py_PDE_Solver.ipynb

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\n",
                "text/plain": "<Figure size 640x480 with 1 Axes>"
              }
            ],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_14a66762f3234d1d993f81fcf4d47c7b",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "14a66762f3234d1d993f81fcf4d47c7b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
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  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Divyanshu-ISM/Oil-and-Gas-data-analysis/blob/master/py_PDE_Solver.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GZcI08w4981N",
        "colab_type": "text"
      },
      "source": [
        "#*Tutorial 1 : Grids and Fields *"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0525WkFL1WQK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 323
        },
        "outputId": "09eb54d2-1a54-4e01-faa6-ed8a848b04e7"
      },
      "source": [
        "!pip install py-pde"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting py-pde\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/e4/64/6620540bdfb2c644ea5525f401744e10846f82e7039f6a6635d0b35efc4d/py_pde-0.9.0-py3-none-any.whl (273kB)\n",
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            "\u001b[?25hRequirement already satisfied: sympy in /usr/local/lib/python3.6/dist-packages (from py-pde) (1.1.1)\n",
            "Requirement already satisfied: numba in /usr/local/lib/python3.6/dist-packages (from py-pde) (0.48.0)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.6/dist-packages (from py-pde) (3.2.2)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from py-pde) (1.18.5)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from py-pde) (1.4.1)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy->py-pde) (1.1.0)\n",
            "Requirement already satisfied: llvmlite<0.32.0,>=0.31.0dev0 in /usr/local/lib/python3.6/dist-packages (from numba->py-pde) (0.31.0)\n",
            "Requirement already satisfied: setuptools in /usr/local/lib/python3.6/dist-packages (from numba->py-pde) (49.2.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->py-pde) (1.2.0)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->py-pde) (2.4.7)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->py-pde) (0.10.0)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->py-pde) (2.8.1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from cycler>=0.10->matplotlib->py-pde) (1.15.0)\n",
            "Installing collected packages: py-pde\n",
            "Successfully installed py-pde-0.9.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "95JF_1W61nhB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from pde import DiffusionPDE, UnitGrid, ScalarField"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6sqdwRaE2We4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        },
        "outputId": "56607df5-e4be-4147-cc4c-8f67933bcbc3"
      },
      "source": [
        "!pip install h5py pandas pyfftw tqdm"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: h5py in /usr/local/lib/python3.6/dist-packages (2.10.0)\n",
            "Requirement already satisfied: pandas in /usr/local/lib/python3.6/dist-packages (1.0.5)\n",
            "Collecting pyfftw\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/dc/77/2a039e2c411b6532ae5b8e5e922d31fdb6140246f92379d9a1dce4872a20/pyFFTW-0.12.0-cp36-cp36m-manylinux1_x86_64.whl (2.6MB)\n",
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            "\u001b[?25hRequirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (4.41.1)\n",
            "Requirement already satisfied: numpy>=1.7 in /usr/local/lib/python3.6/dist-packages (from h5py) (1.18.5)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from h5py) (1.15.0)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas) (2018.9)\n",
            "Requirement already satisfied: python-dateutil>=2.6.1 in /usr/local/lib/python3.6/dist-packages (from pandas) (2.8.1)\n",
            "Installing collected packages: pyfftw\n",
            "Successfully installed pyfftw-0.12.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YhqLEM5F1GqO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from pde import *\n",
        "import numpy as np\n",
        "import scipy\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sk-anTle1Tva",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 515,
          "referenced_widgets": [
            "315e6fd9b6ef4bde9e06400aa5df4e52",
            "324b6f8230fe4cd2afe7dc53e1f8cac4",
            "735d1884d5ea4ecc94e493b25e2a6b1e",
            "c7fe4f432729425599af51fb9db5b128",
            "38f68fa3b66a4724ada152ff38e18586",
            "15e15d8091a443048f6b60d73c368a5d",
            "935bfb1c94ae486c89cd67baad0df015",
            "b0f273df7e4848758e4b32f5b779b2ad"
          ]
        },
        "outputId": "d4716599-5d34-4927-efc9-553078d2fab6"
      },
      "source": [
        "plt.style.use('default')\n",
        "eq = DiffusionPDE(diffusivity=0.1)                  # define the pde\n",
        "grid = UnitGrid([64, 64])                           # generate grid\n",
        "state = ScalarField.random_uniform(grid, 0.2, 0.3)  # generate initial condition\n",
        "\n",
        "result = eq.solve(state, t_range=10)\n",
        "result.plot()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "315e6fd9b6ef4bde9e06400aa5df4e52",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=10.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<pde.tools.plotting.PlotReference at 0x7f4738e93e88>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ePWVkH3U2hd8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "32d213b1-4109-445b-8fc9-3e04c9a43c7f"
      },
      "source": [
        "result.data.shape"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(64, 64)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Udbj1olm28mJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# plt.plot(result.data[0], result.data[1])\n",
        "# plt.show()"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UXw7R8HJ4PmO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4rHxWqTF4QN1",
        "colab_type": "text"
      },
      "source": [
        "#Showing the Dynamic Diffusion History."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3av_xy843f_w",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000,
          "referenced_widgets": [
            "bcc9fca0317a4464bcc5b1d553bbe373",
            "526c08dd92414fad9dd12535ebbdf3ea",
            "9f073f54722b4a87a31022de1e2ae1c2",
            "fecc9fbd80014704b9e4d59866c1b01a",
            "8d0e12721a7d479db04181ab58bb40e5",
            "939fa5d3e7b9449783ae17c5ea221cbb",
            "e35a248fce3b4d2baebd2275aa415ad9",
            "d55a25bb7dd149e5858657a86fea165b",
            "369747c6c421431ea22f1edc025f8e24",
            "41f80986cd1d4d17a0caf3c55f1e1216"
          ]
        },
        "outputId": "8ad799b3-a97a-454b-d378-44b43d28b6a5"
      },
      "source": [
        "eq = DiffusionPDE()                                 # define the pde\n",
        "grid = UnitGrid([16, 16])                           # generate grid\n",
        "state = ScalarField.random_uniform(grid, 0.2, 0.3)  # generate initial condition\n",
        "\n",
        "storage = MemoryStorage()\n",
        "\n",
        "trackers = [\n",
        "    'progress',                    # show progress bar during simulation\n",
        "    'steady_state',                # abort when steady state is reached\n",
        "    storage.tracker(interval=1),   # store data every simulation time unit\n",
        "    PlotTracker(show=True),        # show images during simulation\n",
        "    # print some output every 5 real seconds:\n",
        "    PrintTracker(interval=RealtimeIntervals(duration=5))\n",
        "\n",
        "]\n",
        "\n",
        "eq.solve(state, 10, dt=0.1, tracker=trackers)\n",
        "\n",
        "storage[0].plot(colorbar=True)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "bcc9fca0317a4464bcc5b1d553bbe373",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=10.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "369747c6c421431ea22f1edc025f8e24",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "Output()"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "t=0, c=0.249±0.0294\n",
            "t=0.1, c=0.249±0.0188\n",
            "t=0.2, c=0.249±0.0138\n",
            "t=0.3, c=0.249±0.011\n",
            "t=5.6, c=0.249±0.00266\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "Spent more time on handling trackers (2.059099370999996) than on the actual simulation (1.0252078720000037)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<pde.tools.plotting.PlotReference at 0x7f4735bfb708>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x5Q87ASA4-22",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1DbxenIf5A2n",
        "colab_type": "text"
      },
      "source": [
        "#Setting a Boundary Condition."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ul0Y94DY4CHT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521,
          "referenced_widgets": [
            "5bf13700383e4ca899bd1d588e2b424d",
            "507c05b669564825b6451dc644294781",
            "a48ae9e3aed247d7bcc9df86657b3f9c",
            "1582ba9e943f49c5977b67c983d1c387",
            "ebddb2759e6242ccaa9e7a34ffdad57d",
            "545f95ae27474ac1806242c95627d6e0",
            "4ab6883689a64f03b43bb6178412694b",
            "581f781216374a869f845e18f3e4a6f8"
          ]
        },
        "outputId": "c1e97ffa-1146-4d05-b896-ce5df14fcda6"
      },
      "source": [
        "grid = UnitGrid([16, 16], periodic=[False, True])   # generate grid\n",
        "state = ScalarField.random_uniform(grid, 0.2, 0.3)  # generate initial condition\n",
        "\n",
        "# set boundary conditions `bc` for all axes\n",
        "bc_x_left = {'type': 'derivative', 'value': 0.1}\n",
        "bc_x_right = {'type': 'value', 'value': 0}\n",
        "bc_x = [bc_x_left, bc_x_right]\n",
        "bc_y = 'periodic'\n",
        "eq = DiffusionPDE(bc=[bc_x, bc_y])\n",
        "\n",
        "result = eq.solve(state, t_range=10, dt=0.005)\n",
        "result.plot(colorbar=True)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "5bf13700383e4ca899bd1d588e2b424d",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=10.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<pde.tools.plotting.PlotReference at 0x7f4735e62208>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YM2e4spw5EUr",
        "colab_type": "text"
      },
      "source": [
        "# Making a movie."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mJPJgE734fYQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 457,
          "referenced_widgets": [
            "922a6a4484f54b61b401b10fc56422e5",
            "bac4ba1bf92b4cd7aa0c76a8ab48b567",
            "90ecce188190499d935dc60932c7fc63",
            "e48229355c7240b48bc1d3e4778b2527",
            "9365a90db26f4d3aa6efc853fd31db1f",
            "6537aaf82fb249fa9e52408202925990",
            "10fd0dbf217343e8bef2f9e2a37c5b53",
            "ab796b0cce294583b48db416e4bc2493",
            "647266755f464a1583591215bbd07782",
            "10598d0fcd0d4000b0a88e21d43d8026"
          ]
        },
        "outputId": "e1a8830d-2a42-4f1a-9a6c-40a330f9db74"
      },
      "source": [
        "eq = DiffusionPDE()                                 # define the physics\n",
        "grid = UnitGrid([16, 16])                           # generate grid\n",
        "state = ScalarField.random_uniform(grid, 0.2, 0.3)  # generate initial condition\n",
        "\n",
        "storage = MemoryStorage()               # create storage\n",
        "tracker = storage.tracker(interval=1)   # create associated tracker\n",
        "\n",
        "eq.solve(state, t_range=2, dt=0.005, tracker=tracker)\n",
        "\n",
        "# create movie from stored data\n",
        "movie_scalar(storage, '/tmp/diffusion.mov')"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "922a6a4484f54b61b401b10fc56422e5",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "Output()"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "90ecce188190499d935dc60932c7fc63",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=3.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rpe-sxa26LaB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Practicing..."
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nm3YihbS5JeJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "grid = UnitGrid([32,32])"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8e99Ex7f6SWt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "outputId": "c8bef48f-f6af-4565-f1da-b239d58532ed"
      },
      "source": [
        "grid.plot()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ql19++YVEuIpdjgBgh4u+y3HDhg365z//qblz5+rVV1/VFVdcoalTp2r9+vU6ffp0p8oCANBRnd62//HHH2vlypV64YUXlJSUpB//+Me67777NHTo0IvVsVO+eYfGLkeyg9CFbHez/dSFbOfzTu/QOrXL8ciRI9qyZYu2bNmi7t2769Zbb9X+/ft11VVXacmSJVqwYEFn4i8qdjmSHbQuZLub7acuZHfMBV9yPH36tP70pz/p+9//vnJycrRu3TrNnz9fhw8f1urVq7V161a99tprWrx48UUrCQCAkwt+h5aRkaGWlhbdeeed+vDDD3XNNdecdebmm29WamrqRSkIAMD5uOCB9vTTT+sHP/iBevbs2eaZ1NRU1dTUdKoYAAAX4oIH2k9+8pOu6AEAQKewKQQAYAVPB9qOHTs0bdo0ZWZmKiEhQRs2bGj1+KxZs5SQkNDqNmXKFI/aAgD8rFMf2++sxsZGjRo1SnfffbdmzJhxzjNTpkzRypUr4z9HIpEO/btYfUV2ELqQ7W62n7qQ7XzeSae/WH2xJCQkqLS0VAUFBfH7Zs2apfr6+rPeubWnublZzc3N8Z8bGhqUlZV1UbsCANx30Vdfua2srExpaWnKy8vT3LlzdezYsXbPl5SUKBqNxm8MMwAIB1+/Q1u7dq169+6t3NxcVVdX65FHHlFSUpIqKirUvXv3c+a09Q6N1VdkB6EL2e5m+6kL2c7nu3T1VVe744474v88YsQIjRw5UoMHD1ZZWZkmTJhwzj8TiUTO+Xs2Vl+RHbQuZLub7acuZHeM7y85/rdBgwapX79+qqqq8roKAMBnAjXQvvzySx07dkwZGRleVwEA+IynlxxPnDjR6t1WTU2N9u7dqz59+qhPnz564oknNHPmTKWnp6u6uloPPfSQhgwZosmTJ3vYGgDgR54OtF27dunmm2+O/1xcXCxJKiws1IoVK7Rv3z6tXr1a9fX1yszM1KRJk/SrX/2qw99FAwDYy9OBNn78eLX3Icu3337bxTYAgCAL1O/QAABoCwMNAGAFX38P7WJilyPZQehCtrvZfupCtvN5J77ZFNJVGhoaFI1Gva4BAOikwO9yBADgfITmkiO7HMkOQhey3c32Uxeync87Cc1AY5cj2UHrQra72X7qQnbHcMkRAGAFBhoAwAoMNACAFRhoAAArMNAAAFZgoAEArMBAAwBYITTfQ2OXI9lB6EK2u9l+6kK283kn7HIEAAQCuxwBAKEQmkuO7HIkOwhdyHY3209dyHY+7yQ0A41djmQHrQvZ7mb7qQvZHcMlRwCAFRhoAAArMNAAAFZgoAEArMBAAwBYgYEGALBCaD62z+orsoPQhWx3s/3UhWzn805YfQUACARWXwEAQiE0lxxZfUV2ELqQ7W62n7qQ7XzeSWgGGquvyA5aF7LdzfZTF7I7hkuOAAArMNAAAFZgoAEArMBAAwBYgYEGALACAw0AYAUGGgDACqH5Hhq7HMkOQhey3c32Uxeync87YZcjACAQ2OUIAAiF0FxyZJcj2UHoQra72X7qQrbzeSehGWjsciQ7aF3IdjfbT13I7hguOQIArMBAAwBYgYEGALACAw0AYAUGGgDACp4OtB07dmjatGnKzMxUQkKCNmzY0OpxY4wee+wxZWRkqFevXpo4caIOHDjgUVsAgJ95+rH9xsZGjRo1SnfffbdmzJhx1uNLlizRs88+q9WrVys3N1ePPvqoJk+erM8++0w9e/a8oH8Xq6/IDkIXst3N9lMXsp3POzI+IcmUlpbGf25paTHp6enmqaeeit9XX19vIpGIeeWVV9rMaWpqMrFYLH47dOiQkcSNGzdu3AJ+i8Vi7c4R3/4OraamRrW1tZo4cWL8vmg0qrFjx6qioqLNP1dSUqJoNBq/ZWVluVEXAOAx324Kqa2tlaSzVp4MGDAg/ti5LFy4UMXFxfGfGxoalJWVxeorsgPRhWx3s/3UhWzn8058O9A6KhKJKBKJnHU/q6/IDloXst3N9lMXsjvGt5ccv3k3VVdX1+r+urq6dt9pAQDCybcDLTc3V+np6dq2bVv8voaGBn3wwQfKz8/3sBkAwI88veR44sQJVVVVxX+uqanR3r171adPH2VnZ2v+/Pn69a9/raFDh8Y/tp+ZmamCggIPWwMA/MjTgbZr1y7dfPPN8Z+/+TBHYWGhVq1apYceekiNjY265557VF9frxtvvFGbN2++4O+gAQDs5+lAGz9+vL7+Ctq5JSQkaPHixVq8eLGLrQAAQeTb36EBAHAhGGgAACtY9z20trDLkewgdCHb3Ww/dSHb+byTBNPeL7Es0NDQoGg06nUNAEAnxWIxpaSktPk4lxwBAFYIzSVHdjmSHYQuZLub7acuZDufdxKagcYuR7KD1oVsd7P91IXsjuGSIwDACgw0AIAVGGgAACsw0AAAVmCgAQCswEADAFghNB/bZ/UV2UHoQra72X7qQrbzeSesvgIABAKrrwAAoRCaS46sviI7CF3IdjfbT13Idj7vJDQDjdVXZAetC9nuZvupC9kdwyVHAIAVGGgAACsw0AAAVmCgAQCswEADAFiBgQYAsAIDDQBghdB8D41djmQHoQvZ7mb7qQvZzuedsMsRABAI7HIEAIRCaC45ssuR7CB0IdvdbD91Idv5vJPQDDR2OZIdtC5ku5vtpy5kdwyXHAEAVmCgAQCswEADAFiBgQYAsAIDDQBgBQYaAMAKofnYPquvyA5CF7LdzfZTF7Kdzzth9RUAIBBYfQUACIXQXHJk9RXZQehCtrvZfupCtvN5J6EZaKy+IjtoXch2N9tPXcjuGC45AgCswEADAFiBgQYAsAIDDQBgBQYaAMAKvh5oixYtUkJCQqvbsGHDvK4FAPAh339s/+qrr9bWrVvjP19yie8rAwA84PvpcMkll7T7hejzxS5HsoPQhWx3s/3UhWzn8058vctx0aJFeuqppxSNRtWzZ0/l5+erpKRE2dnZbf6Z5uZmNTc3x39uaGhQVlaWG3UBAF0o0Lscx44dq1WrVmnz5s1asWKFampqdNNNN+n48eNt/pmSkhJFo9H4jWEGAOHg63do/6u+vl45OTlaunSpZs+efc4zbb1DY5cj2UHoQra72X7qQrbzead3aL7/Hdp/S01N1ZVXXqmqqqo2z0QiEUUikbPuZ5cj2UHrQra72X7qQnbH+PqS4/86ceKEqqurlZGR4XUVAIDP+HqgPfDAAyovL9cXX3yh999/X7fddpu6d++uO++80+tqAACf8fUlxy+//FJ33nmnjh07pv79++vGG2/Uzp071b9/f6+rAQB8xtcDbe3atV5XAAAEhK8vOQIAcL4YaAAAKzDQAABW8PXv0C4mdjmSHYQuZLub7acuZDufdxKoTSEd0dDQoGg06nUNAEAnBXqXIwAA5ys0lxzZ5Uh2ELqQ7W62n7qQ7XzeSWgGGrscyQ5aF7LdzfZTF7I7hkuOAAArMNAAAFZgoAEArMBAAwBYgYEGALACAw0AYIXQfGyf1VdkB6EL2e5m+6kL2c7nnbD6CgAQCKy+AgCEQmguObL6iuwgdCHb3Ww/dSHb+byT0Aw0Vl+RHbQuZLub7acuZHcMlxwBAFZgoAEArMBAAwBYgYEGALACAw0AYAUGGgDACgw0AIAVQvM9NHY5kh2ELmS7m+2nLmQ7n3fCLkcAQCCwyxEAEAqhueTILkeyg9CFbHez/dSFbOfzTkIz0NjlSHbQupDtbrafupDdMVxyBABYgYEGALACAw0AYAUGGgDACgw0AIAVGGgAACuE5mP7rL4iOwhdyHY3209dyHY+74TVVwCAQGD1FQAgFEJzyZHVV2QHoQvZ7mb7qQvZzuedhGagsfqK7KB1IdvdbD91IbtjuOQIALACAw0AYAUGGgDACgw0AIAVGGgAACsEYqAtX75cV1xxhXr27KmxY8fqww8/9LoSAMBnfD/QXn31VRUXF+vxxx/Xxx9/rFGjRmny5Mk6evSo19UAAD7i+++hLV26VHPmzNFdd90lSXr++ef1xhtv6A9/+IMefvjh885hlyPZQehCtrvZfupCtvN5J77e5Xjq1Cn17t1b69evV0FBQfz+wsJC1dfXa+PGjWf9mebmZjU3N8d/jsViys7OdqUvAKDr1NfXt7ub19eXHP/973/rzJkzZ609GTBggGpra8/5Z0pKShSNRuM3hhkA2OH48ePtPu77S44XauHChSouLo7/XF9fr5ycHB08eNDqrfsNDQ3KysrSoUOH2t1GHWRheI4Sz9M2YXieXf0cjTE6fvy4MjMz2z3n64HWr18/de/eXXV1da3ur6ura3PRcCQSUSQSOev+aDRq7X+Z/ltKSor1zzMMz1HiedomDM+zK5/j+bwh8fUlx8TERI0ePVrbtm2L39fS0qJt27YpPz/fw2YAAL/x9Ts0SSouLlZhYaGuvfZajRkzRsuWLVNjY2P8U48AAEhS90WLFi3yukR7hg8frtTUVP3mN7/Rb3/7W0nSyy+/rLy8vPPO6N69u8aPH69LLvH9/O6UMDzPMDxHiedpmzA8Tz88R19/bB8AgPPl69+hAQBwvhhoAAArMNAAAFZgoAEArGD1QLP9r51ZtGiREhISWt2GDRvmda1O27Fjh6ZNm6bMzEwlJCRow4YNrR43xuixxx5TRkaGevXqpYkTJ+rAgQMete04p+c5a9ass17fKVOmeNS2Y0pKSnTdddcpOTlZaWlpKigoUGVlZaszTU1NKioqUt++fZWUlKSZM2eetUzB787neY4fP/6s1/Pee+/1qHHHrFixQiNHjox/gTo/P19vvfVW/HGvX0trB1pY/tqZq6++WkeOHInf3n33Xa8rdVpjY6NGjRql5cuXn/PxJUuW6Nlnn9Xzzz+vDz74QJdeeqkmT56spqYml5t2jtPzlKQpU6a0en1feeUVFxt2Xnl5uYqKirRz505t2bJFp0+f1qRJk1ptUF+wYIFef/11rVu3TuXl5Tp8+LBmzJjhYesLdz7PU5LmzJnT6vVcsmSJR407ZuDAgXryySe1e/du7dq1S7fccoumT5+uTz/9VJIPXktjqTFjxpiioqL4z2fOnDGZmZmmpKTEw1YX1+OPP25GjRrldY0uJcmUlpbGf25paTHp6enmqaeeit9XX19vIpGIeeWVV7yoeFH87/M0xpjCwkIzffp0jxp1jaNHjxpJpry83Bjz9WvXo0cPs27duviZzz//3EgyFRUVXtXstP99nsYY853vfMf87Gc/87BV17jsssvMCy+84IvX0sp3aKdOndLu3bs1ceLE+H3dunXTxIkTVVFR4WGzi+/AgQPKzMzUoEGD9KMf/UgHDx70ulKXqqmpUW1tbavXNhqNauzYsda9tpJUVlamtLQ05eXlae7cuTp27JjXlTolFotJkvr06SNJ2r17t06fPt3q9Rw2bJiys7MD/Xr+7/P8xssvv6x+/fpp+PDhWrhwoU6ePOlFvYvizJkzWrt2rRobG5Wfn++L19LKr62399fO/P3vf/eo1cU3duxYrVq1Snl5eTpy5IieeOIJ3XTTTfrkk0+UnJzsdb0u8c1fG3Qhf6VQUE2ZMkUzZsxQbm6uqqur9cgjj2jq1KmqqKhQ9+7dva53wVpaWjR//nzdcMMNGj58uKSvX8/ExESlpqa2Ohvk1/Ncz1OSfvjDHyonJ0eZmZnat2+ffvGLX6iyslJ//vOfPWx74fbv36/8/Hw1NTUpKSlJpaWluuqqq7R3717PX0srB1pYTJ06Nf7PI0eO1NixY5WTk6PXXntNs2fP9rAZLoY77rgj/s8jRozQyJEjNXjwYJWVlWnChAkeNuuYoqIiffLJJ1b8nrc9bT3Pe+65J/7PI0aMUEZGhiZMmKDq6moNHjzY7ZodlpeXp7179yoWi2n9+vUqLCxUeXm517UkWfqhkI78tTM2SE1N1ZVXXqmqqiqvq3SZb16/sL22kjRo0CD169cvkK/vvHnztGnTJr3zzjsaOHBg/P709HSdOnVK9fX1rc4H9fVs63mey9ixYyUpcK9nYmKihgwZotGjR6ukpESjRo3SM88844vX0sqBFta/dubEiROqrq5WRkaG11W6TG5urtLT01u9tg0NDfrggw+sfm0l6csvv2pgkp0AAAPCSURBVNSxY8cC9foaYzRv3jyVlpZq+/btys3NbfX46NGj1aNHj1avZ2VlpQ4ePBio19PpeZ7L3r17JSlQr+e5tLS0qLm52R+vpSsfPfHA2rVrTSQSMatWrTKfffaZueeee0xqaqqpra31utpF8/Of/9yUlZWZmpoa895775mJEyeafv36maNHj3pdrVOOHz9u9uzZY/bs2WMkmaVLl5o9e/aYf/zjH8YYY5588kmTmppqNm7caPbt22emT59ucnNzzVdffeVx8wvT3vM8fvy4eeCBB0xFRYWpqakxW7duNd/+9rfN0KFDTVNTk9fVz9vcuXNNNBo1ZWVl5siRI/HbyZMn42fuvfdek52dbbZv32527dpl8vPzTX5+voetL5zT86yqqjKLFy82u3btMjU1NWbjxo1m0KBBZty4cR43vzAPP/ywKS8vNzU1NWbfvn3m4YcfNgkJCeYvf/mLMcb719LagWaMMb/73e9Mdna2SUxMNGPGjDE7d+70utJFdfvtt5uMjAyTmJhoLr/8cnP77bebqqoqr2t12jvvvGMknXUrLCw0xnz90f1HH33UDBgwwEQiETNhwgRTWVnpbekOaO95njx50kyaNMn079/f9OjRw+Tk5Jg5c+YE7v+Qnev5STIrV66Mn/nqq6/MfffdZy677DLTu3dvc9ttt5kjR454V7oDnJ7nwYMHzbhx40yfPn1MJBIxQ4YMMQ8++KCJxWLeFr9Ad999t8nJyTGJiYmmf//+ZsKECfFhZoz3ryV/fQwAwApW/g4NABA+DDQAgBUYaAAAKzDQAABWYKABAKzAQAMAWIGBBgCwAgMNAGAFBhoAwAoMNACAFRhoAAArMNCAAPrXv/6l9PR0/d///V/8vvfff1+JiYmt/voOIExYTgwE1JtvvqmCggK9//77ysvL0zXXXKPp06dr6dKlXlcDPMFAAwKsqKhIW7du1bXXXqv9+/fro48+UiQS8boW4AkGGhBgX331lYYPH65Dhw5p9+7dGjFihNeVAM/wOzQgwKqrq3X48GG1tLToiy++8LoO4CneoQEBderUKY0ZM0bXXHON8vLytGzZMu3fv19paWleVwM8wUADAurBBx/U+vXr9be//U1JSUn6zne+o2g0qk2bNnldDfAElxyBACorK9OyZcv00ksvKSUlRd26ddNLL72kv/71r1qxYoXX9QBP8A4NAGAF3qEBAKzAQAMAWIGBBgCwAgMNAGAFBhoAwAoMNACAFRhoAAArMNAAAFZgoAEArMBAAwBYgYEGALDC/wN37qaXtIRHHQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r92IReg66bp7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "outputId": "33539cb0-5ed9-4245-d869-057065216f6f"
      },
      "source": [
        "grid = CartesianGrid([[0, 2], [0, 1]], [16, 32])\n",
        "grid.plot(title=f'Area={grid.volume}')"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PTNu2bc19991X5Sa367OwsLCwsNh3sfp2fZ/OfD1w4ECdPHlSkyZNUl5enuLi4rRhwwb3BdlHjhzx+ITor3/9qwICAvTXv/5Vx44dU/PmzdW/f3/97W9/89UhAACAOsSn8xj5AvMY0aZNmzZt2vZt19l5jHyNeYxo06ZNmzZt+7WtZqvb9QEAAKzEwAgAAMCFgREAAICL315jxDxGtGnTpk2btv3aVvPbu9IAAID9WH1XGqfSAAAAXPz2VBrzGNGmTZs2bdr2a1vNbwdGzGNEmzZt2rRp269tNU6lAQAAuDAwAgAAcPHbU2ncrk+bNm3atGnbr201btcHAAC2we36AAAAXuK3p9K4XZ82bdq0adO2X9tqfjsw4nZ92rRp06ZN235tq3EqDQAAwIWBEQAAgAsDIwAAABe/vcaIeYxo06ZNmzZt+7WtxjxGAADANpjHCAAAwEv89lQa8xjRpk2bNm3a9mtbzW8HRsxjRJs2bdq0aduvbTVOpQEAALgwMAIAAHBhYAQAAODit9cYMY8Rbdq0adOmbb+21ZjHCAAA2AbzGAEAAHiJ355KYx4j2rRp06ZN235tq/ntwIh5jGjTpk2bNm37ta3GqTQAAAAXBkYAAAAuDIwAAABc/PYaI+Yxok2bNm3atO3XthrzGAEAANtgHiMAAAAv8dtTacxjRJs2bdq0aduvbTWfD4zmz5+vmTNnKi8vT127dtWLL76o+Pj4Src/c+aMnn76aa1evVqnT59Wy5YtNXfuXN15553V6jKPEW3atGnTpm2/ttV8OjBauXKlUlNTlZaWpoSEBM2dO1fJyck6cOCAIiIiym1fWlqqPn36KCIiQm+//bZiYmL07bffKjw83Ad7DwAA6hqfDoxmz56tESNGaNiwYZKktLQ0rVu3TosXL9b48ePLbb948WKdPn1aW7duVf369SVJrVq18uYuAwCAOsxnA6PS0lLt3LlTEyZMcK8LDAxUUlKSsrOzK3zOe++9p8TERI0aNUrvvvuumjdvrgceeEDjxo1TUFBQhc8pKSlRSUmJ++fCwkJJ3K5PmzZt2rRp27FtOeMjx44dM5LM1q1bPdY/+eSTJj4+vsLndOjQwTgcDvPwww+bHTt2mIyMDNO0aVPzzDPPVNqZPHmykcTCwsLCwsJSB5aCgoIaHY/8kq1u13c6nYqIiNCrr76qbt26aeDAgXr66aeVlpZW6XMmTJiggoIC93L06FEv7jEAALATn51Ka9asmYKCgpSfn++xPj8/v9Lb6KOiolS/fn2P02bXX3+98vLyVFpaquDg4HLPcTgccjgc5dZzuz5t2rRp06Ztv7bVfDYwCg4OVrdu3ZSZmamUlBRJP38ilJmZqdGjR1f4nJtvvllvvvmmnE6nAgN//rDrn//8p6KioiocFF0Mt+vTpk2bNm3a9mtbzaen0lJTU7Vw4UItW7ZMX331lR599FEVFxe771IbMmSIx8XZjz76qE6fPq3HH39c//znP7Vu3TpNmzZNo0aN8tUhAACAOsSnt+sPHDhQJ0+e1KRJk5SXl6e4uDht2LDB/XHZkSNH3J8MSVJsbKw2btyosWPHqkuXLoqJidHjjz+ucePG+eoQAABAHeLzma9Hjx5d6amzrKyscusSExP12WefWbxXAADAH/l8YOQrzGNEmzZt2rRp269ttQBjjPFarRYoLCxUWFiYr3cDAABchoKCAoWGhlr2+raaxwgAAMBKfnsqjXmMaNOmTZs2bfu1rea3AyPmMaJNmzZt2rTt17Yap9IAAABcGBgBAAC4MDACAABw8dtrjJjHiDZt2rRp07Zf22rMYwQAAGyDeYwAAAC8xG9PpTGPEW3atGnTpm2/ttX8dmDEPEa0adOmTZu2/dpW41QaAACACwMjAAAAl2oPjIYOHaotW7ZYsS8AAAA+Ve1rjAoKCpSUlKSWLVtq2LBhGjp0qGJiYqzYN0sxjxFt2rRp06Ztv7bVLmseo5MnT2r58uVatmyZvvzySyUlJWn48OEaMGCA6tevb8V+1hjmMQIAwL5q5TxGzZs3V2pqqr744gtt27ZN7dq10+DBgxUdHa2xY8fq66+/run9BAAAsNwV3a5//Phxbdq0SZs2bVJQUJDuvPNO7dmzRzfccIOef/55jR07tqb2s8YxjxFt2rRp06Ztv7bVqj0w+vHHH/Xee+9pyZIl+uCDD9SlSxeNGTNGDzzwgPujrTVr1ujhhx+u1QMj5jGiTZs2bdq07de2WrUHRlFRUXI6nRo0aJC2b9+uuLi4ctv07t1b4eHhNbKDAAAA3lLtgdGcOXN07733KiQkpNJtwsPDlZube0U7BgAA4G3VHhgNHjzYiv3wOm7Xp02bNm3atO3Xttpl3a5vZ9yuDwCAfdXK2/UBAADqoiu6Xd/OuF2fNm3atGnTtl/ban47MOJ2fdq0adOmTdt+batxKg0AAMCFgREAAIALAyMAAAAXv73GiHmMaNOmTZs2bfu1rcY8RgAAwDaYxwgAAMBL/PZUGvMY0aZNmzZt2vZrW81vB0bMY0SbNm3atGnbr201TqUBAAC4MDACAABwYWAEAADgUiuuMZo/f75mzpypvLw8de3aVS+++KLi4+Mv+byMjAwNGjRIAwYM0Nq1a6vVZB4j2rRp06ZN235tyxkfy8jIMMHBwWbx4sVm3759ZsSIESY8PNzk5+df9Hm5ubkmJibG3HrrrWbAgAFV7hUUFBhJLCwsLCwsLDZcCgoKrnTocVE+P5U2e/ZsjRgxQsOGDdMNN9ygtLQ0NWzYUIsXL670OWVlZXrwwQc1ZcoUtWnTxot7CwAA6jKfnkorLS3Vzp07NWHCBPe6wMBAJSUlKTs7u9LnPfvss4qIiNDw4cP197///aKNkpISlZSUuH8uLCyUxDxGtGnTpk2bth3bVvPpwOjUqVMqKysrd7CRkZHav39/hc/55JNPtGjRIuXk5FSpMX36dE2ZMqXceuYxok2bNm3atO3XtprPT6VVR1FRkQYPHqyFCxeqWbNmVXrOhAkTVFBQ4F6OHj1q8V4CAAC78uknRs2aNVNQUJDy8/M91ufn51d4muvQoUM6fPiw+vfv717ndDolSfXq1dOBAwfUtm1bj+c4HA45HA4L9h4AANQ1Pv3EKDg4WN26dVNmZqZ7ndPpVGZmphITE8ttf91112nPnj3KyclxL3fddZd69+6tnJwcxcbGenP3AQBAHePzeYxSU1M1dOhQde/eXfHx8Zo7d66Ki4s1bNgwSdKQIUMUExOj6dOnKyQkRJ06dfJ4fnh4uCSVW38pzGNEmzZt2rRp269tNZ8PjAYOHKiTJ09q0qRJysvLU1xcnDZs2OC+IPvIkSMKDKz5D7batWtX469ZVd66sp42bdq0adOua22rBRhjjK93wpsKCwsVFhbm690AAACXoaCgQKGhoZa9vs8/MfIV5jGiTZs2bdq07de2mt8OjJjHiDZt2rRp07Zf22q2mscIAADASgyMAAAAXPz2VBq369OmTZs2bdr2a1uNu9IAAIBtWH1XGqfSAAAAXPz2VBq369OmTZs2bdr2a1vNbwdG3K5PmzZt2rRp269tNU6lAQAAuDAwAgAAcGFgBAAA4OK31xgxjxFt2rRp06Ztv7bVmMcIAADYBvMYAQAAeInfnkpjHiPatGnTpk3bfm2r+e3AiHmMaNOmTZs2bfu1rcapNAAAABcGRgAAAC4MjAAAAFz89hoj5jGiTZs2bdq07de2GvMYAQAA22AeIwAAAC/x21NpzGNEmzZt2rRp269tNb8dGDGPEW3atGnTpm2/ttU4lQYAAODCwAgAAMCFgREAAICL315jxDxGtGnTpk2btv3aVmMeIwAAYBvMYwQAAOAlfnsqjXmMaNOmTZs2bfu1rea3AyPmMaJNmzZt2rTt17Yap9IAAABcGBgBAAC4+O2pNG7Xp02bNm3atO3Xthq36wMAANvgdn0AAAAvqRWn0ubPn6+ZM2cqLy9PXbt21Ysvvqj4+PgKt124cKFef/117d27V5LUrVs3TZs2rdLtK8Pt+rRp06ZNm7b92lbz+cBo5cqVSk1NVVpamhISEjR37lwlJyfrwIEDioiIKLd9VlaWBg0apB49eigkJETPPfec+vbtq3379ikmJqbKXW7Xp02bNm3atO3XtprPT6XNnj1bI0aM0LBhw3TDDTcoLS1NDRs21OLFiyvcPj09Xf/zP/+juLg4XXfddXrttdfkdDqVmZnp5T0HAAB1jU8HRqWlpdq5c6eSkpLc6wIDA5WUlKTs7OwqvcbZs2f1448/qmnTphU+XlJSosLCQo8FAACgIj4dGJ06dUplZWXlzhtGRkYqLy+vSq8xbtw4RUdHewyu/tP06dMVFhbmXmJjY694vwEAQN3k82uMrsSMGTOUkZGhrKwshYSEVLjNhAkTlJqa6v65sLBQsbGxzGNEmzZt2rRp27BtOeNDJSUlJigoyKxZs8Zj/ZAhQ8xdd9110efOnDnThIWFmc8//7xazYKCAiOJhYWFhYWFxYZLQUFBtccb1eHTU2nBwcHq1q2bx4XTFy6kTkxMrPR5zz//vKZOnaoNGzaoe/fu3thVAADgB3x+Ki01NVVDhw5V9+7dFR8fr7lz56q4uFjDhg2TJA0ZMkQxMTGaPn26JOm5557TpEmT9Oabb6pVq1bua5EaN26sxo0bV7nLPEa0adOmTZu2/dpW8/nAaODAgTp58qQmTZqkvLw8xcXFacOGDe5/AUeOHFFg4P//YOvll19WaWmp7rnnHo/XmTx5sp555pkqd5nHiDZt2rRp07Zf22o+HxhJ0ujRozV69OgKH8vKyvL4+fDhw9bvEAAA8Es+n+ARAACgtmBgBAAA4FIrTqX5AvMY0aZNmzZt2vZrWy3AGGO8VqsFCgsLFRYW5uvdAAAAl6GgoEChoaGWvT6n0gAAAFz89lQa8xjRpk2bNm3a9mtbzW8HRsxjRJs2bdq0aduvbTVOpQEAALgwMAIAAHBhYAQAAODit9cYMY8Rbdq0adOmbb+21ZjHCAAA2AbzGAEAAHiJ355KYx4j2rRp06ZN235tq/ntwIh5jGjTpk2bNm37ta3GqTQAAAAXBkYAAAAufnsqjdv1adOmTZs2bfu1rcbt+gAAwDa4XR8AAMBL/PZUGrfr06ZNmzZt2vZrW81vB0bcrk+bNm3atGnbr201TqUBAAC4MDACAABwYWAEAADg4rfXGDGPEW3atGnTpm2/ttWYxwgAANgG8xgBAAB4id+eSmMeI9q0adOmTdt+bav57cCIeYxo06ZNmzZt+7Wtxqk0AAAAFwZGAAAALgyMAAAAXPz2GiPmMaJNmzZt2rTt17Ya8xgBAADbYB4jAAAAL/HbU2nMY0SbNm3atGnbr201vx0YMY8Rbdq0adOmbb+21TiVBgAA4FIrBkbz589Xq1atFBISooSEBG3fvv2i27/11lu67rrrFBISos6dO2v9+vVe2lMAAFCX+XxgtHLlSqWmpmry5MnatWuXunbtquTkZJ04caLC7bdu3apBgwZp+PDh2r17t1JSUpSSkqK9e/d6ec8BAEBd4/NrjGbPnq0RI0Zo2LBhkqS0tDStW7dOixcv1vjx48ttP2/ePN1+++168sknJUlTp07Vpk2b9NJLLyktLa3KXeYxok2bNm3atO3XtpzxoZKSEhMUFGTWrFnjsX7IkCHmrrvuqvA5sbGxZs6cOR7rJk2aZLp06VLh9ufPnzcFBQXu5ciRI0YSCwsLCwsLiw2XM2fO1MwgpBI+PZV26tQplZWVlbsFLzIyUnl5eRU+Jy8vr1rbT58+XWFhYe7l2muvrZmdBwAAXvf9999b+vo+P5VmtQkTJig1NdX985kzZ9SyZUsdOXLEr2bALiwsVGxsrI4ePWrpjKG1DcfNcfsDjpvj9gcFBQW69tpr1bRpU0s7Ph0YNWvWTEFBQcrPz/dYn5+fX+nkiy1atKjW9g6HQw6Ho9z6sLAwv/oDdUFoaCjH7Uc4bv/CcfsXfz3uwEBrT3b59FRacHCwunXrpszMTPc6p9OpzMxMJSYmVvicxMREj+0ladOmTZVuDwAAUFU+P5WWmpqqoUOHqnv37oqPj9fcuXNVXFzsvkttyJAhiomJ0fTp0yVJj0hjupIAAAzmSURBVD/+uHr27KkXXnhB/fr1U0ZGhnbs2KFXX33Vl4cBAADqgKBnnnnmGV/uQKdOnRQeHq6//e1vmjVrliQpPT1dHTp0kPTz7fn16tVTSkqKJCk2NlbXX3+9Zs6cqRkzZig/P1+LFi3SzTffXOVmUFCQevXqpXr1fD4u9CqOm+P2Bxw3x+0POG7rjjvAGGMse3UAAAAb8fnM1wAAALUFAyMAAAAXBkYAAAAuDIwAAABc6sTAaP78+WrVqpVCQkKUkJCg7du3X3T7t956S9ddd51CQkLUuXNnrV+/3uNxY4wmTZqkqKgoNWjQQElJSfr666+tPITLUp3jXrhwoW699VZdddVVuuqqq5SUlFRu+4ceekgBAQEey+233271YVRbdY576dKl5Y4pJCTEY5u6+H736tWr3HEHBASoX79+7m1q+/u9ZcsW9e/fX9HR0QoICNDatWsv+ZysrCzdeOONcjgcateunZYuXVpum+r+98Lbqnvcq1evVp8+fdS8eXOFhoYqMTFRGzdu9NjmmWeeKfdeX3fddVYeRrVV97izsrIq/DP+y6+Hqmvvd0W/twEBAerYsaN7Gzu839OnT9dNN92kJk2aKCIiQikpKTpw4MAln+eNv79tPzBauXKlUlNTNXnyZO3atUtdu3ZVcnKyTpw4UeH2W7du1aBBgzR8+HDt3r1bKSkpSklJ0d69e93bPP/88/rf//1fpaWladu2bWrUqJGSk5N1/vx5bx3WJVX3uLOysjRo0CBt3rxZ2dnZio2NVd++fXXs2DGP7W6//XYdP37cvaxYscIbh1Nl1T1u6efZYf/zmL799luPx+vi+7169WqPY967d6+CgoJ07733emxXm9/v4uJide3aVfPnz6/S9rm5uerXr5969+6tnJwcjRkzRo888ojHIOFy/vx4W3WPe8uWLerTp4/Wr1+vnTt3qnfv3urfv792797tsV3Hjh093utPPvnEit2/bNU97gsOHDjgcVwRERHux+ri+z1v3jyP4z169KiaNm1a7ne7tr/fH3/8sUaNGqXPPvtMmzZt0o8//qi+ffuquLi40ud47e9vS7+i1gvi4+PNqFGj3D+XlZWZ6OhoM3369Aq3v++++0y/fv081iUkJJg//vGPxhhjnE6nadGihZk5c6b78TNnzhiHw2FWrFhhwRFcnuoe9y/99NNPpkmTJmbZsmXudUOHDjUDBgyo8X2tSdU97iVLlpiwsLBKX89f3u85c+aYJk2amB9++MG9zg7v9wWSzJo1ay66zVNPPWU6duzosW7gwIEmOTnZ/fOV/nv0tqocd0VuuOEGM2XKFPfPkydPNl27dq3JXbNUVY578+bNRpL597//Xek2/vB+r1mzxgQEBJjDhw+719nt/TbGmBMnThhJ5uOPP650G2/9/W3rT4xKS0u1c+dOJSUludcFBgYqKSlJ2dnZFT4nOzvbY3tJSk5Odm+fm5urvLw8j23CwsKUkJBQ6Wt62+Uc9y+dPXtWP/74Y7kv48vKylJERIQ6dOigRx991PJvMa6Oyz3uH374QS1btlRsbKwGDBigffv2uR/zl/d70aJFuv/++9WoUSOP9bX5/a6uS/1u18S/RztwOp0qKioq97v99ddfKzo6Wm3atNGDDz6oI0eO+GgPa1ZcXJyioqLUp08fffrpp+71/vJ+L1q0SElJSWrZsqXHeru93wUFBZJ00S+I9dbf37YeGJ06dUplZWWKjIz0WB8ZGVnuPPMFeXl5F93+wv9W5zW97XKO+5fGjRun6Ohojz9At99+u15//XVlZmbqueee08cff6w77rhDZWVlNbr/l+tyjrtDhw5avHix3n33Xb3xxhtyOp3q0aOHvvvuO0n+8X5v375de/fu1SOPPOKxvra/39VV2e92YWGhzp07VyO/N3Ywa9Ys/fDDD7rvvvvc6xISErR06VJt2LBBL7/8snJzc3XrrbeqqKjIh3t6ZaKiopSWlqZ33nlH77zzjmJjY9WrVy/t2rVLUs38d7K2+9e//qX/+7//K/e7bbf32+l0asyYMbr55pvVqVOnSrfz1t/f/jWXOCRJM2bMUEZGhrKysjwuRL7//vvd/9y5c2d16dJFbdu2VVZWlm677TZf7OoVS0xM9PiC4R49euj666/XK6+8oqlTp/pwz7xn0aJF6ty5s+Lj4z3W18X329+9+eabmjJlit59912Pa23uuOMO9z936dJFCQkJatmypVatWqXhw4f7YlevWIcOHdxfHSX9/Lt96NAhzZkzR8uXL/fhnnnPsmXLFB4e7v7KrAvs9n6PGjVKe/furTXXQdn6E6NmzZopKChI+fn5Huvz8/PVokWLCp/TokWLi25/4X+r85redjnHfcGsWbM0Y8YMffDBB+rSpctFt23Tpo2aNWumgwcPXvE+14QrOe4L6tevr1//+tfuY6rr73dxcbEyMjKq9B/D2vZ+V1dlv9uhoaFq0KBBjfz5qc0yMjL0yCOPaNWqVeVON/xSeHi42rdvb9v3ujLx8fHuY6rr77cxRosXL9bgwYMVHBx80W1r8/s9evRovf/++9q8ebOuueaai27rrb+/bT0wCg4OVrdu3ZSZmele53Q6lZmZ6fEpwX9KTEz02F6SNm3a5N6+devWatGihcc2hYWF2rZtW6Wv6W2Xc9zSz1frT506VRs2bFD37t0v2fnuu+/0/fffKyoqqkb2+0pd7nH/p7KyMu3Zs8d9THX5/ZZ+vrW1pKREf/jDHy7ZqW3vd3Vd6ne7Jv781FYrVqzQsGHDtGLFCo8pGSrzww8/6NChQ7Z9ryuTk5PjPqa6/H5LP9/VdfDgwSr9n57a+H4bYzR69GitWbNGH330kVq3bn3J53jt7+9qXTZeC2VkZBiHw2GWLl1qvvzySzNy5EgTHh5u8vLyjDHGDB482IwfP969/aeffmrq1atnZs2aZb766iszefJkU79+fbNnzx73NjNmzDDh4eHm3XffNf/4xz/MgAEDTOvWrc25c+e8fnyVqe5xz5gxwwQHB5u3337bHD9+3L0UFRUZY4wpKioyTzzxhMnOzja5ubnmww8/NDfeeKP51a9+Zc6fP++TY6xIdY97ypQpZuPGjebQoUNm586d5v777zchISFm37597m3q4vt9wS233GIGDhxYbr0d3u+ioiKze/dus3v3biPJzJ492+zevdt8++23xhhjxo8fbwYPHuze/ptvvjENGzY0Tz75pPnqq6/M/PnzTVBQkNmwYYN7m0v9e6wNqnvc6enppl69emb+/Pkev9tnzpxxb/PnP//ZZGVlmdzcXPPpp5+apKQk06xZM3PixAmvH19lqnvcc+bMMWvXrjVff/212bNnj3n88cdNYGCg+fDDD93b1MX3+4I//OEPJiEhocLXtMP7/eijj5qwsDCTlZXl8ef27Nmz7m189fe37QdGxhjz4osvmmuvvdYEBweb+Ph489lnn7kf69mzpxk6dKjH9qtWrTLt27c3wcHBpmPHjmbdunUejzudTjNx4kQTGRlpHA6Hue2228yBAwe8cSjVUp3jbtmypZFUbpk8ebIxxpizZ8+avn37mubNm5v69eubli1bmhEjRtSq/4BcUJ3jHjNmjHvbyMhIc+edd5pdu3Z5vF5dfL+NMWb//v1Gkvnggw/KvZYd3u8Lt2P/crlwnEOHDjU9e/Ys95y4uDgTHBxs2rRpY5YsWVLudS/277E2qO5x9+zZ86LbG/PztAVRUVEmODjYxMTEmIEDB5qDBw9698AuobrH/dxzz5m2bduakJAQ07RpU9OrVy/z0UcflXvduvZ+G/PzLegNGjQwr776aoWvaYf3u6JjluTxO+urv78DXDsIAADg92x9jREAAEBNYmAEAADgwsAIAADAhYERAACACwMjAAAAFwZGAAAALgyMAAAAXBgYAQAAuDAwAgAAcGFgBAAA4MLACAAAwIWBEQDbO3nypFq0aKFp06a5123dulXBwcHKzMz04Z4BsBu+RBZAnbB+/XqlpKRo69at6tChg+Li4jRgwADNnj3b17sGwEYYGAGoM0aNGqUPP/xQ3bt31549e/T555/L4XD4ercA2AgDIwB1xrlz59SpUycdPXpUO3fuVOfOnX29SwBshmuMANQZhw4d0r/+9S85nU4dPnzY17sDwIb4xAhAnVBaWqr4+HjFxcWpQ4cOmjt3rvbs2aOIiAhf7xoAG2FgBKBOePLJJ/X222/riy++UOPGjdWzZ0+FhYXp/fff9/WuAbARTqUBsL2srCzNnTtXy5cvV2hoqAIDA7V8+XL9/e9/18svv+zr3QNgI3xiBAAA4MInRgAAAC4MjAAAAFwYGAEAALgwMAIAAHBhYAQAAODCwAgAAMCFgREAAIALAyMAAAAXBkYAAAAuDIwAAABcGBgBAAC4/D/L7B0ckUnBRwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SHbMFiYu6nxc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "outputId": "b8bf9b2b-4849-406b-fed2-49bb1b5d9b9b"
      },
      "source": [
        "\n",
        "grid = PolarGrid(5, 16)\n",
        "grid.plot(title=f'Area={grid.volume:.3g}')"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fge3RNSE6yQN",
        "colab_type": "text"
      },
      "source": [
        "#ScalarFields\n",
        "\n",
        "Scalar fields represent scalar quantities that depend on position. In this package, scalar fields are represented by their values at the support points of the discretized grids discussed above. Consequently, one first has to construct a grid and pass it to the ScalarField class to construct a scalar field."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qkISUqiv6uV0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 455
        },
        "outputId": "798a66c8-3ab7-4375-8f5a-30726540b45f"
      },
      "source": [
        "grid = UnitGrid([20,20])\n",
        "grid.plot()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-CSYKsn87VTa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "P = np.ones([20,20])\n",
        "P = P*2000"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ROQteWP_7elo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# P is now the initial Pressure value containing scalar field. "
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3ZkrylX57fg-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "field = ScalarField(grid=grid , data = P)"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3NJacqnj7-MG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3ZsKo6dq7z_w",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df = pd.DataFrame(field.data)"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ytQUc-ZZ72Hu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 669
        },
        "outputId": "58ff9a7b-853f-43ab-eaac-710368038ff1"
      },
      "source": [
        "df #just to display the various pressure values in each grid block."
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>10</th>\n",
              "      <th>11</th>\n",
              "      <th>12</th>\n",
              "      <th>13</th>\n",
              "      <th>14</th>\n",
              "      <th>15</th>\n",
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              "      <th>17</th>\n",
              "      <th>18</th>\n",
              "      <th>19</th>\n",
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              "      <th>0</th>\n",
              "      <td>2000.0</td>\n",
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              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
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              "      <th>1</th>\n",
              "      <td>2000.0</td>\n",
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              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
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              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "      <td>2000.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        0       1       2       3   ...      16      17      18      19\n",
              "0   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "1   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "2   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "3   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "4   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "5   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "6   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "7   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "8   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "9   2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "10  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "11  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "12  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "13  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "14  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "15  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "16  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "17  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "18  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "19  2000.0  2000.0  2000.0  2000.0  ...  2000.0  2000.0  2000.0  2000.0\n",
              "\n",
              "[20 rows x 20 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-WKVGO6u8Bm1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "outputId": "e93bfd49-7b53-4ee9-a853-083ceb4cfde0"
      },
      "source": [
        "import seaborn as sns\n",
        "sns.heatmap(df)\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nYO7ZSBf8SH8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "outputId": "a0c56f3b-8f24-4b5a-ba16-e9a3b60a1141"
      },
      "source": [
        "#or simply\n",
        "field.plot(colorbar=True)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<pde.tools.plotting.PlotReference at 0x7f4731a00748>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sawfqMx_8qoR",
        "colab_type": "text"
      },
      "source": [
        "#Values at individual points can be determined by interpolation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "33YbgWue9GpE",
        "colab_type": "text"
      },
      "source": [
        "#Initializing with a random normal distribution."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "drtbrPVG8ffu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "outputId": "cd14d634-ddfb-42c6-99be-b2e7eb6e77c9"
      },
      "source": [
        "\n",
        "field = ScalarField.random_normal(grid)\n",
        "field.plot(title=f'Average={field.average:.3f}', colorbar=True);\n",
        "\n"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_8jT1GLh8wvD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VJe7wws2-H99",
        "colab_type": "text"
      },
      "source": [
        "# **Tutorial 2 : Solving Pre-Defined PDEs **"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6JXOgwOY-W0B",
        "colab_type": "text"
      },
      "source": [
        "In the simplest case, a PDE evolves a field in time. To reflect this in code, we first define an initial state and then use a simple PDE to evolve it in time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NK4PO4Aq-NDL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "DiffusionPDE?"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yDmc9AxP-pV-",
        "colab_type": "text"
      },
      "source": [
        "$ \\frac {\\partial P} {\\partial t} =  \\eta \\nabla^2 P $"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SH77Oqx6CJrz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "08e92495-08b3-4f7e-b815-22b7a073f931"
      },
      "source": [
        "P[:,0] = 150\n",
        "\n",
        "P"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.],\n",
              "       [ 150., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000., 2000.,\n",
              "        2000., 2000.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tifMEjh6-kw5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "eq = DiffusionPDE(diffusivity=0.1)"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PvrU3lWt_aaW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "grid = UnitGrid([20,20])"
      ],
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i8IjEetS_iPd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "state_i = ScalarField(grid=grid , data = P)"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EWZ1_xzy_xGz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "outputId": "84a590ce-8aeb-46f4-e13c-27c66939f482"
      },
      "source": [
        "state_i.plot(title='Initial Pressure condition', colorbar=True )"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<pde.tools.plotting.PlotReference at 0x7f4738f6c308>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EQKBqrbh_27n",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 66,
          "referenced_widgets": [
            "86291f64d16449cdb8ba04197605509c",
            "67f08559f1f242e6bf0faff40be468d5",
            "3e2dddf882cb4684a17c2defc8ddca25",
            "fc77ab0e1cbb4b1b83663e6ebd464a32",
            "f34e3552ca014cef8b49006ffc405c5c",
            "e3696e51ada848689f28dd28bcc66157",
            "ede1c5b9e7264d9fb21000596c8ad9df",
            "396f1a372eab46d08fe8d3aaa05d8cda"
          ]
        },
        "outputId": "c0e33c1c-97cf-4f2a-faab-20b498478ef4"
      },
      "source": [
        "result = eq.solve(state_i , t_range= 10 , dt = 0.0001)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "86291f64d16449cdb8ba04197605509c",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=10.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fRC-01AXAkd7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "outputId": "a507a7a6-3f10-44c7-cd0d-d6c2d08e9559"
      },
      "source": [
        "result.plot(title='Pressure COndition after t = 10' , colorbar=True)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<pde.tools.plotting.PlotReference at 0x7f4735d34988>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XqtK5fZFAtfg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k_N9bnk_C1gq",
        "colab_type": "text"
      },
      "source": [
        "##Example 2 :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0nSSZc0LC0eL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "g = UnitGrid([50,50])"
      ],
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OJQv6_gvC6rS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "eq = DiffusionPDE()"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9Ob49X3YDqwR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "ScalarField.from_expression?"
      ],
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9cg95wyYC97m",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# i_state = from_expression(grid = g , expression = 'exp(-(x**2 + y**2) * 100)')\n",
        "\n",
        "# i_state.plot(title='Initial state')"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tq-BFeq8DOoK",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000,
          "referenced_widgets": [
            "27f591df95a34196b4895632dc5575e4",
            "c4cc66bfac61428eacde716b79dfdebe",
            "312075024449481bad0a5f2e59cb07b0",
            "99efc145c032444b9638863a58090c21",
            "919996dd973b42f99f7e16cc4ed1f6ef",
            "497a843b694e4c5db6ff0bca62034668",
            "152f4b8e0de947bba586db8b0814e9c8",
            "75d668da7c9144c1a4719c6207260310",
            "b5e3c10abf4f4222818abebbc15690c7",
            "14a66762f3234d1d993f81fcf4d47c7b"
          ]
        },
        "outputId": "88a6dc32-1609-4e16-8b3f-35ae3ab85549"
      },
      "source": [
        "# eq = DiffusionPDE()                                 # define the pde\n",
        "                          # generate grid\n",
        "# state = ScalarField.random_uniform(grid, 0.2, 0.3)  # generate initial condition\n",
        "\n",
        "storage = MemoryStorage()\n",
        "\n",
        "trackers = [\n",
        "    'progress',                    # show progress bar during simulation\n",
        "    'steady_state',                # abort when steady state is reached\n",
        "    storage.tracker(interval=1),   # store data every simulation time unit\n",
        "    PlotTracker(show=True),        # show images during simulation\n",
        "    # print some output every 5 real seconds:\n",
        "    PrintTracker(interval=RealtimeIntervals(duration=1))\n",
        "\n",
        "]\n",
        "\n",
        "eq.solve(state_i, 10, dt=0.1, tracker=trackers)\n",
        "\n",
        "storage[0].plot(colorbar=True)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "27f591df95a34196b4895632dc5575e4",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=10.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "b5e3c10abf4f4222818abebbc15690c7",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "Output()"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "t=0, c=1.91e+03±403\n",
            "t=0.1, c=1.91e+03±363\n",
            "t=0.2, c=1.91e+03±334\n",
            "t=0.3, c=1.91e+03±312\n",
            "t=0.7, c=1.91e+03±260\n",
            "t=7.7, c=1.91e+03±126\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "Spent more time on handling trackers (2.0656715190000057) than on the actual simulation (1.0967218609999954)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<pde.tools.plotting.PlotReference at 0x7f4730ba73c8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wJCR0I0hGdTE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# gri = CartesianGrid([[0, 2 * np.pi]] * 2, 64)\n",
        "# bcs = [{'value': 'sin(y)'}, {'value': 'sin(x)'}]\n",
        "\n",
        "# field_zero = ScalarField(gri)\n",
        "# result_laplace = field_zero.solve_poisson(bcs)\n",
        "# result_laplace.plot(title=\"Solution to Laplace's equation\", colorbar=True)"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w2efL_x9E37R",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gDx0oCDnkyCy",
        "colab_type": "text"
      },
      "source": [
        "$ \\frac {\\partial^2 P} {\\partial x^2} = \\frac {\\partial P} {\\partial t} $\n"
      ]
    }
  ]
}