Markov_Chain_SteadyState.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "authorship_tag": "ABX9TyNRIYSgq4AS+bfLm8FjWmSt",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/bominwang/MCMC_library/blob/main/Markov_Chain_SteadyState.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **A demo for illustrete the steady state nature of Markov Chains**\n",
        "\n",
        "According to income levels, individuals can be categorized into low-income, middle-income, and high-income levels. Assuming that the income level of offspring is significantly influenced by their parental generation, the transition probabilities between these levels can be described using a state transition matrix. Assuming the transition matrix is as follows:\n",
        "\n",
        "\n",
        "\\\n",
        "\\begin{matrix}\n",
        " & \\text{Low Income} & \\text{Middle Income} & \\text{High Income} \\\\\n",
        "\\text{Low Income} & P_{LL} & P_{LM} & P_{LH} \\\\\n",
        "\\text{Middle Income} & P_{ML} & P_{MM} & P_{MH} \\\\\n",
        "\\text{High Income} & P_{HL} & P_{HM} & P_{HH} \\\\\n",
        "\\end{matrix}\n",
        "\n",
        "\n",
        "In this matrix:\n",
        "- $P_{LL}$ represents the probability of transitioning from low income to low income.\n",
        "- $P_{LM}$ represents the probability of transitioning from low income to middle income.\n",
        "- $P_{LH}$ represents the probability of transitioning from low income to high income.\n",
        "- $P_{ML}$ represents the probability of transitioning from middle income to low income.\n",
        "- $P_{MM}$ represents the probability of transitioning from middle income to middle income.\n",
        "- $P_{MH}$ represents the probability of transitioning from middle income to high income.\n",
        "- $P_{HL}$ represents the probability of transitioning from high income to low income.\n",
        "- $P_{HM}$ represents the probability of transitioning from high income to middle income.\n",
        "- $P_{HH}$ represents the probability of transitioning from high income to high income.\n",
        "\n",
        "Suppose the initial distribution proportions $\\pi_{0}$ within the current population are as follows:\n",
        "\n",
        "\\begin{bmatrix}\n",
        "0.21 & 0.68 & 0.11\n",
        "\\end{bmatrix}\n",
        "\n",
        "the transform matrix of state as follows :\n",
        "\n",
        "\\begin{bmatrix}\n",
        "0.65 & 0.28 & 0.07 \\\\\n",
        "0.15 & 0.67 & 0.18 \\\\\n",
        "0.12 & 0.36 & 0.52 \\\\\n",
        "\\end{bmatrix}\n",
        "\n",
        "The convergence process of a Markov chain can be observed based on the following functions."
      ],
      "metadata": {
        "id": "-awmdt-onRgR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!nvcc --version"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lzHJlh8LBtuK",
        "outputId": "1217f2ac-f322-4901-a1f7-c775bfd2c2e3"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "nvcc: NVIDIA (R) Cuda compiler driver\n",
            "Copyright (c) 2005-2022 NVIDIA Corporation\n",
            "Built on Wed_Sep_21_10:33:58_PDT_2022\n",
            "Cuda compilation tools, release 11.8, V11.8.89\n",
            "Build cuda_11.8.r11.8/compiler.31833905_0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "pBYf6mY1nHI4",
        "outputId": "12a334a2-3640-4274-c295-a869885b52ba"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Transform matrix:\n",
            " [[0.65 0.28 0.07]\n",
            " [0.15 0.67 0.18]\n",
            " [0.12 0.36 0.52]]\n",
            "Initial state is: \n",
            " [[0.21 0.68 0.11]]\n",
            "the 0-th state is [[0.2517 0.554  0.1943]]\n",
            "the 10-th state is [[0.28646357 0.4885367  0.22499973]]\n",
            "the 20-th state is [[0.28650132 0.4885216  0.22497708]]\n",
            "the 30-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 40-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 50-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 60-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 70-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 80-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 90-th state is [[0.28650138 0.48852158 0.22497704]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Fixfj66+/Fre/+OKLKCkpwZdffonc3FwMGDAAI0aMwPXr18U2+fn52LlzJ3bt2oVdu3YhMzMTKSkpAICVK1ciIiICkyZNwpUrV3DlyhUEBARIGt/mJvnLD+9bt29t5uP5iYju7tYN4F3/1j/u25cBJ1ebmlZUVGDlypVIS0tDbGwsAKBbt24YOnQo1q1bh+rqamzevBmurvX9paWlYfTo0XjvvffEL/v18vLCqlWroFQq0aNHD6SmpuLGjRt4++23AfwaiPbv34+YmBjx2DNmzMDzzz8PAFizZg3S09Oxfv16JCQk4IMPPkBAQADS0tKgUCjQs2dPXL58GXPmzEFiYqL45cL9+/dHUlISAKB79+5IS0uDwWDAE088gf379yMnJwclJSXilwi///772LlzJ/71r39h8uTJAOrPMG3cuBFubm4AgPHjx8NgMGDZsmXQarVwcnKCi4sL9Hp90/9MmhEDi614SYiIqN04deoUampqMGLEiAa3hYSEiGEFAB5++GFYLBacOXNGDCx9+vQRAwQA6HQ69O3bV3ytUqng7e2NkpISq/4jIiLE3x0cHBAWFoZTp06Jx46IiIBCobA6dmVlJS5evIguXboAqA8sv+Xn5yceJy8vD5WVlfD29rZqc/PmTeTn54uvAwMDxbDy+z7kiIHFVry1mYjINo4u9Wc77HFcGzk7O9/74RwdrV4rFIoG11kslns+li3Hvn2cyspK+Pn5ISMj4479PDw8bOpDjjiHxVa3b23m4/mJiO5Ooai/NNPay2/OSvyR7t27w9nZGQaD4Y5tvXr1Ql5eHqqqqsR1Bw4cEC/93KtDhw6Jv9fV1SE3Nxe9evUSj52VlQXhN/NxDhw4ADc3N3Tu3Nmm/gcMGACj0QgHBwcEBwdbLT4+PjbX6eTkBLPZbHP7lsbAYivxDAsfz09E1NZpNBrMmTMHCQkJ2Lx5M/Lz83Ho0CGsX78e48aNg0ajQWxsLE6cOIG9e/di5syZGD9+vHg56F6sXr0an332GU6fPo3p06fj559/xiuvvAIAmDZtGi5cuICZM2fi9OnT+Pzzz5GUlIT4+Hiry093ExkZiYiICIwZMwZ79uxBYWEhDh48iPnz5+O7776zuc7AwEBkZ2ejsLAQpaWl4tmXc+fO4dixYzAajbh58yaOHTuGY8eOoba2ZZ9TxktCtro9h6W6HKipANRud29PRESytmDBAjg4OCAxMRGXL1+Gn58fpkyZAhcXF3z11Vd44403MGjQILi4uOD555/H8uXLm+W4KSkpSElJwbFjxxAcHIwvvvhCPPPRqVMn7N69G7Nnz0ZISAi8vLzw6quv4p133rG5f4VCgd27d2P+/PmIi4vD1atXodfr8eijj0oKXG+99RZiY2PRu3dv3Lx5EwUFBQgMDMRrr71mdSv2Qw89BADi9paiEASJ94HJkMlkglarRXl5Odzd3VvuQCld6gPLtGzAt2fLHYeIqI2orq5GQUEBgoKCoNFo7F2OrBUWFiIoKAhHjx5t1SfE2tvd/o5I+fzmJSEpxHksnHhLRETUmhhYpBDnsXDiLRERUWviHBYpxGex8AwLERFJExgYiHYwC8NueIZFituP5+etzURERK2KgUWK24/n563NRERErYqBRQo+np+IiMguGFik0P7mabe8DklERNRqGFikcPMHoADqqoEb1+xdDRER0X2DgUUKByegwy9PCeSdQkRERK2GgUUq3tpMRETU6hhYpBIfHsfAQkRE7dewYcMwa9Ysq3V5eXl46aWXEBAQAGdnZ/Tq1QsrV65slXr44DipOvYC8DlQ+B/gT1PsXQ0REVGryc3Nha+vL7Zu3YqAgAAcPHgQkydPhkqlwowZM1r02DzDIlWv0fU/z35d/63NRETUJlksFqSmpiI4OBhqtRpdunTBsmXLAADHjx/H8OHD4ezsDG9vb0yePBmVlZXivhMnTsSYMWPw7rvvQqfTwcPDA4sXL0ZdXR1mz54NLy8vdO7cGR9++KG4T2FhIRQKBbZt24YhQ4ZAo9Ggb9++Vt98DACZmZkYPHgw1Go1/Pz8MHfuXNTV1Ynbhw0bhtdffx0JCQnw8vKCXq/HwoULrfooKyvDa6+9ho4dO8Ld3R3Dhw9HXl6euH3hwoUIDQ3Fli1bEBgYCK1Wi5iYGFRUVIjvLzMzEytXroRCoYBCoUBhYSFeeeUVrFy5Eo899hi6du2Kl19+GXFxcdixY0ez/bk0hoFFKl0fwLs7YK4BzqTbuxoiItkRBAE3bt1o9UXqY+/nzZuHlJQULFiwACdPnsTHH38MnU6HqqoqREVFwdPTE4cPH8ann36Kb7755o4zCN9++y0uX76Mffv2Yfny5UhKSsLTTz8NT09PZGdnY8qUKfjLX/6CixetpxDMnj0bb775Jo4ePYqIiAiMHj0a167V33l66dIlPPXUUxg0aBDy8vKwZs0arF+/HkuXLrXqY9OmTXB1dUV2djZSU1OxePFifP311+L2F198ESUlJfjyyy+Rm5uLAQMGYMSIEbh+/brYJj8/Hzt37sSuXbuwa9cuZGZmIiUlBQCwcuVKREREYNKkSbhy5QquXLmCgICABsexvLwcXl5eksa+KRRCO/hiAylfT90svl0K7Psr0PNpIOajlj8eEZFMVVdXo6CgAEFBQdBoNACAG7duIPzj8FavJfv/ZcPF0cWmthUVFejYsSPS0tLw2muvWW1bt24d5syZgwsXLsDV1RUAsHv3bowePRqXL1+GTqfDxIkTkZGRgZ9++glKZf2//Xv27AlfX1/s27cPAGA2m6HVavHPf/4TMTExKCwsRFBQEFJSUjBnzhwAQF1dHYKCgjBz5kwkJCRg/vz5+N///V+cOnUKCoUCAPDBBx9gzpw5KC8vh1KpxLBhw2A2m/Gf//xHrHnw4MEYPnw4UlJSsH//fowaNQolJSVQq9Vim+DgYCQkJGDy5MlYuHAh/vrXv8JoNMLNzQ0AkJCQgH379uHQoUMA6s/khIaGYsWKFY2O48GDB/HYY4/h//7v/zBy5MgG2zT0d+Q2KZ/fPMPSFH3+XP/z7NdAtcm+tRARkWSnTp1CTU0NRowY0eC2kJAQMawAwMMPPwyLxYIzZ86I6/r06SOGFQDQ6XTo16+f+FqlUsHb2xslJSVW/UdERIi/Ozg4ICwsDKdOnRKPHRERIYaV28eurKy0OlPTv39/qz79/PzE4+Tl5aGyshLe3t7o0KGDuBQUFCA/P1/cJzAwUAwrv+/DFidOnMCzzz6LpKSkRsNKc+Kk26bw7V1/WejaWeDHr4D+L9q7IiIi2XB2cEb2/8u2y3Ftbutse9vGODo6Wr1WKBQNrrNYLPd8LFuOffs4lZWV8PPzQ0ZGxh37eXh42NTHHzl58iRGjBiByZMn45133pFWfBPxDEtTKBS/nmX54TP71kJEJDMKhQIuji6tvvz2rMQf6d69O5ydnWEwGO7Y1qtXL+Tl5aGqqkpcd+DAASiVSvTo0eOex+f2JReg/pJQbm4uevXqJR47KyvLaj7OgQMH4Obmhs6dO9vU/4ABA2A0GuHg4IDg4GCrxcfHx+Y6nZycYDab71j/ww8/4PHHH0dsbKw4Sbk1NCmwrF69GoGBgdBoNAgPD0dOTk6jbTdu3CjOML69/P4aliAISExMhJ+fH5ydnREZGYmzZ882pbTW02dM/c9z3/CyEBFRG6PRaDBnzhwkJCRg8+bNyM/Px6FDh7B+/XqMGzcOGo0GsbGxOHHiBPbu3YuZM2di/Pjx0Ol093zs1atX47PPPsPp06cxffp0/Pzzz3jllVcAANOmTcOFCxcwc+ZMnD59Gp9//jmSkpIQHx9vdfnpbiIjIxEREYExY8Zgz549KCwsxMGDBzF//nx89913NtcZGBiI7OxsFBYWorS0FBaLBSdOnMDjjz+OkSNHIj4+HkajEUajEVevXm3SWEghObBs374d8fHxSEpKwpEjRxASEoKoqKi7Xvdyd3cXZxlfuXIF58+ft9qempqKVatWYe3atcjOzoarqyuioqJQXV0t/R21Ft/egM+D9XcL/ci7hYiI2poFCxbgzTffRGJiInr16oWxY8eipKQELi4u+Oqrr3D9+nUMGjQIL7zwAkaMGIG0tLRmOW5KSgpSUlIQEhKC/fv344svvhDPfHTq1Am7d+9GTk4OQkJCMGXKFLz66quSLrsoFArs3r0bjz76KOLi4vDggw8iJiYG58+flxS43nrrLahUKvTu3RsdO3ZEUVER/vWvf+Hq1avYunUr/Pz8xGXQoEGSx0EyQaLBgwcL06dPF1+bzWbB399fSE5ObrD9hx9+KGi12kb7s1gsgl6vF/7617+K68rKygS1Wi188sknNtVUXl4uABDKy8ttexPNxbBUEJLcBeHjl1r3uEREMnHz5k3h5MmTws2bN+1diuwVFBQIAISjR4/au5RWdbe/I1I+vyWdYamtrUVubi4iIyPFdUqlEpGRkcjKymp0v8rKSjzwwAMICAjAs88+ix9++EHcVlBQAKPRaNWnVqtFeHh4o33W1NTAZDJZLXbBy0JEREStQlJgKS0thdlsvuOUkk6ng9FobHCfHj16YMOGDfj888+xdetWWCwWDBkyRLw96/Z+UvpMTk6GVqsVl8YeZtPieFmIiIioVbT4XUIRERGYMGECQkND8dhjj2HHjh3o2LEj/v73vze5z3nz5qG8vFxcLly40IwVS6BQAL3H1P/Ou4WIiOguAgMDIQgCQkND7V1KmyQpsPj4+EClUqG4uNhqfXFxMfR6vU19ODo64qGHHsK5c+cAQNxPSp9qtRru7u5Wi9389iFyBfvsVwcREVE7JimwODk5YeDAgVb3rVssFhgMBqsn992N2WzG8ePH4efnBwAICgqCXq+36tNkMiE7O9vmPu3KtxfQ+1nAcgv45CXgUq69KyIiImp3JF8Sio+Px7p167Bp0yacOnUKU6dORVVVFeLi4gAAEyZMwLx588T2ixcvxp49e/DTTz/hyJEjePnll3H+/HnxuxsUCgVmzZqFpUuX4osvvsDx48cxYcIE+Pv7Y8yYMc3zLluSQgH8+R9A0KNAbSWw9Xmg5JS9qyIialVC2/9aOmohzfV3Q/Kj+ceOHYurV68iMTERRqMRoaGhSE9PFyfNFhUVWT3c5ueff8akSZNgNBrh6emJgQMH4uDBg+jdu7fYJiEhAVVVVZg8eTLKysowdOhQpKen3/GAOdly1AAxHwObxwCXvqv/+Uo64BVk78qIiFrU7ce737hxo1ked0/tT21tLYD671a6F/y25uZ04zqwcRRQchLweAB4aRug6/3H+xERtWFXrlxBWVkZfH194eIi7RH51L5ZLBZcvnwZjo6O6NKlyx1/N6R8fvPLD5uTixcw/jNgQzTwcwGwJgII+BMwcGL9PBcn2772nIioLbl9g4SUb/ql+4dSqWwwrEjFMywtoawISJ8HnPkSEH754ii1Fuj19K/PbvEJrj8Lo7y3U2RERHJhNptx69Yte5dBMuPk5NTo9yBJ+fxmYGlJpivAsY+AI5vqQ8zvqZwAFx/A2QPQaAGNB6B2AxycAJUacNDU/650qF8UKkCprP+pUP5uuZ1cFb/5/faq32z7vSYnXp7yJSK6r2jcgb7PN2uXDCxyY7EABRnA+YNA6dn65dq5+ifkEhERtQXe3YGZtn/bsy04h0VulEqg2/D65TaLGSi/CNy8DtwsA6rLgeoyoKayPsjU/bKYawFL3S+L+ZelDoAACAIgWOoX4Nd1t38H7nz9W20/qxIRUWtx87Pr4RlY7EWpAjwfqF+IiIjorlr8u4SIiIiI7hUDCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREclekwLL6tWrERgYCI1Gg/DwcOTk5Ni037Zt26BQKDBmzBir9RMnToRCobBaoqOjm1IaERERtUOSA8v27dsRHx+PpKQkHDlyBCEhIYiKikJJScld9yssLMRbb72FRx55pMHt0dHRuHLlirh88sknUksjIiKidkpyYFm+fDkmTZqEuLg49O7dG2vXroWLiws2bNjQ6D5msxnjxo3DokWL0LVr1wbbqNVq6PV6cfH09JRaGhEREbVTkgJLbW0tcnNzERkZ+WsHSiUiIyORlZXV6H6LFy+Gr68vXn311UbbZGRkwNfXFz169MDUqVNx7do1KaURERFRO+YgpXFpaSnMZjN0Op3Vep1Oh9OnTze4z/79+7F+/XocO3as0X6jo6Px3HPPISgoCPn5+Xj77bfx5JNPIisrCyqV6o72NTU1qKmpEV+bTCYpb4OIiIjaGEmBRaqKigqMHz8e69atg4+PT6PtYmJixN/79euH/v37o1u3bsjIyMCIESPuaJ+cnIxFixa1SM1EREQkP5IuCfn4+EClUqG4uNhqfXFxMfR6/R3t8/PzUVhYiNGjR8PBwQEODg7YvHkzvvjiCzg4OCA/P7/B43Tt2hU+Pj44d+5cg9vnzZuH8vJycblw4YKUt0FERERtjKQzLE5OThg4cCAMBoN4a7LFYoHBYMCMGTPuaN+zZ08cP37cat0777yDiooKrFy5EgEBAQ0e5+LFi7h27Rr8/Pwa3K5Wq6FWq6WUTkRERG2Y5EtC8fHxiI2NRVhYGAYPHowVK1agqqoKcXFxAIAJEyagU6dOSE5OhkajQd++fa329/DwAABxfWVlJRYtWoTnn38eer0e+fn5SEhIQHBwMKKiou7x7REREVF7IDmwjB07FlevXkViYiKMRiNCQ0ORnp4uTsQtKiqCUmn7lSaVSoXvv/8emzZtQllZGfz9/TFy5EgsWbKEZ1GIiIgIAKAQBEGwdxH3ymQyQavVory8HO7u7vYuh4iIiGwg5fOb3yVEREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESy16TAsnr1agQGBkKj0SA8PBw5OTk27bdt2zYoFAqMGTPGar0gCEhMTISfnx+cnZ0RGRmJs2fPNqU0IiIiaockB5bt27cjPj4eSUlJOHLkCEJCQhAVFYWSkpK77ldYWIi33noLjzzyyB3bUlNTsWrVKqxduxbZ2dlwdXVFVFQUqqurpZZHRERE7ZDkwLJ8+XJMmjQJcXFx6N27N9auXQsXFxds2LCh0X3MZjPGjRuHRYsWoWvXrlbbBEHAihUr8M477+DZZ59F//79sXnzZly+fBk7d+6U/IaIiIio/ZEUWGpra5Gbm4vIyMhfO1AqERkZiaysrEb3W7x4MXx9ffHqq6/esa2goABGo9GqT61Wi/Dw8Eb7rKmpgclkslqIiIio/ZIUWEpLS2E2m6HT6azW63Q6GI3GBvfZv38/1q9fj3Xr1jW4/fZ+UvpMTk6GVqsVl4CAAClvg4iIiNqYFr1LqKKiAuPHj8e6devg4+PTbP3OmzcP5eXl4nLhwoVm65uIiIjkx0FKYx8fH6hUKhQXF1utLy4uhl6vv6N9fn4+CgsLMXr0aHGdxWKpP7CDA86cOSPuV1xcDD8/P6s+Q0NDG6xDrVZDrVZLKZ2IiIjaMElnWJycnDBw4EAYDAZxncVigcFgQERExB3te/bsiePHj+PYsWPi8swzz+Dxxx/HsWPHEBAQgKCgIOj1eqs+TSYTsrOzG+yTiIiI7j+SzrAAQHx8PGJjYxEWFobBgwdjxYoVqKqqQlxcHABgwoQJ6NSpE5KTk6HRaNC3b1+r/T08PADAav2sWbOwdOlSdO/eHUFBQViwYAH8/f3veF4LERER3Z8kB5axY8fi6tWrSExMhNFoRGhoKNLT08VJs0VFRVAqpU2NSUhIQFVVFSZPnoyysjIMHToU6enp0Gg0UssjIiKidkghCIJg7yLulclkglarRXl5Odzd3e1dDhEREdlAyuc3v0uIiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkr0mBZfXq1QgMDIRGo0F4eDhycnIabbtjxw6EhYXBw8MDrq6uCA0NxZYtW6zaTJw4EQqFwmqJjo5uSmlERETUDjlI3WH79u2Ij4/H2rVrER4ejhUrViAqKgpnzpyBr6/vHe29vLwwf/589OzZE05OTti1axfi4uLg6+uLqKgosV10dDQ+/PBD8bVarW7iWyIiIqL2RiEIgiBlh/DwcAwaNAhpaWkAAIvFgoCAAMycORNz5861qY8BAwZg1KhRWLJkCYD6MyxlZWXYuXOntOp/YTKZoNVqUV5eDnd39yb1QURERK1Lyue3pEtCtbW1yM3NRWRk5K8dKJWIjIxEVlbWH+4vCAIMBgPOnDmDRx991GpbRkYGfH190aNHD0ydOhXXrl1rtJ+amhqYTCarhYiIiNovSZeESktLYTabodPprNbrdDqcPn260f3Ky8vRqVMn1NTUQKVS4YMPPsATTzwhbo+OjsZzzz2HoKAg5Ofn4+2338aTTz6JrKwsqFSqO/pLTk7GokWLpJROREREbZjkOSxN4ebmhmPHjqGyshIGgwHx8fHo2rUrhg0bBgCIiYkR2/br1w/9+/dHt27dkJGRgREjRtzR37x58xAfHy++NplMCAgIaPH3QURERPYhKbD4+PhApVKhuLjYan1xcTH0en2j+ymVSgQHBwMAQkNDcerUKSQnJ4uB5fe6du0KHx8fnDt3rsHAolarOSmXiIjoPiJpDouTkxMGDhwIg8EgrrNYLDAYDIiIiLC5H4vFgpqamka3X7x4EdeuXYOfn5+U8oiIiKidknxJKD4+HrGxsQgLC8PgwYOxYsUKVFVVIS4uDgAwYcIEdOrUCcnJyQDq55uEhYWhW7duqKmpwe7du7FlyxasWbMGAFBZWYlFixbh+eefh16vR35+PhISEhAcHGx12zMRERHdvyQHlrFjx+Lq1atITEyE0WhEaGgo0tPTxYm4RUVFUCp/PXFTVVWFadOm4eLFi3B2dkbPnj2xdetWjB07FgCgUqnw/fffY9OmTSgrK4O/vz9GjhyJJUuW8LIPERERAWjCc1jkiM9hISIianta7DksRERERPbAwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREstekwLJ69WoEBgZCo9EgPDwcOTk5jbbdsWMHwsLC4OHhAVdXV4SGhmLLli1WbQRBQGJiIvz8/ODs7IzIyEicPXu2KaURERFROyQ5sGzfvh3x8fFISkrCkSNHEBISgqioKJSUlDTY3svLC/Pnz0dWVha+//57xMXFIS4uDl999ZXYJjU1FatWrcLatWuRnZ0NV1dXREVFobq6uunvjIiIiNoNhSAIgpQdwsPDMWjQIKSlpQEALBYLAgICMHPmTMydO9emPgYMGIBRo0ZhyZIlEAQB/v7+ePPNN/HWW28BAMrLy6HT6bBx40bExMT8YX8mkwlarRbl5eVwd3eX8naIiIjITqR8fks6w1JbW4vc3FxERkb+2oFSicjISGRlZf3h/oIgwGAw4MyZM3j00UcBAAUFBTAajVZ9arVahIeHN9pnTU0NTCaT1UJERETtl6TAUlpaCrPZDJ1OZ7Vep9PBaDQ2ul95eTk6dOgAJycnjBo1Cn/729/wxBNPAIC4n5Q+k5OTodVqxSUgIEDK2yAiIqI2plXuEnJzc8OxY8dw+PBhLFu2DPHx8cjIyGhyf/PmzUN5ebm4XLhwofmKJSIiItlxkNLYx8cHKpUKxcXFVuuLi4uh1+sb3U+pVCI4OBgAEBoailOnTiE5ORnDhg0T9ysuLoafn59Vn6GhoQ32p1aroVarpZROREREbZikMyxOTk4YOHAgDAaDuM5iscBgMCAiIsLmfiwWC2pqagAAQUFB0Ov1Vn2aTCZkZ2dL6pOIiIjaL0lnWAAgPj4esbGxCAsLw+DBg7FixQpUVVUhLi4OADBhwgR06tQJycnJAOrnm4SFhaFbt26oqanB7t27sWXLFqxZswYAoFAoMGvWLCxduhTdu3dHUFAQFixYAH9/f4wZM6b53ikRERG1WZIDy9ixY3H16lUkJibCaDQiNDQU6enp4qTZoqIiKJW/nripqqrCtGnTcPHiRTg7O6Nnz57YunUrxo4dK7ZJSEhAVVUVJk+ejLKyMgwdOhTp6enQaDTN8BaJiIiorZP8HBY54nNYiIiI2p4Wew4LERERkT0wsBAREZHsMbAQERGR7DGwEBERkexJvkuIWkZNnRklphpcq6pFZXUdKmtuobLGjKqaOlTfMqO2zoJas0X8abYI1osgQBAAiyDA8stPCICA+vW/nVotoP5FQ9OtbZmB3fanaRMRkVR6rRpLx/Sz2/EZWFqRIAgoNtXg+4tlOH6pHD9cNuFy2U0Um6rx841b9i6PiIioUV07utr1+AwsLUwQBOSe/xkfZxfhP+dKcbWiptG2Tg5KdOygRge1AzpoHOCqdkAHtQoaRxXUDko4qZRwclDCUaWEg1IBlVIJlRJQKhVQKRRQKhRQKCD+VKD+wXy//f22278qoLijDsWdq4iI6D7nprFvZGBgaSGm6lvYefQSPjpUhDPFFeJ6pQJ4UOeGfp206N9Ziy7ertC7a6BzV0Pr7GgVKoiIiKgeA0sL2H64CIv+fRI3as0AAI2jEqP7++P5gZ0R0tkDzk4qO1dIRETUtjCwNKM6swXv7j6NDQcKAADBvh0wLrwLnnuoM7QujnaujoiIqO1iYGkm5TdvYeYnR7Hvx6sAgP+KfBCvjwjmJR4iIqJmwMDSDApKq/DqpsP46WoVnB1VWP7/heDJfn72LouIiKjdYGC5R2U3avHi2iyUVtbAX6vBPyaEoW8nrb3LIiIialcYWO7Rim/OorSyBt06uuKTyX+Cr5vG3iURERG1O3w0/z04W1yBLYfOAwCWPNuXYYWIiKiFMLA0kSAIWLzrJMwWAVF9dBgS7GPvkoiIiNotBpYmMpwqwX/OlsJJpcT8p3rbuxwiIqJ2jYGlCWrqzFj6fycBAK89EoQu3i52roiIiKh9Y2Bpgo0HClF47QZ83dSY9niwvcshIiJq9xhYJCqpqMbfvj0HAJgT3RMd1LzRioiIqKUxsEi0bt9PqKypQ0iAB/78UCd7l0NERHRfYGCRKONM/aP3//JoVyiVfOw+ERFRa2BgkaDYVI2zJZVQKICHu/E2ZiIiotbCwCLB/rOlAID+nbT89mUiIqJWxMAiwYFz9YHlYT4kjoiIqFUxsNhIEATs/yWwDGVgISIialUMLDY6V1KJkooaqB2UGPCAp73LISIiuq8wsNjo9tmVwUFe0Diq7FwNERHR/YWBxUacv0JERGQ/DCw2uGW24NBP1wFw/goREZE9MLDYIO9CGSpr6uDp4ojefu72LoeIiOi+w8Big9vzV4YE+/DptkRERHbAwGKDA7ydmYiIyK4YWP5AZU0djhaVAWBgISIishcGlj+QU3ANdRYBXbxcEODlYu9yiIiI7ktNCiyrV69GYGAgNBoNwsPDkZOT02jbdevW4ZFHHoGnpyc8PT0RGRl5R/uJEydCoVBYLdHR0U0prdntP3sNAG9nJiIisifJgWX79u2Ij49HUlISjhw5gpCQEERFRaGkpKTB9hkZGXjppZewd+9eZGVlISAgACNHjsSlS5es2kVHR+PKlSvi8sknnzTtHTWz/eeuAuDlICIiInuSHFiWL1+OSZMmIS4uDr1798batWvh4uKCDRs2NNj+o48+wrRp0xAaGoqePXvin//8JywWCwwGg1U7tVoNvV4vLp6e9n/8fYmpGj8WV0KhACK6edu7HCIiovuWpMBSW1uL3NxcREZG/tqBUonIyEhkZWXZ1MeNGzdw69YteHl5Wa3PyMiAr68vevTogalTp+LatWuN9lFTUwOTyWS1tASjqRrdfTugj787vFydWuQYRERE9MccpDQuLS2F2WyGTqezWq/T6XD69Gmb+pgzZw78/f2tQk90dDSee+45BAUFIT8/H2+//TaefPJJZGVlQaW683t7kpOTsWjRIimlN0n/zh74Ov4x3Kw1t/ixiIiIqHGSAsu9SklJwbZt25CRkQGNRiOuj4mJEX/v168f+vfvj27duiEjIwMjRoy4o5958+YhPj5efG0ymRAQENBidTs78csOiYiI7EnSJSEfHx+oVCoUFxdbrS8uLoZer7/rvu+//z5SUlKwZ88e9O/f/65tu3btCh8fH5w7d67B7Wq1Gu7u7lYLERERtV+SAouTkxMGDhxoNWH29gTaiIiIRvdLTU3FkiVLkJ6ejrCwsD88zsWLF3Ht2jX4+flJKY+IiIjaKcl3CcXHx2PdunXYtGkTTp06halTp6KqqgpxcXEAgAkTJmDevHli+/feew8LFizAhg0bEBgYCKPRCKPRiMrKSgBAZWUlZs+ejUOHDqGwsBAGgwHPPvssgoODERUV1Uxvk4iIiNoyyXNYxo4di6tXryIxMRFGoxGhoaFIT08XJ+IWFRVBqfw1B61Zswa1tbV44YUXrPpJSkrCwoULoVKp8P3332PTpk0oKyuDv78/Ro4ciSVLlkCtVt/j2yMiIqL2QCEIgmDvIu6VyWSCVqtFeXk557MQERG1EVI+v/ldQkRERCR7DCxEREQkewwsREREJHsMLERERCR7DCxEREQkewwsREREJHsMLERERCR7DCxEREQkewwsREREJHsMLERERCR7DCxEREQkewwsREREJHsMLERERCR7DCxEREQkewwsREREJHsO9i6gvbhluYXT107jSMkR5Bbn4uS1kzALZiihhEKhgEqhgqPKES4OLnB2cIaroytcHF2gUWmgcdDA2cEZGgcN1Co1HJWOcFI5wVHpCEelIxyUDlApVFApVVAqlFAp6n8qFUqxf4VCAfF/CgUANPr7bylw5zpbNNQXERG1X2qVGj29etrt+Aws96jOUoelh5Zid8Fu3Ky7ae9yiIiIWkSgeyD+/ed/2+34DCz3aEXuCvzv2f8FALg7uWOA7wAM0A1AqG8oXBxcYBEs4lJjrsHNupu4UXcDN27dwI26G6iuq0a1uRo3b91Etbka1XXVuGW59etivgWzYK5fLGbUCXUwW8wQIEAQBFgEC8yCGQAgCALE/wmCVZ0Cfn19e9tv1zXm9/0QEdH9Se+qt+vxGVjuQXpBOjad3AQASH4kGU8FPQWlgtOCiIiImhsDSxP9+POPSDyYCAB4te+reLrr03auiIiIqP3i6YAmMNWaMGvvLNysu4k/+f0JMx+aae+SiIiI2jUGFoksggXz/jMPFyouwN/VH6mPpkKlVNm7LCIionaNgUWibae3Yd/FfVCr1Pjvx/8bnhpPe5dERETU7jGwSJR5MRMAMDVkKnp797ZzNURERPcHBhYJBEHAD9d+AAD8ye9Pdq6GiIjo/sHAIsGlyksorymHg9IB3T2727scIiKi+wYDiwQnr50EADzo+SCcVE52roaIiOj+wcAiwe3LQX28+9i5EiIiovsLA4sEDCxERET2wcBiI0EQcLK0/pIQ7w4iIiJqXQwsNrpQcQEVtyrgpHRCsEewvcshIiK6rzCw2Oj25aAeXj3gqHK0czVERET3FwYWG92+Q4iXg4iIiFofA4uNOOGWiIjIfhhYbGARLOIZlj4+DCxEREStjYHFBudN51F1qwoalQZdtV3tXQ4REdF9p0mBZfXq1QgMDIRGo0F4eDhycnIabbtu3To88sgj8PT0hKenJyIjI+9oLwgCEhMT4efnB2dnZ0RGRuLs2bNNKa1F/HbCrYPSwc7VEBER3X8kB5bt27cjPj4eSUlJOHLkCEJCQhAVFYWSkpIG22dkZOCll17C3r17kZWVhYCAAIwcORKXLl0S26SmpmLVqlVYu3YtsrOz4erqiqioKFRXVzf9nTWjH0o5f4WIiMieFIIgCFJ2CA8Px6BBg5CWlgYAsFgsCAgIwMyZMzF37tw/3N9sNsPT0xNpaWmYMGECBEGAv78/3nzzTbz11lsAgPLycuh0OmzcuBExMTF/2KfJZIJWq0V5eTnc3d2lvB2bxH4ZiyMlR7Bs6DI80+2ZZu+fiIjofiTl81vSGZba2lrk5uYiMjLy1w6USkRGRiIrK8umPm7cuIFbt27By8sLAFBQUACj0WjVp1arRXh4eKN91tTUwGQyWS0txWwx49T1UwB4hoWIiMheJAWW0tJSmM1m6HQ6q/U6nQ5Go9GmPubMmQN/f38xoNzeT0qfycnJ0Gq14hIQECDlbUhSaCrEzbqbcHZwRqB7YIsdh4iIiBrXqncJpaSkYNu2bfjss8+g0Wia3M+8efNQXl4uLhcuXGjGKq3dnnDby6sXVEpVix2HiIiIGifplhcfHx+oVCoUFxdbrS8uLoZer7/rvu+//z5SUlLwzTffoH///uL62/sVFxfDz8/Pqs/Q0NAG+1Kr1VCr1VJKb7LbE275hFsiIiL7kXSGxcnJCQMHDoTBYBDXWSwWGAwGRERENLpfamoqlixZgvT0dISFhVltCwoKgl6vt+rTZDIhOzv7rn22FvEJt3xgHBERkd1IfqhIfHw8YmNjERYWhsGDB2PFihWoqqpCXFwcAGDChAno1KkTkpOTAQDvvfceEhMT8fHHHyMwMFCcl9KhQwd06NABCoUCs2bNwtKlS9G9e3cEBQVhwYIF8Pf3x5gxY5rvnTZBnaUOZ66fAcAJt0RERPYkObCMHTsWV69eRWJiIoxGI0JDQ5Geni5Omi0qKoJS+euJmzVr1qC2thYvvPCCVT9JSUlYuHAhACAhIQFVVVWYPHkyysrKMHToUKSnp9/TPJfm8FP5T6g2V8PV0RUPuD9g11qIiIjuZ5KfwyJHLfUclpIbJdj10y5U11VjWui0ZuuXiIiIpH1+8znzd+Hr4otX+r5i7zKIiIjue/zyQyIiIpI9BhYiIiKSPQYWIiIikj0GFiIiIpI9BhYiIiKSPQYWIiIikj0GFiIiIpI9BhYiIiKSPQYWIiIikj0GFiIiIpI9BhYiIiKSPQYWIiIikj0GFiIiIpK9dvFtzYIgAKj/mmoiIiJqG25/bt/+HL+bdhFYKioqAAABAQF2roSIiIikqqiogFarvWsbhWBLrJE5i8WCy5cvw83NDQqFoln7NplMCAgIwIULF+Du7t6sfZM1jnXr4Vi3Ho516+FYt57mGmtBEFBRUQF/f38olXefpdIuzrAolUp07ty5RY/h7u7O/wO0Eo516+FYtx6OdevhWLee5hjrPzqzchsn3RIREZHsMbAQERGR7DGw/AG1Wo2kpCSo1Wp7l9LucaxbD8e69XCsWw/HuvXYY6zbxaRbIiIiat94hoWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4HlLlavXo3AwEBoNBqEh4cjJyfH3iW1ecnJyRg0aBDc3Nzg6+uLMWPG4MyZM1ZtqqurMX36dHh7e6NDhw54/vnnUVxcbKeK24+UlBQoFArMmjVLXMexbj6XLl3Cyy+/DG9vbzg7O6Nfv3747rvvxO2CICAxMRF+fn5wdnZGZGQkzp49a8eK2yaz2YwFCxYgKCgIzs7O6NatG5YsWWL1XTQc66bbt28fRo8eDX9/fygUCuzcudNquy1je/36dYwbNw7u7u7w8PDAq6++isrKynsvTqAGbdu2TXBychI2bNgg/PDDD8KkSZMEDw8Pobi42N6ltWlRUVHChx9+KJw4cUI4duyY8NRTTwldunQRKisrxTZTpkwRAgICBIPBIHz33XfCn/70J2HIkCF2rLrty8nJEQIDA4X+/fsLb7zxhrieY908rl+/LjzwwAPCxIkThezsbOGnn34SvvrqK+HcuXNim5SUFEGr1Qo7d+4U8vLyhGeeeUYICgoSbt68acfK255ly5YJ3t7ewq5du4SCggLh008/FTp06CCsXLlSbMOxbrrdu3cL8+fPF3bs2CEAED777DOr7baMbXR0tBASEiIcOnRI+M9//iMEBwcLL7300j3XxsDSiMGDBwvTp08XX5vNZsHf319ITk62Y1XtT0lJiQBAyMzMFARBEMrKygRHR0fh008/FducOnVKACBkZWXZq8w2raKiQujevbvw9ddfC4899pgYWDjWzWfOnDnC0KFDG91usVgEvV4v/PWvfxXXlZWVCWq1Wvjkk09ao8R2Y9SoUcIrr7xite65554Txo0bJwgCx7o5/T6w2DK2J0+eFAAIhw8fFtt8+eWXgkKhEC5dunRP9fCSUANqa2uRm5uLyMhIcZ1SqURkZCSysrLsWFn7U15eDgDw8vICAOTm5uLWrVtWY9+zZ0906dKFY99E06dPx6hRo6zGFOBYN6cvvvgCYWFhePHFF+Hr64uHHnoI69atE7cXFBTAaDRajbVWq0V4eDjHWqIhQ4bAYDDgxx9/BADk5eVh//79ePLJJwFwrFuSLWOblZUFDw8PhIWFiW0iIyOhVCqRnZ19T8dvF19+2NxKS0thNpuh0+ms1ut0Opw+fdpOVbU/FosFs2bNwsMPP4y+ffsCAIxGI5ycnODh4WHVVqfTwWg02qHKtm3btm04cuQIDh8+fMc2jnXz+emnn7BmzRrEx8fj7bffxuHDh/H666/DyckJsbGx4ng29N8UjrU0c+fOhclkQs+ePaFSqWA2m7Fs2TKMGzcOADjWLciWsTUajfD19bXa7uDgAC8vr3sefwYWspvp06fjxIkT2L9/v71LaZcuXLiAN954A19//TU0Go29y2nXLBYLwsLC8O677wIAHnroIZw4cQJr165FbGysnatrX/7nf/4HH330ET7++GP06dMHx44dw6xZs+Dv78+xbud4SagBPj4+UKlUd9wtUVxcDL1eb6eq2pcZM2Zg165d2Lt3Lzp37iyu1+v1qK2tRVlZmVV7jr10ubm5KCkpwYABA+Dg4AAHBwdkZmZi1apVcHBwgE6n41g3Ez8/P/Tu3dtqXa9evVBUVAQA4njyvyn3bvbs2Zg7dy5iYmLQr18/jB8/Hv/1X/+F5ORkABzrlmTL2Or1epSUlFhtr6urw/Xr1+95/BlYGuDk5ISBAwfCYDCI6ywWCwwGAyIiIuxYWdsnCAJmzJiBzz77DN9++y2CgoKstg8cOBCOjo5WY3/mzBkUFRVx7CUaMWIEjh8/jmPHjolLWFgYxo0bJ/7OsW4eDz/88B235//444944IEHAABBQUHQ6/VWY20ymZCdnc2xlujGjRtQKq0/ulQqFSwWCwCOdUuyZWwjIiJQVlaG3Nxcsc23334Li8WC8PDweyvgnqbstmPbtm0T1Gq1sHHjRuHkyZPC5MmTBQ8PD8FoNNq7tDZt6tSpglarFTIyMoQrV66Iy40bN8Q2U6ZMEbp06SJ8++23wnfffSdEREQIERERdqy6/fjtXUKCwLFuLjk5OYKDg4OwbNky4ezZs8JHH30kuLi4CFu3bhXbpKSkCB4eHsLnn38ufP/998Kzzz7LW22bIDY2VujUqZN4W/OOHTsEHx8fISEhQWzDsW66iooK4ejRo8LRo0cFAMLy5cuFo0ePCufPnxcEwbaxjY6OFh566CEhOztb2L9/v9C9e3fe1tzS/va3vwldunQRnJychMGDBwuHDh2yd0ltHoAGlw8//FBsc/PmTWHatGmCp6en4OLiIvz5z38Wrly5Yr+i25HfBxaOdfP597//LfTt21dQq9VCz549hX/84x9W2y0Wi7BgwQJBp9MJarVaGDFihHDmzBk7Vdt2mUwm4Y033hC6dOkiaDQaoWvXrsL8+fOFmpoasQ3Huun27t3b4H+jY2NjBUGwbWyvXbsmvPTSS0KHDh0Ed3d3IS4uTqioqLjn2hSC8JvHAxIRERHJEOewEBERkewxsBAREZHsMbAQERGR7DGwEBERkewxsBAREZHsMbAQERGR7DGwEBERkewxsBAREZHsMbAQERGR7DGwEBERkewxsBAREZHsMbAQERGR7P3/FJYFvTBBYkYAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time taken (NumPy): 0.19352197647094727 seconds\n",
            "the 0-th state is [[0.2517 0.554  0.1943]]\n",
            "the 10-th state is [[0.28646357 0.4885367  0.22499973]]\n",
            "the 20-th state is [[0.28650132 0.4885216  0.22497708]]\n",
            "the 30-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 40-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 50-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 60-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 70-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 80-th state is [[0.28650138 0.48852158 0.22497704]]\n",
            "the 90-th state is [[0.28650138 0.48852158 0.22497704]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Fixfj66+/Fre/+OKLKCkpwZdffonc3FwMGDAAI0aMwPXr18U2+fn52LlzJ3bt2oVdu3YhMzMTKSkpAICVK1ciIiICkyZNwpUrV3DlyhUEBARIGt/mJvnLD+9bt29t5uP5iYju7tYN4F3/1j/u25cBJ1ebmlZUVGDlypVIS0tDbGwsAKBbt24YOnQo1q1bh+rqamzevBmurvX9paWlYfTo0XjvvffEL/v18vLCqlWroFQq0aNHD6SmpuLGjRt4++23AfwaiPbv34+YmBjx2DNmzMDzzz8PAFizZg3S09Oxfv16JCQk4IMPPkBAQADS0tKgUCjQs2dPXL58GXPmzEFiYqL45cL9+/dHUlISAKB79+5IS0uDwWDAE088gf379yMnJwclJSXilwi///772LlzJ/71r39h8uTJAOrPMG3cuBFubm4AgPHjx8NgMGDZsmXQarVwcnKCi4sL9Hp90/9MmhEDi614SYiIqN04deoUampqMGLEiAa3hYSEiGEFAB5++GFYLBacOXNGDCx9+vQRAwQA6HQ69O3bV3ytUqng7e2NkpISq/4jIiLE3x0cHBAWFoZTp06Jx46IiIBCobA6dmVlJS5evIguXboAqA8sv+Xn5yceJy8vD5WVlfD29rZqc/PmTeTn54uvAwMDxbDy+z7kiIHFVry1mYjINo4u9Wc77HFcGzk7O9/74RwdrV4rFIoG11kslns+li3Hvn2cyspK+Pn5ISMj4479PDw8bOpDjjiHxVa3b23m4/mJiO5Ooai/NNPay2/OSvyR7t27w9nZGQaD4Y5tvXr1Ql5eHqqqqsR1Bw4cEC/93KtDhw6Jv9fV1SE3Nxe9evUSj52VlQXhN/NxDhw4ADc3N3Tu3Nmm/gcMGACj0QgHBwcEBwdbLT4+PjbX6eTkBLPZbHP7lsbAYivxDAsfz09E1NZpNBrMmTMHCQkJ2Lx5M/Lz83Ho0CGsX78e48aNg0ajQWxsLE6cOIG9e/di5syZGD9+vHg56F6sXr0an332GU6fPo3p06fj559/xiuvvAIAmDZtGi5cuICZM2fi9OnT+Pzzz5GUlIT4+Hiry093ExkZiYiICIwZMwZ79uxBYWEhDh48iPnz5+O7776zuc7AwEBkZ2ejsLAQpaWl4tmXc+fO4dixYzAajbh58yaOHTuGY8eOoba2ZZ9TxktCtro9h6W6HKipANRud29PRESytmDBAjg4OCAxMRGXL1+Gn58fpkyZAhcXF3z11Vd44403MGjQILi4uOD555/H8uXLm+W4KSkpSElJwbFjxxAcHIwvvvhCPPPRqVMn7N69G7Nnz0ZISAi8vLzw6quv4p133rG5f4VCgd27d2P+/PmIi4vD1atXodfr8eijj0oKXG+99RZiY2PRu3dv3Lx5EwUFBQgMDMRrr71mdSv2Qw89BADi9paiEASJ94HJkMlkglarRXl5Odzd3VvuQCld6gPLtGzAt2fLHYeIqI2orq5GQUEBgoKCoNFo7F2OrBUWFiIoKAhHjx5t1SfE2tvd/o5I+fzmJSEpxHksnHhLRETUmhhYpBDnsXDiLRERUWviHBYpxGex8AwLERFJExgYiHYwC8NueIZFituP5+etzURERK2KgUWK24/n563NRERErYqBRQo+np+IiMguGFik0P7mabe8DklERNRqGFikcPMHoADqqoEb1+xdDRER0X2DgUUKByegwy9PCeSdQkRERK2GgUUq3tpMRETU6hhYpBIfHsfAQkRE7dewYcMwa9Ysq3V5eXl46aWXEBAQAGdnZ/Tq1QsrV65slXr44DipOvYC8DlQ+B/gT1PsXQ0REVGryc3Nha+vL7Zu3YqAgAAcPHgQkydPhkqlwowZM1r02DzDIlWv0fU/z35d/63NRETUJlksFqSmpiI4OBhqtRpdunTBsmXLAADHjx/H8OHD4ezsDG9vb0yePBmVlZXivhMnTsSYMWPw7rvvQqfTwcPDA4sXL0ZdXR1mz54NLy8vdO7cGR9++KG4T2FhIRQKBbZt24YhQ4ZAo9Ggb9++Vt98DACZmZkYPHgw1Go1/Pz8MHfuXNTV1Ynbhw0bhtdffx0JCQnw8vKCXq/HwoULrfooKyvDa6+9ho4dO8Ld3R3Dhw9HXl6euH3hwoUIDQ3Fli1bEBgYCK1Wi5iYGFRUVIjvLzMzEytXroRCoYBCoUBhYSFeeeUVrFy5Eo899hi6du2Kl19+GXFxcdixY0ez/bk0hoFFKl0fwLs7YK4BzqTbuxoiItkRBAE3bt1o9UXqY+/nzZuHlJQULFiwACdPnsTHH38MnU6HqqoqREVFwdPTE4cPH8ann36Kb7755o4zCN9++y0uX76Mffv2Yfny5UhKSsLTTz8NT09PZGdnY8qUKfjLX/6CixetpxDMnj0bb775Jo4ePYqIiAiMHj0a167V33l66dIlPPXUUxg0aBDy8vKwZs0arF+/HkuXLrXqY9OmTXB1dUV2djZSU1OxePFifP311+L2F198ESUlJfjyyy+Rm5uLAQMGYMSIEbh+/brYJj8/Hzt37sSuXbuwa9cuZGZmIiUlBQCwcuVKREREYNKkSbhy5QquXLmCgICABsexvLwcXl5eksa+KRRCO/hiAylfT90svl0K7Psr0PNpIOajlj8eEZFMVVdXo6CgAEFBQdBoNACAG7duIPzj8FavJfv/ZcPF0cWmthUVFejYsSPS0tLw2muvWW1bt24d5syZgwsXLsDV1RUAsHv3bowePRqXL1+GTqfDxIkTkZGRgZ9++glKZf2//Xv27AlfX1/s27cPAGA2m6HVavHPf/4TMTExKCwsRFBQEFJSUjBnzhwAQF1dHYKCgjBz5kwkJCRg/vz5+N///V+cOnUKCoUCAPDBBx9gzpw5KC8vh1KpxLBhw2A2m/Gf//xHrHnw4MEYPnw4UlJSsH//fowaNQolJSVQq9Vim+DgYCQkJGDy5MlYuHAh/vrXv8JoNMLNzQ0AkJCQgH379uHQoUMA6s/khIaGYsWKFY2O48GDB/HYY4/h//7v/zBy5MgG2zT0d+Q2KZ/fPMPSFH3+XP/z7NdAtcm+tRARkWSnTp1CTU0NRowY0eC2kJAQMawAwMMPPwyLxYIzZ86I6/r06SOGFQDQ6XTo16+f+FqlUsHb2xslJSVW/UdERIi/Ozg4ICwsDKdOnRKPHRERIYaV28eurKy0OlPTv39/qz79/PzE4+Tl5aGyshLe3t7o0KGDuBQUFCA/P1/cJzAwUAwrv+/DFidOnMCzzz6LpKSkRsNKc+Kk26bw7V1/WejaWeDHr4D+L9q7IiIi2XB2cEb2/8u2y3Ftbutse9vGODo6Wr1WKBQNrrNYLPd8LFuOffs4lZWV8PPzQ0ZGxh37eXh42NTHHzl58iRGjBiByZMn45133pFWfBPxDEtTKBS/nmX54TP71kJEJDMKhQIuji6tvvz2rMQf6d69O5ydnWEwGO7Y1qtXL+Tl5aGqqkpcd+DAASiVSvTo0eOex+f2JReg/pJQbm4uevXqJR47KyvLaj7OgQMH4Obmhs6dO9vU/4ABA2A0GuHg4IDg4GCrxcfHx+Y6nZycYDab71j/ww8/4PHHH0dsbKw4Sbk1NCmwrF69GoGBgdBoNAgPD0dOTk6jbTdu3CjOML69/P4aliAISExMhJ+fH5ydnREZGYmzZ882pbTW02dM/c9z3/CyEBFRG6PRaDBnzhwkJCRg8+bNyM/Px6FDh7B+/XqMGzcOGo0GsbGxOHHiBPbu3YuZM2di/Pjx0Ol093zs1atX47PPPsPp06cxffp0/Pzzz3jllVcAANOmTcOFCxcwc+ZMnD59Gp9//jmSkpIQHx9vdfnpbiIjIxEREYExY8Zgz549KCwsxMGDBzF//nx89913NtcZGBiI7OxsFBYWorS0FBaLBSdOnMDjjz+OkSNHIj4+HkajEUajEVevXm3SWEghObBs374d8fHxSEpKwpEjRxASEoKoqKi7Xvdyd3cXZxlfuXIF58+ft9qempqKVatWYe3atcjOzoarqyuioqJQXV0t/R21Ft/egM+D9XcL/ci7hYiI2poFCxbgzTffRGJiInr16oWxY8eipKQELi4u+Oqrr3D9+nUMGjQIL7zwAkaMGIG0tLRmOW5KSgpSUlIQEhKC/fv344svvhDPfHTq1Am7d+9GTk4OQkJCMGXKFLz66quSLrsoFArs3r0bjz76KOLi4vDggw8iJiYG58+flxS43nrrLahUKvTu3RsdO3ZEUVER/vWvf+Hq1avYunUr/Pz8xGXQoEGSx0EyQaLBgwcL06dPF1+bzWbB399fSE5ObrD9hx9+KGi12kb7s1gsgl6vF/7617+K68rKygS1Wi188sknNtVUXl4uABDKy8ttexPNxbBUEJLcBeHjl1r3uEREMnHz5k3h5MmTws2bN+1diuwVFBQIAISjR4/au5RWdbe/I1I+vyWdYamtrUVubi4iIyPFdUqlEpGRkcjKymp0v8rKSjzwwAMICAjAs88+ix9++EHcVlBQAKPRaNWnVqtFeHh4o33W1NTAZDJZLXbBy0JEREStQlJgKS0thdlsvuOUkk6ng9FobHCfHj16YMOGDfj888+xdetWWCwWDBkyRLw96/Z+UvpMTk6GVqsVl8YeZtPieFmIiIioVbT4XUIRERGYMGECQkND8dhjj2HHjh3o2LEj/v73vze5z3nz5qG8vFxcLly40IwVS6BQAL3H1P/Ou4WIiOguAgMDIQgCQkND7V1KmyQpsPj4+EClUqG4uNhqfXFxMfR6vU19ODo64qGHHsK5c+cAQNxPSp9qtRru7u5Wi9389iFyBfvsVwcREVE7JimwODk5YeDAgVb3rVssFhgMBqsn992N2WzG8ePH4efnBwAICgqCXq+36tNkMiE7O9vmPu3KtxfQ+1nAcgv45CXgUq69KyIiImp3JF8Sio+Px7p167Bp0yacOnUKU6dORVVVFeLi4gAAEyZMwLx588T2ixcvxp49e/DTTz/hyJEjePnll3H+/HnxuxsUCgVmzZqFpUuX4osvvsDx48cxYcIE+Pv7Y8yYMc3zLluSQgH8+R9A0KNAbSWw9Xmg5JS9qyIialVC2/9aOmohzfV3Q/Kj+ceOHYurV68iMTERRqMRoaGhSE9PFyfNFhUVWT3c5ueff8akSZNgNBrh6emJgQMH4uDBg+jdu7fYJiEhAVVVVZg8eTLKysowdOhQpKen3/GAOdly1AAxHwObxwCXvqv/+Uo64BVk78qIiFrU7ce737hxo1ked0/tT21tLYD671a6F/y25uZ04zqwcRRQchLweAB4aRug6/3H+xERtWFXrlxBWVkZfH194eIi7RH51L5ZLBZcvnwZjo6O6NKlyx1/N6R8fvPLD5uTixcw/jNgQzTwcwGwJgII+BMwcGL9PBcn2772nIioLbl9g4SUb/ql+4dSqWwwrEjFMywtoawISJ8HnPkSEH754ii1Fuj19K/PbvEJrj8Lo7y3U2RERHJhNptx69Yte5dBMuPk5NTo9yBJ+fxmYGlJpivAsY+AI5vqQ8zvqZwAFx/A2QPQaAGNB6B2AxycAJUacNDU/650qF8UKkCprP+pUP5uuZ1cFb/5/faq32z7vSYnXp7yJSK6r2jcgb7PN2uXDCxyY7EABRnA+YNA6dn65dq5+ifkEhERtQXe3YGZtn/bsy04h0VulEqg2/D65TaLGSi/CNy8DtwsA6rLgeoyoKayPsjU/bKYawFL3S+L+ZelDoAACAIgWOoX4Nd1t38H7nz9W20/qxIRUWtx87Pr4RlY7EWpAjwfqF+IiIjorlr8u4SIiIiI7hUDCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREckeAwsRERHJHgMLERERyR4DCxEREclekwLL6tWrERgYCI1Gg/DwcOTk5Ni037Zt26BQKDBmzBir9RMnToRCobBaoqOjm1IaERERtUOSA8v27dsRHx+PpKQkHDlyBCEhIYiKikJJScld9yssLMRbb72FRx55pMHt0dHRuHLlirh88sknUksjIiKidkpyYFm+fDkmTZqEuLg49O7dG2vXroWLiws2bNjQ6D5msxnjxo3DokWL0LVr1wbbqNVq6PV6cfH09JRaGhEREbVTkgJLbW0tcnNzERkZ+WsHSiUiIyORlZXV6H6LFy+Gr68vXn311UbbZGRkwNfXFz169MDUqVNx7do1KaURERFRO+YgpXFpaSnMZjN0Op3Vep1Oh9OnTze4z/79+7F+/XocO3as0X6jo6Px3HPPISgoCPn5+Xj77bfx5JNPIisrCyqV6o72NTU1qKmpEV+bTCYpb4OIiIjaGEmBRaqKigqMHz8e69atg4+PT6PtYmJixN/79euH/v37o1u3bsjIyMCIESPuaJ+cnIxFixa1SM1EREQkP5IuCfn4+EClUqG4uNhqfXFxMfR6/R3t8/PzUVhYiNGjR8PBwQEODg7YvHkzvvjiCzg4OCA/P7/B43Tt2hU+Pj44d+5cg9vnzZuH8vJycblw4YKUt0FERERtjKQzLE5OThg4cCAMBoN4a7LFYoHBYMCMGTPuaN+zZ08cP37cat0777yDiooKrFy5EgEBAQ0e5+LFi7h27Rr8/Pwa3K5Wq6FWq6WUTkRERG2Y5EtC8fHxiI2NRVhYGAYPHowVK1agqqoKcXFxAIAJEyagU6dOSE5OhkajQd++fa329/DwAABxfWVlJRYtWoTnn38eer0e+fn5SEhIQHBwMKKiou7x7REREVF7IDmwjB07FlevXkViYiKMRiNCQ0ORnp4uTsQtKiqCUmn7lSaVSoXvv/8emzZtQllZGfz9/TFy5EgsWbKEZ1GIiIgIAKAQBEGwdxH3ymQyQavVory8HO7u7vYuh4iIiGwg5fOb3yVEREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESy16TAsnr1agQGBkKj0SA8PBw5OTk27bdt2zYoFAqMGTPGar0gCEhMTISfnx+cnZ0RGRmJs2fPNqU0IiIiaockB5bt27cjPj4eSUlJOHLkCEJCQhAVFYWSkpK77ldYWIi33noLjzzyyB3bUlNTsWrVKqxduxbZ2dlwdXVFVFQUqqurpZZHRERE7ZDkwLJ8+XJMmjQJcXFx6N27N9auXQsXFxds2LCh0X3MZjPGjRuHRYsWoWvXrlbbBEHAihUr8M477+DZZ59F//79sXnzZly+fBk7d+6U/IaIiIio/ZEUWGpra5Gbm4vIyMhfO1AqERkZiaysrEb3W7x4MXx9ffHqq6/esa2goABGo9GqT61Wi/Dw8Eb7rKmpgclkslqIiIio/ZIUWEpLS2E2m6HT6azW63Q6GI3GBvfZv38/1q9fj3Xr1jW4/fZ+UvpMTk6GVqsVl4CAAClvg4iIiNqYFr1LqKKiAuPHj8e6devg4+PTbP3OmzcP5eXl4nLhwoVm65uIiIjkx0FKYx8fH6hUKhQXF1utLy4uhl6vv6N9fn4+CgsLMXr0aHGdxWKpP7CDA86cOSPuV1xcDD8/P6s+Q0NDG6xDrVZDrVZLKZ2IiIjaMElnWJycnDBw4EAYDAZxncVigcFgQERExB3te/bsiePHj+PYsWPi8swzz+Dxxx/HsWPHEBAQgKCgIOj1eqs+TSYTsrOzG+yTiIiI7j+SzrAAQHx8PGJjYxEWFobBgwdjxYoVqKqqQlxcHABgwoQJ6NSpE5KTk6HRaNC3b1+r/T08PADAav2sWbOwdOlSdO/eHUFBQViwYAH8/f3veF4LERER3Z8kB5axY8fi6tWrSExMhNFoRGhoKNLT08VJs0VFRVAqpU2NSUhIQFVVFSZPnoyysjIMHToU6enp0Gg0UssjIiKidkghCIJg7yLulclkglarRXl5Odzd3e1dDhEREdlAyuc3v0uIiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkr0mBZfXq1QgMDIRGo0F4eDhycnIabbtjxw6EhYXBw8MDrq6uCA0NxZYtW6zaTJw4EQqFwmqJjo5uSmlERETUDjlI3WH79u2Ij4/H2rVrER4ejhUrViAqKgpnzpyBr6/vHe29vLwwf/589OzZE05OTti1axfi4uLg6+uLqKgosV10dDQ+/PBD8bVarW7iWyIiIqL2RiEIgiBlh/DwcAwaNAhpaWkAAIvFgoCAAMycORNz5861qY8BAwZg1KhRWLJkCYD6MyxlZWXYuXOntOp/YTKZoNVqUV5eDnd39yb1QURERK1Lyue3pEtCtbW1yM3NRWRk5K8dKJWIjIxEVlbWH+4vCAIMBgPOnDmDRx991GpbRkYGfH190aNHD0ydOhXXrl1rtJ+amhqYTCarhYiIiNovSZeESktLYTabodPprNbrdDqcPn260f3Ky8vRqVMn1NTUQKVS4YMPPsATTzwhbo+OjsZzzz2HoKAg5Ofn4+2338aTTz6JrKwsqFSqO/pLTk7GokWLpJROREREbZjkOSxN4ebmhmPHjqGyshIGgwHx8fHo2rUrhg0bBgCIiYkR2/br1w/9+/dHt27dkJGRgREjRtzR37x58xAfHy++NplMCAgIaPH3QURERPYhKbD4+PhApVKhuLjYan1xcTH0en2j+ymVSgQHBwMAQkNDcerUKSQnJ4uB5fe6du0KHx8fnDt3rsHAolarOSmXiIjoPiJpDouTkxMGDhwIg8EgrrNYLDAYDIiIiLC5H4vFgpqamka3X7x4EdeuXYOfn5+U8oiIiKidknxJKD4+HrGxsQgLC8PgwYOxYsUKVFVVIS4uDgAwYcIEdOrUCcnJyQDq55uEhYWhW7duqKmpwe7du7FlyxasWbMGAFBZWYlFixbh+eefh16vR35+PhISEhAcHGx12zMRERHdvyQHlrFjx+Lq1atITEyE0WhEaGgo0tPTxYm4RUVFUCp/PXFTVVWFadOm4eLFi3B2dkbPnj2xdetWjB07FgCgUqnw/fffY9OmTSgrK4O/vz9GjhyJJUuW8LIPERERAWjCc1jkiM9hISIianta7DksRERERPbAwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREssfAQkRERLLHwEJERESyx8BCREREstekwLJ69WoEBgZCo9EgPDwcOTk5jbbdsWMHwsLC4OHhAVdXV4SGhmLLli1WbQRBQGJiIvz8/ODs7IzIyEicPXu2KaURERFROyQ5sGzfvh3x8fFISkrCkSNHEBISgqioKJSUlDTY3svLC/Pnz0dWVha+//57xMXFIS4uDl999ZXYJjU1FatWrcLatWuRnZ0NV1dXREVFobq6uunvjIiIiNoNhSAIgpQdwsPDMWjQIKSlpQEALBYLAgICMHPmTMydO9emPgYMGIBRo0ZhyZIlEAQB/v7+ePPNN/HWW28BAMrLy6HT6bBx40bExMT8YX8mkwlarRbl5eVwd3eX8naIiIjITqR8fks6w1JbW4vc3FxERkb+2oFSicjISGRlZf3h/oIgwGAw4MyZM3j00UcBAAUFBTAajVZ9arVahIeHN9pnTU0NTCaT1UJERETtl6TAUlpaCrPZDJ1OZ7Vep9PBaDQ2ul95eTk6dOgAJycnjBo1Cn/729/wxBNPAIC4n5Q+k5OTodVqxSUgIEDK2yAiIqI2plXuEnJzc8OxY8dw+PBhLFu2DPHx8cjIyGhyf/PmzUN5ebm4XLhwofmKJSIiItlxkNLYx8cHKpUKxcXFVuuLi4uh1+sb3U+pVCI4OBgAEBoailOnTiE5ORnDhg0T9ysuLoafn59Vn6GhoQ32p1aroVarpZROREREbZikMyxOTk4YOHAgDAaDuM5iscBgMCAiIsLmfiwWC2pqagAAQUFB0Ov1Vn2aTCZkZ2dL6pOIiIjaL0lnWAAgPj4esbGxCAsLw+DBg7FixQpUVVUhLi4OADBhwgR06tQJycnJAOrnm4SFhaFbt26oqanB7t27sWXLFqxZswYAoFAoMGvWLCxduhTdu3dHUFAQFixYAH9/f4wZM6b53ikRERG1WZIDy9ixY3H16lUkJibCaDQiNDQU6enp4qTZoqIiKJW/nripqqrCtGnTcPHiRTg7O6Nnz57YunUrxo4dK7ZJSEhAVVUVJk+ejLKyMgwdOhTp6enQaDTN8BaJiIiorZP8HBY54nNYiIiI2p4Wew4LERERkT0wsBAREZHsMbAQERGR7DGwEBERkexJvkuIWkZNnRklphpcq6pFZXUdKmtuobLGjKqaOlTfMqO2zoJas0X8abYI1osgQBAAiyDA8stPCICA+vW/nVotoP5FQ9OtbZmB3fanaRMRkVR6rRpLx/Sz2/EZWFqRIAgoNtXg+4tlOH6pHD9cNuFy2U0Um6rx841b9i6PiIioUV07utr1+AwsLUwQBOSe/xkfZxfhP+dKcbWiptG2Tg5KdOygRge1AzpoHOCqdkAHtQoaRxXUDko4qZRwclDCUaWEg1IBlVIJlRJQKhVQKRRQKhRQKCD+VKD+wXy//f22278qoLijDsWdq4iI6D7nprFvZGBgaSGm6lvYefQSPjpUhDPFFeJ6pQJ4UOeGfp206N9Ziy7ertC7a6BzV0Pr7GgVKoiIiKgeA0sL2H64CIv+fRI3as0AAI2jEqP7++P5gZ0R0tkDzk4qO1dIRETUtjCwNKM6swXv7j6NDQcKAADBvh0wLrwLnnuoM7QujnaujoiIqO1iYGkm5TdvYeYnR7Hvx6sAgP+KfBCvjwjmJR4iIqJmwMDSDApKq/DqpsP46WoVnB1VWP7/heDJfn72LouIiKjdYGC5R2U3avHi2iyUVtbAX6vBPyaEoW8nrb3LIiIialcYWO7Rim/OorSyBt06uuKTyX+Cr5vG3iURERG1O3w0/z04W1yBLYfOAwCWPNuXYYWIiKiFMLA0kSAIWLzrJMwWAVF9dBgS7GPvkoiIiNotBpYmMpwqwX/OlsJJpcT8p3rbuxwiIqJ2jYGlCWrqzFj6fycBAK89EoQu3i52roiIiKh9Y2Bpgo0HClF47QZ83dSY9niwvcshIiJq9xhYJCqpqMbfvj0HAJgT3RMd1LzRioiIqKUxsEi0bt9PqKypQ0iAB/78UCd7l0NERHRfYGCRKONM/aP3//JoVyiVfOw+ERFRa2BgkaDYVI2zJZVQKICHu/E2ZiIiotbCwCLB/rOlAID+nbT89mUiIqJWxMAiwYFz9YHlYT4kjoiIqFUxsNhIEATs/yWwDGVgISIialUMLDY6V1KJkooaqB2UGPCAp73LISIiuq8wsNjo9tmVwUFe0Diq7FwNERHR/YWBxUacv0JERGQ/DCw2uGW24NBP1wFw/goREZE9MLDYIO9CGSpr6uDp4ojefu72LoeIiOi+w8Big9vzV4YE+/DptkRERHbAwGKDA7ydmYiIyK4YWP5AZU0djhaVAWBgISIishcGlj+QU3ANdRYBXbxcEODlYu9yiIiI7ktNCiyrV69GYGAgNBoNwsPDkZOT02jbdevW4ZFHHoGnpyc8PT0RGRl5R/uJEydCoVBYLdHR0U0prdntP3sNAG9nJiIisifJgWX79u2Ij49HUlISjhw5gpCQEERFRaGkpKTB9hkZGXjppZewd+9eZGVlISAgACNHjsSlS5es2kVHR+PKlSvi8sknnzTtHTWz/eeuAuDlICIiInuSHFiWL1+OSZMmIS4uDr1798batWvh4uKCDRs2NNj+o48+wrRp0xAaGoqePXvin//8JywWCwwGg1U7tVoNvV4vLp6e9n/8fYmpGj8WV0KhACK6edu7HCIiovuWpMBSW1uL3NxcREZG/tqBUonIyEhkZWXZ1MeNGzdw69YteHl5Wa3PyMiAr68vevTogalTp+LatWuN9lFTUwOTyWS1tASjqRrdfTugj787vFydWuQYRERE9MccpDQuLS2F2WyGTqezWq/T6XD69Gmb+pgzZw78/f2tQk90dDSee+45BAUFIT8/H2+//TaefPJJZGVlQaW683t7kpOTsWjRIimlN0n/zh74Ov4x3Kw1t/ixiIiIqHGSAsu9SklJwbZt25CRkQGNRiOuj4mJEX/v168f+vfvj27duiEjIwMjRoy4o5958+YhPj5efG0ymRAQENBidTs78csOiYiI7EnSJSEfHx+oVCoUFxdbrS8uLoZer7/rvu+//z5SUlKwZ88e9O/f/65tu3btCh8fH5w7d67B7Wq1Gu7u7lYLERERtV+SAouTkxMGDhxoNWH29gTaiIiIRvdLTU3FkiVLkJ6ejrCwsD88zsWLF3Ht2jX4+flJKY+IiIjaKcl3CcXHx2PdunXYtGkTTp06halTp6KqqgpxcXEAgAkTJmDevHli+/feew8LFizAhg0bEBgYCKPRCKPRiMrKSgBAZWUlZs+ejUOHDqGwsBAGgwHPPvssgoODERUV1Uxvk4iIiNoyyXNYxo4di6tXryIxMRFGoxGhoaFIT08XJ+IWFRVBqfw1B61Zswa1tbV44YUXrPpJSkrCwoULoVKp8P3332PTpk0oKyuDv78/Ro4ciSVLlkCtVt/j2yMiIqL2QCEIgmDvIu6VyWSCVqtFeXk557MQERG1EVI+v/ldQkRERCR7DCxEREQkewwsREREJHsMLERERCR7DCxEREQkewwsREREJHsMLERERCR7DCxEREQkewwsREREJHsMLERERCR7DCxEREQkewwsREREJHsMLERERCR7DCxEREQkewwsREREJHsO9i6gvbhluYXT107jSMkR5Bbn4uS1kzALZiihhEKhgEqhgqPKES4OLnB2cIaroytcHF2gUWmgcdDA2cEZGgcN1Co1HJWOcFI5wVHpCEelIxyUDlApVFApVVAqlFAp6n8qFUqxf4VCAfF/CgUANPr7bylw5zpbNNQXERG1X2qVGj29etrt+Aws96jOUoelh5Zid8Fu3Ky7ae9yiIiIWkSgeyD+/ed/2+34DCz3aEXuCvzv2f8FALg7uWOA7wAM0A1AqG8oXBxcYBEs4lJjrsHNupu4UXcDN27dwI26G6iuq0a1uRo3b91Etbka1XXVuGW59etivgWzYK5fLGbUCXUwW8wQIEAQBFgEC8yCGQAgCALE/wmCVZ0Cfn19e9tv1zXm9/0QEdH9Se+qt+vxGVjuQXpBOjad3AQASH4kGU8FPQWlgtOCiIiImhsDSxP9+POPSDyYCAB4te+reLrr03auiIiIqP3i6YAmMNWaMGvvLNysu4k/+f0JMx+aae+SiIiI2jUGFoksggXz/jMPFyouwN/VH6mPpkKlVNm7LCIionaNgUWibae3Yd/FfVCr1Pjvx/8bnhpPe5dERETU7jGwSJR5MRMAMDVkKnp797ZzNURERPcHBhYJBEHAD9d+AAD8ye9Pdq6GiIjo/sHAIsGlyksorymHg9IB3T2727scIiKi+wYDiwQnr50EADzo+SCcVE52roaIiOj+wcAiwe3LQX28+9i5EiIiovsLA4sEDCxERET2wcBiI0EQcLK0/pIQ7w4iIiJqXQwsNrpQcQEVtyrgpHRCsEewvcshIiK6rzCw2Oj25aAeXj3gqHK0czVERET3FwYWG92+Q4iXg4iIiFofA4uNOOGWiIjIfhhYbGARLOIZlj4+DCxEREStjYHFBudN51F1qwoalQZdtV3tXQ4REdF9p0mBZfXq1QgMDIRGo0F4eDhycnIabbtu3To88sgj8PT0hKenJyIjI+9oLwgCEhMT4efnB2dnZ0RGRuLs2bNNKa1F/HbCrYPSwc7VEBER3X8kB5bt27cjPj4eSUlJOHLkCEJCQhAVFYWSkpIG22dkZOCll17C3r17kZWVhYCAAIwcORKXLl0S26SmpmLVqlVYu3YtsrOz4erqiqioKFRXVzf9nTWjH0o5f4WIiMieFIIgCFJ2CA8Px6BBg5CWlgYAsFgsCAgIwMyZMzF37tw/3N9sNsPT0xNpaWmYMGECBEGAv78/3nzzTbz11lsAgPLycuh0OmzcuBExMTF/2KfJZIJWq0V5eTnc3d2lvB2bxH4ZiyMlR7Bs6DI80+2ZZu+fiIjofiTl81vSGZba2lrk5uYiMjLy1w6USkRGRiIrK8umPm7cuIFbt27By8sLAFBQUACj0WjVp1arRXh4eKN91tTUwGQyWS0txWwx49T1UwB4hoWIiMheJAWW0tJSmM1m6HQ6q/U6nQ5Go9GmPubMmQN/f38xoNzeT0qfycnJ0Gq14hIQECDlbUhSaCrEzbqbcHZwRqB7YIsdh4iIiBrXqncJpaSkYNu2bfjss8+g0Wia3M+8efNQXl4uLhcuXGjGKq3dnnDby6sXVEpVix2HiIiIGifplhcfHx+oVCoUFxdbrS8uLoZer7/rvu+//z5SUlLwzTffoH///uL62/sVFxfDz8/Pqs/Q0NAG+1Kr1VCr1VJKb7LbE275hFsiIiL7kXSGxcnJCQMHDoTBYBDXWSwWGAwGRERENLpfamoqlixZgvT0dISFhVltCwoKgl6vt+rTZDIhOzv7rn22FvEJt3xgHBERkd1IfqhIfHw8YmNjERYWhsGDB2PFihWoqqpCXFwcAGDChAno1KkTkpOTAQDvvfceEhMT8fHHHyMwMFCcl9KhQwd06NABCoUCs2bNwtKlS9G9e3cEBQVhwYIF8Pf3x5gxY5rvnTZBnaUOZ66fAcAJt0RERPYkObCMHTsWV69eRWJiIoxGI0JDQ5Geni5Omi0qKoJS+euJmzVr1qC2thYvvPCCVT9JSUlYuHAhACAhIQFVVVWYPHkyysrKMHToUKSnp9/TPJfm8FP5T6g2V8PV0RUPuD9g11qIiIjuZ5KfwyJHLfUclpIbJdj10y5U11VjWui0ZuuXiIiIpH1+8znzd+Hr4otX+r5i7zKIiIjue/zyQyIiIpI9BhYiIiKSPQYWIiIikj0GFiIiIpI9BhYiIiKSPQYWIiIikj0GFiIiIpI9BhYiIiKSPQYWIiIikj0GFiIiIpI9BhYiIiKSPQYWIiIikj0GFiIiIpK9dvFtzYIgAKj/mmoiIiJqG25/bt/+HL+bdhFYKioqAAABAQF2roSIiIikqqiogFarvWsbhWBLrJE5i8WCy5cvw83NDQqFoln7NplMCAgIwIULF+Du7t6sfZM1jnXr4Vi3Ho516+FYt57mGmtBEFBRUQF/f38olXefpdIuzrAolUp07ty5RY/h7u7O/wO0Eo516+FYtx6OdevhWLee5hjrPzqzchsn3RIREZHsMbAQERGR7DGw/AG1Wo2kpCSo1Wp7l9LucaxbD8e69XCsWw/HuvXYY6zbxaRbIiIiat94hoWIiIhkj4GFiIiIZI+BhYiIiGSPgYWIiIhkj4HlLlavXo3AwEBoNBqEh4cjJyfH3iW1ecnJyRg0aBDc3Nzg6+uLMWPG4MyZM1ZtqqurMX36dHh7e6NDhw54/vnnUVxcbKeK24+UlBQoFArMmjVLXMexbj6XLl3Cyy+/DG9vbzg7O6Nfv3747rvvxO2CICAxMRF+fn5wdnZGZGQkzp49a8eK2yaz2YwFCxYgKCgIzs7O6NatG5YsWWL1XTQc66bbt28fRo8eDX9/fygUCuzcudNquy1je/36dYwbNw7u7u7w8PDAq6++isrKynsvTqAGbdu2TXBychI2bNgg/PDDD8KkSZMEDw8Pobi42N6ltWlRUVHChx9+KJw4cUI4duyY8NRTTwldunQRKisrxTZTpkwRAgICBIPBIHz33XfCn/70J2HIkCF2rLrty8nJEQIDA4X+/fsLb7zxhrieY908rl+/LjzwwAPCxIkThezsbOGnn34SvvrqK+HcuXNim5SUFEGr1Qo7d+4U8vLyhGeeeUYICgoSbt68acfK255ly5YJ3t7ewq5du4SCggLh008/FTp06CCsXLlSbMOxbrrdu3cL8+fPF3bs2CEAED777DOr7baMbXR0tBASEiIcOnRI+M9//iMEBwcLL7300j3XxsDSiMGDBwvTp08XX5vNZsHf319ITk62Y1XtT0lJiQBAyMzMFARBEMrKygRHR0fh008/FducOnVKACBkZWXZq8w2raKiQujevbvw9ddfC4899pgYWDjWzWfOnDnC0KFDG91usVgEvV4v/PWvfxXXlZWVCWq1Wvjkk09ao8R2Y9SoUcIrr7xite65554Txo0bJwgCx7o5/T6w2DK2J0+eFAAIhw8fFtt8+eWXgkKhEC5dunRP9fCSUANqa2uRm5uLyMhIcZ1SqURkZCSysrLsWFn7U15eDgDw8vICAOTm5uLWrVtWY9+zZ0906dKFY99E06dPx6hRo6zGFOBYN6cvvvgCYWFhePHFF+Hr64uHHnoI69atE7cXFBTAaDRajbVWq0V4eDjHWqIhQ4bAYDDgxx9/BADk5eVh//79ePLJJwFwrFuSLWOblZUFDw8PhIWFiW0iIyOhVCqRnZ19T8dvF19+2NxKS0thNpuh0+ms1ut0Opw+fdpOVbU/FosFs2bNwsMPP4y+ffsCAIxGI5ycnODh4WHVVqfTwWg02qHKtm3btm04cuQIDh8+fMc2jnXz+emnn7BmzRrEx8fj7bffxuHDh/H666/DyckJsbGx4ng29N8UjrU0c+fOhclkQs+ePaFSqWA2m7Fs2TKMGzcOADjWLciWsTUajfD19bXa7uDgAC8vr3sefwYWspvp06fjxIkT2L9/v71LaZcuXLiAN954A19//TU0Go29y2nXLBYLwsLC8O677wIAHnroIZw4cQJr165FbGysnatrX/7nf/4HH330ET7++GP06dMHx44dw6xZs+Dv78+xbud4SagBPj4+UKlUd9wtUVxcDL1eb6eq2pcZM2Zg165d2Lt3Lzp37iyu1+v1qK2tRVlZmVV7jr10ubm5KCkpwYABA+Dg4AAHBwdkZmZi1apVcHBwgE6n41g3Ez8/P/Tu3dtqXa9evVBUVAQA4njyvyn3bvbs2Zg7dy5iYmLQr18/jB8/Hv/1X/+F5ORkABzrlmTL2Or1epSUlFhtr6urw/Xr1+95/BlYGuDk5ISBAwfCYDCI6ywWCwwGAyIiIuxYWdsnCAJmzJiBzz77DN9++y2CgoKstg8cOBCOjo5WY3/mzBkUFRVx7CUaMWIEjh8/jmPHjolLWFgYxo0bJ/7OsW4eDz/88B235//444944IEHAABBQUHQ6/VWY20ymZCdnc2xlujGjRtQKq0/ulQqFSwWCwCOdUuyZWwjIiJQVlaG3Nxcsc23334Li8WC8PDweyvgnqbstmPbtm0T1Gq1sHHjRuHkyZPC5MmTBQ8PD8FoNNq7tDZt6tSpglarFTIyMoQrV66Iy40bN8Q2U6ZMEbp06SJ8++23wnfffSdEREQIERERdqy6/fjtXUKCwLFuLjk5OYKDg4OwbNky4ezZs8JHH30kuLi4CFu3bhXbpKSkCB4eHsLnn38ufP/998Kzzz7LW22bIDY2VujUqZN4W/OOHTsEHx8fISEhQWzDsW66iooK4ejRo8LRo0cFAMLy5cuFo0ePCufPnxcEwbaxjY6OFh566CEhOztb2L9/v9C9e3fe1tzS/va3vwldunQRnJychMGDBwuHDh2yd0ltHoAGlw8//FBsc/PmTWHatGmCp6en4OLiIvz5z38Wrly5Yr+i25HfBxaOdfP597//LfTt21dQq9VCz549hX/84x9W2y0Wi7BgwQJBp9MJarVaGDFihHDmzBk7Vdt2mUwm4Y033hC6dOkiaDQaoWvXrsL8+fOFmpoasQ3Huun27t3b4H+jY2NjBUGwbWyvXbsmvPTSS0KHDh0Ed3d3IS4uTqioqLjn2hSC8JvHAxIRERHJEOewEBERkewxsBAREZHsMbAQERGR7DGwEBERkewxsBAREZHsMbAQERGR7DGwEBERkewxsBAREZHsMbAQERGR7DGwEBERkewxsBAREZHsMbAQERGR7P3/FJYFvTBBYkYAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time taken (Cupy): 0.2075977325439453 seconds\n",
            "the steady state is [[0.28650138 0.48852158 0.22497704]]\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import cupy as cp\n",
        "import matplotlib.pyplot as plt\n",
        "import time\n",
        "\n",
        "def state_transform(transform_matrix, initial_state, steps_transform=1000, adaptive_flag=False, cp_flag=False):\n",
        "    if cp_flag:\n",
        "        initial_state = cp.array(initial_state.reshape(1, -1))\n",
        "        transform_matrix = cp.array(transform_matrix.reshape(initial_state.shape[1], initial_state.shape[1]))\n",
        "        history = cp.zeros(shape=[steps_transform, initial_state.shape[1]], dtype=cp.float32)\n",
        "    else:\n",
        "        initial_state = np.array(initial_state.reshape(1, -1))\n",
        "        transform_matrix = np.array(transform_matrix.reshape(initial_state.shape[1], initial_state.shape[1]))\n",
        "        history = np.zeros(shape=[steps_transform, initial_state.shape[1]], dtype=np.float32)\n",
        "\n",
        "    if adaptive_flag is False:\n",
        "        final_state = initial_state\n",
        "        for i in range(steps_transform):\n",
        "            if cp_flag:\n",
        "                final_state = cp.dot(final_state, transform_matrix)\n",
        "            else:\n",
        "                final_state = np.dot(final_state, transform_matrix)\n",
        "\n",
        "            history[i, :] = final_state.squeeze()\n",
        "\n",
        "            if i % 10 == 0:\n",
        "                print(f'the {i}-th state is {final_state}')\n",
        "        if cp_flag:\n",
        "          plt.figure()\n",
        "          for dim in range(initial_state.shape[1]):\n",
        "            plt.plot([i for i in range(steps_transform)], history[:, dim].get(), label=f'component{dim}')\n",
        "          plt.legend()\n",
        "          plt.show()\n",
        "\n",
        "        else:\n",
        "          plt.figure()\n",
        "          for dim in range(initial_state.shape[1]):\n",
        "            plt.plot([i for i in range(steps_transform)], history[:, dim], label=f'component{dim}')\n",
        "          plt.legend()\n",
        "          plt.show()\n",
        "\n",
        "\n",
        "    else:\n",
        "      final_state = initial_state\n",
        "      state_last = None\n",
        "      while state_last is None or not (cp.array_equal(final_state, state_last) if cp_flag else np.array_equal(final_state, state_last)):\n",
        "        state_last = cp.copy(final_state) if cp_flag else np.copy(final_state)\n",
        "        if cp_flag:\n",
        "            final_state = cp.dot(final_state, transform_matrix)\n",
        "        else:\n",
        "            final_state = np.dot(final_state, transform_matrix)\n",
        "\n",
        "      print(f'the steady state is {final_state}')\n",
        "\n",
        "    return final_state\n",
        "\n",
        "if __name__ == '__main__':\n",
        "    # Numpy\n",
        "    P = np.array([[0.65, 0.28, 0.07],[0.15, 0.67, 0.18],[0.12, 0.36, 0.52]]).reshape(3, 3)\n",
        "    print(f'Transform matrix:\\n {P}')\n",
        "    initial = np.array([0.21,0.68,0.11]).reshape(1, 3)\n",
        "    print(f'Initial state is: \\n {initial}')\n",
        "    start_time = time.time()\n",
        "    final_state = state_transform(transform_matrix=P, initial_state=initial, steps_transform=100, adaptive_flag=False)\n",
        "    end_time = time.time()\n",
        "    print(f'Time taken (NumPy): {end_time - start_time} seconds')\n",
        "    # Cupy\n",
        "    P = cp.array([[0.65, 0.28, 0.07],[0.15, 0.67, 0.18],[0.12, 0.36, 0.52]]).reshape(3, 3)\n",
        "    initial = cp.array([0.21,0.68,0.11]).reshape(1, 3)\n",
        "    start_time = time.time()\n",
        "    final_state = state_transform(transform_matrix=P, initial_state=initial, steps_transform=100, adaptive_flag=False, cp_flag =True)\n",
        "    end_time = time.time()\n",
        "    print(f'Time taken (Cupy): {end_time - start_time} seconds')\n",
        "    final_state = state_transform(transform_matrix=P, initial_state=initial, adaptive_flag=True, cp_flag =True)"
      ]
    }
  ]
}