{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "irCdVIKDw9IF", "outputId": "681c0ed2-219e-4190-c38c-b51faea0895c" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Step # 1\n", "[0.9901 0.01 0.01 ]\n", "\n", "Step # 2\n", "[0.019801 0.9901 0.9901 ]\n", "\n", "Step # 3\n", "[0.98039701 0.019801 0.019801 ]\n", "\n", "Step # 4\n", "[0.02940696 0.98039701 0.98039701]\n", "\n", "Step # 5\n", "[0.97088711 0.02940696 0.02940696]\n", "\n", "Step # 6\n", "[0.03882176 0.97088711 0.97088711]\n", "\n", "Step # 7\n", "[0.96156646 0.03882176 0.03882176]\n", "\n", "Step # 8\n", "[0.04804921 0.96156646 0.96156646]\n", "\n", "Step # 9\n", "[0.95243128 0.04804921 0.04804921]\n", "\n", "Step # 10\n", "[0.05709303 0.95243128 0.95243128]\n", "\n", "Step # 11\n", "[0.9434779 0.05709303 0.05709303]\n", "\n", "Step # 12\n", "[0.06595688 0.9434779 0.9434779 ]\n", "\n", "Step # 13\n", "[0.93470269 0.06595688 0.06595688]\n", "\n", "Step # 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99\n", "[0.68460905 0.31857671 0.31857671]\n", "\n", "Step # 100\n", "[0.32223704 0.68460905 0.68460905]\n", "\n", "Step # 101\n", "[0.68098533 0.32223704 0.32223704]\n", "\n" ] } ], "source": [ "import numpy as np\n", "\n", "eps = 0.01\n", "#T = np.array([[1/3., 1/3., 1/3.], [1/2., 1/2., 0], [0, 1/4., 3/4.]]) # Example 1\n", "T = np.array([[0+eps, 1/2.-eps/2, 1/2.-eps/2], [1, 0, 0], [1, 0, 0]]) # Example 2\n", "\n", "\n", "p0 = np.array([1, 0, 0])\n", "\n", "prev_p = p0\n", "p = T.dot(prev_p)\n", "step = 0\n", "while not np.allclose(p, prev_p):\n", "#while not np.array_equal(p, prev_p):\n", " step += 1\n", " prev_p = p\n", " p = T.dot(prev_p)\n", " print(\"Step #\", step)\n", " print(p)\n", " print()\n", " if step > 100:\n", " break\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" }, "colab": { "provenance": [] } }, "nbformat": 4, "nbformat_minor": 0 }