{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import numpy as np\n",
        "import scipy.optimize as opt\n",
        "\n",
        "# Define the two probability distributions p and q\n",
        "n, m = 10, 10  # Probability distributions of size 10\n",
        "p = torch.rand(n)\n",
        "q = torch.rand(m)\n",
        "\n",
        "# Normalize the distributions to have a total area of 1\n",
        "p /= p.sum()\n",
        "q /= q.sum()\n",
        "\n",
        "# Create a cost matrix based on the distance between elements in the support\n",
        "cost_matrix = torch.zeros((n, m), dtype=torch.float)\n",
        "\n",
        "for i in range(n):\n",
        "    for j in range(m):\n",
        "        cost_matrix[i][j] = torch.abs(torch.tensor(i - j, dtype=torch.float))\n",
        "\n",
        "# Set up the optimization problem to compute the Wasserstein distance\n",
        "T = nn.Parameter(torch.zeros((n, m), requires_grad=True))\n",
        "\n",
        "# Define the optimizer\n",
        "optimizer = optim.Adam([T], lr=0.01)\n",
        "\n",
        "# Number of optimization steps\n",
        "num_steps = 1000\n",
        "\n",
        "# Lists to store Wasserstein distances during optimization\n",
        "wasserstein_distances = []\n",
        "\n",
        "# Lists to store distributions p and q for plotting\n",
        "p_values = []\n",
        "q_values = []\n",
        "\n",
        "# Optimization loop to find the optimal transport matrix T and plot Wasserstein distances\n",
        "for step in range(num_steps):\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    # Calculate the cost of transporting the mass from p to q\n",
        "    transport_cost = torch.sum(T * cost_matrix)\n",
        "\n",
        "    # Ensure that the transport matrix sums to the correct marginals\n",
        "    row_marginals = torch.sum(T, dim=1, keepdim=True)\n",
        "    col_marginals = torch.sum(T, dim=0, keepdim=True)\n",
        "\n",
        "    loss = torch.sum(T * cost_matrix) + torch.norm(row_marginals - p.view(-1, 1), p=1) + torch.norm(col_marginals - q.view(1, -1), p=1)\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    wasserstein_distances.append(transport_cost.item())\n",
        "    p_values.append(p.detach().numpy())\n",
        "    q_values.append(q.detach().numpy())\n",
        "\n",
        "# Plot the Transport matrix\n",
        "plt.figure(figsize=(8, 8))\n",
        "sns.heatmap(T.detach().numpy(), cmap=\"Blues\", xticklabels=False, yticklabels=False)\n",
        "plt.title(\"Transport Matrix\")\n",
        "plt.show()\n",
        "\n",
        "# Plot the Cost matrix\n",
        "plt.figure(figsize=(8, 8))\n",
        "sns.heatmap(cost_matrix.numpy(), cmap=\"coolwarm\", xticklabels=False, yticklabels=False)\n",
        "plt.title(\"Cost Matrix\")\n",
        "plt.show()\n",
        "\n",
        "# Plot Wasserstein distances over iterations\n",
        "plt.figure(figsize=(8, 4))\n",
        "plt.plot(range(num_steps), wasserstein_distances)\n",
        "plt.title(\"Wasserstein Distance over Optimization\")\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Wasserstein Distance\")\n",
        "plt.grid()\n",
        "plt.show()\n",
        "\n",
        "# Plot probability distributions p and q\n",
        "plt.figure(figsize=(8, 4))\n",
        "plt.plot(range(n), p_values[-1], label='p', color='blue', marker='o')\n",
        "plt.plot(range(m), q_values[-1], label='q', color='red', marker='s')\n",
        "plt.title(\"Probability Distributions p and q\")\n",
        "plt.xlabel(\"Support Point\")\n",
        "plt.ylabel(\"Probability\")\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "KXqh5YFNVZk8",
        "outputId": "7c828381-1311-4ac2-c408-ca5f9158e3c8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 2 Axes>"
            ],
            "image/png": 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2AEACFHUAAAnQfgUAsmGhRK4kdQAACZDUAQDZsFAiV842AEACFHUAAAnQfgUAsmGhRK4kdQAACZDUAQDZsFAiV842AEACJHUAQDZcU5crSR0AQAIUdQAACdB+BQCyYaFErpxtAIAESOoAgGxI6nLlbAMAJEBRBwCQAO1XACAbFe5TlydJHQBAAiR1AEA2LJTIlbMNAJAASR0AkA3Pfs2VpA4AIAGKOgCABGi/AgDZsFAiV842AEACJHUAQDYslMiVpA4AIAGKOgCABGi/AgDZsFAiV842AEACJHUAQDYslMiVpA4AIAGSOgAgG66py5WzDQCQAEUdAEACtF8BgGxYKJErSR0AQAIkdQBANiyUyJWzDQCQAEUdAEACtF8BgGxYKJErRd1H0J3TZpR7Ci1kfLkn8IHdcHLvck8BACJCUQcAZMVCiVw52wAACZDUAQDZkNTlytkGAEiAog4AIAHarwBANtzSJFeSOgCABEjqAIBsWCiRK2cbACABijoAgARovwIA2bBQIleSOgBgu9atW7coFApbbePHN/yM8lmzZm01tnXr1jnPemuSOgAgGx+RhRJPP/10bN68uf71s88+G5/+9KdjxIgR2zxml112iWXLltW/LnwIUklFHQCwXevYsWPJ62uuuSZ69uwZxx133DaPKRQKUVVVlfXUmuWjUUIDADRDXV1drF+/vmSrq6t7z+M2bdoUs2fPjnPOOafR9G3Dhg3RtWvX2HfffePUU0+N5557riWn/74o6gCAbBQKZdtqamqiQ4cOJVtNTc17Tvn++++PdevWxZgxY7Y55sADD4w777wzHnjggZg9e3Zs2bIl+vfvHy+++GILnrzmKxSLxWJTBrY5YkLWc2E7c86VDV+A+lFyw8m9yz0FgEa1LuOFVm0+e0fZvnvdv5+1VTJXWVkZlZWVjR43ePDgaNWqVTz00ENN/q633norevfuHSNHjozp06e/r/m2BNfUAQCZKOfigaYUcP9o1apV8cgjj8SPf/zjZh230047xRFHHBHLly9v1nEtTfsVACAiZs6cGXvttVcMHTq0Wcdt3rw5fv/730fnzp0zmlnTSOoAgEx8GG7z0VRbtmyJmTNnxujRo2PHHUvLo1GjRsXee+9df03etGnT4hOf+ETsv//+sW7durjuuuti1apVcd5555Vj6vUUdQDAdu+RRx6J1atXxznnnLPVe6tXr46Kiv9rbr722msxduzYqK2tjd122y369OkTTzzxRBx00EF5TnkrijoAYLt3wgknxLbWji5YsKDk9U033RQ33XRTDrNqHkUdAJCNj073NQkWSgAAJEBSBwBk4qO0UCIFkjoAgAQo6gAAEqD9CgBkQvs1X5I6AIAESOoAgExI6vIlqQMASICkDgDIhKQuX5I6AIAEKOoAABKg/QoAZEP3NVeSOgCABEjqAIBMWCiRL0kdAEACFHUAAAnQfgUAMqH9mi9JHQBAAiR1AEAmJHX5ktQBACRAUgcAZEJSly9JHQBAAhR1AAAJ0H4FALKh+5orSR0AQAIkdQBAJiyUyJekDgAgAYo6AIAEaL8CAJnQfs2XpA4AIAGSOgAgE5K6fEnqAAASIKkDALIhqMuVpA4AIAGKOgCABGi/AgCZsFAiX5I6AIAESOoAgExI6vLV5KLunCvHZzmP3Nw5bUa5p8DfpPFnkcbfixtO7l3uKQDwAWm/AgAkQPsVAMiE9mu+JHUAAAmQ1AEAmZDU5UtSBwCQAEkdAJANQV2uJHUAAAlQ1AEAJED7FQDIhIUS+ZLUAQAkQFIHAGRCUpcvSR0AQAIUdQAACdB+BQAyof2aL0kdAEACJHUAQDYEdbmS1AEAJEBSBwBkwjV1+ZLUAQAkQFEHAJAA7VcAIBPar/mS1AEAJEBSBwBkQlKXL0kdAEACFHUAAAnQfgUAMqH9mi9JHQCwXZs6dWoUCoWSrVevXo0ec99990WvXr2idevWceihh8bPfvaznGa7bYo6ACAbhTJuzXTwwQfHn//85/rtV7/61TbHPvHEEzFy5Mg499xz43e/+10MGzYshg0bFs8++2zzv7gFKeoAgO3ejjvuGFVVVfXbnnvuuc2x3/rWt2LIkCFx6aWXRu/evWP69Onx8Y9/PG699dYcZ7w1RR0AkJy6urpYv359yVZXV7fN8X/84x+jS5cu0aNHjzjzzDNj9erV2xy7cOHCGDRoUMm+wYMHx8KFC1ts/u+Hog4AyMQ/XqeW51ZTUxMdOnQo2WpqahqcZ9++fWPWrFkxd+7cuO2222LFihXxqU99Kv761782OL62tjY6depUsq9Tp05RW1vb4uewOax+BQCSU11dHRMnTizZV1lZ2eDYE088sf6/DzvssOjbt2907do1fvjDH8a5556b6TxbkqIOAMhEOW9pUllZuc0i7r3suuuu8U//9E+xfPnyBt+vqqqKNWvWlOxbs2ZNVFVVva/vaynarwAA77Jhw4Z44YUXonPnzg2+369fv3j00UdL9s2bNy/69euXx/S2SVEHAGSiUCjf1hyXXHJJPP7447Fy5cp44okn4rTTTosddtghRo4cGRERo0aNiurq6vrxF110UcydOzduuOGGeP7552Pq1Knxm9/8JiZMmNCSp6/ZtF8BgO3aiy++GCNHjoxXX301OnbsGMccc0w8+eST0bFjx4iIWL16dVRU/F8O1r9//5gzZ05Mnjw5rrjiijjggAPi/vvvj0MOOaRcPyEiFHUAwHbu3nvvbfT9BQsWbLVvxIgRMWLEiIxm9P4o6gCATHj2a75cUwcAkABJHQCQCUFdviR1AAAJUNQBACRA+xUAyISFEvmS1AEAJEBSBwBkQlCXL0kdAEACJHUAQCYqKkR1eZLUAQAkQFEHAJAA7VcAIBMWSuRLUgcAkABJHQCQCTcfzpekDgAgAYo6AIAEaL8CAJnQfc2XpA4AIAGSOgAgExZK5EtSBwCQAEkdAJAJSV2+JHUAAAloclJ3w8m9s5xHjsaXewIf2J3TZpR7CvxNOn8WH/2/FxEp/TsF0HzarwBAJnRf86X9CgCQAEkdAJAJCyXyJakDAEiAog4AIAHarwBAJnRf8yWpAwBIgKQOAMiEhRL5ktQBACRAUgcAZEJQly9JHQBAAhR1AAAJ0H4FADJhoUS+JHUAAAmQ1AEAmRDU5UtSBwCQAEUdAEACtF8BgExYKJEvSR0AQAIkdQBAJgR1+ZLUAQAkQFIHAGTCNXX5ktQBACRAUQcAkADtVwAgE7qv+ZLUAQAkQFIHAGTCQol8SeoAABKgqAMASID2KwCQCd3XfEnqAAASIKkDADJhoUS+JHUAAAmQ1AEAmZDU5UtSBwCQAEUdAEACtF8BgEzovuZLUgcAkABJHQCQCQsl8iWpAwBIgKIOACAB2q8AQCZ0X/MlqQMAtms1NTVx1FFHxc477xx77bVXDBs2LJYtW9boMbNmzYpCoVCytW7dOqcZN0xSBwBk4qOyUOLxxx+P8ePHx1FHHRVvv/12XHHFFXHCCSfEH/7wh2jXrt02j9tll11Kir9y/15FHQCwXZs7d27J61mzZsVee+0VixcvjmOPPXabxxUKhaiqqsp6ek2m/QoAJKeuri7Wr19fstXV1TXp2Ndffz0iInbfffdGx23YsCG6du0a++67b5x66qnx3HPPfeB5fxCKOgAgE4VC+baampro0KFDyVZTU/Oec96yZUtcfPHF8clPfjIOOeSQbY478MAD484774wHHnggZs+eHVu2bIn+/fvHiy++2JKnsFm0XwGA5FRXV8fEiRNL9lVWVr7ncePHj49nn302fvWrXzU6rl+/ftGvX7/61/3794/evXvHd7/73Zg+ffr7m/QHpKgDADJRUcaFA5WVlU0q4t5twoQJ8dOf/jR++ctfxj777NOsY3faaac44ogjYvny5c06riVpvwIA27VisRgTJkyIn/zkJzF//vzo3r17sz9j8+bN8fvf/z46d+6cwQybRlIHAGTiI3JHkxg/fnzMmTMnHnjggdh5552jtrY2IiI6dOgQbdq0iYiIUaNGxd57711/Xd60adPiE5/4ROy///6xbt26uO6662LVqlVx3nnnle13KOoAgO3abbfdFhERAwYMKNk/c+bMGDNmTERErF69Oioq/q/B+dprr8XYsWOjtrY2dtttt+jTp0888cQTcdBBB+U17a0o6gCA7VqxWHzPMQsWLCh5fdNNN8VNN92U0YzeH0UdAJCJcj9hYXtjoQQAQAIkdQBAJioEdbmS1AEAJEBRBwCQAO1XACATFkrkS1IHAJAASR0AkAlBXb62u6LuhpN7l3sKLWB8uSfQIu6cNqPcU+Bv0vmz+Oj/3Ujj3yigHLa7og4AyEchRHV5ck0dAEACFHUAAAnQfgUAMuGJEvmS1AEAJEBSBwBkws2H8yWpAwBIgKIOACAB2q8AQCZ0X/MlqQMASICkDgDIRIWoLleSOgCABEjqAIBMCOryJakDAEiAog4AIAHarwBAJjxRIl+SOgCABEjqAIBMCOryJakDAEiAog4AIAHarwBAJjxRIl+SOgCABEjqAIBMyOnyJakDAEiApA4AyISbD+dLUgcAkABFHQBAArRfAYBMVOi+5kpSBwCQAEkdAJAJCyXyJakDAEiAog4AIAHarwBAJnRf8yWpAwBIgKQOAMiEhRL5ktQBACRAUgcAZMLNh/MlqQMASICiDgAgAdqvAEAmLJTIl6QOACABkjoAIBNyunxJ6gAAEqCoAwBIgPYrAJCJCgslciWpAwBIgKQOAMiEoC5fkjoAgARI6gCATLj5cL4kdQAACVDUAQAkQPsVAMiE7mu+JHUAAAmQ1AEAmXDz4XxJ6gAAEqCoAwBIgPYrAJAJ3dd8SeoAgO3ejBkzolu3btG6devo27dvLFq0qNHx9913X/Tq1Stat24dhx56aPzsZz/LaabbpqgDADJRKBTKtjXHD37wg5g4cWJMmTIlfvvb38bhhx8egwcPjpdffrnB8U888USMHDkyzj333Pjd734Xw4YNi2HDhsWzzz7bEqftfVPUAQDbtRtvvDHGjh0bZ599dhx00EFx++23R9u2bePOO+9scPy3vvWtGDJkSFx66aXRu3fvmD59enz84x+PW2+9NeeZl1LUAQDJqauri/Xr15dsdXV1W43btGlTLF68OAYNGlS/r6KiIgYNGhQLFy5s8LMXLlxYMj4iYvDgwdscnxcLJT6Cbji5d7mn0ELGl3sCH9id02aUewq8Sxp/Hh/9vxcRKf07xQdRzuSopqYmrrrqqpJ9U6ZMialTp5bsW7t2bWzevDk6depUsr9Tp07x/PPPN/jZtbW1DY6vra394BP/ABR1AEByqqurY+LEiSX7KisryzSbfCjqAIBMNHfBQkuqrKxsUhG35557xg477BBr1qwp2b9mzZqoqqpq8Jiqqqpmjc+La+oAgO1Wq1atok+fPvHoo4/W79uyZUs8+uij0a9fvwaP6devX8n4iIh58+Ztc3xeJHUAQCYqPiI3H544cWKMHj06jjzyyDj66KPj5ptvjo0bN8bZZ58dERGjRo2KvffeO2pqaiIi4qKLLorjjjsubrjhhhg6dGjce++98Zvf/Ca+973vlfNnKOoAgO3b5z//+XjllVfiyiuvjNra2vjYxz4Wc+fOrV8MsXr16qio+L/mZv/+/WPOnDkxefLkuOKKK+KAAw6I+++/Pw455JBy/YSIUNQBAMSECRNiwoQJDb63YMGCrfaNGDEiRowYkfGsmkdRBwBk4qPSfk2FhRIAAAmQ1AEAmSjnLU22R5I6AIAEKOoAABKg/QoAZMJCiXxJ6gAAEiCpAwAyYZ1EviR1AAAJkNQBAJmoENXlSlIHAJAARR0AQAK0XwGATEiO8uV8AwAkQFIHAGTCOol8SeoAABKgqAMASID2KwCQCfepy5ekDgAgAZI6ACATgrp8SeoAABIgqQMAMlEhqcuVpA4AIAGKOgCABGi/AgCZcEuTfEnqAAASIKkDADIhqMuXpA4AIAGKOgCABGi/AgCZcJ+6fEnqAAASIKkDADJRCFFdniR1AAAJkNQBAJlwTV2+JHUAAAlQ1AEAJED7FQDIhPZrviR1AAAJkNQBAJkoePhrriR1AAAJUNQBACRA+xUAyISFEvmS1AEAJEBSBwBkwjqJfEnqAAASIKkDADJRIarLlaQOACABijoAgARovwIAmXBLk3xJ6gAAEiCpAwAyYZ1EviR1AAAJUNQBACRA+xUAyERF6L/mSVFH2dxwcu9yT6EFjC/3BFrEndNmlHsK/E06fxYf/b8bafwbxfZEUQcAZMJCiXy5pg4AIAGSOgAgE24+nC9JHQBAAhR1AAAJ0H4FADJRYaVEriR1AAAJkNQBAJkQ1OVLUgcAkABFHQBAArRfAYBMWCiRL0kdAEATrFy5Ms4999zo3r17tGnTJnr27BlTpkyJTZs2NXrcgAEDolAolGxf/OIXW3x+kjoAIBOpBXXPP/98bNmyJb773e/G/vvvH88++2yMHTs2Nm7cGNdff32jx44dOzamTZtW/7pt27YtPj9FHQBAEwwZMiSGDBlS/7pHjx6xbNmyuO22296zqGvbtm1UVVVlOj/tVwAgOXV1dbF+/fqSra6ursW/5/XXX4/dd9/9Pcd9//vfjz333DMOOeSQqK6ujjfeeKPF56KoAwAyUVHGraamJjp06FCy1dTUtOjvW758edxyyy0xbty4RsedccYZMXv27Hjssceiuro67rnnnjjrrLNadC4R2q8AQIKqq6tj4sSJJfsqKysbHHv55ZfHtdde2+jnLV26NHr16lX/+qWXXoohQ4bEiBEjYuzYsY0ee/7559f/96GHHhqdO3eO448/Pl544YXo2bPne/2UJlPUAQCZKJRxpURlZeU2i7h/NGnSpBgzZkyjY3r06FH/33/6059i4MCB0b9///je977X7Ln17ds3It5J+hR1AAAtpGPHjtGxY8cmjX3ppZdi4MCB0adPn5g5c2ZUVDT/SrYlS5ZERETnzp2bfWxjXFMHAGSiUMYtCy+99FIMGDAg9ttvv7j++uvjlVdeidra2qitrS0Z06tXr1i0aFFERLzwwgsxffr0WLx4caxcuTIefPDBGDVqVBx77LFx2GGHtej8JHUAAE0wb968WL58eSxfvjz22WefkveKxWJERLz11luxbNmy+tWtrVq1ikceeSRuvvnm2LhxY+y7774xfPjwmDx5covPT1EHANAEY8aMec9r77p161Zf4EVE7LvvvvH4449nPLN3KOoAgEx49mu+XFMHAJAASR0AkAk5Xb4kdQAACVDUAQAkQPsVAMiEdRL5ktQBACRAUgcAZKKcz37dHknqAAASIKkDADIhOcqX8w0AkABFHQBAArRfAYBMWCiRL0kdAEACJHUAQCbkdPmS1AEAJEBRBwCQAO1XACATFkrkS1IHAJAASR0AkAnJUb6cbwCABEjqAIBMuKYuX5I6AIAEKOoAABKg/QoAZELzNV+SOgCABEjqAIBMWCeRL0kdAEACFHUAAAnQfgUAMlFhqUSuJHUAAAmQ1AEAmbBQIl+SOgCABEjqAIBMFFxTlytJHQBAAhR1AAAJ0H4FADJhoUS+JHUAAAmQ1AEAmXDz4Xwp6uADuOHk3uWeQgsZX+4JtIg7p80o9xT4mzT+LNL4ezHjtFT+neK9aL8CACRAUgcAZMJCiXxJ6gAAEiCpAwAyIanLl6QOACABkjoAIBOe/ZovSR0AQAIUdQAACdB+BQAyUaH7mitJHQBAAiR1AEAmLJTIl6QOACABijoAgARovwIAmfBEiXxJ6gAAEiCpAwAyYaFEviR1AAAJkNQBAJlw8+F8SeoAABKgqAMASID2KwCQCQsl8iWpAwBIgKQOAMiEmw/nS1IHAJAARR0AQAK0XwGATOi+5ktSBwDQRN26dYtCoVCyXXPNNY0e8+abb8b48eNjjz32iPbt28fw4cNjzZo1LT43SR0AkImKRFdKTJs2LcaOHVv/euedd250/Fe+8pV4+OGH47777osOHTrEhAkT4rOf/Wz8+te/btF5KeoAAJph5513jqqqqiaNff311+OOO+6IOXPmxD//8z9HRMTMmTOjd+/e8eSTT8YnPvGJFpuX9isAkJy6urpYv359yVZXV9cin33NNdfEHnvsEUcccURcd9118fbbb29z7OLFi+Ott96KQYMG1e/r1atX7LfffrFw4cIWmc/fKeoAgEwUyrjV1NREhw4dSraampoP/JsuvPDCuPfee+Oxxx6LcePGxTe+8Y346le/us3xtbW10apVq9h1111L9nfq1Clqa2s/8HzeTfsVAEhOdXV1TJw4sWRfZWVlg2Mvv/zyuPbaaxv9vKVLl0avXr1KPvOwww6LVq1axbhx46Kmpmabn58XRR0AkI0yrpOorKxscpE1adKkGDNmTKNjevTo0eD+vn37xttvvx0rV66MAw88cKv3q6qqYtOmTbFu3bqStG7NmjVNvi6vqRR1AMB2rWPHjtGxY8f3deySJUuioqIi9tprrwbf79OnT+y0007x6KOPxvDhwyMiYtmyZbF69ero16/f+55zQxR1AEAmCondfnjhwoXx1FNPxcCBA2PnnXeOhQsXxle+8pU466yzYrfddouIiJdeeimOP/74uPvuu+Poo4+ODh06xLnnnhsTJ06M3XffPXbZZZe44IILol+/fi268jVCUQcA0CSVlZVx7733xtSpU6Ouri66d+8eX/nKV0qus3vrrbdi2bJl8cYbb9Tvu+mmm6KioiKGDx8edXV1MXjw4PjOd77T4vNT1AEANMHHP/7xePLJJxsd061btygWiyX7WrduHTNmzIgZM2ZkOT1FHQCQjUQfKPGh5T51AAAJkNQBAJkQ1OVLUgcAkABFHQBAArRfAYBs6L/mSlIHAJAASR0AkInUnijxYSepAwBIgKQOAMiEmw/nS1IHAJAARR0AQAK0XwGATOi+5ktSBwCQAEkdAJANUV2uJHUAAAlQ1AEAJED7FQDIhCdK5EtSBwCQAEkdAJAJT5TIl6QOACABkjoAIBOCunxJ6gAAElAoFovFpgx88+2spwLwwUx6aGm5p/CB3TltRrmnQGL+93e3lu27n1n917J99+H77Vy27y4X7VcAIBv6r7nSfgUASICkDgDIhJsP50tSBwCQAEUdAEACtF8BgEx4okS+JHUAAAmQ1AEAmRDU5UtSBwCQAEkdAJANUV2uJHUAAAlQ1AEAJED7FQDIhCdK5EtSBwCQAEkdAJAJNx/Ol6QOACABijoAgARovwIAmdB9zZekDgAgAZI6ACAborpcSeoAABIgqQMAMuHmw/mS1AEAJEBRBwCQAO1XACATniiRL0kdAEACJHUAQCYEdfmS1AEAJEBRBwCQAO1XACAb+q+5ktQBACRAUgcAZMITJfIlqQMASICkDgDIhJsP50tSBwCQAEUdAEACtF8BgEzovuZLUgcAkABJHQCQDVFdriR1AAAJUNQBACRA+xUAyIQnSuRLUgcA0AQLFiyIQqHQ4Pb0009v87gBAwZsNf6LX/xii89PUgcAZCK1J0r0798//vznP5fs+9rXvhaPPvpoHHnkkY0eO3bs2Jg2bVr967Zt27b4/BR1AABN0KpVq6iqqqp//dZbb8UDDzwQF1xwQRTeo4Jt27ZtybFZ0H4FAJJTV1cX69evL9nq6upa9DsefPDBePXVV+Pss89+z7Hf//73Y88994xDDjkkqqur44033mjRuUQo6gCAjBTKuNXU1ESHDh1Ktpqamhb9fXfccUcMHjw49tlnn0bHnXHGGTF79ux47LHHorq6Ou65554466yzWnQuERGFYrFYbMrAN99u8e8GaFGTHlpa7il8YHdOm1HuKZCY//3drWX77pVr3yzbd3feubBVMldZWRmVlZVbjb388svj2muvbfTzli5dGr169ap//eKLL0bXrl3jhz/8YQwfPrxZc5s/f34cf/zxsXz58ujZs2ezjm2Ma+oAgGyUcaHEtgq4hkyaNCnGjBnT6JgePXqUvJ45c2bsscceccoppzR7bn379o2IUNQBALSkjh07RseOHZs8vlgsxsyZM2PUqFGx0047Nfv7lixZEhERnTt3bvaxjXFNHQCQiUIZ/y9L8+fPjxUrVsR555231XsvvfRS9OrVKxYtWhQRES+88EJMnz49Fi9eHCtXrowHH3wwRo0aFccee2wcdthhLTovSR0AQDPccccd0b9//5Jr7P7urbfeimXLltWvbm3VqlU88sgjcfPNN8fGjRtj3333jeHDh8fkyZNbfF6KOgCAZpgzZ8423+vWrVu8ew3qvvvuG48//nge01LUAQDZSO2JEh92rqkDAEiApA4AyISgLl+SOgCABCjqAAASoP0KAGTCQol8SeoAABIgqQMAMiKqy5OiDkjGDSf3LvcUWsD4ck+gRdw5bUa5pwDbHUUdAJAJ19TlyzV1AAAJUNQBACRA+xUAyITua74kdQAACZDUAQCZsFAiX5I6AIAEKOoAABKg/QoAZKJgqUSuJHUAAAmQ1AEA2RDU5UpSBwCQAEkdAJAJQV2+JHUAAAlQ1AEAJED7FQDIhCdK5EtSBwCQAEkdAJAJNx/Ol6QOACABijoAgARovwIA2dB9zZWkDgAgAZI6ACATgrp8SeoAABIgqQMAMuHmw/mS1AEAJEBRBwCQAO1XACATniiRL0kdAEACJHUAQCYslMiXpA4AIAGKOgCABCjqAAASoKgDAEiAhRIAQCYslMiXpA4AIAGSOgAgE24+nC9JHQBAAhR1AAAJ0H4FADJhoUS+JHUAAAmQ1AEAmRDU5UtSBwCQAEUdAEACtF8BgGzov+ZKUgcAkABJHQCQCU+UyJekDgAgAZI6ACATbj6cL0kdAEACFHUAAAnQfgUAMqH7mi9JHQBAAiR1AEA2RHW5ktQBACRAUQcAkADtVwAgE54okS9JHQBAE1199dXRv3//aNu2bey6664Njlm9enUMHTo02rZtG3vttVdceuml8fbbbzf6uX/5y1/izDPPjF122SV23XXXOPfcc2PDhg3NmpuiDgDIRKFQvi0rmzZtihEjRsSXvvSlBt/fvHlzDB06NDZt2hRPPPFE3HXXXTFr1qy48sorG/3cM888M5577rmYN29e/PSnP41f/vKXcf755zdrboVisVhsysA3Gy8wAWgBkx5aWu4ptIg7p80o9xT4m//93a1l++5y1g6tM77AbNasWXHxxRfHunXrSvb/53/+Z5x00knxpz/9KTp16hQREbfffntcdtll8corr0SrVq22+qylS5fGQQcdFE8//XQceeSRERExd+7c+MxnPhMvvvhidOnSpUlzktQBAMmpq6uL9evXl2x1dXWZf+/ChQvj0EMPrS/oIiIGDx4c69evj+eee26bx+y66671BV1ExKBBg6KioiKeeuqpJn93k+vYrCteACJmnNa73FNoETNOK186xIdHOWuHqV+viauuuqpk35QpU2Lq1KmZfm9tbW1JQRcR9a9ra2u3ecxee+1Vsm/HHXeM3XfffZvHNERSBwAkp7q6Ol5//fWSrbq6usGxl19+eRQKhUa3559/Pudf0HzyNwAgOZWVlVFZWdmksZMmTYoxY8Y0OqZHjx5N+qyqqqpYtGhRyb41a9bUv7etY15++eWSfW+//Xb85S9/2eYxDVHUAQDbtY4dO0bHjh1b5LP69esXV199dbz88sv1LdV58+bFLrvsEgcddNA2j1m3bl0sXrw4+vTpExER8+fPjy1btkTfvn2b/N3arwAATbR69epYsmRJrF69OjZv3hxLliyJJUuW1N9T7oQTToiDDjoo/uVf/iWeeeaZ+PnPfx6TJ0+O8ePH1yeHixYtil69esVLL70UERG9e/eOIUOGxNixY2PRokXx61//OiZMmBBf+MIXmrzyNaIZtzQBANjejRkzJu66666t9j/22GMxYMCAiIhYtWpVfOlLX4oFCxZEu3btYvTo0XHNNdfEjju+0yBdsGBBDBw4MFasWBHdunWLiHduPjxhwoR46KGHoqKiIoYPHx7f/va3o3379k2em6IOACAB2q8AAAlQ1AEAJEBRBwCQAEUdAEACFHUAAAlQ1AEAJEBRBwCQAEUdAEACFHUAAAlQ1AEAJEBRBwCQgP8Ptgyra20zLk0AAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "\n",
        "# Define the two probability distributions p and q\n",
        "n, m = 10, 10  # Probability distributions of size 10\n",
        "p = np.random.rand(n)\n",
        "q = np.random.rand(m)\n",
        "\n",
        "# Normalize the distributions to have a total area of 1\n",
        "p /= p.sum()\n",
        "q /= q.sum()\n",
        "\n",
        "# Create a cost matrix based on the distance between elements in the support\n",
        "cost_matrix = np.zeros((n, m), dtype=float)\n",
        "\n",
        "for i in range(n):\n",
        "    for j in range(m):\n",
        "        cost_matrix[i][j] = np.abs(i - j)\n",
        "\n",
        "# Flatten the cost matrix for the linear programming\n",
        "c = cost_matrix.flatten()\n",
        "\n",
        "# Define equality constraints for row and column sums\n",
        "A_eq = []\n",
        "b_eq = np.concatenate((p, q))\n",
        "\n",
        "for i in range(n):\n",
        "    row_constraint = np.zeros(n * m)\n",
        "    row_constraint[i * m: (i + 1) * m] = 1\n",
        "    A_eq.append(row_constraint)\n",
        "\n",
        "for j in range(m):\n",
        "    col_constraint = np.zeros(n * m)\n",
        "    col_constraint[j::m] = 1\n",
        "    A_eq.append(col_constraint)\n",
        "\n",
        "# Use linear programming to find the optimal transport plan\n",
        "result = opt.linprog(c, A_eq=A_eq, b_eq=b_eq, method=\"highs\")\n",
        "\n",
        "# Reshape the result into a matrix\n",
        "T = result.x.reshape((n, m))\n",
        "\n",
        "# Calculate the Wasserstein distance\n",
        "wasserstein_distance = np.sum(T * cost_matrix)\n",
        "\n",
        "print(f'Wasserstein Distance: {wasserstein_distance:.4f}')\n",
        "\n",
        "# Plot the Transport matrix\n",
        "plt.figure(figsize=(8, 8))\n",
        "sns.heatmap(T, cmap=\"Blues\", xticklabels=False, yticklabels=False)\n",
        "plt.title(\"Transport Matrix\")\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 700
        },
        "id": "XZ7QMOKqWp_u",
        "outputId": "31c4e80d-f201-4933-d4f3-6f12aeb82026"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Wasserstein Distance: 1.1257\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Define the two probability distributions p and q\n",
        "n, m = 10, 10  # Probability distributions of size 10\n",
        "p = np.random.rand(n)\n",
        "q = np.random.rand(m)\n",
        "\n",
        "# Normalize the distributions to have a total area of 1\n",
        "p /= p.sum()\n",
        "q /= q.sum()\n",
        "\n",
        "# Create a cost matrix based on the distance between elements in the support\n",
        "cost_matrix = np.zeros((n, m), dtype=float)\n",
        "\n",
        "for i in range(n):\n",
        "    for j in range(m):\n",
        "        cost_matrix[i][j] = np.abs(i - j)\n",
        "\n",
        "# Flatten the cost matrix for the linear programming\n",
        "c = cost_matrix.flatten()\n",
        "\n",
        "# Define equality constraints for row and column sums\n",
        "A_eq = []\n",
        "b_eq = np.concatenate((p, q))\n",
        "\n",
        "for i in range(n):\n",
        "    row_constraint = np.zeros(n * m)\n",
        "    row_constraint[i * m: (i + 1) * m] = 1\n",
        "    A_eq.append(row_constraint)\n",
        "\n",
        "for j in range(m):\n",
        "    col_constraint = np.zeros(n * m)\n",
        "    col_constraint[j::m] = 1\n",
        "    A_eq.append(col_constraint)\n",
        "\n",
        "# Use linear programming to find the optimal transport plan\n",
        "result = opt.linprog(c, A_eq=A_eq, b_eq=b_eq, method=\"highs\")\n",
        "\n",
        "# Reshape the result into a matrix\n",
        "T = result.x.reshape((n, m))\n",
        "\n",
        "# Calculate the Wasserstein distance\n",
        "wasserstein_distance = np.sum(T * cost_matrix)\n",
        "\n",
        "print(f'Wasserstein Distance: {wasserstein_distance:.4f}')\n",
        "\n",
        "# Plot the Probability Distributions p and q\n",
        "plt.figure(figsize=(12, 4))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.bar(range(n), p, label='p', color='blue')\n",
        "plt.title(\"Distribution p\")\n",
        "plt.xlabel(\"Support Point\")\n",
        "plt.ylabel(\"Probability\")\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.bar(range(m), q, label='q', color='red')\n",
        "plt.title(\"Distribution q\")\n",
        "plt.xlabel(\"Support Point\")\n",
        "plt.ylabel(\"Probability\")\n",
        "plt.show()\n",
        "\n",
        "# Plot the Cost Matrix\n",
        "plt.figure(figsize=(8, 8))\n",
        "sns.heatmap(cost_matrix, cmap=\"coolwarm\", xticklabels=False, yticklabels=False)\n",
        "plt.title(\"Cost Matrix\")\n",
        "plt.show()\n",
        "\n",
        "# Plot the Transport Matrix\n",
        "plt.figure(figsize=(8, 8))\n",
        "sns.heatmap(T, cmap=\"Blues\", xticklabels=False, yticklabels=False)\n",
        "plt.title(\"Transport Matrix\")\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "WOUZBdyyW4oS",
        "outputId": "dba3972c-c274-4836-cae7-a8531205683f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Wasserstein Distance: 1.9079\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 2 Axes>"
            ],
            "image/png": 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B9X7nnHNOR0oVEbHPPvvEM888E+3t7bkLKi0/AKChvf7669HrfWla7969o1qt5l5DQgUAJNGrd/c4KX3GjBlxwQUXxLBhw2L8+PHxP//zP3HxxRfHySefnHsNBRUA0NAuu+yy+Na3vhVnnHFGvPTSSzFkyJA47bTT4rzzzsu9hoIKAEiiu3yXX1NTU1xyySVxySWXbPMaZqgAAApSUAEAFKTlBwAkUc9zqLa3xvmkAACJSKgAgCS6y1B6LUioAAAKklABAElIqAAAyE1BBQBQkJYfAJCEYxMAAMhNQgUAJGEoHQCA3BRUAAAFafkBAEkYSgcAIDcJFQCQRslQOgAAOUmoAIAkHJsAAEBuCioAgIK0/ACAJBybAABAbhIqACAJQ+kAAOSmoAIAKEjLDwBIwlA6AAC5SagAgCQMpQMAkJuECgBIQkIFAEBuCioAgIK0/ACANBybAABAXhIqACCJUslQOgAAOSmoAAAK0vIDAJLwXX4AAOQmoQIAknBSOgAAuUmoAIA0zFABAJCXggoAoCAtPwAgCUPpAADkJqECAJIolRont8ldUO05riXlPuiCJ1evrfcW6NBT/lzsUu8N1MbAMfXeQWF7DK33Dmqjqd4bqIHd670BupXGKR0BABLR8gMA0jCUDgBAXhIqACCJkpPSAQDIS0IFACThYE8AAHJTUAEAFKTlBwCk0UAnpTfOJwUA2IoRI0ZEqVTa4jV37tzca0ioAIAkustQ+sqVK2Pz5s0dP69ZsyY++9nPxnHHHZd7DQUVANDjVCqVqFQqna6Vy+Uol8tb3NvS0vl7WS+88MIYPXp0TJ48OffztPwAgB6nvb09mpubO73a29s/8n1vvfVW/OxnP4uTTz45SqX8CZuECgBIo44npbe1tUVra2una1tLp97vl7/8Zbz66qvxpS99qUvPU1ABAD3OB7X3PsqVV14Z06ZNiyFDhnTpfQoqACCJrrTM/hI888wzcfvtt8cvfvGLLr/XDBUAQEQsXrw4Bg0aFNOnT+/yeyVUAEAadZyh6qpqtRqLFy+O2bNnxw47dL086j6fFAAgkdtvvz2effbZOPnkk7fp/RIqAKDhTZ06NbIs2+b3K6gAgCS6y0nptaDlBwBQkIQKAEij1Di5TeN8UgCARBRUAAAFafkBAGkYSgcAIC8JFQCQRMlQOgAAeSmoAAAK0vIDANIwlA4AQF4SKgAgiVKvxsltGueTAgAkIqECANIomaECACAnBRUAQEFafgBAGobSAQDIS0IFAKRhKB0AgLwUVAAABWn5AQBJOCkdAIDcJFQAQBqlxsltGueTAgAkIqECANLo5dgEAAByUlABABSk5QcAJFEylA4AQF4SKgAgDUPpAADkpaACAChIyw8ASMNQOgAAeUmoAIA0SobSAQDISUIFAKTRq3Fym8b5pAAAieROqMaO7Cm1V0u9N8CfPbl6bb23QIee8udil3pvoLiBY+q9g5rYY2i9d1BcU703QLei5QcApOHYBAAA8pJQAQBp+C4/AADyUlABABSk5QcApGEoHQCAvCRUAEAavssPAIC8JFQAQBq+yw8AgLwUVAAABWn5AQBpGEoHACAvCRUAkIaDPQEAyEtBBQA0vOeeey7+8R//MT7+8Y9Hv379Yp999olVq1blfr+WHwCQRjc5h+qVV16JSZMmxRFHHBG//vWvo6WlJR5//PHYZZddcq+hoAIAGtpFF10Ue+yxRyxevLjj2siRI7u0RvcoHQGA7qdUqturUqnEhg0bOr0qlcpWt3nTTTfFQQcdFMcdd1wMGjQo9t9//7jiiiu69FEVVABAj9Pe3h7Nzc2dXu3t7Vu998knn4xFixbFnnvuGcuWLYvTTz89vvrVr8ZVV12V+3lafgBAGnU8NqGtrS1aW1s7XSuXy1u9t1qtxkEHHRTf+c53IiJi//33jzVr1sSPfvSjmD17dq7nKagAgB6nXC5/YAH1foMHD45x48Z1uvaJT3wi/uM//iP387T8AICGNmnSpHjsscc6XVu7dm0MHz489xoSKgAgjW7yXX5nnXVWHHroofGd73wnjj/++HjggQfi8ssvj8svvzz3GhIqAKChffKTn4wbb7wxrr766pgwYUKcf/75cckll8SJJ56Yew0JFQCQRjc52DMi4uijj46jjz56m9/ffT4pAMBfKAUVAEBBWn4AQBJZNxlKrwUJFQBAQRIqACCNOp6Uvr01zicFAEhEQgUApCGhAgAgLwUVAEBBWn4AQBKOTQAAIDcJFQCQhqF0AADyUlABABSk5QcApGEoHQCAvCRUAEAavRont2mcTwoAkIiCCgCgIC0/ACAJJ6UDAJCbhAoASMNJ6QAA5CWhAgCSyCRUAADkpaACAChIyw8ASMOxCQAA5CWhAgCSMJQOAEBuCioAgIK0/ACANAylAwCQl4QKAEijgYbScxdUowe+knIf29Eu9d5ADbTUewP82ZOr19Z7C3TSE/5s9IR/R0XEwDH13kFhewyt9w5qo2+9N9AgJFQAQBKZGSoAAPJSUAEAFKTlBwCk0UBD6Y3zSQEAEpFQAQBJZGEoHQCAnBRUAAAFafkBAElkhtIBAMhLQgUApCGhAgAgLwkVAJCE7/IDACA3BRUAQEFafgBAEo5NAAAgNwkVAJCGoXQAAPJSUAEAFKTlBwAkYSgdAIDcJFQAQBJZGEoHAGgICxYsiFKp1Ok1duzYLq0hoQIAkuhOM1Tjx4+P22+/vePnHXboWomkoAIAepxKpRKVSqXTtXK5HOVyeav377DDDrH77rtv8/O6T+kIAJBTe3t7NDc3d3q1t7d/4P2PP/54DBkyJEaNGhUnnnhiPPvss116noQKAEijjielt7W1RWtra6drH5ROHXzwwbFkyZLYe++94/nnn4+FCxfG3/zN38SaNWuiqakp1/MUVABAj/Nh7b33mzZtWsc/T5w4MQ4++OAYPnx4XHfddfFP//RPudZQUAEASWTddLJo5513jr322iueeOKJ3O/pnp8UACCRjRs3xrp162Lw4MG536OgAgAa2te//vVYsWJFPP3003HPPffEscceG717945Zs2blXkPLDwBIIqvjUHpX/OEPf4hZs2bF//3f/0VLS0scdthhcd9990VLS0vuNRRUAEBDu+aaawqvoaACAJLoTielF9U4nxQAIBEJFQCQRBbdY4aqFiRUAAAFKagAAArS8gMAkjCUDgBAbhIqACCJ7nKwZy1IqAAAClJQAQAUpOUHACThHCoAAHKTUAEASTg2AQCA3CRUAEASZqgAAMhNQQUAUJCWHwCQhKF0AAByk1ABAEkYSgcAIDcFFQBAQVp+AEAShtIBAMhNQgUAJGEoHQCA3BRUAAAF5W757fH2Eyn3sf0MHFPvHdTALvXeQI201HsD/NmTq9fWewt06Cl/LnrAv6d6xH8v6vu/qKyk5QcAQE6G0gGAJLJMQgUAQE4SKgAgiayBcpvG+aQAAIkoqAAACtLyAwCScFI6AAC5SagAgCQkVAAA5KagAgAoSMsPAEhCyw8AgNwkVABAEhIqAAByk1ABAElkmYQKAICcFFQAAAVp+QEASRhKBwAgNwkVAJCEhAoAgNwUVAAABWn5AQBJaPkBAJCbhAoASMJJ6QAA5CahAgCSqJqhAgAgLwUVAMCfXXjhhVEqlWLevHldep+WHwCQRHc7NmHlypXx4x//OCZOnNjl90qoAICGt3HjxjjxxBPjiiuuiF122aXL71dQAQBJZFmpbq9KpRIbNmzo9KpUKh+417lz58b06dNjypQp2/RZFVQAQI/T3t4ezc3NnV7t7e1bvfeaa66Jhx566AN/PQ8zVABAj9PW1hatra2drpXL5S3u+/3vfx9f+9rX4rbbbou+fftu8/MUVABAEvUcSi+Xy1stoN7vwQcfjJdeeikOOOCAjmubN2+Ou+66K77//e9HpVKJ3r17f+Q6CioAoGF95jOfiYcffrjTtTlz5sTYsWPjX/7lX3IVUxEKKgAgke7wXX5NTU0xYcKETtf69+8fH//4x7e4/mEMpQMAFCShAgCS6G4He75r+fLlXX6PhAoAoCAFFQBAQVp+AEAS3WEovVYkVAAABUmoAIAkqvXewHYkoQIAKEhBBQBQkJYfAJCEoXQAAHKTUAEASXTXk9K3hYQKAKAgCRUAkIQZKgAAclNQAQAUpOUHACRhKB0AgNwkVABAEtWs3jvYfiRUAAAFKagAAArS8gMAkmikofTcBVXTH9ak3Md2s8fQeu+gBgaOqfcOamSXem+gBlrqvQHe48nVa+u9BTr0hD8bPeHfUREH1HsDDUJCBQAk4aR0AAByk1ABAElkjk0AACAvBRUAQEFafgBAEtUGOjZBQgUAUJCECgBIwrEJAADkpqACAChIyw8ASMI5VAAA5CahAgCSyBybAABAXgoqAICCtPwAgCSqhtIBAMhLQgUAJOGkdAAAcpNQAQBJONgTAIDcFFQAAAVp+QEASVSdlA4AQF4SKgAgCUPpAADkpqACAChIyw8ASMJJ6QAA5CahAgCSqBpKBwAgLwkVAJCEYxMAAMhNQQUAUJCWHwCQROa7/AAAyEtBBQAkUc3q9+qKRYsWxcSJE2PAgAExYMCAOOSQQ+LXv/51l9ZQUAEADW3o0KFx4YUXxoMPPhirVq2KI488MmbOnBmPPPJI7jXMUAEADW3GjBmdfr7gggti0aJFcd9998X48eNzraGgAgCSqOc5VJVKJSqVSqdr5XI5yuXyh75v8+bNcf3118emTZvikEMOyf08LT8AoMdpb2+P5ubmTq/29vYPvP/hhx+Oj33sY1Eul+PLX/5y3HjjjTFu3Ljcz5NQAQBJ1DOhamtri9bW1k7XPiyd2nvvvWP16tWxfv36uOGGG2L27NmxYsWK3EWVggoA6HHytPfeq0+fPjFmzJiIiDjwwANj5cqVcemll8aPf/zjXO9XUAEASVSz7nuwZ7Va3WIG68MoqACAhtbW1hbTpk2LYcOGxWuvvRZLly6N5cuXx7Jly3KvoaACABraSy+9FCeddFI8//zz0dzcHBMnToxly5bFZz/72dxrKKgAgCTqOZTeFVdeeWXhNRybAABQkIQKAEiiuyRUtSChAgAoSEEFAFCQlh8AkERVyw8AgLwkVABAElk3Pim9qyRUAAAFSagAgCQcmwAAQG4KKgCAgrT8AIAkHJsAAEBuEioAIIlGGkrPXVC99cjDKfex3TTVewM1sMfQeu+gRgaOqfcOamCXem+gRlrqvQH+7MnVa+u9BTr0kD8Xn9KM2h78LgMAFKTlBwAk0UgtPwkVAEBBEioAIAnHJgAAkJuECgBIwgwVAAC5KagAAArS8gMAkqhW672D7UdCBQBQkIQKAEjCUDoAALkpqAAACtLyAwCS0PIDACA3CRUAkITv8gMAIDcJFQCQRFbXIarSdn2ahAoAoCAFFQBAQVp+AEASjk0AACA3CRUAkES1Wu8dbD8SKgCAghRUAAAFafkBAEkYSgcAIDcJFQCQhO/yAwAgNwUVAEBBWn4AQBKG0gEAyE1CBQAkkdV1Kr20XZ8moQIAKEhCBQAk4dgEAAByU1ABABSk5QcAJOHYBAAAcpNQAQBJVBtoKl1CBQBQkIIKAKAgLT8AIAlD6QAADaK9vT0++clPRlNTUwwaNCiOOeaYeOyxx7q0hoIKAEgiy+r36ooVK1bE3Llz47777ovbbrst3n777Zg6dWps2rQp9xpafgBAQ/vNb37T6eclS5bEoEGD4sEHH4xPf/rTudZQUAEASVTrOERVqVSiUql0ulYul6NcLn/ke9evXx8REQMHDsz9PC0/AKDHaW9vj+bm5k6v9vb2j3xftVqNefPmxaRJk2LChAm5nyehAgB6nLa2tmhtbe10LU86NXfu3FizZk3cfffdXXqeggoASCKr1u/Zedt77/WVr3wlbrnllrjrrrti6NChXXqvggoAaGhZlsWZZ54ZN954YyxfvjxGjhzZ5TUUVABAElk3Odlz7ty5sXTp0vjVr34VTU1N8cILL0RERHNzc/Tr1y/XGobSAYCGtmjRoli/fn0cfvjhMXjw4I7Xtddem3sNCRUA0NBqkaQpqACAJKp1HErf3rT8AAAKklABAEl0l6H0WpBQAQAUJKECAJKoNk5AJaECACgqd0L1wsrfpdzHdrN7vTdQA0313kCN7NG1U/3/Mg0cU+8d1Mgu9d5AjbTUewP82ZOr19Z7C3QYXO8NNAQtPwAgiayBen5afgAABUmoAIAkGujUBAkVAEBRCioAgIK0/ACAJKqG0gEAyEtCBQAk4bv8AADITUIFACSRVeu9g+1HQgUAUJCCCgCgIC0/ACCJqqF0AADyklABAEk4NgEAgNwUVAAABWn5AQBJ+C4/AAByk1ABAEk00Ey6hAoAoCgJFQCQRGaGCgCAvBRUAAAFafkBAEn4Lj8AAHKTUAEASRhKBwAgNwUVAEBBWn4AQBJafgAA5CahAgCSaKCASkIFAFCUhAoASMIMFQAAuSmoAAAK0vIDAJLIfJcfAAB5SagAgCSqhtIBAMhLQQUAUJCWHwCQhKF0AAByk1ABAEk4KR0AgNwUVAAABWn5AQBJaPkBAJCbhAoASKLq2AQAAPJSUAEASWTVrG6vrrjrrrtixowZMWTIkCiVSvHLX/6yy59VQQUANLRNmzbFvvvuGz/4wQ+2eQ0zVABAQ5s2bVpMmzat0BoKKgAgiXp+l1+lUolKpdLpWrlcjnK5nOR5Wn4AQI/T3t4ezc3NnV7t7e3JniehAgCSqNbxYM+2/68tWltbO11LlU5FKKgAgB4oZXtva7T8AAAKklABAEl0l+/y27hxYzzxxBMdPz/11FOxevXqGDhwYAwbNizXGgoqAKChrVq1Ko444oiOn9+dvZo9e3YsWbIk1xoKKgAgiXoem9AVhx9+eOG95i6oHr/hqUIPonZ2r/cGaqSp3huogT2G1nsHNTJwTL13UCO71HsDNdBS7w3wZ0+uXlvvLdTI4HpvoCFIqACAJLJqtd5b2G78LT8AgIIUVAAABWn5AQBJ1POk9O1NQgUAUJCECgBIorscm1ALEioAgIIUVAAABWn5AQBJdJfv8qsFCRUAQEESKgAgCQkVAAC5SagAgCSqme/yAwAgJwUVAEBBWn4AQBKG0gEAyE1CBQAkIaECACA3BRUAQEFafgBAElmm5QcAQE4SKgAgiWrVSekAAOQkoQIAknBsAgAAuSmoAAAK0vIDAJLIMkPpAADkJKECAJIwlA4AQG4KKgCAgrT8AIAktPwAAMhNQgUAJFF1bAIAAHlJqACAJMxQAQCQm4IKAKAgLT8AIImsaigdAICcJFQAQBKG0gEAyE1BBQBQkJYfAJBE5qR0AADyklABAElUDaUDAJCXhAoASMLBngAA5KagAgAoSMsPAEjCSekAAOQmoQIAknCwJwAAuSmoAAAK0vIDAJIwlA4A0EB+8IMfxIgRI6Jv375x8MEHxwMPPNCl9yuoAIAksmq1bq+uuPbaa6O1tTXmz58fDz30UOy7775x1FFHxUsvvZR7DQUVANDQLr744jj11FNjzpw5MW7cuPjRj34UO+20U/zkJz/JvYaCCgDocSqVSmzYsKHTq1KpbHHfW2+9FQ8++GBMmTKl41qvXr1iypQpce+99+Z+Xu6h9OlvP5Z7UWgUfeu9gRppqfcGauSAem+gFj7VU/5/7uB6b6AGesJnqK+7b55ct2cvWLAgFi5c2Ona/PnzY8GCBZ2uvfzyy7F58+bYbbfdOl3fbbfd4ne/+13u5/lbfgBAj9PW1hatra2drpXL5WTPU1ABAD1OuVzOVUDtuuuu0bt373jxxRc7XX/xxRdj9913z/28npItAwB0WZ8+feLAAw+MO+64o+NatVqNO+64Iw455JDc60ioAICG1traGrNnz46DDjoo/vqv/zouueSS2LRpU8yZMyf3GgoqAKChnXDCCfHHP/4xzjvvvHjhhRdiv/32i9/85jdbDKp/mFKWZY1zLjwAQAJmqAAAClJQAQAUpKACAChIQQUAUJCCCgCgIAUVAEBBCioAgIIUVAAABSmoAAAKUlABABSkoAIAKOj/AUpkisVOjd7/AAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Define the two probability distributions p and q\n",
        "n, m = 10, 10  # Probability distributions of size 10\n",
        "p = torch.rand(n, dtype=torch.float32)\n",
        "q = torch.rand(m, dtype=torch.float32)\n",
        "\n",
        "# Normalize the distributions to have a total area of 1\n",
        "p /= p.sum()\n",
        "q /= q.sum()\n",
        "\n",
        "# Create a cost matrix based on the distance between elements in the support\n",
        "cost_matrix = torch.zeros((n, m), dtype=torch.float32)\n",
        "\n",
        "for i in range(n):\n",
        "    for j in range(m):\n",
        "        cost_matrix[i][j] = abs(i - j)\n",
        "\n",
        "# Set up the optimization problem to compute the Wasserstein distance\n",
        "T = torch.nn.Parameter(torch.zeros((n, m), requires_grad=True, dtype=torch.float32))\n",
        "\n",
        "# Define the optimizer\n",
        "optimizer = optim.Adam([T], lr=0.01)\n",
        "\n",
        "# Number of optimization steps\n",
        "num_steps = 1000\n",
        "\n",
        "# Lists to store Wasserstein distances during optimization\n",
        "wasserstein_distances = []\n",
        "\n",
        "# Lists to store distributions p and q for plotting\n",
        "p_values = []\n",
        "q_values = []\n",
        "\n",
        "# Optimization loop to find the optimal transport matrix T and plot Wasserstein distances\n",
        "for step in range(num_steps):\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    # Calculate the cost of transporting the mass from p to q\n",
        "    transport_cost = torch.sum(T * cost_matrix)\n",
        "\n",
        "    # Ensure that the transport matrix sums to the correct marginals\n",
        "    row_marginals = torch.sum(T, dim=1, keepdim=True)\n",
        "    col_marginals = torch.sum(T, dim=0, keepdim=True)\n",
        "\n",
        "    loss = torch.sum(T * cost_matrix) + torch.norm(row_marginals - p.view(-1, 1), p=1) + torch.norm(col_marginals - q.view(1, -1), p=1)\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    wasserstein_distances.append(transport_cost.item())\n",
        "    p_values.append(p.cpu().numpy())\n",
        "    q_values.append(q.cpu().numpy())\n",
        "\n",
        "# Calculate the final Wasserstein distance\n",
        "wasserstein_distance = transport_cost.item()\n",
        "\n",
        "print(f'Wasserstein Distance: {wasserstein_distance:.4f}')\n",
        "\n",
        "# Plot the Probability Distributions p and q\n",
        "plt.figure(figsize=(12, 4))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.bar(range(n), p_values[-1], label='p', color='blue')\n",
        "plt.title(\"Distribution p\")\n",
        "plt.xlabel(\"Support Point\")\n",
        "plt.ylabel(\"Probability\")\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.bar(range(m), q_values[-1], label='q', color='red')\n",
        "plt.title(\"Distribution q\")\n",
        "plt.xlabel(\"Support Point\")\n",
        "plt.ylabel(\"Probability\")\n",
        "plt.show()\n",
        "\n",
        "# Plot the Transport Matrix\n",
        "plt.figure(figsize=(8, 8))\n",
        "sns.heatmap(T.detach().numpy(), cmap=\"Blues\", xticklabels=False, yticklabels=False)\n",
        "plt.title(\"Transport Matrix\")\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "ZxMYvzB4XK23",
        "outputId": "5c9a7748-a65f-4359-a06e-fe96319377ed",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Wasserstein Distance: -2617.4001\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}