labs/AM2/lab3/lab3_AM2_Bulin_Zhuikov_Lopatenko.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "# @title **[1/5] Run project imports** { run: \"auto\", display-mode: \"form\" }\n",
        "\n",
        "import copy\n",
        "import json\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import numpy.typing as nptp\n",
        "import pathlib\n",
        "import prettytable\n",
        "import threading\n",
        "import typing as tp\n",
        "import warnings\n",
        "\n",
        "from dataclasses import dataclass, field\n",
        "from sys import setrecursionlimit\n",
        "\n",
        "setrecursionlimit(10 ** 9)\n",
        "threading.stack_size(67108864)\n",
        "%config InlineBackend.figure_format = 'retina'"
      ],
      "metadata": {
        "id": "g75XLQ6iXIP5"
      },
      "execution_count": 113,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Ergodic Markov Chain**"
      ],
      "metadata": {
        "id": "dSbpSkD7YGmP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title **[3/5] Initialize Markov Chain**\n",
        "\n",
        "\n",
        "@dataclass()\n",
        "class ErgodicChain:\n",
        "    matrix: nptp.NDArray\n",
        "    eps: float = field(default=1e-6)\n",
        "    num_iter: int = field(default=1000)\n",
        "    errors: tp.List[float] = field(init=False, compare=False)\n",
        "\n",
        "    def __init__(self,\n",
        "                 matrix: tp.Sequence[tp.Sequence[float]],\n",
        "                 eps: float = 1e-6,\n",
        "                 num_iter: int = 1000) -> None:\n",
        "        self.matrix = self.validate_matrix(np.array(matrix))\n",
        "        self.eps = eps\n",
        "        self.num_iter = num_iter\n",
        "        self.errors = []\n",
        "\n",
        "    @staticmethod\n",
        "    def validate_matrix(matrix: nptp.NDArray) -> nptp.NDArray:\n",
        "        if matrix.shape[0] != matrix.shape[1]:\n",
        "            raise ValueError(f'matrix {matrix} should be square')\n",
        "        if np.any(matrix < 0):\n",
        "            raise ValueError(f'matrix {matrix} contains negative values')\n",
        "        if not np.allclose(np.sum(matrix, axis=1), 1):\n",
        "            raise ValueError(f'matrix {matrix} rows should be normalized')\n",
        "        return matrix\n",
        "\n",
        "    @staticmethod\n",
        "    def validate_distribution(base: nptp.NDArray, shape: tp.Tuple[int, int]) -> nptp.NDArray:\n",
        "        validated = copy.deepcopy(base)\n",
        "        if len(validated.shape) > 1:\n",
        "            validated = validated.ravel()\n",
        "        if validated.shape[0] != shape[0]:\n",
        "            raise ValueError(f'base vector shape {validated.shape} should match matrix shape {shape[0]}')\n",
        "        if not np.isclose(np.sum(validated), 1.0):\n",
        "            raise ValueError(f'base vector {validated} {np.sum(validated)}should be normalized')\n",
        "        return validated\n",
        "\n",
        "    def check_criteria(self, distribution: nptp.NDArray, other: nptp.NDArray) -> bool:\n",
        "        norm = float(np.linalg.norm(distribution - other))\n",
        "        self.errors.append(norm)\n",
        "        return norm < self.eps\n",
        "\n",
        "    def solve_numeric(self, base: tp.Sequence[float | tp.Sequence[float]]) -> nptp.NDArray:\n",
        "        self.errors = []\n",
        "        old_base = self.validate_distribution(np.array(base), self.matrix.shape)\n",
        "        new_base = old_base @ self.matrix\n",
        "        for i in range(self.num_iter):\n",
        "            if self.check_criteria(old_base, new_base):\n",
        "                return new_base\n",
        "            old_base, new_base = new_base, new_base @ self.matrix\n",
        "        warnings.warn('Numerical method did not converge, try changing eps and num_iter')\n",
        "        return new_base\n",
        "\n",
        "    def solve_analytic(self) -> nptp.NDArray:\n",
        "        matrix = self.matrix.T - np.eye(self.matrix.shape[0])\n",
        "        matrix[-1, :] = 1\n",
        "        b_term = np.zeros((self.matrix.shape[0], 1))\n",
        "        b_term[-1] = 1\n",
        "        return (np.linalg.inv(matrix) @ b_term).T.ravel()\n",
        "\n",
        "    def __str__(self) -> str:\n",
        "        labels = [f's{i}' for i in range(self.matrix.shape[1])]\n",
        "        table = prettytable.PrettyTable(\n",
        "            field_names=[\"state\"] + labels,\n",
        "        )\n",
        "        table.add_rows(\n",
        "            [[labels[i]] + \\\n",
        "             list(map(lambda x: \"{:.2f}\".format(x), self.matrix[i])) \\\n",
        "             for i in range(self.matrix.shape[0])],\n",
        "        )\n",
        "        return table.get_string()"
      ],
      "metadata": {
        "id": "LfXpgUFtGec6"
      },
      "execution_count": 98,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Benchmark and Tests**"
      ],
      "metadata": {
        "id": "flE16CinLcst"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# @title **[4/5] Initialize MVP Tests** { display-mode: \"form\" }\n",
        "\n",
        "def generate_bases(dim: int, n_bases: int) -> tp.Generator[tp.Sequence[float], None, None]:\n",
        "    for _ in range(n_bases):\n",
        "        matrix = np.random.rand(1, dim)\n",
        "        yield (matrix / np.sum(matrix)).tolist()\n",
        "\n",
        "\n",
        "@dataclass()\n",
        "class ErgodicChainCase:\n",
        "    name: str\n",
        "    bases: tp.Sequence[tp.Sequence[float]]\n",
        "    matrix: tp.Sequence[tp.Sequence[float]]\n",
        "    ground_truth: tp.Sequence[tp.Sequence[float]]\n",
        "    eps: float = 1e-6\n",
        "    num_iter: int = 1000\n",
        "\n",
        "\n",
        "TEST_CHAINS = [\n",
        "    ErgodicChainCase(\n",
        "        name=\"3x3\",\n",
        "        bases=list(generate_bases(3, 2)),\n",
        "        matrix=[\n",
        "            [1/2, 1/4, 1/4],\n",
        "            [1/3, 1/3, 1/3],\n",
        "            [1/2, 1/2, 0],\n",
        "        ],\n",
        "        ground_truth=[\n",
        "            [4/9, 1/3, 2/9],\n",
        "        ],\n",
        "    ),\n",
        "    ErgodicChainCase(\n",
        "        name=\"8x8\",\n",
        "        bases=list(generate_bases(8, 2)),\n",
        "        matrix=[\n",
        "            [1/4, 1/4, 1/4, 1/4, 0, 0, 0, 0],\n",
        "            [1/3, 0, 1/3, 1/3, 0, 0, 0, 0],\n",
        "            [0, 1/4, 1/4, 1/4, 1/4, 0, 0, 0],\n",
        "            [1/3, 1/3, 0, 0, 1/3, 0, 0, 0],\n",
        "            [0, 0, 1/4, 1/4, 1/4, 1/4, 0, 0],\n",
        "            [0, 0, 0, 0, 1/3, 0, 1/3, 1/3],\n",
        "            [0, 0, 0, 0, 0, 1/4, 1/4, 1/2],\n",
        "            [0, 0, 0, 0, 0, 1/2, 0, 1/2],\n",
        "        ],\n",
        "        ground_truth=[\n",
        "            [0.1134893, 0.11199602, 0.1433549, 0.1433549, 0.16724739, 0.12543554, 0.05574913, 0.13937282],\n",
        "        ],\n",
        "    ),\n",
        "]"
      ],
      "metadata": {
        "id": "G8mRB8m-CBCi"
      },
      "execution_count": 103,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# @title **[5/5] Run MVP Tests!** { display-mode: \"form\" }\n",
        "\n",
        "def plot_errors(errors: tp.Sequence[tp.Sequence[float]]) -> None:\n",
        "    fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n",
        "    for i in range(len(errors)):\n",
        "        steps = list(range(1, len(errors[i]) + 1))\n",
        "        ax.scatter(steps, errors[i])\n",
        "        ax.plot(steps, errors[i], label=f'state vector {i}')\n",
        "    ax.set(title='Error function', xlabel='steps', ylabel='error')\n",
        "    ax.legend()\n",
        "    with plt.ion():\n",
        "        plt.grid()\n",
        "        plt.show()\n",
        "\n",
        "for test_id, test in enumerate(TEST_CHAINS):\n",
        "    try:\n",
        "        errors = []\n",
        "        print(f'START-TEST[{test_id}][{test.name}]'.center(80, '~'))\n",
        "        chain = ErgodicChain(test.matrix, test.eps, test.num_iter)\n",
        "        print(chain)\n",
        "        distribution_analytic = chain.solve_analytic()\n",
        "        print(f'Analytic solution: {distribution_analytic}\\n')\n",
        "        for i, base in enumerate(test.bases):\n",
        "            distribution_numeric = chain.solve_numeric(base)\n",
        "            errors.append(chain.errors)\n",
        "            print(f'Numeric solution: {distribution_numeric}')\n",
        "            print(f'base_{i}: {base}\\neps={test.eps}, num_iter={test.num_iter}\\n')\n",
        "    except Exception as e:\n",
        "        warnings.warn(f'Catched exception on {test_id}-{test.name} test: {e}')\n",
        "    else:\n",
        "        plot_errors(errors)\n",
        "        assert np.allclose(distribution_analytic, np.array(test.ground_truth)), \\\n",
        "            f'Oops, matrices do not match'\n",
        "        print(f'END-TEST[{test_id}][{test.name}]'.center(80, '~'), end='\\n\\n\\n\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "lMcM5pQOY3Ne",
        "outputId": "d920775b-a82a-4b08-c789-e71aeed98748"
      },
      "execution_count": 117,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~START-TEST[0][3x3]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
            "+-------+------+------+------+\n",
            "| state |  s0  |  s1  |  s2  |\n",
            "+-------+------+------+------+\n",
            "|   s0  | 0.50 | 0.25 | 0.25 |\n",
            "|   s1  | 0.33 | 0.33 | 0.33 |\n",
            "|   s2  | 0.50 | 0.50 | 0.00 |\n",
            "+-------+------+------+------+\n",
            "Analytic solution: [0.44444444 0.33333333 0.22222222]\n",
            "\n",
            "Numeric solution: [0.44444439 0.33333323 0.22222239]\n",
            "base_0: [[0.49912446067748717, 0.03721929765633627, 0.46365624166617664]]\n",
            "eps=1e-06, num_iter=1000\n",
            "\n",
            "Numeric solution: [0.4444444  0.33333325 0.22222234]\n",
            "base_1: [[0.2326337203788858, 0.3227006983919964, 0.4446655812291177]]\n",
            "eps=1e-06, num_iter=1000\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
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          },
          "metadata": {
            "image/png": {
              "width": 691,
              "height": 392
            }
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~END-TEST[0][3x3]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
            "\n",
            "\n",
            "\n",
            "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~START-TEST[1][8x8]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
            "+-------+------+------+------+------+------+------+------+------+\n",
            "| state |  s0  |  s1  |  s2  |  s3  |  s4  |  s5  |  s6  |  s7  |\n",
            "+-------+------+------+------+------+------+------+------+------+\n",
            "|   s0  | 0.25 | 0.25 | 0.25 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 |\n",
            "|   s1  | 0.33 | 0.00 | 0.33 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 |\n",
            "|   s2  | 0.00 | 0.25 | 0.25 | 0.25 | 0.25 | 0.00 | 0.00 | 0.00 |\n",
            "|   s3  | 0.33 | 0.33 | 0.00 | 0.00 | 0.33 | 0.00 | 0.00 | 0.00 |\n",
            "|   s4  | 0.00 | 0.00 | 0.25 | 0.25 | 0.25 | 0.25 | 0.00 | 0.00 |\n",
            "|   s5  | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 | 0.33 | 0.33 |\n",
            "|   s6  | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.25 | 0.50 |\n",
            "|   s7  | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.50 |\n",
            "+-------+------+------+------+------+------+------+------+------+\n",
            "Analytic solution: [0.1134893  0.11199602 0.1433549  0.1433549  0.16724739 0.12543554\n",
            " 0.05574913 0.13937282]\n",
            "\n",
            "Numeric solution: [0.11348705 0.11199394 0.14335273 0.14335273 0.16724693 0.12543848\n",
            " 0.05575068 0.13937744]\n",
            "base_0: [[0.05300764418222075, 0.15557620929521784, 0.24447840440588292, 0.004172797957913218, 0.10944392441825529, 0.21609386541684486, 0.08467238809614748, 0.13255476622751766]]\n",
            "eps=1e-06, num_iter=1000\n",
            "\n",
            "Numeric solution: [0.11349139 0.11199795 0.14335692 0.14335692 0.16724781 0.1254328\n",
            " 0.05574768 0.13936852]\n",
            "base_1: [[0.24604614056001436, 0.2548949135840568, 0.02594271880002981, 0.06220832326616111, 0.15066729840198687, 0.08179635896730557, 0.04856261095432622, 0.12988163546611936]]\n",
            "eps=1e-06, num_iter=1000\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "image/png": {
              "width": 700,
              "height": 392
            }
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~END-TEST[1][8x8]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n",
            "\n",
            "\n",
            "\n"
          ]
        }
      ]
    }
  ]
}