected\n",
        "   qs = [];  % Actual strength of source term (in m^3/s).\n",
        "\n",
        "   % Contribution from wells\n",
        "   if ~isempty(W)\n",
        "      qi = [qi; vertcat(W.cells)];\n",
        "      qs = [qs; vertcat(state.wellSol.flux)];\n",
        "   end\n",
        "\n",
        "   % Contribution from sources\n",
        "   if ~isempty(src)\n",
        "      qi = [qi; src.cell];\n",
        "      qs = [qs; src.rate];\n",
        "   end\n",
        "\n",
        "   % Assemble all source and sink contributions to each affected cell.\n",
        "   q = sparse(qi, 1, qs, G.cells.num, 1);\n",
        "\n",
        "   % Contribution from boundary conditions\n",
        "   if ~isempty(bc)\n",
        "      ff    = zeros(G.faces.num, 1);\n",
        "\n",
        "      isDir = strcmp('pressure', bc.type);\n",
        "      i     = bc.face(isDir);\n",
        "      if ~isempty(i)\n",
        "         ff(i) = state.flux(i) .* (2*(G.faces.neighbors(i,1)==0) - 1);\n",
        "      end\n",
        "\n",
        "      isNeu = strcmp('flux', bc.type);\n",
        "      ff(bc.face(isNeu)) = bc.value(isNeu);\n",
        "\n",
        "      is_outer = ~all(double(G.faces.neighbors) > 0, 2);\n",
        "      qb = sparse(sum(G.faces.neighbors(is_outer,:), 2), 1, ...\n",
        "         ff(is_outer), G.cells.num, 1);\n",
        "   else\n",
        "      qb = sparse(G.cells.num,1);\n",
        "   end\n",
        "end\n",
        "\n",
        "\n",
        "function [A, pv] = thresholdConnectedComponents(A, pv, maxIn, opt)\n",
        "    % Find strongly connected components in flux-matrix:\n",
        "    [p,r,r]= dmperm(A); %#ok\n",
        "    % Pick components containing more than a single cell\n",
        "    ix = find(diff(r)>1);\n",
        "    if ~isempty(ix)\n",
        "        nc = numel(p);\n",
        "        % Retrieve cell-indices to components, and construct sparse index-mapping\n",
        "        c  = arrayfun(@(b,e)p(b:e)', r(ix), r(ix+1)-1, 'UniformOutput', false);\n",
        "        rc = rldecode( (1:numel(c))', cellfun(@numel, c)');\n",
        "        C  = sparse(vertcat(c{:}), rc, 1, nc, numel(c));\n",
        "        % Compute influx to each component\n",
        "        q_in = full(diag(C'*A*C));\n",
        "        % Threshold\n",
        "        compAboveMax = full((C'*pv)./ (max(q_in, eps*maxIn)) ) > opt.maxTOF;\n",
        "\n",
        "        if any(compAboveMax)\n",
        "            badCells = (vertcat(c{compAboveMax}));\n",
        "            dispif(mrstVerbose, 'Found %d strongly connected components, ', nnz(compAboveMax));\n",
        "            dispif(mrstVerbose, 'total of %d cells, with influx below threshold.\\n', numel(badCells));\n",
        "            % Modify system setting tof to maxTOF and remove upstream connections\n",
        "            A(badCells,:) = sparse((1:numel(badCells))', badCells, maxIn, numel(badCells), nc);\n",
        "            pv(badCells)  = maxIn*opt.maxTOF;\n",
        "        end\n",
        "    end\n",
        "end\n",
        "\n",
        "\n",
        "function checkInput(G, rock, opt)\n",
        "    assert (~all([isempty(opt.src), isempty(opt.bc), isempty(opt.wells)]), ...\n",
        "        'Must have inflow described as boundary conditions, sources, or wells');\n",
        "    assert (isfield(rock, 'poro')         && ...\n",
        "        numel(rock.poro)==G.cells.num,   ...\n",
        "        ['The rock input must have a field poro with porosity ',...\n",
        "        'for each cell in the grid.']);\n",
        "    assert(min(rock.poro) > 0, 'Rock porosities must be positive numbers.');\n",
        "    if ~isempty(opt.maxTOF) && opt.allowInf\n",
        "        warning('Input value for ''maxTOF'' ignored since option ''allowInf'' has value ''true''.')\n",
        "    end\n",
        "    if opt.processCycles && opt.allowInf\n",
        "        warning('Input request to process cycles ignored since option ''allowInf'' has value ''true''.')\n",
        "    end\n",
        "end"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/computeTimeOfFlight.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ptKUX7eNfer0",
        "outputId": "d9b67bb5-7dec-4895-fb52-29b38bd8bcef",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/computeTOFandTracer.m\n",
        "function D = computeTOFandTracer(state, G, rock,  varargin)\n",
        "%Compute time-of-flight and tracer distribution using finite-volume scheme.\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%    D  = computeTOFandTracer(state, G, rock)\n",
        "%    D  = computeTOFandTracer(state, G, rock, 'pn1', pv1, ...)\n",
        "%\n",
        "% DESCRIPTION:\n",
        "%   Construct the basis for flow diagnostic by computing\n",
        "%     1) time-of-flight        :   \\nabla·(v T) = \\phi,\n",
        "%     2) reverse time-of-flight:  -\\nabla·(v T) = \\phi,\n",
        "%     3) stationary tracer     :  ±\\nabla·(v C) = 0\n",
        "%   using a first-order finite-volume method with upwind flux. A majority\n",
        "%   vote is also used to partition the volume and assign each cell to a\n",
        "%   unique tracer. Optionally, the routine can also compute time-of-flight\n",
        "%   values for each influence region by solving localized time-of-flight\n",
        "%   equations\n",
        "%         \\nabla·(v C_i T) = \\phi C_i,\n",
        "%   where C_i is the tracer concentration of each influence region.\n",
        "%\n",
        "%   Finally, first arrival time is computed by a graph algorithm.\n",
        "%\n",
        "% REQUIRED PARAMETERS:\n",
        "%   G     - Grid structure.\n",
        "%\n",
        "%   rock  - Rock data structure.\n",
        "%           Must contain a valid porosity field, 'rock.poro'.\n",
        "%\n",
        "%   state - Reservoir and well solution structure either properly\n",
        "%           initialized from functions 'initResSol' and 'initWellSol'\n",
        "%           respectively, or the results from a call to function\n",
        "%           'solveIncompFlow'.  Must contain valid cell interface fluxes,\n",
        "%           'state.flux'.\n",
        "%\n",
        "% OPTIONAL PARAMETERS (supplied in 'key'/value pairs):\n",
        "%   wells - Well structure as defined by function 'addWell'.  May be empty\n",
        "%           (i.e., wells = []) which is interpreted as a model without any\n",
        "%           wells.\n",
        "%\n",
        "%   src   - Explicit source contributions as defined by function\n",
        "%           'addSource'.  May be empty (i.e., src = []) which is\n",
        "%           interpreted as a reservoir model without explicit sources.\n",
        "%\n",
        "%   bc    - Boundary condition structure as defined by function 'addBC'.\n",
        "%           This structure accounts for all external boundary conditions\n",
        "%           to the reservoir flow.  May be empty (i.e., bc = []) which is\n",
        "%           interpreted as all external no-flow (homogeneous Neumann)\n",
        "%           conditions.\n",
        "%\n",
        "%   tracerWells - Logical index vector indicating subset of wells for which\n",
        "%           tracer-fields will be computed. Empty matrix (default) is\n",
        "%           interpeted as all true, i.e., compute tracer fields for all\n",
        "%           wells.\n",
        "%\n",
        "%   computeWellTOFs - Boolean variable. If true, time-of-flight values are\n",
        "%           computed individually for each influence region by solving\n",
        "%\n",
        "%   firstArrival - Boolean variable. If true, compute first-arrival time by\n",
        "%           a graph algorithm.\n",
        "%\n",
        "%   solver - Function handle to solver for use in TOF/tracer equations.\n",
        "%           Default (empty) is matlab mldivide (i.e., \\)\n",
        "%\n",
        "%   maxTOF - Maximal TOF thresholding to avoid singular/ill-conditioned\n",
        "%           systems. Default (empty) is 50*PVI (pore-volumes-injected).\n",
        "%\n",
        "%   processCycles - Extend TOF thresholding to strongly connected\n",
        "%           components in flux graph by considering Dulmage-Mendelsohn\n",
        "%           decomposition (dmperm). Recommended for highly cyclic flux\n",
        "%           fields. Only takes effect if 'allowInf' is set to false.\n",
        "%\n",
        "% RETURNS:\n",
        "%   D - struct that contains the basis for computing flow diagnostics:\n",
        "%       'inj'     - list of injection wells\n",
        "%       'prod'    - list of production wells\n",
        "%       'tof'     - time-of-flight and reverse time-of-flight returned\n",
        "%                   as an array where the first (G.cells.num x 2) elements\n",
        "%                   contain forward/backward TOF for the whole field, and\n",
        "%                   any other columns optinally contain TOF values for\n",
        "%                   individual influence regions\n",
        "%       'itracer' - steady-state tracer distribution for injectors\n",
        "%       'ipart'   - tracer partition for injectors\n",
        "%       'ifa'     - first-arrival time injectors\n",
        "%       'ptracer' - steady-state tracer distribution for producers\n",
        "%       'ppart'   - tracer partition for producers\n",
        "%       'pfa'     - first-arrival time for producers\n",
        "\n",
        "%{\n",
        "Copyright 2009-2018 SINTEF Digital, Applied Mathematics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "\n",
        "% Process optional parameters\n",
        "opt = struct('bc', [],                ...\n",
        "             'src', [],               ...\n",
        "             'wells', [],             ...\n",
        "             'tracerWells', [],       ...\n",
        "             'solver', [],            ...\n",
        "             'maxTOF', [],            ...\n",
        "             'processCycles', false,  ...\n",
        "             'computeWellTOFs', false, ...\n",
        "             'firstArrival', false);\n",
        "opt = merge_options(opt, varargin{:});\n",
        "if opt.firstArrival\n",
        "  opt.computeWellTOFs = true;\n",
        "end\n",
        "\n",
        "check_input(G, rock, opt);\n",
        "\n",
        "state = validateStateForDiagnostics(state);\n",
        "% If opt.tracerWells is empty include all\n",
        "if isempty(opt.tracerWells)\n",
        "    opt.tracerWells = true(numel(opt.wells), 1);\n",
        "end\n",
        "opt.tracerWells = opt.tracerWells(:)';\n",
        "\n",
        "% Find injectors and producers\n",
        "wflux = getTotalWellSolFlux(state.wellSol);\n",
        "iwells = wflux > 0;\n",
        "D.inj  = find( iwells & opt.tracerWells);\n",
        "D.prod = find(~iwells & opt.tracerWells);\n",
        "\n",
        "% Check that we actually have a meaningful TOF scenario. If all wells are\n",
        "% shut off, return Inf.\n",
        "sum_flux = cell2mat(arrayfun(@(x) sum(abs(x.flux)), state.wellSol, 'UniformOutput', false));\n",
        "if (sum(sum_flux) == 0.0)\n",
        "    D.tof = Inf(G.cells.num, 2);\n",
        "    D.itracer = NaN(G.cells.num, numel(D.inj));\n",
        "    D.ipart = NaN(G.cells.num, 1);\n",
        "    D.ptracer = NaN(G.cells.num, numel(D.prod));\n",
        "    D.ppart = NaN(G.cells.num, 1);\n",
        "    return;\n",
        "end\n",
        "\n",
        "% Compute time-of-flight and tracer partition from injectors\n",
        "t = computeTimeOfFlight(state, G, rock, 'wells', opt.wells,  ...\n",
        "   'tracer', {opt.wells(D.inj).cells}, 'solver', opt.solver, ...\n",
        "   'maxTOF', opt.maxTOF, 'processCycles', opt.processCycles, ...\n",
        "   'computeWellTOFs', opt.computeWellTOFs,                   ...\n",
        "   'firstArrival', opt.firstArrival);\n",
        "D.tof     = t(:,1);\n",
        "D.itracer = t(:,2:numel(D.inj)+1);\n",
        "if opt.computeWellTOFs\n",
        "    D.itof = t(:, numel(D.inj)+2:2*numel(D.inj)+1);\n",
        "    if opt.firstArrival\n",
        "        D.ifa = t(:, 2*numel(D.inj)+2:end);\n",
        "    end\n",
        "end\n",
        "[val,D.ipart] = max(D.itracer,[],2); %#ok<*ASGLU>\n",
        "% set 'non-traced' cells to zero\n",
        "D.ipart(val==0) = 0;\n",
        "\n",
        "% Compute time-of-flight and tracer partition from producers\n",
        "t = computeTimeOfFlight(state, G, rock, 'wells', opt.wells, ...\n",
        "   'tracer', {opt.wells(D.prod).cells}, 'reverse', true, ...\n",
        "   'solver', opt.solver, 'maxTOF', opt.maxTOF, ...\n",
        "   'processCycles', opt.processCycles, ...\n",
        "   'computeWellTOFs', opt.computeWellTOFs, ...\n",
        "   'firstArrival', opt.firstArrival);\n",
        "D.tof(:,2) = t(:,1);\n",
        "D.ptracer  = t(:,2:numel(D.prod)+1);\n",
        "if opt.computeWellTOFs\n",
        "    D.ptof = t(:, numel(D.prod)+2:2*numel(D.prod)+1);\n",
        "    if opt.firstArrival\n",
        "       D.pfa = t(:, 2*numel(D.prod)+2 : end);\n",
        "    end\n",
        "end\n",
        "[val,D.ppart] = max(D.ptracer,[],2);\n",
        "D.ppart(val==0) = 0;\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function check_input(G, rock, opt)\n",
        "   assert(~isempty(opt.wells), 'Wells are required for computeTOFandTracer');\n",
        "   assert(isempty(opt.src), 'Source terms not supported yet');\n",
        "   assert(isempty(opt.bc),  'Boundary conditions not supported yet');\n",
        "\n",
        "   assert (isfield(rock, 'poro')         && ...\n",
        "           numel(rock.poro)==G.cells.num,   ...\n",
        "          ['The rock input must have a field poro with porosity ',...\n",
        "           'for each cell in the grid.']);\n",
        "\n",
        "   assert(min(rock.poro) > 0, 'Rock porosities must be positive numbers.');\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function flux = getTotalWellSolFlux(wellSol)\n",
        "    nw = numel(wellSol);\n",
        "    flux = zeros(1, nw);\n",
        "    for i = 1:nw\n",
        "        ws = wellSol(i);\n",
        "        f = sum(ws.flux);\n",
        "        if isempty(f) || f == 0 && ( isfield(ws, 'sign') && ~isempty(ws.sign) )\n",
        "            % If we have a sign for well and there is no flux defined, set\n",
        "            % it to a small value of right sign instead.\n",
        "            f = sqrt(eps)*ws.sign;\n",
        "        end\n",
        "        flux(i) = f;\n",
        "    end\n",
        "end"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/computeTOFandTracer.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qHaFLAjnjUV9",
        "outputId": "e0407eb5-9082-445f-caab-0a69eeb7c929",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/computeLorenz.m\n",
        "function Lc = computeLorenz(F,Phi)\n",
        "%Compute the Lorenz coefficient\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   Lc = computeLorenz(F, Phi)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   F   - flow capacity\n",
        "%   Phi - storage capacity\n",
        "%\n",
        "% RETURNS:\n",
        "%   Lc  - the Lorenz coefficient, a popular measure of heterogeneity. It is\n",
        "%         equal to twice the area under the curve and above the F=Phi line.\n",
        "%         It varies between 0 (homogeneous displacement) to 1 (infinitely\n",
        "%         heterogeneous displacement).\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `computeFandPhi`, `computeSweep`\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "\n",
        "v      = diff(Phi,1);\n",
        "Lc     = 2*(sum((F(1:end-1,:)+F(2:end,:))/2.*v) - .5);\n",
        "end"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/computeLorenz.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XEDt9LSkemIo",
        "outputId": "8578f008-ba3b-49e9-e59d-dcbd9c47da3a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/getIncompCapillaryPressure.m\n",
        "function varargout = getIncompCapillaryPressure(state, fluid, varargin)\n",
        "%Undocumented Utility Function\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "    varargout = cell(1, nargout);\n",
        "    if isfield(fluid, 'properties')\n",
        "        [varargout{:}] = getPropsLegacy(state, fluid);\n",
        "    else\n",
        "        [varargout{:}] = getPropsAD(state, fluid);\n",
        "    end\n",
        "end\n",
        "\n",
        "function [pc, dpc] = getPropsLegacy(state, fluid)\n",
        "    if isfield(fluid, 'pc')\n",
        "        if nargout > 1\n",
        "            [pc, dpc] = fluid.pc(state);\n",
        "        else\n",
        "            pc = fluid.pc(state);\n",
        "        end\n",
        "    else\n",
        "        pc = [];\n",
        "        dpc = [];\n",
        "    end\n",
        "end\n",
        "\n",
        "function [pc, dpc] = getPropsAD(state, fluid)\n",
        "    if isfield(fluid, 'pcOW')\n",
        "        getDer = nargout > 1;\n",
        "        s = state.s(:, 1);\n",
        "        if getDer\n",
        "            s = initVariablesAD_diagonal(s);\n",
        "        end\n",
        "        pc = fluid.pcOW(s);\n",
        "        if getDer\n",
        "            dpc = pc.jac{1}.diagonal; \n",
        "        end\n",
        "    else\n",
        "        pc = [];\n",
        "        dpc = [];\n",
        "    end\n",
        "end"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/getIncompCapillaryPressure.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FeBm5J74a7EP",
        "outputId": "dbf58deb-0eb2-4c52-c15e-533adb85392e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/checkDrivingForcesIncomp.m\n",
        "function do_solve = checkDrivingForcesIncomp(g, opt)\n",
        "%Check if a solution is necessary for incompressible solvers. \n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   W = addWell(W, G, rock, cellInx)\n",
        "%   W = addWell(W, G, rock, cellInx, 'pn', pv, ...)\n",
        "%\n",
        "% REQUIRED PARAMETERS:\n",
        "%   g       - Valid MRST grid intended for simulation.\n",
        "%\n",
        "%   opt     - Merged options struct with standard incompressible options.\n",
        "%             Specifically, the forces supported by incompTPFA and\n",
        "%             incompMimetic should be included.\n",
        "%\n",
        "%\n",
        "% RETURNS:\n",
        "%\n",
        "%   do_solve - Logical indicating if forces are well specified and should\n",
        "%              be solved. This check verifies that the problem is\n",
        "%              meaningful for incompressible flow.\n",
        "% SEE ALSO:\n",
        "%   `incompMimetic`, `incompTPFA`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "   pressure_bc = ~isempty(opt.bc) && ...\n",
        "                 any(strcmpi('pressure', opt.bc.type));\n",
        "   well_bhp    = ~isempty(opt.wells) && ...\n",
        "                 any(strcmpi('bhp', { opt.wells.type }));\n",
        "   if ~(pressure_bc || well_bhp)\n",
        "      sum_rates = 0;\n",
        "      norm_rates = 0;\n",
        "      if ~isempty(opt.wells)\n",
        "          rates = vertcat(opt.wells.val);\n",
        "          sum_rates = sum(rates);\n",
        "          norm_rates = max(norm_rates, norm(rates, inf));\n",
        "      end\n",
        "      if ~isempty(opt.src)\n",
        "          sum_rates = sum_rates + sum(opt.src.rate);\n",
        "          norm_rates = max(norm_rates, norm(opt.src.rate, inf));\n",
        "      end\n",
        "      if ~isempty(opt.bc)\n",
        "          sum_rates = sum_rates + sum(opt.bc.value);\n",
        "          norm_rates = max(norm_rates, norm(opt.bc.value, inf));\n",
        "      end\n",
        "      if abs(sum_rates) > 1e-12\n",
        "         warning('incomp:MassBalance:NotFulfilled', ...\n",
        "              ['Well rates and flux bc must sum up to 0 \\n', ...\n",
        "               'when there are no bhp constrained wells or pressure bc.'...\n",
        "               'Results may not be reliable.\\n']);\n",
        "      end\n",
        "   end\n",
        "\n",
        "   g_vec = gravity();\n",
        "   % Check if there are gravity components in the grid axes or if the\n",
        "   % pressure functions have been overridden (which means we cannot assume\n",
        "   % anything about the influence of gravity and we play it safe).\n",
        "   grav  = norm(g_vec(1 : g.griddim)) > 0 || isfield(g, 'grav_pressure');\n",
        "\n",
        "   % We assemble and solve a system if there are any external forces or\n",
        "   % sources (e.g., gravity, boundary conditions, explicit source terms,\n",
        "   % injection/production wells or, in the case of the adjoint method, if\n",
        "   % the caller supplied the right hand side directly).\n",
        "   do_solve = grav || ~all([isempty(opt.bc),    ...\n",
        "                            isempty(opt.src),   ...\n",
        "                            isempty(opt.wells), ...\n",
        "                            isempty(opt.bcp)\n",
        "                            ]);\n",
        "   % Assemble (and solve) system even in absence of external driving forces\n",
        "   % if the caller requested 'MatrixOutput'.\n",
        "   do_solve = do_solve || opt.MatrixOutput;\n",
        "\n",
        "   if isfield(opt, 'rhs')\n",
        "       do_solve = do_solve || ~isempty(opt.rhs);\n",
        "   end\n",
        "   if ~do_solve,\n",
        "      warning('incomp:DrivingForce:Missing',                   ...\n",
        "             ['No external driving forces present in model--', ...\n",
        "              'state remains unchanged.\\n']);\n",
        "   end\n",
        "\n",
        "end"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/checkDrivingForcesIncomp.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gLfYlH_Te-T6",
        "outputId": "5d2a602c-a790-46da-b0b9-5d27ab9bf43b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/computeIncompWellPressureDrop.m\n",
        "function dp = computeIncompWellPressureDrop(W, mob, rho, g)\n",
        "%Compute incompressible connection pressure drop for a single well\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   dp = computeIncompWellPressureDrop(W, mob, rho, g)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   W   - Well structure as defined by function addWell.\n",
        "%\n",
        "%   mob - Phase mobilities for each cell in model.\n",
        "%\n",
        "%   rho - Fluid mass densities.  One scalar for each fluid phase.\n",
        "%\n",
        "%   g   - Norm of gravity along z-axis\n",
        "%\n",
        "% RETURNS:\n",
        "%   dp - Column vector of size numel(W.cells).  Contains each completion's\n",
        "%        pressure drop along the well bore from the bottom hole pressure\n",
        "%        reference depth, under certain assumptions for the incompressible,\n",
        "%        linear pressure equation.\n",
        "%\n",
        "% NOTES:\n",
        "%   In order to avoid nonlinear behavior for wells, this function assumes\n",
        "%   that the well bore density is constant for all perforations and is\n",
        "%   equal to the injection composition if the well is an injector,\n",
        "%   either through positive rates or W.sign > 0. If the well is a producer,\n",
        "%   the mixture is assumed to be taken from the perforated cells, with flux\n",
        "%   proportional to the well indices.\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `addWell`, `incompTPFA`, `incompMimetic`, `incompMPFA`\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "   check_input(W, mob, rho)\n",
        "\n",
        "   np = numel(rho);\n",
        "\n",
        "   if is_injector(W)\n",
        "      % We compute a simple mixture of the injected fluids\n",
        "      i = 1 : min(np, size(W.compi, 2));\n",
        "\n",
        "      rhoMix = rho(i) * W.compi(i)';\n",
        "   else\n",
        "      % We compute approximate phase fluxes by taking the fractional flow\n",
        "      % in each cell, weighted by the densities.  The flux is estimated\n",
        "      % roughly as proportional to the well index.\n",
        "      i = 1 : min(np, size(mob, 2));\n",
        "\n",
        "      mobw = mob(W.cells, :);\n",
        "      f    = bsxfun(@rdivide, mobw, sum(mobw, 2));\n",
        "\n",
        "      rhoMix = sum(W.WI .* (f(:, i) * rho(i)')) ./ sum(W.WI);\n",
        "   end\n",
        "\n",
        "   dp = g * (W.dZ * rhoMix);\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function check_input(W, mob, rho)\n",
        "   persistent NI NP NM\n",
        "\n",
        "   nchanged = 0;\n",
        "\n",
        "   if isempty(NI), NI = numel(W.compi); nchanged = nchanged + 1; end\n",
        "   if isempty(NP), NP = numel(rho);     nchanged = nchanged + 1; end\n",
        "   if isempty(NM), NM = size(mob, 2);   nchanged = nchanged + 1; end\n",
        "\n",
        "   [NP, nchanged] = change_if_modified(NP, nchanged, numel(rho));\n",
        "   [NI, nchanged] = change_if_modified(NI, nchanged, numel(W.compi));\n",
        "   [NM, nchanged] = change_if_modified(NM, nchanged, size(mob, 2));\n",
        "\n",
        "   if (nchanged > 0) && ((NI ~= NP) || (NM ~= NP))\n",
        "      np = min([NI, NM, NP]);\n",
        "      pl = '';  if np ~= 1, pl = 's'; end\n",
        "\n",
        "      warning('NumPhase:Inconsistent', ...\n",
        "             ['Inconsistent Number of Phases.  ', ...\n",
        "              'Using %d Phase%s (=min([%d, %d, %d])).'], ...\n",
        "              np, pl, NI, NP, NM);\n",
        "   end\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function tf = is_injector(W)\n",
        "   % A well is an injector if the sign is set (and positive) or the well is\n",
        "   % constrained to a positive rate target.  Otherwise, we assume that the\n",
        "   % well is a producer.\n",
        "   tf = (W.sign > 0) || (strcmpi(W.type, 'rate') && (W.val > 0));\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function [n, count] = change_if_modified(n, count, new)\n",
        "   if n ~= new\n",
        "      n     = new;\n",
        "      count = count + 1;\n",
        "   end\n",
        "end"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/computeIncompWellPressureDrop.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_miC6no1aMV8",
        "outputId": "d90a2902-8685-44dd-aa87-d39b180c06c9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/treatLegacyForceOptions.m\n",
        "function opt = treatLegacyForceOptions(opt)\n",
        "    % Internal function for ensuring that both W and Wells are supported as\n",
        "    % keyword arguments to incompressible solvers.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "    hasWells = isfield(opt, 'wells');\n",
        "    hasW = isfield(opt, 'W');\n",
        "    if hasWells\n",
        "        Wells = opt.wells;\n",
        "    else\n",
        "        Wells = [];\n",
        "    end\n",
        "    if hasW\n",
        "        W = opt.W;\n",
        "    else\n",
        "        W = [];\n",
        "    end\n",
        "    \n",
        "    if ~isempty(W)\n",
        "        assert(isempty(Wells), ...\n",
        "            'Solver cannot have both legacy ''wells'' argument and ''W'' argument at the same time');\n",
        "        opt.wells = W;\n",
        "    end\n",
        "    if ~isempty(Wells)\n",
        "        assert(isempty(W), ...\n",
        "            'Solver cannot have both legacy ''wells'' argument and ''W'' argument at the same time');\n",
        "        opt.W = Wells;\n",
        "    end\n",
        "end"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/treatLegacyForceOptions.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_9FMIhRBbaCq",
        "outputId": "9f4ae23c-9f9d-41ce-b069-5ad27d22b48a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/getIncompProps.m\n",
        "function varargout = getIncompProps(state, fluid)\n",
        "%Undocumented Utility Function\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "    varargout = cell(1, nargout);\n",
        "    if isfield(fluid, 'properties')\n",
        "        [varargout{:}] = getPropsLegacy(state, fluid);\n",
        "    else\n",
        "        [varargout{:}] = getPropsAD(state, fluid);\n",
        "    end\n",
        "end\n",
        "\n",
        "function [rho, kr, mu, dkr] = getPropsLegacy(state, fluid)\n",
        "    [mu, rho] = fluid.properties(state);\n",
        "    s         = fluid.saturation(state);\n",
        "    if nargout < 4\n",
        "        kr = fluid.relperm(s, state);\n",
        "    else\n",
        "        [kr, dkr] = fluid.relperm(s, state);\n",
        "    end\n",
        "end\n",
        "\n",
        "function [rho, kr, mu, dkr] = getPropsAD(state, fluid)\n",
        "    if isfield(state, 'pressure')\n",
        "        p = state.pressure;\n",
        "        p_avg = mean(p);\n",
        "    else\n",
        "        p_avg = 1*atm;\n",
        "    end\n",
        "    \n",
        "    rho = [fluid.rhoWS*fluid.bW(p_avg), ...\n",
        "           fluid.rhoOS*fluid.bO(p_avg)];\n",
        "    mu = [fluid.muW(p), ...\n",
        "           fluid.muO(p)];\n",
        "    getDer = nargout > 3;\n",
        "    s = state.s(:, 1);\n",
        "    if getDer\n",
        "        s = initVariablesAD_diagonal(s);\n",
        "    end\n",
        "    \n",
        "    krW = fluid.krW(s);\n",
        "    so = 1 - s;\n",
        "    if isfield(fluid, 'krOW')\n",
        "        krO = fluid.krOW(so);\n",
        "    else\n",
        "        krO = fluid.krO(so);\n",
        "    end\n",
        "    kr = [value(krW), value(krO)];\n",
        "    if getDer\n",
        "        dkr = [krW.jac{1}.diagonal, krO.jac{1}.diagonal]; \n",
        "    end\n",
        "end"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/getIncompProps.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "50rsDsOIbwvP",
        "outputId": "a0e5ec34-f8ab-450c-f685-da446de4ec78",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/computePressureRHS.m\n",
        "function [ff, gg, hh, gp, dF, dC] = computePressureRHS(g, omega, bc, src)\n",
        "%Compute right-hand side contributions to pressure linear system.\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   [f, g, h, grav, dF, dC] = computePressureRHS(G, omega, bc, src)\n",
        "%\n",
        "% DESCRIPTION:\n",
        "%   The contributions to the right-hand side for mimetic, two-point and\n",
        "%   multi-point discretisations of the equations for pressure and total\n",
        "%   velocity\n",
        "%\n",
        "%     v + lam K·grad (p - g·z omega) = 0\n",
        "%     div v  = q\n",
        "%\n",
        "%   with\n",
        "%             __\n",
        "%             \\    kr_i/\n",
        "%     lam   = /       / mu_i\n",
        "%             -- i\n",
        "%             __\n",
        "%             \\\n",
        "%     omega = /    f_i·rho_i\n",
        "%             -- i\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   G     - Grid data structure.\n",
        "%\n",
        "%   omega - Accumulated phase densities \\rho_i weighted by fractional flow\n",
        "%           functions f_i -- i.e., omega = \\sum_i \\rho_i f_i.  One scalar\n",
        "%           value for each cell in the discretised reservoir model, G.\n",
        "%\n",
        "%   bc    - Boundary condition structure as defined by function 'addBC'.\n",
        "%           This structure accounts for all external boundary conditions to\n",
        "%           the reservoir flow.  May be empty (i.e., bc = struct([])) which\n",
        "%           is interpreted as all external no-flow (homogeneous Neumann)\n",
        "%           conditions.\n",
        "%\n",
        "%   src   - Explicit source contributions as defined by function\n",
        "%           'addSource'.  May be empty (i.e., src = struct([])) which is\n",
        "%           interpreted as a reservoir model without explicit sources.\n",
        "%\n",
        "% RETURNS:\n",
        "%   f, g, h - Pressure (f), source/sink (g), and flux (h) external\n",
        "%             conditions.  In a problem without effects of gravity, these\n",
        "%             values may be passed directly on to linear system solvers\n",
        "%             such as 'schurComplementSymm'.\n",
        "%\n",
        "%   grav    - Pressure contributions from gravity,\n",
        "%\n",
        "%                grav = omega·g·(x_face - x_cell)\n",
        "%\n",
        "%             where\n",
        "%\n",
        "%                omega = \\sum_i f_i\\rho_i,\n",
        "%\n",
        "%             thus grav is a vector with one scalar value for each\n",
        "%             half-face in the model (size(G.cells.faces,1)).\n",
        "%\n",
        "%   dF, dC  - Dirichlet/pressure condition structure.  Logical array 'dF'\n",
        "%             is true for those faces that have prescribed pressures, while\n",
        "%             the corresponding prescribed pressure values are listed in\n",
        "%             'dC'.  The number of elements in 'dC' is SUM(DOUBLE(dF)).\n",
        "%\n",
        "%             This structure may be used to eliminate known face pressures\n",
        "%             from the linear system before calling a system solver (e.g.,\n",
        "%             'schurComplementSymm').\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `addBC`, `addSource`, `computeMimeticIP`, `schurComplementSymm`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "\n",
        "   if isfield(g, 'grav_pressure')\n",
        "       % If provided, use alternate grav_pressure function from the grid\n",
        "       % itself.\n",
        "       gp = g.grav_pressure(g, omega);\n",
        "   else\n",
        "       gp =   grav_pressure(g, omega);\n",
        "   end\n",
        "\n",
        "   ff = zeros(size(gp));\n",
        "   gg = zeros([g.cells.num, 1]);\n",
        "   hh = zeros([g.faces.num, 1]);\n",
        "\n",
        "   % SOURCE TERMS\n",
        "   if ~isempty(src),\n",
        "      % Compatibility check on cell numbers for source terms\n",
        "      assert (max(src.cell) <= g.cells.num && min(src.cell)>0, ...\n",
        "         'Source terms refer to cell not existant in grid.');\n",
        "\n",
        "      % Sum source terms inside each cell and add to rhs\n",
        "      ss = accumarray(src.cell, src.rate)    ;\n",
        "      ii = accumarray(src.cell,    1    ) > 0;\n",
        "      gg(ii) = gg(ii) + ss(ii);\n",
        "   end\n",
        "\n",
        "   dF = false([g.faces.num, 1]);\n",
        "   dC = [];\n",
        "\n",
        "   % BOUNDARY CONDITIONS\n",
        "   if ~isempty(bc),\n",
        "      % Check that bc and g are compatible.\n",
        "      assert (max(bc.face) <= g.faces.num && min(bc.face) > 0, ...\n",
        "         'Boundary condition refer to face not existant in grid.');\n",
        "      assert (all(accumarray(bc.face, 1, [g.faces.num, 1]) <= 1), ...\n",
        "         'There are repeated faces in boundary condition.');\n",
        "\n",
        "      % Pressure (Dirichlet) boundary conditions.\n",
        "      %  1) Extract the faces marked as defining pressure conditions.\n",
        "      %     Define a local numbering (map) of the face indices to the\n",
        "      %     pressure condition values.\n",
        "      %\n",
        "      is_press = strcmpi('pressure', bc.type);\n",
        "      face     = bc.face (is_press);\n",
        "      dC       = bc.value(is_press);\n",
        "      map      = sparse(double(face), 1, 1 : numel(face));\n",
        "\n",
        "      %  2) For purpose of (mimetic) pressure solvers, mark the 'face's as\n",
        "      %     having pressure boundary conditions.  This information will be\n",
        "      %     used to eliminate known pressures from the resulting system of\n",
        "      %     linear equations.  See (e.g.) 'solveIncompFlow' for details.\n",
        "      %\n",
        "      dF(face) = true;\n",
        "\n",
        "      %  3) Enter Dirichlet conditions into system right hand side.\n",
        "      %     Relies implictly on boundary faces being mentioned exactly once\n",
        "      %     in g.cells.faces(:,1).\n",
        "      %\n",
        "      i     =   dF(    g.cells.faces(:,1) );\n",
        "      ff(i) = - dC(map(g.cells.faces(i,1)));\n",
        "\n",
        "      %  4) Reorder Dirichlet conditions according to SORT(face).  This\n",
        "      %     allows the caller to issue statements such as 'X(dF) = dC' even\n",
        "      %     when ISLOGICAL(dF).\n",
        "      %\n",
        "      dC = dC(map(dF));\n",
        "\n",
        "      % Flux (Neumann) boundary conditions.\n",
        "      % Note negative sign due to bc.value representing INJECTION flux.\n",
        "      %\n",
        "      is_flux              = strcmpi('flux', bc.type);\n",
        "      hh(bc.face(is_flux)) = - bc.value(is_flux);\n",
        "   end\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function ff = grav_pressure(g, omega)\n",
        "% computes innerproduct cf (face_centroid - cell_centroid) * g for each face\n",
        "\n",
        "   g_vec = gravity();\n",
        "\n",
        "   if norm(g_vec(1:g.griddim)) > 0,\n",
        "      dim = g.griddim;\n",
        "\n",
        "      assert (1 <= dim && dim < 4);\n",
        "\n",
        "      cellno = rldecode(1 : g.cells.num, diff(g.cells.facePos), 2) .';\n",
        "      cvec   = g.faces.centroids(g.cells.faces(:,1), :) - ...\n",
        "               g.cells.centroids(cellno            , :);\n",
        "      ff     = omega(cellno) .* (cvec * reshape(g_vec(1:dim), [], 1));\n",
        "   else\n",
        "      ff     = zeros([size(g.cells.faces,1), 1]);\n",
        "   end\n",
        "end"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/computePressureRHS.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "spspq7z_NHLy",
        "outputId": "cfe0c6b6-a88e-4034-c977-eff80c72b917",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/initSingleFluid.m\n",
        "function fluid = initSingleFluid(varargin)\n",
        "%Initialize incompressible single phase fluid model.\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   fluid = initSingleFluid('pn1', pv1, ...)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   'pn'/pv - List of 'key'/value pairs defining specific fluid\n",
        "%             characteristics.  The following parameters must be defined:\n",
        "%               - mu  -- Fluid viscosity in units of Pa*s.\n",
        "%               - rho -- Fluid density in units of kilogram/meter^3.\n",
        "%\n",
        "% RETURNS:\n",
        "%   fluid - Fluid data structure as described in 'fluid_structure'\n",
        "%           representing the current state of the fluid within the\n",
        "%           reservoir model.\n",
        "%\n",
        "% EXAMPLE:\n",
        "%   fluid = initSingleFluid('mu' ,    1*centi*poise     , ...\n",
        "%                           'rho', 1014*kilogram/meter^3);\n",
        "%\n",
        "%   s = linspace(0, 1, 1001).'; kr = fluid.relperm(s);\n",
        "%   plot(s, kr), legend('kr')\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `fluid_structure`, `initSimpleFluid`, `solveIncompFlow`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "\n",
        "   opt = struct('mu', [], 'rho', []);\n",
        "   opt = merge_options(opt, varargin{:});\n",
        "\n",
        "   assert ((numel(opt.mu) == 1) && (numel(opt.rho) == 1));\n",
        "\n",
        "   prop = @(  varargin) properties(opt, varargin{:});\n",
        "   kr   = @(s,varargin) relperm(s, opt, varargin{:});\n",
        "\n",
        "   fluid = struct('properties', prop             , ...\n",
        "                  'saturation', @(x,varargin) x.s, ...\n",
        "                  'relperm'   , kr);\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function varargout = properties(opt, varargin)\n",
        "   varargout{1} = opt.mu;\n",
        "   if nargout > 1, varargout{2} = opt.rho; end\n",
        "   if nargout > 2, varargout{3} = []     ; end\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function varargout = relperm(s, varargin)\n",
        "   assert(size(s,2)==1);\n",
        "   varargout{1} = ones(size(s));\n",
        "   if nargout > 1, varargout{2} = zeros(size(s)); end\n",
        "   if nargout > 2, varargout{3} = zeros(size(s)); end\n",
        "end"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/initSingleFluid.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xp4nNl7aN6CL",
        "outputId": "a469460d-9841-4f9d-e818-2f0958b287b9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/modules/getSPE10rock.m\n",
        "function rock = getSPE10rock(varargin)\n",
        "%Define rock properties for Model 2 of tenth SPE CSP\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   rock = getSPE10rock\n",
        "%   rock = getSPE10rock(layers)\n",
        "%   rock = getSPE10rock(I, J, K)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   layers - Which of the 85 model layers to include in a specific test.\n",
        "%            OPTIONAL.  If unspecified, all 85 layers (for a total of\n",
        "%            60-by-220-by-85 == 1,122,000 cells) are included.\n",
        "%\n",
        "%            Some possible values are\n",
        "%               layers = ( 1 : 35).';  %  Tarbert formation\n",
        "%               layers = (36 : 85).';  %  Upper Ness formation\n",
        "%\n",
        "%   I,J,K  - Global Cartesian indices identifying subset of rock data.\n",
        "%            Useful, e.g., in extracting lateral sections.  Arrays must\n",
        "%            satisfy\n",
        "%\n",
        "%               ALL((0 < I) & (I <=  60)) && ...\n",
        "%               ALL((0 < J) & (J <= 220)) && ...\n",
        "%               ALL((0 < K) & (K <=  85))\n",
        "%\n",
        "%            OPTIONAL.  If unspecified, treated as I=1:60,J=1:220,K=1:85\n",
        "%            (i.e., the entire model; 1,122,000 cells).  In other words,\n",
        "%            equivalently to an unspecified 'layers' input.\n",
        "%\n",
        "% RETURNS:\n",
        "%   rock - Rock structure having fields 'perm' and 'poro' pertaining to\n",
        "%          the specified layers or cell subset.\n",
        "%\n",
        "% NOTE:\n",
        "%   The permeability data is returned in strict SI units (metres squared).\n",
        "%\n",
        "% EXAMPLE:\n",
        "%   rock = getSPE10rock(85)\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `getSPE10setup`, `make_spe10_data`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "   assert (all(cellfun(@isnumeric, varargin)), ...\n",
        "           'Input arrays must be numeric.');\n",
        "\n",
        "   % Load data in pre-processed form.\n",
        "   rock = load_mat_file();\n",
        "\n",
        "   % Extract caller's requested subset from 'rock' data\n",
        "   %\n",
        "   % Return only PERM and PORO data and exclude any other information that\n",
        "   % might be stored in on-disk representation of rock data.\n",
        "   %\n",
        "   ix   = define_subset(varargin{:});\n",
        "\n",
        "   rock = struct('perm', rock.perm(ix, :), ...\n",
        "                 'poro', rock.poro(ix   ));\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function ix = define_subset(varargin)\n",
        "   [Nx, Ny, Nz] = deal(60, 220, 85);\n",
        "                                          % ()\n",
        "   [I, J, K]    = deal(1:Nx, 1:Ny, 1:Nz); % Default (entire dataset)\n",
        "\n",
        "   if nargin == 1\n",
        "                                          % (layers)\n",
        "      K = varargin{1};                    % Caller specified ind. layers\n",
        "\n",
        "   elseif nargin == 3\n",
        "                                          % (I, J, K)\n",
        "      [I, J, K] = deal(varargin{:});      % Caller specified box\n",
        "\n",
        "   elseif nargin ~= 0\n",
        "      file = mfilename();\n",
        "      error(['Syntax is\\n\\t'              , ...\n",
        "             'rock = %s         %% or\\n\\t', ...\n",
        "             'rock = %s(layers) %% or\\n\\t', ...\n",
        "             'rock = %s(I, J, K)'], file, file, file);\n",
        "   end\n",
        "\n",
        "   validate_range(I, Nx);\n",
        "   validate_range(J, Ny);\n",
        "   validate_range(K, Nz);\n",
        "\n",
        "   [I, J, K] = ndgrid(I, J, K);\n",
        "\n",
        "   ix = sub2ind([Nx, Ny, Nz], I(:), J(:), K(:));\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function rock = load_mat_file()\n",
        "   %rdir = getDatasetPath('spe10', 'skipAvailableCheck', true);\n",
        "   rdir = '/content/mrst-core/data/SPE10';\n",
        "   rock_file = fullfile(rdir, 'spe10_rock');\n",
        "\n",
        "   if ~exist([rock_file, '.mat'], 'file')\n",
        "      ok = makeSPE10DataAvailable();\n",
        "\n",
        "      if ~ok\n",
        "         error('SPE10Download:Fail', 'Failed to download SPE 10 dataset');\n",
        "      end\n",
        "   end\n",
        "\n",
        "   data = load(rock_file);\n",
        "   rock = data.rock; % Fa-Fa-Fa\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function validate_range(i, n)\n",
        "   assert (all((0 < i) & (i <= n)), ...\n",
        "           '%s outside valid range 1:%d', inputname(1), n);\n",
        "end"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Writing /content/mrst-core/modules/getSPE10rock.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PYG4NJUTXXwb",
        "outputId": "a0ef7c4a-585e-4f04-d10d-ebb09a50d6aa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/params/wells_and_bc/addWell.m\n",
        "function W = addWell(W, G, rock, cellInx, varargin)\n",
        "%Insert a well into the simulation model.\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   W = addWell(W, G, rock, cellInx)\n",
        "%   W = addWell(W, G, rock, cellInx, 'pn', pv, ...)\n",
        "%\n",
        "% REQUIRED PARAMETERS:\n",
        "%   W       - Well structure or empty if no other wells exist.\n",
        "%             Updated upon return.\n",
        "%\n",
        "%   G       - Grid data structure.\n",
        "%\n",
        "%   rock    - Rock data structure.  Must contain valid field `perm`.\n",
        "%\n",
        "%   cellInx - Perforated well cells (vector of cell indices or a logical\n",
        "%             mask with length equal to G.cells.num).\n",
        "%\n",
        "% OPTIONAL PARAMETERS:\n",
        "%   Type -   Well control type. String. Supported values depend on the\n",
        "%            solver in question. Most solvers support at least two options: \n",
        "%              - 'bhp': Controlled by bottom hole pressure (DEFAULT)\n",
        "%              - 'rate': Controlled by total rate.\n",
        "%\n",
        "%   Val    - Well control target value.  Interpretation of this value is\n",
        "%            dependent upon `Type`.  Default value is 0.  If the well\n",
        "%            `Type` is 'bhp', then `Val` is given in unit Pascal and if\n",
        "%            the `Type` is 'rate', then `Val` is given in unit m^3/second.\n",
        "%\n",
        "%   Radius - Well bore radius (in unit of meters).  Either a single,\n",
        "%            scalar value which applies to all perforations or a vector of\n",
        "%            radii (one radius value for each perforation).\n",
        "%            Default value: Radius = 0.1 (i.e., 10 cm).\n",
        "%\n",
        "%   Dir    - Well direction.  Single CHAR or CHAR array.  A single CHAR\n",
        "%            applies to all perforations while a CHAR array defines the\n",
        "%            direction of the corresponding perforation.  In other words,\n",
        "%            Dir(i) is the direction in perforation cellInx(i) in the CHAR\n",
        "%            array case.\n",
        "%\n",
        "%            Supported values for a single perforation are 'x', 'y', or\n",
        "%            'z' (case insensitive) meaning the corresponding cell is\n",
        "%            perforated in the X, Y, or Z direction, respectively.\n",
        "%            Default value: Dir = 'z' (vertical well).\n",
        "%\n",
        "%   InnerProduct - The inner product with which to define the mass matrix.\n",
        "%            String.  Default value = 'ip_tpf'.\n",
        "%            Supported values are 'ip_simple', 'ip_tpf', 'ip_quasitpf',\n",
        "%            and 'ip_rt'.\n",
        "%\n",
        "%   WI     - Well productivity index. Vector of length `nc=numel(cellInx)`.\n",
        "%            Default value: `WI = repmat(-1, [nc, 1])`, whence the\n",
        "%            productivity index will be computed from available grid block\n",
        "%            data in grid blocks containing well completions.\n",
        "%\n",
        "%   Kh     - Permeability thickness.  Vector of length `nc=numel(cellInx)`.\n",
        "%            Default value: `Kh = repmat(-1, [nc, 1])`, whence the thickness\n",
        "%            will be computed from available grid block data in grid\n",
        "%            blocks containing well completions.\n",
        "%\n",
        "%   Skin   - Skin factor for computing effective well bore radius.  Scalar\n",
        "%            value or vector of length `nc=numel(cellInx)`.\n",
        "%            Default value: 0.0 (no skin effect).\n",
        "%\n",
        "%   compi  - Fluid phase composition for injection wells.  Vector of phase\n",
        "%            volume fractions.\n",
        "%            Default value:  `compi = [1, 0, 0]` (water injection)\n",
        "%\n",
        "%   Sign   - Well type: Production (Sign = -1) or Injection (Sign = 1).\n",
        "%            Default value: 0 (Undetermined sign. Will be derived from\n",
        "%            rates if possible).\n",
        "%\n",
        "%   Name   - Well name (string).\n",
        "%            Default value: `sprintf('W%d', numel(W) + 1)`\n",
        "%\n",
        "%   refDepth - Reference depth for the well, i.e. the value for which\n",
        "%            bottom hole pressures are defined. Defaults to the top of\n",
        "%            formation (calculated when refDepth = [])\n",
        "%\n",
        "%   calcReprRad - Whether or not to compute the representative radius of\n",
        "%            each perforation.  The representative radius is needed to\n",
        "%            derive shear thinning calculations in the context of polymer\n",
        "%            injection.  LOGICAL.  Default value: `calcReprRad = true` (do\n",
        "%            calculate the representative radius).  If set to false, the\n",
        "%            resulting well structure cannot be used to simulate polymer\n",
        "%            injection.\n",
        "%\n",
        "%   cellDims - optional cellDims of grid cells\n",
        "%\n",
        "%   lineSegments - nx3 matrix where row k represents x,y, and z-lengths of the \n",
        "%           line segment cooresponding to the part of trajectory traversing \n",
        "%           cell k. If nonempty, well indices will be computed using the \n",
        "%           projected directional well indices, i.e.,\n",
        "%              WI^2 = sum_i WI_i^2,  WI_i = (l_i/d_i)*WI(Dir=i), i = x,y,z\n",
        "%           where l_i and d_i are the segment length and cell dimention in\n",
        "%           direction i, respectively.\n",
        "%\n",
        "% RETURNS:\n",
        "%   W - Updated (or freshly created) well structure, each element of which\n",
        "%       has the following fields:\n",
        "%         - cells:   Grid cells perforated by this well (== cellInx).\n",
        "%         - type:    Well control type (== Type).\n",
        "%         - val:     Target control value (== Val).\n",
        "%         - r:       Well bore radius (== Radius).\n",
        "%         - dir:     Well direction (== Dir).\n",
        "%         - WI:      Well productivity index.\n",
        "%         - dZ: Displacement of each well perforation measured from\n",
        "%           'highest' horizontal contact (i.e., the 'TOP' contact with the\n",
        "%           minimum 'Z' value counted amongst all cells perforated by this\n",
        "%           well).\n",
        "%         - name:    Well name (== Name).\n",
        "%         - compi:   Fluid composition--only used for injectors (== Comp_i).\n",
        "%         - sign:    Injection (+) or production (-) flag.\n",
        "%         - status:  Boolean indicating if the well is open or shut.\n",
        "%         - cstatus: One entry per perforation, indicating if the completion is open.\n",
        "%         - lims:    Limits for the well. Contains subfields for the types\n",
        "%           of limits applicable to the well (bhp, rate, orat, ...)\n",
        "%           Injectors generally have upper limits, while producers have\n",
        "%           lower limits.\n",
        "%         - rR:      The representative radius for the wells, which is used\n",
        "%           in the shear thinning calculation when polymer is involved in\n",
        "%           the simulation.  Empty if 'calcReprRad' is false.\n",
        "%\n",
        "% EXAMPLE:\n",
        "%   incompTutorialWells\n",
        "%\n",
        "% NOTE:\n",
        "%   Wells in one/two-dimensional grids are not well defined in terms of\n",
        "%   computing well indices. However, such wells are often useful for\n",
        "%   simulation scenarios where the exact value of well indices is not of\n",
        "%   great importance. For this reason, we make the following approximations\n",
        "%   when addWell is used to compute e.g. horizontal wells in 2D:\n",
        "%\n",
        "%       - K_z is assumed to be the harmonic average of K_x and K_y:\n",
        "%         K_z = 1/(1/K_x + 1/K_y).\n",
        "%       - The depth of a grid block is assumed to be unit length (1 meter)\n",
        "%\n",
        "%   This generally produces reasonable ranges for the WI field, but it is\n",
        "%   the user's responsibility to keep these assumptions in mind.\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `verticalWell`, `addSource`, `addBC`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2020 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "addpath '/content/mrst-core/params'\n",
        "\n",
        "mrstNargInCheck(4, [], nargin);\n",
        "\n",
        "if isempty(cellInx) || (islogical(cellInx) && ~any(cellInx))\n",
        "   warn_empty_cell_index_range(numel(W), varargin{:});\n",
        "   return\n",
        "end\n",
        "\n",
        "if islogical(cellInx)\n",
        "    assert(numel(cellInx) == G.cells.num, ...\n",
        "    'Logical mask does not match number of grid cells.');\n",
        "    cellInx = find(cellInx);\n",
        "end\n",
        "numC = numel(cellInx);\n",
        "\n",
        "\n",
        "opt = struct('InnerProduct', 'ip_tpf',                     ...\n",
        "             'Dir'         , 'z',                          ...\n",
        "             'Name'        , sprintf('W%d', numel(W) + 1), ...\n",
        "             'Radius'      , 0.1,                          ...\n",
        "             'Type'        , 'bhp',                        ...\n",
        "             'Val'         , 0,                            ...\n",
        "             'Comp_i'      , [],                           ...\n",
        "             'compi'       , [],                           ...\n",
        "             'WI'          , repmat(-1, [numC, 1]),        ...\n",
        "             'Kh'          , repmat(-1, [numC, 1]),        ...\n",
        "             'Skin'        , zeros(numC, 1),               ...\n",
        "             'refDepth'    , [],                           ...\n",
        "             'lims'        , [],                           ...\n",
        "             'vfp_index'   , [],                           ...\n",
        "             'cp'          , [],                           ...\n",
        "             'components'  , [],                           ...\n",
        "             'heel'        , [],                           ...\n",
        "             'Sign'        , 0,                            ...\n",
        "             'calcReprRad' , true,                         ...\n",
        "             'cellDims'    , [],                           ...\n",
        "             'lineSegments', []);\n",
        "\n",
        "opt = merge_options(opt, varargin{:});\n",
        "\n",
        "if ~isempty(opt.Comp_i)\n",
        "    % Legacy keyword - check that injection phase composition is not doubly\n",
        "    % specified with different values.\n",
        "    if numel(opt.compi) ~= numel(opt.Comp_i) || any(opt.compi ~= opt.Comp_i)\n",
        "        assert(isempty(opt.compi), ...\n",
        "            ['Ambigious injection phase composition. Both ''compi'' and ', ...\n",
        "            '''Comp_i'' was specified with different values.']);\n",
        "        opt.compi = opt.Comp_i;\n",
        "    end\n",
        "    opt.Comp_i = [];\n",
        "end\n",
        "\n",
        "if isempty(opt.compi)\n",
        "    opt.compi = [1, 0, 0];\n",
        "end\n",
        "\n",
        "% Expand scalar values to vectors equal to the number of cells\n",
        "if numel(opt.WI) == 1\n",
        "    opt.WI = repmat(opt.WI, numC, 1);\n",
        "end\n",
        "if numel(opt.Skin) == 1\n",
        "    opt.Skin = repmat(opt.Skin, numC, 1);\n",
        "end\n",
        "if numel(opt.Kh) == 1\n",
        "    opt.Kh = repmat(opt.Kh, numC, 1);\n",
        "end\n",
        "\n",
        "WI = reshape(opt.WI, [], 1);\n",
        "\n",
        "assert (numel(WI) == numC, ...\n",
        "        'Provided WI should be one entry per perforated cell.')\n",
        "assert (numel(opt.Kh) == numC, ...\n",
        "        'Provided Kh should be one entry per perforated cell.')\n",
        "assert (numel(opt.Skin) == numC || numel(opt.Skin) == 1, ...\n",
        "       ['Provided Skin should be one entry per perforated cell or ', ...\n",
        "        'a single entry for all perforated cells']);\n",
        "\n",
        "if numel(opt.Skin) == 1\n",
        "   opt.Skin = opt.Skin(ones([numC, 1]));\n",
        "end\n",
        "\n",
        "% Set reference depth default value.\n",
        "if isempty(opt.refDepth)\n",
        "   dispif(mrstVerbose(), ...\n",
        "       ['Defaulting reference depth to top of formation for well %s. Please', ...\n",
        "       ' specify ''refDepth'' optional argument to ''addWell'' if you require bhp', ...\n",
        "       ' at a specific depth.\\n'], opt.Name);\n",
        "   g_vec = gravity();\n",
        "   dims  = G.griddim;\n",
        "   if norm(g_vec(1:dims)) > 0\n",
        "      g_vec = g_vec ./ norm(g_vec);\n",
        "      opt.refDepth = min(G.nodes.coords * g_vec(1:dims)');\n",
        "   else\n",
        "      opt.refDepth = 0;\n",
        "   end\n",
        "end\n",
        "ip = opt.InnerProduct;\n",
        "\n",
        "if opt.calcReprRad\n",
        "   % Compute the representative radius for the grid block in which the well\n",
        "   % is completed.  It is needed for computing the shear rate of the wells.\n",
        "   rR = radiusRep(G, opt.Radius, opt.Dir, reshape(cellInx, [], 1));\n",
        "else\n",
        "   rR = [];\n",
        "end\n",
        "\n",
        "% Initialize Well index - WI. ---------------------------------------------\n",
        "% Check if we need to calculate WI or if it is supplied.\n",
        "\n",
        "compWI = WI < 0;\n",
        "\n",
        "if any(compWI) % calculate WI for the cells in compWI\n",
        "    if isempty(opt.lineSegments)\n",
        "        WI(compWI) = computeWellIndex(G, rock, opt.Radius, reshape(cellInx, [], 1), ...\n",
        "            'Dir', opt.Dir, ...\n",
        "            'Skin', opt.Skin, ...\n",
        "            'cellDims', opt.cellDims, ...\n",
        "            'Kh', opt.Kh, ...\n",
        "            'InnerProduct', ip, ...\n",
        "            'Subset', compWI);\n",
        "    else\n",
        "        len = opt.lineSegments;\n",
        "        assert(all(size(opt.lineSegments)== [numC, 3]), ...\n",
        "            'Expected format of input ''segments'' is [%d, 3], got [%d, %d]', ...\n",
        "            numC, size(len,1), size(len,2));\n",
        "        d = {'x', 'y', 'z'}; \n",
        "        tmp = 0; \n",
        "        if isempty(opt.cellDims)\n",
        "            [dx, dy, dz] = cellDims(G, cellInx);\n",
        "            opt.cellDims = [dx, dy, dz];\n",
        "        end\n",
        "        for k = 1:3\n",
        "            WI_d = computeWellIndex(G, rock, opt.Radius, reshape(cellInx, [], 1), ...\n",
        "                   'Dir', d{k}, ...\n",
        "                   'Skin', opt.Skin, ...\n",
        "                   'cellDims', opt.cellDims, ...\n",
        "                   'Kh', opt.Kh, ...\n",
        "                   'InnerProduct', ip, ...\n",
        "                   'Subset', compWI);         \n",
        "            tmp = tmp + ( (len(compWI, k)./opt.cellDims(compWI, k)).*WI_d ).^2;\n",
        "        end\n",
        "        WI(compWI) = sqrt(tmp);\n",
        "    end\n",
        "end\n",
        "\n",
        "% Set well sign (injection = 1 or production = -1)\n",
        "% for bhp wells or rate controlled wells with rate = 0.\n",
        "if opt.Sign ~= 0\n",
        "   if sum(opt.Sign == [-1, 1]) ~= 1\n",
        "      error(msgid('Sign:NonUnit'), 'Sign must be -1 or 1');\n",
        "   end\n",
        "   if strcmp(opt.Type, 'rate') && (sign(opt.Val) ~= 0) ...\n",
        "         && (opt.Sign ~= sign(opt.Val))\n",
        "      warning(msgid('Sign'), ...\n",
        "             ['Given sign does not match sign of given value. ', ...\n",
        "              'Setting w.sign = sign( w.val )']);\n",
        "      opt.Sign = sign(opt.Val);\n",
        "   end\n",
        "else\n",
        "   if strcmp(opt.Type, 'rate')\n",
        "      if opt.Val == 0\n",
        "         warning(msgid('Sign'), 'Given value is zero, prod or inj ???');\n",
        "      else\n",
        "         opt.Sign = sign(opt.Val);\n",
        "      end\n",
        "   end\n",
        "end\n",
        "\n",
        "% Add well to well structure. ---------------------------------------------\n",
        "%\n",
        "if numel(opt.Radius) == 1\n",
        "    opt.Radius = repmat(opt.Radius, numC, 1);\n",
        "end\n",
        "W  = [W; struct('cells'     , reshape(cellInx, [], 1), ...\n",
        "                'type'      , opt.Type,             ...\n",
        "                'val'       , opt.Val,              ...\n",
        "                'r'         , opt.Radius,           ...\n",
        "                'dir'       , opt.Dir,              ...\n",
        "                'rR'        , rR,                   ...\n",
        "                'WI'        , WI,                   ...\n",
        "                'dZ'        , getDeltaZ(G, reshape(cellInx, [], 1), ...\n",
        "                                           opt.refDepth, opt.Name), ...\n",
        "                'heel'      , opt.heel,             ...\n",
        "                'name'      , opt.Name,             ...\n",
        "                'compi'     , opt.compi,            ...\n",
        "                'refDepth'  , opt.refDepth,         ...\n",
        "                'defaulted' , [],                   ...\n",
        "                'lims'      , opt.lims,             ...\n",
        "                'cp'        , opt.cp,               ...\n",
        "                'components', opt.components,      ...\n",
        "                'sign'      , opt.Sign,             ...\n",
        "                'status'    , true,                 ...\n",
        "                'vfp_index' , opt.vfp_index,        ...\n",
        "                'cstatus'   , true(numC,1))];\n",
        "\n",
        "if numel(W(end).dir) == 1\n",
        "   W(end).dir = repmat(W(end).dir, [numel(W(end).cells), 1]);\n",
        "end\n",
        "assert (numel(W(end).dir) == numel(W(end).cells));\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "% Private helper functions follow\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function dZ = getDeltaZ(G, cells, refDepth, wellName)\n",
        "direction = gravity();\n",
        "dims      = G.griddim;\n",
        "if norm(direction(1:dims)) > 0\n",
        "   direction = direction ./ norm(direction(1:dims));\n",
        "else\n",
        "   direction      = zeros(1, dims);\n",
        "   if dims > 2\n",
        "      direction(end) = 1;\n",
        "   end\n",
        "end\n",
        "xyz = G.cells.centroids(cells, :);\n",
        "bad = any(~isfinite(xyz), 1);\n",
        "if norm(direction(bad))\n",
        "    % We allow nan/inf coordinates, but not if the corresponding \"down\"\n",
        "    % direction has magnitude in those dimensions.\n",
        "    error('Non-finite centroids in dimensions: %s', num2str(find(bad)));\n",
        "end\n",
        "xyz(isnan(xyz)) = 0;\n",
        "Z = xyz * direction(1:dims).';\n",
        "dZ = Z - refDepth;\n",
        "if any(dZ < -max(eps(Z), eps(refDepth)))\n",
        "    warning('RefDepth:BelowTopConnection', ...\n",
        "           ['Reference depth for well BHP in well ''%s'' is set ', ...\n",
        "            'below well''s top-most reservoir connection'], wellName);\n",
        "end\n",
        "if isfield(G, 'nodes')\n",
        "    % Grid with nodes\n",
        "    delta = max(G.nodes.coords)-min(G.nodes.coords);\n",
        "elseif isfield(G.faces, 'centroids')\n",
        "    % Possibly a coarse grid\n",
        "    delta = max(G.faces.centroids)-min(G.faces.centroids);\n",
        "else\n",
        "    % Skip check\n",
        "    delta = inf(1, G.griddim);\n",
        "end\n",
        "\n",
        "if max(dZ) > delta*direction(1:dims).' && norm(gravity()) > 0\n",
        "    msg = ['Pressure drop distance from BHP reference depth to ', ...\n",
        "           'selected perforation exceeds total thickness of model ', ...\n",
        "           'in well ''%s''.'];\n",
        "    if refDepth == 0\n",
        "        msg = [msg, ' BHP reference depth is defaulted to zero. ', ...\n",
        "               'Consider setting a different value.'];\n",
        "    else\n",
        "        msg = [msg, ' Please check refDepth value.'];\n",
        "    end\n",
        "    warning('RefDepth:PDropExceedsThickness', msg, wellName)\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "% A function to compute the representative radius of the grid block in\n",
        "% which the well is completed.\n",
        "% rR = sqrt(re * rw).\n",
        "% Here, rw is the wellbore radius, re is the area equivalent radius of the\n",
        "% grid block where the well is completed, which means the circle with radius\n",
        "% re has the same area as the cross section of the grid block in the\n",
        "% completion's orthogonal direction.\n",
        "% The current formulation theoretically only works for Cartisian grids,\n",
        "% while it has been working well for the cases we have,\n",
        "% including some corner-point grids.\n",
        "% TODO: REMAIN TO BE VERIFIED for really twisted grids.\n",
        "function rr = radiusRep(G, radius, welldir, cells)\n",
        "\n",
        "if(isfield(G,'nodes'))\n",
        "   [dx, dy, dz] = cellDims(G, cells);\n",
        "elseif isfield(G.faces, 'centroids')\n",
        "   [dx, dy, dz] = cellDimsCG(G, cells);\n",
        "else\n",
        "   warning('RepRad:FaceGeomMissing', ...\n",
        "           'Face geometry missing, will not compute representative radius')\n",
        "   [dx, dy, dz] = deal(nan(G.cells.num, 1));\n",
        "end\n",
        "\n",
        "welldir = lower(welldir);\n",
        "if numel(welldir) == 1\n",
        "    welldir = repmat(welldir, numel(cells), 1);\n",
        "end\n",
        "re = zeros(size(welldir, 1), 1);\n",
        "\n",
        "% The following formulation only works for Cartisian mesh\n",
        "ci = welldir == 'x';\n",
        "re(ci) = sqrt(dy(ci) .* dz(ci) / pi);\n",
        "\n",
        "ci = welldir == 'y';\n",
        "re(ci) = sqrt(dx(ci) .* dz(ci) / pi);\n",
        "\n",
        "ci = welldir == 'z';\n",
        "re(ci) = sqrt(dy(ci) .* dx(ci) / pi);\n",
        "\n",
        "rr = sqrt( re .* radius);\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function warn_empty_cell_index_range(nW, varargin)\n",
        "[opt, ign] = merge_options(struct('Name', ''), varargin{:});    %#ok<ASGLU>\n",
        "\n",
        "name = opt.Name;\n",
        "if isempty(name), name = sprintf('%d', nW + 1); end\n",
        "\n",
        "warning('Empty:CellIndexSelection', ...\n",
        "        'Empty Cell Selection in Well ''%s''. Well Ignored.', name);\n"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Overwriting /content/mrst-core/params/wells_and_bc/addWell.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FQXCYdiwYxR5",
        "outputId": "1a786c22-234a-4f49-e08a-b157f2f94bbb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "%%writefile /content/mrst-core/solvers/computeTrans.m\n",
        "function T = computeTrans(G, rock, varargin)\n",
        "%Compute transmissibilities.\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   T = computeTrans(G, rock)\n",
        "%   T = computeTrans(G, rock, 'pn', pv, ...)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   G    - Grid structure as described by grid_structure.\n",
        "%\n",
        "%   rock - Rock data structure with valid field `perm`.  The permeability\n",
        "%          is assumed to be in measured in units of metres squared (m^2).\n",
        "%          Use function `darcy` to convert from darcies to m^2, e.g::\n",
        "%\n",
        "%                 perm = convertFrom(perm, milli*darcy)\n",
        "%\n",
        "%          if the permeability is provided in units of millidarcies.\n",
        "%\n",
        "%          The field rock.perm may have ONE column for a scalar\n",
        "%          permeability in each cell, TWO/THREE columns for a diagonal\n",
        "%          permeability in each cell (in 2/3 D) and THREE/SIX columns for a\n",
        "%          symmetric full tensor permeability.  In the latter case, each\n",
        "%          cell gets the permeability tensor::\n",
        "%\n",
        "%                 K_i = [ k1  k2 ]      in two space dimensions\n",
        "%                       [ k2  k3 ]\n",
        "%\n",
        "%                 K_i = [ k1  k2  k3 ]  in three space dimensions\n",
        "%                       [ k2  k4  k5 ]\n",
        "%                       [ k3  k5  k6 ]\n",
        "%\n",
        "%\n",
        "% OPTIONAL PARAMETERS:\n",
        "%\n",
        "%   K_system - Define the system permeability is defined in valid values\n",
        "%              are `xyz` and `loc_xyz`.\n",
        "%\n",
        "%   cellCenters - Compute transmissibilities based on supplied\n",
        "%                 `cellCenters` rather than default `G.cells.centroids`\n",
        "%\n",
        "%   cellFaceCenters - Compute transmissibilities based on supplied\n",
        "%                     `cellFaceCenters` rather then default\n",
        "%                     `G.faces.centroids(G.cells.faces(:,1), :)`\n",
        "%\n",
        "%   fixNegative     - Take absolute value of negative transmissibilities if\n",
        "%                     present. This typically happens if the grid cell\n",
        "%                     geometry is degenerate, for instance with a centroid\n",
        "%                     outside the cell. Default: true.\n",
        "%\n",
        "% RETURNS:\n",
        "%   T - half-transmissibilities for each local face of each grid cell in\n",
        "%       the grid.  The number of half-transmissibilities equals the number\n",
        "%       of rows in `G.cells.faces`.\n",
        "%\n",
        "% NOTE:\n",
        "%   Face normals are assumed to have length equal to the corresponding face\n",
        "%   areas. This property is guaranteed by function `computeGeometry`.\n",
        "%\n",
        "% SEE ALSO:\n",
        "%   `computeGeometry`, `permTensor`, `makeRock`.\n",
        "\n",
        "%{\n",
        "Copyright 2009-2020 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "MRST is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "MRST is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "%}\n",
        "\n",
        "   addpath '/content/mrst-core/utils/gridtools'\n",
        "   addpath '/content/mrst-core/params/rock' \n",
        "\n",
        "   opt = struct('verbose'        , false, ...\n",
        "                'grdecl'         , []   , ...\n",
        "                'K_system'       , 'xyz', ...\n",
        "                'cellCenters'    , []   , ...\n",
        "                'fixNegative'    , true, ...\n",
        "                'cellFaceCenters', []   );\n",
        "   opt = merge_options(opt, varargin{:});\n",
        "\n",
        "   dispif(opt.verbose, 'Computing one-sided transmissibilities...\\t');\n",
        "   t0 = ticif(opt.verbose);\n",
        "\n",
        "   switch lower(opt.K_system)\n",
        "      case 'xyz',     T = htrans_xyz  (G, rock, opt);\n",
        "      case 'loc_xyz', T = htrans_local(G, rock, opt);\n",
        "\n",
        "      otherwise\n",
        "         error(msgid('PermSys:Unknown'), ...\n",
        "               'Unknown permeability coordinate system ''%s''.', ...\n",
        "               opt.K_system);\n",
        "   end\n",
        "   if opt.fixNegative\n",
        "      T = handle_negative_trans(T, opt);\n",
        "   end\n",
        "   T = handle_ntg(T, rock, G);\n",
        "   \n",
        "   if isstruct(opt.grdecl) && numel(opt.grdecl) == 1\n",
        "      m = getMultipliers(G, opt.grdecl);\n",
        "      T = T .* m;\n",
        "   end\n",
        "\n",
        "   tocif(opt.verbose, t0);\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function T = htrans_xyz(G, rock, opt)\n",
        "   [C, N, cellNo] = cell_geometry(G, opt);\n",
        "   [K, i, j] = permTensor(rock, G.griddim);\n",
        "\n",
        "   assert (size(K,1) == G.cells.num, ...\n",
        "          ['Permeability must be defined in active cells only.\\n', ...\n",
        "           'Got %d tensors, expected %d (== number of cells).'],   ...\n",
        "           size(K,1), G.cells.num);\n",
        "\n",
        "   % Compute T = C'*K*N / C'*C. Loop-based to limit memory use.\n",
        "   T = zeros(size(cellNo));\n",
        "   for k = 1 : size(i, 2)\n",
        "      T = T + (C(:, i(k)) .* K(cellNo, k) .* N(:, j(k)));\n",
        "   end\n",
        "\n",
        "   T = T ./ sum(C .* C, 2);\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function T = htrans_local(G, rock, opt)\n",
        "   if size(rock.perm, 2) == 1\n",
        "      rock.perm = repmat(rock.perm, [1, G.griddim]);\n",
        "   end\n",
        "\n",
        "   if size(rock.perm, 2) ~= size(G.cartDims, 2)\n",
        "      error(msgid('PermSys:Inconsistent'),                 ...\n",
        "           ['Permeability coordinate system ''loc_xyz'' ', ...\n",
        "            'is only valid for diagonal tensors.']);\n",
        "   end\n",
        "\n",
        "   assert (size(rock.perm, 1) == G.cells.num, ...\n",
        "          ['Permeability must be defined in active cells only.\\n', ...\n",
        "           'Got %d tensors, expected %d (== number of cells).'],   ...\n",
        "           size(rock.perm,1), G.cells.num);\n",
        "\n",
        "   [C, N, cellNo] = cell_geometry(G, opt);\n",
        "\n",
        "   dim = ceil(G.cells.faces(:,2) / 2);\n",
        "   ind = sub2ind(size(rock.perm), cellNo, double(dim));\n",
        "   T   = reshape(rock.perm(ind), [], 1) .* ...\n",
        "         sum(C .* N, 2) ./ sum(C .* C, 2);\n",
        "     \n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function [C, N, cellNo] = cell_geometry(G, opt)\n",
        "   % Vectors from cell centroids to face centroids\n",
        "   cellNo = gridCellNo(G);\n",
        "\n",
        "   if ~isempty(opt.cellCenters)\n",
        "      C = opt.cellCenters;\n",
        "   else\n",
        "      C = G.cells.centroids;\n",
        "   end\n",
        "\n",
        "   if ~isempty(opt.cellFaceCenters)\n",
        "      C = opt.cellFaceCenters - C(cellNo,:);\n",
        "   else\n",
        "      C = G.faces.centroids(G.cells.faces(:,1), :) - C(cellNo,:);\n",
        "   end\n",
        "\n",
        "   % Outward-pointing normal vectors\n",
        "   cf  = G.cells.faces(:,1);\n",
        "   sgn = 2*(cellNo == G.faces.neighbors(cf, 1)) - 1;\n",
        "   N   = bsxfun(@times, sgn, G.faces.normals(cf, :));\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function T = handle_ntg(T, rock, G)\n",
        "if isfield(rock, 'ntg') && size(G.cells.faces, 2) == 2\n",
        "    cellNo = gridCellNo(G);\n",
        "    dim    = ceil(G.cells.faces(:,2) / 2);\n",
        "    m      = rock.ntg(cellNo);\n",
        "    m(dim==3) = 1;\n",
        "    T = m.*T;\n",
        "end\n",
        "end\n",
        "    \n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function T = handle_negative_trans(T, opt)\n",
        "   is_neg = T < 0;\n",
        "\n",
        "   if any(is_neg)\n",
        "      dispif(opt.verbose, ...\n",
        "            ['\\nWarning:\\n\\t%d negative transmissibilities.\\n\\t', ...\n",
        "             'Replaced by absolute values...\\n'], sum(is_neg));\n",
        "\n",
        "      T(is_neg) = -T(is_neg);\n",
        "   end\n",
        "end\n",
        "\n",
        "%--------------------------------------------------------------------------\n",
        "\n",
        "function multipliers = getMultipliers(G, grdecl)\n",
        "%Extract multipliers from grdecl.FAULTS and grdecl.MULT*\n",
        "%\n",
        "% SYNOPSIS:\n",
        "%   m = getMultipliers(G, rock)\n",
        "%\n",
        "% PARAMETERS:\n",
        "%   G       - Grid data structure as described by grid_structure.\n",
        "%\n",
        "%   grdecl  - Raw ECLIPSE data field as read by (???).  The fields FAULTS\n",
        "%             MULTX, MULTY and MULTZ all contain transmissibility\n",
        "%             multipliers.  These are interpreted as one-sided multipliers,\n",
        "%             i.e multiplicative modifiers for the half-face\n",
        "%             transmissibilities computed in this file.\n",
        "%\n",
        "% RETURNS:\n",
        "%   m - half-transmissibilities multipliers for all faces.\n",
        "\n",
        "   multipliers = ones(size(G.cells.faces, 1), 1);\n",
        "\n",
        "   % do fault multiplicators which are in grdecl.FAULTS.('fault_name')\n",
        "   dirstruct = struct('X', 1, 'Y', 3, 'Z', 5);\n",
        "   if isfield(grdecl,'FAULTS')\n",
        "      faults = struct2cell(grdecl.FAULTS);\n",
        "      for i = 1:numel(faults)\n",
        "\n",
        "         fault = faults{i};\n",
        "\n",
        "         % Skip if there are no fault multipliers.\n",
        "         if ~isfield(fault, 'multflt')\n",
        "            continue;\n",
        "         end\n",
        "\n",
        "         for j = 1 : numel(fault.dir)\n",
        "            dirnum = dirstruct.(fault.dir(j));\n",
        "            region = fault.cells(j,:);\n",
        "\n",
        "            if region(dirnum) ~= region(dirnum+1)\n",
        "               error(['Wrong fault ind direction ', fault.dir(j)]);\n",
        "            end\n",
        "\n",
        "            % For each half-face...\n",
        "            for side = 0 : 1\n",
        "               % Find cell indices in G corresponding to region\n",
        "               region(dirnum:dirnum+1) = region(dirnum:dirnum+1) + side;\n",
        "\n",
        "               [X,Y,Z] = ndgrid(region(1) : region(2), ...\n",
        "                                region(3) : region(4), ...\n",
        "                                region(5) : region(6));\n",
        "               ind = sub2ind(G.cartDims, X(:), Y(:), Z(:));\n",
        "               c   = cart2active(G, ind);\n",
        "\n",
        "               % Set multiplier of cellFace with the correct tag\n",
        "               cf  = mcolon(G.cells.facePos(c), G.cells.facePos(c+1)-1);\n",
        "               tag = dirnum + 1 - side;\n",
        "               cf  = cf(G.cells.faces(cf,2) == tag);\n",
        "               multipliers(cf) = fault.multflt;\n",
        "            end\n",
        "         end\n",
        "      end\n",
        "   end\n",
        "\n",
        "   %assume MULT?M is not used\n",
        "   vecstruct=[];\n",
        "   dirstruct=[];\n",
        "   if isfield(grdecl,'MULTX')\n",
        "      vecstruct = [vecstruct, grdecl.MULTX];\n",
        "      dirstruct = [dirstruct, 2];\n",
        "      mult      = ones(G.cartDims);\n",
        "      multx     = reshape(grdecl.MULTX, G.cartDims);\n",
        "      mult(2:end,:,:) = multx(1:end-1, :, :);\n",
        "      vecstruct = [vecstruct, mult(:)];\n",
        "      dirstruct = [dirstruct, 1];%set the direction number\n",
        "   end\n",
        "\n",
        "   if isfield(grdecl,'MULTY')\n",
        "      vecstruct = [vecstruct, grdecl.MULTY];\n",
        "      dirstruct = [dirstruct, 4];\n",
        "      mult      = ones(G.cartDims);\n",
        "      multx     = reshape(grdecl.MULTY, G.cartDims);\n",
        "      mult(:,2:end,:) = multx(:, 1:end-1, :);\n",
        "      vecstruct = [vecstruct, mult(:)];\n",
        "      dirstruct = [dirstruct, 3];\n",
        "   end\n",
        "\n",
        "   if isfield(grdecl,'MULTZ')\n",
        "      vecstruct = [vecstruct, grdecl.MULTZ];\n",
        "      dirstruct = [dirstruct, 6];\n",
        "      mult      = ones(G.cartDims);\n",
        "      multx     = reshape(grdecl.MULTZ, G.cartDims);\n",
        "      mult(:,:,2:end) = multx(:, :, 1:end-1);\n",
        "      vecstruct = [vecstruct, mult(:)];\n",
        "      dirstruct = [dirstruct, 5];\n",
        "   end\n",
        "\n",
        "   if ~isempty(vecstruct)\n",
        "      % do multipliers\n",
        "      for i = 1:length(dirstruct)\n",
        "         vec   = vecstruct(:, i);\n",
        "         dir   = dirstruct(i);\n",
        "         b     = cumsum(G.cells.faces(:, 2) == dir);\n",
        "         cfind = cumsum(double(diff(G.cells.facePos)));%facepos\n",
        "         numf  = b(cfind)-[0; b(cfind(1:end-1))];\n",
        "         ci    = G.cells.faces(:,2) == dirstruct(i);\n",
        "         mult  = rldecode(vec(G.cells.indexMap), numf);\n",
        "\n",
        "         multipliers(ci) = mult;\n",
        "      end\n",
        "   end\n",
        "end"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Overwriting /content/mrst-core/solvers/computeTrans.m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1suPOKOfO8Se"
      },
      "source": [
        "# %%writefile /content/mrst-core/modules/getDatasetPath.m\n",
        "# function pth = getDatasetPath(name, varargin)\n",
        "# %Get the path of a dataset (optionally: try to download it if missing)\n",
        "# %\n",
        "# % SYNOPSIS:\n",
        "# %   pth = getDatasetPath(name)\n",
        "# %   pth = getDatasetPath(name, 'pn1', pv1, ...)\n",
        "# %\n",
        "# % REQUIRED PARAMETERS:\n",
        "# %   name    -  The name of the dataset. Must be known to MRST, see\n",
        "# %              `getAvailableDatasets` for details.\n",
        "# %\n",
        "# % OPTIONAL PARAMETERS:\n",
        "# %   download - Boolean indicating if the functions should attempt to\n",
        "# %              download the dataset if it is missing. Default: Enabled.\n",
        "# %\n",
        "# %   askBeforeDownload - Boolean. If the download option is enabled, setting\n",
        "# %                       this to true will prompt the user before starting a\n",
        "# %                       potentially large download. Default: Enabled.\n",
        "# %\n",
        "# %   skipAvailableCheck -\n",
        "# %              Boolean flag indicating whether or not to omit checking for\n",
        "# %              presence of data on disk.  This is mainly intended for the\n",
        "# %              case of needing to manually download objects into the\n",
        "# %              dataset's containing directory through some external means.\n",
        "# %              Default value: `skipAvailableCheck = false` (*do* check if\n",
        "# %              the dataset is available).\n",
        "# %\n",
        "# % RETURNS:\n",
        "# %   pth      - Path to dataset.\n",
        "# %\n",
        "# % NOTE: \n",
        "# %   If this function returns, the dataset will be present at the path\n",
        "# %   given. Any other situation will result in an error being thrown.\n",
        "# %\n",
        "# %   Using `skipAvailableCheck` bypasses this basic safety measure of MRST's\n",
        "# %   dataset handling.  Consequently, said option should be used only when\n",
        "# %   circumstances so dictate.\n",
        "# % \n",
        "# % SEE ALSO:\n",
        "# %   `mrstdatasetGUI`, `downloadDataset`.\n",
        "\n",
        "# %{\n",
        "# Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "# This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "# MRST is free software: you can redistribute it and/or modify\n",
        "# it under the terms of the GNU General Public License as published by\n",
        "# the Free Software Foundation, either version 3 of the License, or\n",
        "# (at your option) any later version.\n",
        "\n",
        "# MRST is distributed in the hope that it will be useful,\n",
        "# but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "# GNU General Public License for more details.\n",
        "\n",
        "# You should have received a copy of the GNU General Public License\n",
        "# along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "# %}\n",
        "\n",
        "#     opt = struct('download',          true, ...\n",
        "#                  'askBeforeDownload', true, ...\n",
        "#                  'skipAvailableCheck', false);\n",
        "#     opt = merge_options(opt, varargin{:});\n",
        "#     [info, present] = getDatasetInfo(name);\n",
        "\n",
        "#     if present || opt.skipAvailableCheck,\n",
        "#         % Return path to dataset\n",
        "#         pth = fullfile(mrstDataDirectory(), info.name);\n",
        "#     else\n",
        "#         if opt.download\n",
        "#             % We want to attempt a download\n",
        "#             [pth, ok] = downloadDataset(name, opt.askBeforeDownload);\n",
        "#             if ~ok\n",
        "#                 error(['Unable to load dataset ''', info.name,...\n",
        "#                        ''' due to aborted/missing download']);\n",
        "#             end\n",
        "#         else\n",
        "#             % Nothing more to do, throw error\n",
        "#             error(['Dataset ''', info.name, ''' not found. ', ...\n",
        "#                    'Consider running ''downloadDataset(''', info.name, ''')''']);\n",
        "#         end\n",
        "#     end \n",
        "# end\n"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6YWytBo3PR9N"
      },
      "source": [
        "# %%writefile /content/mrst-core/modules/getDatasetInfo.m\n",
        "# function [info, present] = getDatasetInfo(name)\n",
        "# % Get info struct for a given dataset.\n",
        "# %\n",
        "# % SYNOPSIS:\n",
        "# %   [info, present] = getDatasetInfo('datasetname')\n",
        "# %\n",
        "# % REQUIRED PARAMETERS:\n",
        "# %   name    - Dataset name. Must be known to MRST.\n",
        "# %\n",
        "# %\n",
        "# % RETURNS:\n",
        "# %   info    - Info struct as defined by datasetInfoStruct with containing\n",
        "# %             metadata about the dataset with the supplied name.\n",
        "# %\n",
        "# % SEE ALSO:\n",
        "# %   `datasetInfoStruct`, `getDatasetPath`, `listDatasetExamples`\n",
        "\n",
        "# %{\n",
        "# Copyright 2009-2019 SINTEF Digital, Mathematics & Cybernetics.\n",
        "\n",
        "# This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).\n",
        "\n",
        "# MRST is free software: you can redistribute it and/or modify\n",
        "# it under the terms of the GNU General Public License as published by\n",
        "# the Free Software Foundation, either version 3 of the License, or\n",
        "# (at your option) any later version.\n",
        "\n",
        "# MRST is distributed in the hope that it will be useful,\n",
        "# but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "# GNU General Public License for more details.\n",
        "\n",
        "# You should have received a copy of the GNU General Public License\n",
        "# along with MRST.  If not, see <http://www.gnu.org/licenses/>.\n",
        "# %}\n",
        "\n",
        "\n",
        "#     dname = ['dataset_', lower(name)];\n",
        "#     if exist(dname, 'file') == 2\n",
        "#         [info, present] = eval([dname, '()']);\n",
        "#     else\n",
        "#         error(['Dataset ''', name, ''' is not known to MRST.']);\n",
        "#     end\n",
        "# end"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jys-NOqOS9h2"
      },
      "source": [
        "!mkdir /content/mrst-core/data"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tK_ndM8KSOCP"
      },
      "source": [
        "!mv /content/reservoir_datasets/MRST/SPE10 /content/mrst-core/data"
      ],
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vb30aobYvLRF"
      },
      "source": [
        "### Execution"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SdDtdx_46x76"
      },
      "source": [
        "out = !octave -W '/content/MRST-simulations/simulations/computeLorenzSPE10.m'"
      ],
      "execution_count": 71,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CSPjl4mu5kQx",
        "outputId": "60aec4af-a1c2-43b7-e5cb-99aaf8da760f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Parsing the output\n",
        "length_Lc = 85\n",
        "length_F_Phi = 13201\n",
        "length_Ev_tD = 12859\n",
        "\n",
        "Lc = out[2:2+length_Lc]\n",
        "F = out[(2+length_Lc)+3:((2+length_Lc)+3)+length_F_Phi]\n",
        "Phi = out[(((2+length_Lc)+3)+length_F_Phi)+3:((((2+length_Lc)+3)+length_F_Phi)+3)+length_F_Phi]\n",
        "\n",
        "Ev = out[(((((2+length_Lc)+3)+length_F_Phi)+3)+length_F_Phi)+3:((((((2+length_Lc)+3)+length_F_Phi)+3)+length_F_Phi)+3)+length_Ev_tD]\n",
        "tD = out[(((((((2+length_Lc)+3)+length_F_Phi)+3)+length_F_Phi)+3)+length_Ev_tD)+3:((((((((2+length_Lc)+3)+length_F_Phi)+3)+length_F_Phi)+3)+length_Ev_tD)+3)+length_Ev_tD]\n",
        "\n",
        "Lc = np.float64(Lc)\n",
        "F = np.float64(F)\n",
        "Phi = np.float64(Phi)\n",
        "# Ev = np.float64(Ev)\n",
        "# tD = np.float64(tD)\n",
        "\n",
        "len(Ev)"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "12859"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 102
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LG39aKh1-ae7",
        "outputId": "c6633014-1380-4e8c-8ce4-812ea60eaa3a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(Phi, F)\n",
        "plt.show()"
      ],
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NCaLEQGZwtZq"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "Lc = np.float64(out[2:-1])"
      ],
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XDBwC1kvyJVE",
        "outputId": "4f16af47-4229-4d6e-cd23-777419af39ad",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "Lc"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.36969, 0.39434, 0.48656, 0.35775, 0.39666, 0.35629, 0.37631,\n",
              "       0.40714, 0.51976, 0.40509, 0.42647, 0.50229, 0.65744, 0.38819,\n",
              "       0.46035, 0.4108 , 0.30107, 0.35475, 0.32217, 0.51444, 0.48854,\n",
              "       0.28145, 0.30003, 0.3194 , 0.31818, 0.48985, 0.65746, 0.34528,\n",
              "       0.44821, 0.42484, 0.34226, 0.43168, 0.28213, 0.34788, 0.44405,\n",
              "       0.29617, 0.71977, 0.63132, 0.62016, 0.68264, 0.63049, 0.46444,\n",
              "       0.59139, 0.63447, 0.5881 , 0.59196, 0.62834, 0.78076, 0.77342,\n",
              "       0.77323, 0.48429, 0.46139, 0.48068, 0.57147, 0.49656, 0.57867,\n",
              "       0.47038, 0.58704, 0.62813, 0.64257, 0.78199, 0.77524, 0.68637,\n",
              "       0.72538, 0.58025, 0.70117, 0.69763, 0.63174, 0.46748, 0.76795,\n",
              "       0.46066, 0.5239 , 0.47362, 0.49434, 0.73015, 0.73867, 0.63465,\n",
              "       0.44521, 0.47327, 0.43732, 0.40858, 0.50038, 0.49387, 0.52234,\n",
              "       0.39854])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bvIAus9t6r80"
      },
      "source": [
        "## Optimize Faulted Model program (doesn't work)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "30_SQtBXmUPZ"
      },
      "source": [
        "# setStateFunction function is in SetFunctionGrouping\n",
        "# There is difference in line 124 StateFunctionGrouping\n",
        "# where the function in laptop vs mrst bitbucket is different\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dMAN4xZRQ1GN",
        "outputId": "55667188-98a2-4ca4-9b01-d8e8c00ed099",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!octave -W '/content/mrst-autodiff/optimization/examples/optimizeFaultedModel.m'"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/bin/bash: octave: command not found\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "icSdhOOHN6wA",
        "outputId": "2acf1bd5-524c-4613-ac93-3ec4997cc2ed",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!octave -W help.m"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "warning: function ./help.m shadows a core library function\n",
            "warning: function ./addpath.m shadows a built-in function\n",
            "error: invalid use of script /content/addpath.m in index expression\n",
            "error: called from\n",
            "    help at line 2 column 1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZiyCXljXO0cF",
        "outputId": "a36fadc8-59ff-4075-8e08-e57f807fd328",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!octave -W '/content/mrst-core/params/rock/makeRock.m'"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "warning: function ./help.m shadows a core library function\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EXXFDBpGLsro"
      },
      "source": [
        "!octave -W '/content/mrst-core/startup.m'"
      ],
      "execution_count": 17,
      "outputs": []
    }
  ]
}