demo_sparsity_constrained_optimal_transport.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyMUlbK4v1KUkWgxHkielXNs",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/liutianlin0121/sparsity-constrained-ot-demo/blob/main/demo_sparsity_constrained_optimal_transport.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Sparsity-constrained optimal transport\n",
        "\n",
        "This is a colab to demonstrate sparsity-constrained optimal transport, as proposed in our work:\n",
        "\n",
        "> Liu, T., Puigcerver, J., & Blondel, M. (2023). [Sparsity-constrained optimal transport](https://openreview.net/forum?id=yHY9NbQJ5BP). \n",
        "Proceedings of the Eleventh International Conference on Learning Representations (ICLR).\n",
        "\n",
        "\n",
        "In this notebook, we focus on 1D demos (transporting between 1D distributions). For more demos including the applications in 2D, color transfer, and vision mixture-of-experts models, please refer to the [vmoe](https://github.com/google-research/vmoe/tree/main/vmoe/projects/sparsity_constrained_ot) repository.\n"
      ],
      "metadata": {
        "id": "Et0GPaQgGuJa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Prepare 1D optimal transport data"
      ],
      "metadata": {
        "id": "1r72jfRS7Yx8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!git clone https://github.com/PythonOT/POT.git -q\n",
        "\n",
        "import sys, os\n",
        "%cd /content/POT\n",
        "%pip install -e . -q\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pylab as pl\n",
        "import ot\n",
        "import ot.plot\n",
        "from ot.datasets import make_1D_gauss as gauss\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yOxshwjj7aED",
        "outputId": "fe7207a8-b443-413c-f00f-742291f1f345"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "fatal: destination path 'POT' already exists and is not an empty directory.\n",
            "/content/POT\n",
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Checking if build backend supports build_editable ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build editable ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing editable metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Building editable for POT (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n = 100  # number of bins\n",
        "x = np.arange(n, dtype=np.float64) # bin positions\n",
        "\n",
        "# 1D Gaussian distributions\n",
        "a = gauss(n, m=20, s=5)  # m= mean, s= std\n",
        "b = gauss(n, m=60, s=10)\n",
        "\n",
        "# loss matrix\n",
        "M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\n",
        "M /= M.max()\n",
        "\n",
        "\n",
        "# plot the distributions\n",
        "pl.figure(1, figsize=(6.4, 3))\n",
        "pl.plot(x, a, 'b', label='Source distribution')\n",
        "pl.plot(x, b, 'r', label='Target distribution')\n",
        "pl.legend()\n",
        "\n",
        "# plot distributions and loss matrix\n",
        "\n",
        "pl.figure(2, figsize=(5, 5))\n",
        "ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 780
        },
        "id": "RmxkM6zM7bul",
        "outputId": "633fc3c4-f84e-4694-c6cc-65b129d58621"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 3 Axes>"
            ],
            "image/png": 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d2L0baNECOP98u0dj7qab5OvUqfJHBaUEBmkioppomqS6AeAvf5FFWk503nny+fTu3dzcJIUwSBMR1WTxYmDVKtm85Oqr7R5NeG63/BEByB8V3NwkJTBIExHVxDeLHjIEaNTI3rFEMmKE/DGxcqX8cUFJj0GaiCicHTsCNZvHjLF3LNFo1AgYPFiOn37a3rGQJRikiYjCmTJFKkz16gV07mz3aKLj+2Ni9mz5I4OSGoM0EZGZw4clSAPA6NH2jiUWJ58s93EfPgy8/LLdo6FaYpAmIjLz/vvA9u3AUUcBF19s92hiM2qUfJ06Ve6dpqTFIE1EZOb55+Xr1VcD2dn2jiVWAwdK8Y3Nm4GPP7Z7NFQLDNJERME2bQoEN1+VqWSSmwsMGybHvp3SKCkxSBMRBZs6Ve4zPvtsoFUru0ej5rrr5Ou8ecDWrfaOhZQxSBMR6VVVBRZc+QJdMmrTBujdG/B6gZdesns0pIhBmohI7913gZ07geJi4IIL7B5N7fgWkL34oqz2pqTDIE1EpOe77WrECKBOHXvHUlsXXSSr07dtAz780O7RkAIGaSIin40bgfnzAZdLgnSyy84Ghg+XY98fH5RUGKSJiHx8n92efTZQWmrvWKxyzTXy9YMPgP/9z96xUMwYpImIAOOCsZEj7R2LlU44ATj9dFlANm2a3aOhGDFIExEBssNYWRnQuDFw/vl2j8Zavnu9X3yRO5AlGQZpIiIg8Jnt8OFAVpatQ7HcJZfIDmRbtshn7pQ0GKSJiLZsAT76SI59n+Gmktxc4Ior5HjqVHvHQjFhkCYievll2WGsTx+gdWu7RxMfvpT3v/8taX1KCgzSRJTeqqsDq7qTcZ/uaLVvD3TvLpuavPKK3aOhKDFIE1F6++gjuTWpYUPZ/COV+Vatv/iirPYmx2OQJqL05vuMdtgwICfH3rHE22WXAfn5wE8/AZ9+avdoKAoM0kSUvnbskCpRQGqnun3q1QOGDJFj7kCWFBikiSh9TZsmn0n36gW0bWv3aBLDl/KeMwf49Vd7x0IRMUgTUXryeuWzWSA9ZtE+nTsDXboAlZXAv/5l92goAgZpIkpPCxYAmzYBBQXAwIF2jyaxfLPpKVPk1jNyLAZpIkpPL7wgX//8Z6BuXXvHkmiDBwP16wNr1wL//a/do6EaMEgTUfrZsQOYO1eOR42ydSi2yMsLLCB7/nl7x0I1YpAmovTz8suyYKxnT9nkIx1dd518fftt4Jdf7B0LhcUgTUTppbo6cG+0L1Clo5NPBrp2lRKd3IHMsRikiSi9/Oc/wObNUhUq3RaMBfOl+qdM4Q5kDsUgTUTpxfcZ7LBhUh0qnQ0aJDuQbdgALFxo92jIBIM0EaWPrVsDO4z5bkNKZ/Xqyep2gAvIHIpBmojSxwsvSFr3jDPSZ4exSK6/Xr7OnQts22brUCgUgzQRpYeKisCCsdGj7R2Lk7RvD5x+uiyo437ejsMgTUTp4e23gV27gKZNgQED7B6Ns/j+aJkyRbYLJcdgkCai9PDMM/L1uuuAOnXsHYvTXHQR0KQJUFYmhTfIMRikiSj1rVoFfPklkJmZXsU0olWnTmAhne+PGXIEBmkiSn2+wHPppTJjpFAjR8ofMZ9/Dnz7rd2joSMYpIkotf32GzBjhhxzwVh4TZtK2hsAnnrK3rGQH4M0EaW2KVOAgweBTp2AXr3sHo2z3XijfH31VeDXX+0dCwFgkCaiVFZZCTz9tBzffDPgctk7Hqfr1Uv28z50iJubOASDNBGlrrfeArZvB4qLZQtMqpnLJX/MAPI5fkWFveMhBmkiSlGaBvzzn3I8ejSQlWXveJLFpZfK59NlZcAbb9g9mrTHIE1EqemLL4Dly4GcnEC1J4osKwsYM0aO//lP+WOHbMMgTUSpyTeLvuIK4Kij7B1LsrnuOqkQtmoV8Omndo8mrTFIE1Hq+fHHwM5ZN91k71iSUcOGwPDhcvzII7YOJd0xSBNR6nnkEUnTXnAB0K6d3aNJTrfeCmRkAB99BKxcafdo0haDNBGllq1bgddek+MJE+wdSzI77rjAiviHHrJ3LGmMQZqIUstjjwFVVVIzunt3u0eT3MaPl69vvQWsX2/vWNIUgzQRpY5ffw3URPYFGFLXoQPQvz/g9fKzaZswSBNR6njqKeDAAaBzZ+CPf7R7NKnB95HB9OnAtm32jiUNMUgTUWrYvRt4/HE5njCBW4BapVcv4PTT5SOESZPsHk3aYZAmotTw978DHg9w0knAJZfYPZrUMnGifJ06Fdi82d6xpBkGaSJKfr/8Ajz5pBz/7W9y6xBZ54wzgDPPlNn0Aw/YPZq0wu9kIkp+Dz8M7N8vFZwuuMDu0aSm+++Xr9OmARs22DuWNMIgTUTJbccOqdgESCDhZ9Hx0bMncO65QHW1ZCsoIRikiSi53X+/1D/u2RPo18/u0aQ2X3B+7TXg22/tHUuaYJAmouT1/ffACy/I8eTJnEXHW9euUspS04BbbmGFrARgkCai5HXLLbLRxsUXy21CFH8PPyzlLOfPBz74wO7RpDwGaSJKTh9+CHz8MVCnjgQOSozjjgtUFrvlFlnxTXHDIE1EyaeqSgIEANx4I9Cqlb3jSTd33gkcfTSwdi3w/PN2jyalMUgTUfJ59lnghx+ARo2Au+6yezTpp6AgsIjs3nvlPnWKCwZpIkouW7bITA4AHnwQKCy0dThp65prgI4dgd9/B8aNs3s0KYtBmoiSh6YBo0fLxiW9egHXXmv3iNJXZqZUHHO55Jas+fPtHlFKYpAmouTx9tvAvHmyWOyFF7j9p91OPRW44QY5HjVKKpCRpfgdTkTJYc+eQEAYPx5o187W4dARDzwAHHsssHFjoBAHWYZBmoicT9NkplZWBhx/PHDHHXaPiHzy8mQhHyCVyD7/3N7xpBgGaSJyvn/9C3jjDcDtluOcHLtHRHrnnw8MHy4bywwdKovJyBIM0kTkbBs2AGPGyPHf/gZ062bveMjck08CLVsCW7dK1oNbhlqCQZqInKuyUmZm+/YBvXsDt99u94gonLw8YOZMWfX95ptS0pJqjUGaiJzJd7vV0qVyL/Srr0q6m5zr1FMDm5z85S/y/45qhUGaiJzpmWeAF1+U+3BnzgRKSuweEUXj9tvlM+qKCuDCC4Ht2+0eUVJjkCYi51mwABg7Vo4feQQ491xbh0MxyMiQzU3atQN27JBAffCg3aNKWgzSROQsq1dLzeLqauCKKwKFNCh55OcD774LNGwILFsm6woOH7Z7VEmJQZqInOPHH4Gzz5aNS3r2DGw7ScmnZUvgrbek9vScOcBVV8ktWhQTBmkicoaNG4GzzpKKSiefDLz/Pu+HTnZ9+gCzZ8uCv9dek4WAvDUrJgzSRGS/778HzjhDFhm1awd8/DGrW6WKCy6QAO1ySe3pa69l6jsGDNJEZK/PPwdOO002wWjTRqopHXWU3aMiKw0aBLz8siwqe+klWUy2f7/do0oKDNJEZJ9Zs4yfQS9aBDRpYveoKB6GDwfeeUc+wnj/fUmF8/asiBikiSjxDh2SzS4GD5b7aQcMAP7v/4BGjeweGcXTgAHAwoWBVd+dOgH/+Y/do3I0BmkiSqwffgB69ACee07+PWGC1InOzbV3XJQYPXoAX30FdOwoiwTPOQe48075Y41CMEgTUWIcPAjcfbf8cl61Sj53/vBDYNIkbveZblq3lkDtK8QxaZLMqj/91O6ROQ6DNBHFl9cr98uedBLwwANAVRXQv78E6nPOsXt0ZJecHMmmzJ4NFBXJPfJ9+sgGNhs32j06x2CQJqL4qK4G5s6Ve54HDpSSk02bSsB+7z3gmGPsHiE5waWXSoC+/nq5Teu114ATTgBGjgQ2bbJ7dLZjkCYia/36q+y33bo1cNFFss1nfj5w773yefQll3AXMTIqLASefVaqZvXrJ/dRT50qu5adf758LJKmu5W5NI3bv1Dq8Hg8KCgoQHl5OfLz8+0eTvr47TfZq3n2bFml7dusorBQZki33ioreomi8cUXUvJSv/K7SRP5A2/gQLldLzPTvvEFiefvHQZpSikM0glSVia30Hz+uVSsWrnSuN1jly5yi9WgQUDduvaNk5Lb2rWyS9krr8i99D4FBUDv3rKNbPfust7Bxi1kGaSJosQgbaHKStkFbPNmWcjzww/y+OYbYNu20P4dO8rniwMHymeKRFapqJAMzVtvScbm99+Nz9epA7RvD5x4ouxad8IJQIsW8jjqqLh/vMIgTRQl/w/Lrl3OCdLhfsT07TUde73yNfjha6+uluPqankcPiyPqip5VFbKL7mKCtlE5MABuR1q3z5g717A45FZyu7d8ti1S2bKv/4a/j25XEDbtkC3bjKbOfNM7hRGiVFdLZmbBQvklq3ly2v+Xs3OltXjxcUSsBs2BBo0kNl4Xp6sl6hbV+7Tr1tX+vsedeoEHpmZcqug75GRIV+PPppBmiha/h8WAA4J0cktJwdo3lxmJCecIIG5XTugc2egfn27R0ckf6hu3iy39PmyPRs2SFu8tx11uQCvN65B2jmfvBORGt9f9BkZgb/2MzMDM4CsLOPswDdrqF9fZhJ5eTKz8D18sw7fzIMrscnJXK5AavvCC43PVVRIVqisDNixQxY4/v67ZIw8Hnns3SuZJV+GyZd1qqgIZKOqqgJZKn3mKiP+N0gxSFNq2rJF0lhWsyJghTuHvt3lCvzbd6x/uN3GPkQUKjtbMkHNm8fn/AlIRDNIU2oqKIhPkCYi8knAH8nczISIiMihGKSJiIgciuluSim+mxU8Ho/NIyGidOH7fROPm6UYpCml/PbbbwCAkpISm0dCROnmt99+Q0FBgaXnZJCmlNLwyP7QW7ZssfyHxSk8Hg9KSkqwdetW52zYYjG+x9SRDu+zvLwczZo18//+sRKDNKWUjCP3LRYUFKTsLwSf/Px8vscUkA7vEUiP95kRh/umuXCMiIjIoRikiYiIHIpBmlJKdnY27r33XmRnZ9s9lLjhe0wN6fAegfR4n/F8jyywQURE5FCcSRMRETkUgzQREZFDMUgTERE5FIM0ERGRQzFIExERORSDNKWMZ555Bi1atEBOTg66deuGpUuX2j0kZZMnT8Ypp5yCvLw8NG7cGBdeeCHWrl1r6HPo0CGMHj0ajRo1Qv369XHJJZdg586dNo249h566CG4XC6MHTvW35YK73Hbtm3485//jEaNGiE3NxcdOnTA8uXL/c9rmoZ77rkHTZo0QW5uLvr27Yv169fbOOLYVVdX4+6770ZpaSlyc3PRsmVL3H///YaCE8n2Pv/73//i/PPPR9OmTeFyuTB37lzD89G8n927d2Po0KHIz89HYWEhRowYgX379sU2EI0oBcyaNUvLysrSXn75Ze3777/Xrr32Wq2wsFDbuXOn3UNT0q9fP23atGnad999p61atUr705/+pDVr1kzbt2+fv8+oUaO0kpISbcGCBdry5cu17t27az179rRx1OqWLl2qtWjRQjvppJO0m266yd+e7O9x9+7dWvPmzbXhw4drS5Ys0TZu3Kh9/PHH2oYNG/x9HnroIa2goECbO3eutnr1au2CCy7QSktLtYMHD9o48tg8+OCDWqNGjbR58+ZpmzZt0mbPnq3Vr19fe+KJJ/x9ku19fvDBB9qdd96pvfPOOxoAbc6cOYbno3k/55xzjtaxY0ftq6++0j7//HOtVatW2uDBg2MaB4M0pYRTTz1VGz16tP/f1dXVWtOmTbXJkyfbOCrr7Nq1SwOgffbZZ5qmadqePXu0OnXqaLNnz/b3+eGHHzQA2uLFi+0appK9e/dqrVu31ubPn6/17t3bH6RT4T3efvvt2mmnnRb2ea/XqxUXF2uPPvqov23Pnj1adna29vrrrydiiJbo37+/dvXVVxvaLr74Ym3o0KGapiX/+wwO0tG8nzVr1mgAtGXLlvn7fPjhh5rL5dK2bdsW9bWZ7qakV1lZiRUrVqBv377+toyMDPTt2xeLFy+2cWTWKS8vBxCo8rVixQpUVVUZ3nObNm3QrFmzpHvPo0ePRv/+/Q3vBUiN9/jvf/8bXbt2xcCBA9G4cWN07twZU6dO9T+/adMmlJWVGd5jQUEBunXrljTvEQB69uyJBQsWYN26dQCA1atXY9GiRTj33HMBpM779Inm/SxevBiFhYXo2rWrv0/fvn2RkZGBJUuWRH0tVsGipPfrr7+iuroaRUVFhvaioiL8+OOPNo3KOl6vF2PHjkWvXr3Qvn17AEBZWRmysrJQWFho6FtUVISysjIbRqlm1qxZ+Prrr7Fs2bKQ51LhPW7cuBHPPfccxo0bhzvuuAPLli3DjTfeiKysLAwbNsz/Psy+d5PlPQLA+PHj4fF40KZNG7jdblRXV+PBBx/E0KFDASBl3qdPNO+nrKwMjRs3NjyfmZmJhg0bxvSeGaSJHG706NH47rvvsGjRIruHYqmtW7fipptuwvz585GTk2P3cOLC6/Wia9eumDRpEgCgc+fO+O677/D8889j2LBhNo/OOm+++SZmzJiBmTNnol27dli1ahXGjh2Lpk2bptT7tAPT3ZT0jjrqKLjd7pBVvzt37kRxcbFNo7LGmDFjMG/ePHzyySc49thj/e3FxcWorKzEnj17DP2T6T2vWLECu3btwsknn4zMzExkZmbis88+w5NPPonMzEwUFRUl/Xts0qQJTjzxRENb27ZtsWXLFgDwv49k/97961//ivHjx2PQoEHo0KEDrrjiCtx8882YPHkygNR5nz7RvJ/i4mLs2rXL8Pzhw4exe/fumN4zgzQlvaysLHTp0gULFizwt3m9XixYsAA9evSwcWTqNE3DmDFjMGfOHCxcuBClpaWG57t06YI6deoY3vPatWuxZcuWpHnPZ511Fr799lusWrXK/+jatSuGDh3qP07299irV6+QW+fWrVuH5s2bAwBKS0tRXFxseI8ejwdLlixJmvcIAAcOHEBGhjGcuN1ueL1eAKnzPn2ieT89evTAnj17sGLFCn+fhQsXwuv1olu3btFfrNbL3ogcYNasWVp2drb2yiuvaGvWrNFGjhypFRYWamVlZXYPTcn111+vFRQUaJ9++qm2Y8cO/+PAgQP+PqNGjdKaNWumLVy4UFu+fLnWo0cPrUePHjaOuvb0q7s1Lfnf49KlS7XMzEztwQcf1NavX6/NmDFDq1u3rvbaa6/5+zz00ENaYWGh9u6772rffPONNmDAAEffmmRm2LBh2jHHHOO/Beudd97RjjrqKO22227z90m297l3715t5cqV2sqVKzUA2mOPPaatXLlS27x5s6Zp0b2fc845R+vcubO2ZMkSbdGiRVrr1q15Cxalr6eeekpr1qyZlpWVpZ166qnaV199ZfeQlAEwfUybNs3f5+DBg9pf/vIXrUGDBlrdunW1iy66SNuxY4d9g7ZAcJBOhff43nvvae3bt9eys7O1Nm3aaFOmTDE87/V6tbvvvlsrKirSsrOztbPOOktbu3atTaNV4/F4tJtuuklr1qyZlpOTox133HHanXfeqVVUVPj7JNv7/OSTT0x/BocNG6ZpWnTv57ffftMGDx6s1a9fX8vPz9euuuoqbe/evTGNg/WkiYiIHIqfSRMRETlU3IJ0Ku2jTEREZIe4pLvfeOMNXHnllXj++efRrVs3PP7445g9ezbWrl0bcnN3MK/Xi+3btyMvLw8ul8vqoVGK0zQNe/fuRdOmTUNWmxIRJZu4BOlu3brhlFNOwdNPPw1AAm9JSQluuOEGjB8/vsbX/u9//0NJSYnVQ6I0s3XrVsN9xUREycjyHcd8+yhPmDDB31bTPsoVFRWoqKjw/9v3N8PWrVuRn59v9fAoyf3yC9CqlRzv2QMEJ1s8Hg9KSkqQl5eX8LEREVnN8iAd6z7KkydPxsSJE0Pa8/PzGaQpxN698jUzEygoMO/T13UpLm1wjTUXNPvIxWWeRndlhPl4Rt/fpI/hYx19ij5Mu7G/7th3HX1bhtu0r+Ecbl0ffbvv2K0ff+BYywgzbrf5e9AMfVxh24LPrenOp7ldNfbXv86bGe58+mOYt+uG5fWN1R3aFnIO3euM/UOv48007xv2WD8mk9dqmVpIW+i1dX0yzY+h64Mj7S5dmyvTG+jq1h3r2uvUORw4dlf7j7My5Thb15btDvTNzazyH+fojuu5KwN93Lr2TJng1c0IPJ/nPuQ/rq87zs846D+um1Ghaw/0yTMcy3XyXJquLfAfvn5GYCvbjOL41cW2/UO7CRMmoLy83P/YunWr3UMiB6s68vNZp4694yAiSgTLZ9Kx7qOcnZ2N7Oxsq4dBKcoXpDMTVRrGt2RDP8PUAjMG/SxZ8+pmGxlh+ntDZ9X6ZSEur66vfpapa9fPPl267sjwhl4D1brjwJRKPytzVev66GfV/lN4Q9sAuHR/42sw76OfVevfm3bktS6Etkm7nuFN6vrrxxIqIzBBM8w8jfSvND9jxpF2r0lbcHs4+v8j3iOvzdC9Lsx/vfDn0783/5H5ezFeO/JYzRYpGdsCZ6wO7uiX4NpN8bxcRmDmDq/uPzx0s/R4Xt7qE6biPsrkHIeO/FykaNEkIiKDuPz9MW7cOAwbNgxdu3bFqaeeiscffxz79+/HVVddFY/LURo5eORjpbp17R0HEVEixCVIX3755fjll19wzz33oKysDJ06dcJHH30UspiMKFb798vX3NwEX1h/p6LVqW/9oiYrUt8ZYdLrDkx9G1PctU99h0vmWpH6DpfiVk19ew0p6dqnvo2vY+o7LsKkvuOZ7o7b2xkzZgzGjBkTr9NTmvKVFm7QwNZhEBElhO2ru4lisXu3fG3Y0N5xEBElQoLzEES188sv8rVRIxsHYXXq22TFt1xGLfVtuuI7+DqxpL7N0t6AJalvsxXfcg611HekFd9AbVLfkVPcsaS+zVZ8S7ta6tt8xTdgReo73LaUTH3HH2fSlFR+/lm+Nm9u6zCIiBKCM2lKKps2ydfSUnvH4WfFrDrCfdRymehn1RHvow6+ToRZdcTFZID6rDrCfdRyjlhm1dHfRw3EOquu+T5qGQVn1cFnNJ9V2xB6kjTacSZNSWXNGvnasqW94yAiSgQGaUoaW7YA//ufTOa6dLF7NERE8ZekCQBKR198IV87dQLq1bN1KOYUU9+xbCEql4mQ+o5lC9Hg65ikvmO6jxqwOfWttoUoEE3qO/otRGUkTH0Hn5Gp79hxJk1JY84c+dq7t73jICJKFAZpSgq//ALMnSvHV15p61CIiBImiSb9lM6mTZMKWKecAnTsaPdoohBD6lu1epZcxiT1rVo9K/g6/uSk4haiQMTUt2r1LDmHWVUtPWenvlWrZ0l7YlPfqluIhrbLGR1zH7VNl4wFZ9LkeNu2AQ8+KMejRtk7FiKiRGKQJse74QbA4wFOPRUYNszu0RARJY7DJ/qU7l5+WRaMZWYCL74YPqtq4HIZ0812i5T6Vq2eBZimvpWrZwFhUt8WVM8CTFPfqtWzpH9o6lu1elZof11vX5UpxepZcsXQ1Ldq9SzpH5r6Vq2eFfra0PdjRfUsY7sDtxC16ZKRcCZNjvXaa8A118jxHXcAHTrYOx4iokRjkCZHmjFDUtuaBowcCdx7r90jIiJKPAdO7imdVVXJIrH775fs7DXXAM89Z8zaRsWQVnZ46lu1ehZgmvpWrZ4l/XVj9aW+VatnAQlPfatWz5L++rGEUq+eZWw3W91tRepbdcU3EE3qW22zE+Mrw7Ux9V0ThwyDCPjuO7kHeuVK+fd11wHPPqsQoImIUgR//ZHtDh8GHn5Y9uNeuRJo2BCYNQt4/nkGaCJKb5xJk20qK4FXXwUeegjYsEHazjsPmDIFaNKkFid2ZQSlkB2e+lYtcRnc35eWVixxCYRJfSuWuASiSH2r7vMNmKa+1UtcAolOfVuxz7f09/Wt/WYnQLjUd+33+Ta+MlybA1PfNkdJBmlKuAMH5HaqRx+VqlaAzJ4ffRS46ipjzCIiSmcM0pQwu3fLLPmf/wR27ZK2Jk2AW2+VFdz169s7PiIip2GQprg6eBB47z25perDD2X1NgC0aAHcfjswfDiQkxOHC+tSxY5PfSuWuJRmk/6qJS4B09S3aolLOYfuLSQg9a1e4hKIlPpW3+c7+NWhZ3RiiUtAt5GLodUpJS6BdEh9M0iT5aqrgYULJTC/8w6wd2/guU6dgJtvBgYPBurUsW2IRERJgUGaLHH4MPDVVxKUZ80CduwIPNe8OTBkCDB0KNCunX1jJCJKNgzSpOznn4GPP5bHggVSBMOnYUPgssskMPfsmdhbqVwZLkNKOO1S36olLgHT1Ld6iUsgYupbscQlECb1rVjiUtr1QlPf1pS41L9arcRlcLvpOHTHdpa4lP6JSH2nbh6aQZqitn8/8NlnwEcfSWBet874fMOGQL9+wKBBwDnnAFlZ9oyTiChVMEhTWIcOAStWAIsWAfPnA59/Lvc2+7jdQPfuEpj79ZPNSKKqUpUA+gVV6TarVq2eBYSZVStXzwIizapVtxAF7JhVq1XPAsLNqtWqZ9XUbjoO3TFn1ckntd4N1crOncCXX8rjiy8kQOuDMiCfL/uC8plnAoWFtgyViCgtMEinKa8XWLNGgrEvKP/0U2i/xo2BXr2AM86QwHz88dxshIgoURik08T27TIzXrECWLIEWLwYKC839nG5ZPV1r16y2KtXL+C445IwKAdtC5puqW/V6llyGZPUt2r1rODrmKS+raieBQRS36rVs+QckVLfaluIAolJfatWz5L2xKa+VbcQDW2XMzrmPuo4SP53QCH0Adn30N8S5VOvHtCtWyAgd+/O9DURkZMwSCe5aANyRgbQpg3Qtas8evYEOnYEMvkdQETkWPwVnSS8XmDjRmDVKmD1avlaU0Bu21ZWW/senTrJzDktZLiMaVYrUt9OSXsDkVPfqtWzANPUt3L1LCCK1LfiFqKAaepbtXqW9K859W1F9SxAt9WmYvUsuWJo6lu1epb0T2zq24rqWcZ2B24hapHkHHWKO3AA+PbbQDBevRr45htg377QvmkfkImIUhiDtI00DSgrM86OV6+WTUK8Jn/CZmcDHTpImrpjR+DkkxmQiYhSGYN0ghw+DKxdawzIq1YBv/xi3r9xYwnAnTpJQO7USW5/4mfIUdKndq1IfTtxxTdgnvpWrZ4FmKa+VatnSX/dWE1T3xZUzwISkvpWrZ4V2v9IT+XqWcZ2s9XdVqe+Vatnhb42dEtUK1Lfjq+eVQvJM9IkUl4u6Wl9QP7uO6CiIrRvRgZwwgnGYNyxI1BcnNgxExGR8zBI14KmAVu2hM6ON20y75+XB5x0knGG3L49kJubsCETEVESYZCOkqYBmzcDy5cHHitWAHv2mPcvKQlNV5eWJrYaVLpyuVyGFK0lqW+nb3YCBMaiWj0ruL/vv5Vi9SwgitS3avUswDz1rbrPNxAx9a1aPUv668cSyorUtxX7fEt/3Vj8q7HVVnwD4VLftd/n2/jKcG3Jn/p29uhstG2bMSAvXw78+mtov8xM2aXLF4h9Qblhw0SPmIiIUg2DNIBdu0IDstn9x5mZkq72bQjSpYsE6OzsxI+ZiIhSX1oG6R07gE8/BT75RB4bNoT2yciQANy1K3DKKfK1QwcgJyfhw6VYZWQY05VWpL5TdJ9vaY6Q+lYtcQlETn0rlrgEEp/6Vi9xCZilvtX3+Q5+degZrU59W7HZCaDbyMXQ6pQSl4ATQ6LzRhQHu3ZJUPYF5h9/ND7vcskKa18w7tpV0tZ169owWCIioiNSMkjv3m2cKX//vfF5l0uCcJ8+8vjDH4CCAjtGSkREFF7KBOnqamD+fODFF4F335XNQ/Q6dAgE5dNP58KulOZyGVKuVqS+06HEpTSbpL5VS1wCEVPfqiUu5Ry6t+BLfSuWuAQip77VS1wCZqlva0pc6l+tVuIyuN10HLpjO0tcSv/0Sn07YxS1sHkzMG0a8PLLwNatgfa2bYEzz5Sg3Ls3cNRR9o2RiIhIRVIG6epqYM4cmTX/5z+ByUKDBsAVVwAjRsgqbCIiomQWU5CePHky3nnnHfz444/Izc1Fz5498fDDD+OEE07w9zl06BBuueUWzJo1CxUVFejXrx+effZZFBUVWTLg6mrg8suBt98OtJ15JnDNNcBFF3H1NUFSrGFSrqqpb+USl3Kh6MceT4qpb9USl0Dk1Ld6iUvALPWtus83EEXqW7HEpbTr+Ze26/oiTN+AyKlvtRKXNbWbjkN3nB6pb3vnsjHtf/XZZ59h9OjR+OqrrzB//nxUVVXhj3/8I/bv3+/vc/PNN+O9997D7Nmz8dlnn2H79u24+OKLLRmspgFjx0qAzsoCJkyQ26cWLAAGD2aAJiKi1BLTnwgfffSR4d+vvPIKGjdujBUrVuD0009HeXk5XnrpJcycORNnnnkmAGDatGlo27YtvvrqK3Tv3r1Wg330UeDpp+X41VeByy6r1ekoRblcLsMMzZJZtWr1LBmQrj35ZtWq1bPkMhFm1crVswCzWbUV1bOARM2q1bYQBTirDr6+6haioe3Om1XXaifp8vJyAEDDI0ulV6xYgaqqKvTt29ffp02bNmjWrBkWL15seo6Kigp4PB7Dw8yuXcD48XJ8550M0ERElPqUg7TX68XYsWPRq1cvtG/fHgBQVlaGrKwsFBYWGvoWFRWhrKzM9DyTJ09GQUGB/1FSUmLar1Ej2YYTAF5/Hdi5U3XkREREyUF57j569Gh89913WLRoUa0GMGHCBIwbN87/b4/HYxqo3W5g3jygRw9g40bgvPOAuXOBY46p1eUpFWW4DOlSS1LfqtWzgvonZepbtXoWEDn1rVo9K/g6/uSk4haiQMTUt2r1LDmHWVUtvdqnvlWrZ8kVa059q1bPkvb4p76tqJ4V2i5ntfs+aqWZ9JgxYzBv3jx88sknOPbYY/3txcXFqKysxJ6g+o07d+5EcXGx6bmys7ORn59veIRTVAR89JHMqpcvB5o1CwTrqiqVd0JERORcMQVpTdMwZswYzJkzBwsXLkRpaanh+S5duqBOnTpYsGCBv23t2rXYsmULevToYcmAjz9edhb7wx/kD+/335dbr0pK5DPr9estuQwREZHtYpqvjx49GjNnzsS7776LvLw8/+fMBQUFyM3NRUFBAUaMGIFx48ahYcOGyM/Pxw033IAePXrUemW3XufOwH//C6xdKzuNvfKKfEb98MPy6N0bGDRIdhs7/nhjBo/SgCvDkBa1JPWtWj3LNx6T/v5vTKekvQHz1Ldq9SwgYupbuXoWECb1bUH1LMA09a1aPUv6h6a+VatnhfY/0lO5epax3Sz1rVo9S/qHpr5Vq2eFvjZ0S1TrU9/RbCEaPy5Ni/43hCtMtJs2bRqGDx8OILCZyeuvv27YzCRcujuYx+NBQUEBysvLa0x961VVyefVL74o6XD9z32TJhKszzhDvrZsyaCdyjweDy4rvTUoUAS+xQ3f7vpvlDDtpj8e+gCsmf+6MQRp4xMmbQ4K0npmPygu8+SbIUiH62/Sx/A7RR+kw7Qb++uOfdfRt2W4TfsazqEP0vp2Qx/fuXUBMyPMuN3m78Hwx6HbFbYt+Nya7nya21Vjf/3rvJnhzqc/hnm7/m8l31jdoW0h59D/LWroH3od/R8RxnGEOdaPyeS1WqYW0hZ6bV2fTPNj6PrgSLtL1+bKDPz8ut2B4w2X34V4iSlIJ4JKkNbbuhV47TXZLnTxYqCiwvj8sccGCm306QO0aGHNuMkZGKQtxCB9pA+DNIO0YJBG7YO03qFDEqh9JSuXLAldYNaihaTHTz1V6kmfdBKQnV2ry5KNPB4PLmv51/CBVDFgh/0xSYeAHS715MSAHe4aVgRsfQC2ImC7aw7iweeOFLANfS0O2OECs2rA1l/DioBteN7qgK1rCxewNw25A/GSlAU2opWTE5gxA8CBA8CXXwaC9rJlwM8/y2P6dOlTp46UtezaNfBo317aiYiIEimlg3SwunWBvn3lAQD79gGLFgFffCG3dC1bBvz2G/D11/KYMkX6ZWcDnToZA3fbtuHXnBAREVkhrYJ0sPr1gXPOkQcgmcYtWyRYL18eeJSXS6p8yZLAa+vWlVXmnTtLAO/YUWbcLPLhABluGNZhGlYYq636Vq2eBUSx6jvZNzsB1Fd9K1bPAoz/z/z/LxWrZwFRrPpW3ecbMF31rV49CzBb9R1uPawVq76t2Odb+vv61n6zE0C3kYuh1fy9WLHqO9w+3/GU1kE6mMsFNG8uj0svlTavV3Y40wfuFSuA/ftlBv7FF4HXu91AmzYSsDt1CgTvxo3teDdERJTsGKQjyMgAWrWSx+DB0lZdDaxbJwF79Wpg1Sp5/PYb8P338pg5M3COJk2MQbtTJzkf0+VERFQTBmkFbrd8Jt22LXDFFdKmacD27RKs9YF7wwZgxw55fPhh4Bx168oCNX3g7tBBUvBUSxku6FOalqS+VUtcApFT36m0zzcQW+pbtcQlYJr6Vi1xKefQvYUEpL7VS1wCZqlva0pcBr86NJmeSiUupX/NY41un+/4YZC2iMslxT6OOQbo3z/Qvm8f8O23xuD9zTey0jz4c26XS2bYvqDt+3rMMdyAhYgoHTFIx1n9+lK5S791eXW17DG+enUgcK9eLTPx9evl8dZbgf4NGxqDdseOMovPykrwmyEiooRikLaBb4FZmzbA5ZcH2n/5xZgqX70a+OEHYPduYOFCefj47ufu0iXw6NCBG7EAskGFZlh4aUHqW7XEZfB1TFLfKVviEoic+lYtcQmYpr7VS1wCEVPfiiUugTCpb8USl9Ku51/aruuLMH0DYkt9q5W4DG43HYfuOFlT3/HEIO0gRx9tvI8bkF3T1qwxpstXr5bbwnz3c0+dKn3r1JHbwLp2ZeAmIkoFDNIOl5MDnHyyPHw0TXZJW7HC+Ni9G1i5Uh7BgdsXtLt2TYPA7XYbFv5YMatWrp4FRJxVK1fPkgvBERRn1arVs4Aws2rl6llApFm1avUsIFGzarXqWUA0s+qa76OWK3JWHQ8M0knI5QJKS+Xhu59b04DNmyVY++7lDg7cL74ofbOyJGD36iWPnj15LzcRkRMxSKcIl0uKhbRoAVxyibTVFLgXL5bH3/8ufVu1CgTsXr1kYVpGRrirERFRIjBIp7Bwgfunn2SntC+/lK/ffy/3c2/YECg0UlgoK9J9Qbt7dyA316Y3EiuXy5COtCL1HcsWotI/htR3LFuIBvVP9tR3TFuIApFT37FsIQrElPqO6T5qIGLqO5YtRKV/zanvWLYQDe2v652A1HcsW4hKf/tS39GMNZ4YpNOM717sVq2AYcOk7fffga++CgTtJUuAPXtk8xXfBizZ2cDppwP9+sle5yeeyHu3iYjijUGa0KABcO658gCAw4dlBblvtr1oEbBtGzB/vjxuvVU2WOnXTx59+8q93EREZC2XFraavT08Hg8KCgpQXl6O/Px8u4dDkOzljz8CH38sj08/lVvDfDIygFNOkYB97rlAt272zbI9Hg8u73CvMeWqP9anvvXt+tSytzq03ZB+1RWJN5xDnxM3bzf9cdNfWzNP4BlS38YnTNoc9SMdYPZN4TJf+GBIfYfrb9LHpb+GPvUdpt3YX3dsdp0Mt2lfwzn0qW99u6GPrwKYLg2dEWbcbvP3YPjIxe0K2xZ8bk13Ps3titz/yLE3M9z59Mcwb9d/AuEbqzu0LeQc+k94DP1Dr6NPyxvHEeZYP6Zwr83UIlw78HO2aewtiBcuDaKIXC5ZSDZ2rKS/d++WYD1uHNCuncSgJUuAv/1NPsc+7jjgzjvl/m4iIlLHIE0xy80F/vhH4B//AL77Dti6FXjpJeCyy4C8PLmHe9IkCeCdO8sK8m3b7B41EVHyYbqbLHXwIPDee8Brr8ms+/CRFZUuF3DGGcCf/ywlP+O1Utzj8eDyThONK2utSH2HS0kz9a0mGVPfhpS0BalvfSrbitS326QtpF0t9a1/nRWp73ApbtXUt/4aVqe+fWnvcNcGgI23jEO8cCZNlsrNlRn1v/8NlJUBzz0HnHaaxIpPPgFGjJBNWB55BNi71+7REhE5G4M0xU2jRsCoUcDnnwObNkkKvFkzYOdO4PbbgebNgfvuA377ze6REhE5E9PdlFBVVcCMGcDkycC6ddJWrx5w/fWy2KywsHbn93g8uPzk+43pZitS32YrvgFLUt9hfwRVU99h+joy9R3uNgDV1HeY5y1JfYdLr6umvs1WfAeNI5bUd/gUd+1T32YrvgH11LfZiu/gvrGkvs1WfMv4QvvWeGyS+jZb8R3cvuE2prspRdSpAwwfLiu/33xTamPv3y+Ly9q3l1XjREQkGKTJFm43MHCgFP6YN092QNu2TXYzGzUK2LfP7hESEdmPO46RrVwuoH9/Wfk9YQLw1FPACy8A//kP8PrrsjFKrLQMl6E0oEGY/ZQj7/WtVuJSzlHzXt+qJS6BMHt9p+g+39IcYa9v1RKXQOS9vhVLXAJR7PWtWuIS8Ke+1UtcApH2+lbf5zv41aFndGKJSyDw3qLZ5zueOJMmR6hXD3jySWDBAllQtmkTcNZZsiUpEVG6YpAmRznzTOCbb2Q/8P37ZZvRL76we1RERPZgupscJz8fePdd4PzzgYUL5XPqhQtlf/CoZGQYUoNWpL5VS1wCUaS+VUtcAqap73QocSnNJqlv1RKXQMTUt2qJSzmH7i34Ut+KJS6BMKlvxRKX0q4Xmvq2psSl/tVqJS6D203HoTtOXInL+OFMmhypbl3ZuaxPH1lENnSosagHEVE6YJAmx6pbF5gzB2jaFFi/Hrj/frtHRESUWEx3k6MVFABPPw1cfLFsJTpoENChQ4QXuY1/e1qR+jZf8Q1YkvoOk3JVTX2brviWJ0L6SnvqpL5NV3wDlqS+TVd8A8qp74grvgEHpb5DV3yH9g2InPoOt0o6WVPf8cOZNDneRRcBAwZIsY7HHrN7NEREicOZNCWF226TxWRvvAE8/rjMsMNyuUJm0z7Ks+qI91EDqrPqSPdRS98YZtWR7qOWJ6B7Qtee3LPqiPdRA+qz6kj3UQMxzapjuo8aiDirjnQftYxVdVZd833Uxr5GiZhVR5pRS1/dOCyeVccTZ9KUFHr0AE48UUphvv663aMhIkoMBmlKCi4XcOWVcvz++/aOhYgoUZjupqRxxhny9csvJfOYEeZPTC0jw5iudHjqO5YtRKV/hNR3LFuIyhOm/f2pZaekvYHIqe9YthAFYkt9x7KFKBBF6ltxC1HA9Psyli1EZazRp75j2UI0tL+ut2+rzZi2EDW2m6W+Y1lMJv0DrNpGNF44k6ak0bkzkJMD7N4NrF1r92iIiOKPQZqSRlaWlLYEpNQlEVGqY7qbkkppKbBkiRTgCMvtMqbvrEh9K1fPAiKmvhWrZ0l/k9S3avUseSK0vxNXfAPmqW/V6llAxNS3cvUsIEzq24LqWUBCUt+q1bNC+x/pqVw9y9hutrrb6tS33WlvzqQpqZSWytcagzQRUYpgkKakcswx8nXnTnvHQUSUCEx3U1Jp2FC+7t4dvo+WkRF+cwYnpr5Vq2cBpqlv1epZ0myS+nb6ZidAYCyq1bOC+5ukvlWrZ0l/3Vh9/49Vq2cB5qlv1S1EgYipb9XqWdJfP5ZQVqS+rdhCVPrrxnLktXav+OZMmpKKL0j/9pu94yAiSgQGaUoqeXnydf9+e8dBRJQITHdTUsnNla8HDtTQKXh1twWpb9XqWUA0qW/F6lmAaepbtXoWECb1naL7fEtzDKlvxepZQJjUt2L1LCDxqW/16lmAWepbfZ/v4FeHntHq1Lfdm53Uaib90EMPweVyYezYsf62Q4cOYfTo0WjUqBHq16+PSy65BDu5yocs4gvSBw/aOw4iokRQDtLLli3DCy+8gJNOOsnQfvPNN+O9997D7Nmz8dlnn2H79u24+OKLaz1QIkA2NAGAqip7x0FElAhK6e59+/Zh6NChmDp1Kh544AF/e3l5OV566SXMnDkTZ555JgBg2rRpaNu2Lb766it0797dmlFT2qpTR77WFKS1DFdQQqz2qW/lfb6BKFLfaiUu5Rwm6VXVEpeAaeo7HUpcSnOE1LdqiUvANPWtWuJSzqF7C77vKcUSl0Dk1Ld6iUvALPVtTYlL/avVSlwGt5uOQ3ccLvUdT0oz6dGjR6N///7o27evoX3FihWoqqoytLdp0wbNmjXD4sWLTc9VUVEBj8djeBCFE02QJiJKFTHPpGfNmoWvv/4ay5YtC3murKwMWVlZKCwsNLQXFRWhrKzM9HyTJ0/GxIkTYx0GpSnf5ETT5OFKzB+zRES2iClIb926FTfddBPmz5+PnJwcSwYwYcIEjBs3zv9vj8eDkpISS85NqUefQQwXpDV3BmBIT+uec2DqW7XEpYxVNy7ffxzVEpfB1zmS5lUucSkXgiNYkfpWLXEJmKa+1UtcAmapb9V9voEoUt+KJS6lXc+/tF3XF2H6BkROfauVuKyp3XQcumMvEvO9HVO6e8WKFdi1axdOPvlkZGZmIjMzE5999hmefPJJZGZmoqioCJWVldizZ4/hdTt37kRxcbHpObOzs5Gfn294EIWj/12n/51ERJSKYppJn3XWWfj2228NbVdddRXatGmD22+/HSUlJahTpw4WLFiASy65BACwdu1abNmyBT169LBu1JS2nDhJIyKKl5iCdF5eHtq3b29oq1evHho1auRvHzFiBMaNG4eGDRsiPz8fN9xwA3r06MGV3WSJaD6D1twuBCem/K/X94sl9a26zzcQMfWtXOISME19K5e4BMxT36olLgFn/lWlmPpWLXEJhEl9K5e4BMxS31aUuAQSlfpW2+cbcGbqO54s33Hsn//8JzIyMnDJJZegoqIC/fr1w7PPPmv1ZShNOfF3PhFRvNQ6SH/66aeGf+fk5OCZZ57BM888U9tTE4WIKki7XUFLOmo/q7akehZgPntRrZ4FmM6qVatnAWFm1arVs4L6O/IvrBhm1arVs+QyJrNq1epZwdfxfz8obiEKRJxVq1bPknOYVdXSq/2sWrV6llyx5ll1NFuIxhMLbBARETkUgzQlLadMxoiI4oVVsCipRLVwLGRbUD211Ldq9Sw5R4JT34rVs6S/SepbtXqWPGHa3/8/0kl/aUVKfatWzwJMU9/K1bOAMKlvC6pnAabfl6rVs6R/hJ8nw0nUUt/q1bOM7Wap71irZ1mNM2kiIiKHYpAmIiJyKKa7KalEm+42vEb/nOGZ6FPfqluISv8IqW/l6lmAaepbtXoWYJr6Vq2eJc0RUt9OXPENmKe+VatnAaapb9XqWdJfN1bf/2PV6llAwlPfqtWzpL9+LKGsTn2r3kdtFc6kiYiIHIpBmoiIyKGY7qaU4810GVJeeqqpbyuqZ0n/RKS+FatnAaapb9XqWUAUqW+nb3YCBMaiWj0ruL9/Fb5a9SwgTOpbsXoWEEXqW3ULUcA09a1ePQswS32rbyEa/OrQ1Hc0W4jGE2fSREREDsUgTURE5FBMd1PK0TJchtSWFalv5epZQMTUt2r1LCBc6lutepacwyS9qlo9C4ic+k7Rfb6lOULqW7V6FmCa+latniXn0L2FBKS+1atnAWapb2uqZwW/OjSZztXdRERE5McgTURE5FBMd1PK0dxByTFLUt9qJS6ByKlv5X2+AdPUt2qJSxmrbly+9Kpqicvg65ikvtOhxKU0m6S+VUtcAqapb/USl0DE1LdiiUsgTOpbscSltOv5l7br+iJM34DYUt+R9/mOJ86kiYiIHIpBmoiIyKGY7qaUo7mBcIku9dS3WonLkPYEpL6VS1wCpqlv5RKXQMTUt3KJS7kQHEEx9a1a4hIIk/pWLnEJREp9q+7zDSQq9a22zzcQTeo78j7f8cSZNBERkUNxJk0pRxaORf6LN5ZZtWr1LGmPMKtW3UIUMJ+9qFbPAkxn1arVs4AoZtWq1bOApJ9Vq1bPksuYzKpVq2cFX8dkVm1F9Swg8H2sWj1LzmFWVUvPjll1/HAmTURE5FAM0kRERA7FdDelHEnNxbbYI1LqW7V6lvSPkKqzonoWEL/Ut2L1LOkfIfWtWj0rqL8/teyUtDcQOfWtWj0LME19K1fPAqJIfStuIQqYfl+qVs+S/qE/T6rVs0L763of+T0Q3Rai8cOZNBERkUMxSBMRETkU092UcrxuV9CWfc5OfatWz5JzmPRRrp4FmKa+VatnAZFT36rVs+SJ0P5OXPENmKe+VatnAaapb9XqWdJfN1bT1LcF1bOAuKW+VatnSX/9WEJFt4Vo/HAmTURE5FAM0kRERA7FdDelHM1tLMhuRepbvXoWECn1rbqFqPRPROpbsXoWEDH1rVo9S5pNUt9O3+wECIxFtXpWcH//Kny16llAFKlv1epZgHnqW3ULUcA09a1ePQtweuqbM2kiIiKHYpAmIiJyKKa7KeUEr+62IvWtXj1Lrqo7U0h/K6pnSf8je20rVs8CwqW+1apnyTlqTn2rVs8CwqS+U3Sfb2mOkPpWrZ4FRE59K1bPAhKT+lavngVESn1Hs893PHEmTURE5FAM0kRERA7FdDelnJpWdzsx9a1c4hIwTX0r7/MNmKa+VUtcylh14zJLr6qWuARMU9/pUOJSmk1S36olLoGIqW/VEpdyDt1b8KW+FUtcAmFS34olLqVdLzT1Hc0+3/HEmTQREZFDMUgTERE5FNPdlHK0oD89rUl9q+3zHe5svqv6RmLe1xmpb+USl0Dk1Ldqicvg6xxJ9SqXuJQLwREUU9+qJS6ByKlv9RKXgFnqW3Wfb8CO1HdsJS6txpk0ERGRQzFIExERORTT3ZRytDDZM6A2qe/al7gMfmXgjGolLkPafak91X2+AfMUo2qJSyBi6lu5xCVgnvpWLXEJJH3qW7XEpVwmQupbucQlYJb6tqLEJRD4PlYtcSnniJT6jrzPdzxxJk1ERORQnElTyvG6o/vrM7ZZtVr1LCDyrFq1epa0h84CLKmeBSRkVq1aPQsIM6tWrZ4V1D8pZ9Wq1bOAyLNq1epZwdfxfz8obiEKmH5fqlbPkv4Rfp4MJzGfVccTZ9JEREQOxSBNRETkUEx3U8rR3C54wyzLCidS6lt1C1EgcupbtXqW9A9N1alWz5JzmPRRrp4FREx9K1bPkv4mqW/V6lnyhGl/f2rZKWlvwDz1rVo9C4iY+laungWESX1bUD0LSEjqO7otROOHM2kiIiKHijlIb9u2DX/+85/RqFEj5ObmokOHDli+fLn/eU3TcM8996BJkybIzc1F3759sX79eksHTURElA5iSnf//vvv6NWrF/r06YMPP/wQRx99NNavX48GDRr4+zzyyCN48sknMX36dJSWluLuu+9Gv379sGbNGuTk5Fj+BoiCeTOBDMNdjrVPfVtRPcs3Nv954pT6Vt1CVPonOPWtWj0LME19q1bPkuYIqW8nrvgGAmNRrZ4V3N8k9a1aPUv668bq+3+sWj0LME99q24hCkRMfUe3hWj8xBSkH374YZSUlGDatGn+ttLSUv+xpml4/PHHcdddd2HAgAEAgH/9618oKirC3LlzMWjQIIuGTURElPpiSnf/+9//RteuXTFw4EA0btwYnTt3xtSpU/3Pb9q0CWVlZejbt6+/raCgAN26dcPixYtNz1lRUQGPx2N4EBERUYwz6Y0bN+K5557DuHHjcMcdd2DZsmW48cYbkZWVhWHDhqGsrAwAUFRUZHhdUVGR/7lgkydPxsSJExWHTxRKcwdvOVD71Ld69azgdt25j/z0qVfPktEE97eiepb0P7LhiGL1LCCa1Ldi9SzANPWtWj0LiCL1neybnQDqqW/F6llAmNS3YvUsIPGp72h+nuIppqt4vV6cfPLJmDRpEjp37oyRI0fi2muvxfPPP688gAkTJqC8vNz/2Lp1q/K5iIiIUklMQbpJkyY48cQTDW1t27bFli1bAADFxcUAgJ07dxr67Ny50/9csOzsbOTn5xseREREFGO6u1evXli7dq2hbd26dWjevDkAWURWXFyMBQsWoFOnTgAAj8eDJUuW4Prrr7dmxEQRBFfBsiL1rV49C4iU+lavniVX1Y8ytG/tU9/K+3wDUaS+1apnyTlM0quq1bOAyKnvVNrnG4gt9a1aPQswTX2rVs+Sc+jegu97SrF6FhA59R3NPt/xFFOQvvnmm9GzZ09MmjQJl112GZYuXYopU6ZgypQpAACXy4WxY8figQceQOvWrf23YDVt2hQXXnhhPMZPRESUsmIK0qeccgrmzJmDCRMm4G9/+xtKS0vx+OOPY+jQof4+t912G/bv34+RI0diz549OO200/DRRx/xHmkiIqIYuTTNKfkZ4fF4UFBQgPLycn4+TSH27QPy8uT4wAEgN9f4vMfjQfeHXoJLlykLd6xPLbuqdalvk/769JzhHLrXhW03vDa0v6FNl3bMOGzerj+G4XxH9lmu9kbuq09Nhmv3/WrQpwy9Yc5tOJ/JOYKPj6QpDb9+DOerNm83rDwOtPvPYzb+oPawv/LCXcffFOZ1Jn1Dru8UrjBbcLjMP8YwpL7N+po9D8mqBvro89OukDZjX91xuOtkuEPaDefQp7717YY++nPrUt8ZJuN2m4wfxo9bPv7mfsQL9+4mIiJyKAZpIiIih2KpSko5WpR/ejpn1bfaPt/hzqZa4jKk3ZciVt3nG4i46lu5xCVguupbucQlEHHVt3KJS7kQHEFx1bdqiUsgzKpv5RKXgNmqbytKXAJRrPoOs893PHEmTURE5FAM0kRERA7FdDelHG9m+PRw2Nfojs1S36olLmtq1++2HdoWdO4YUt+qJS6l3aRUnxUlLgHzFKNqiUvANPWtWuISiCL1rVriEkj61LdqiUu5jEnqW7XEZfB1/N8Pivt8AxFT39Hs8x1PnEkTERE5FGfSlHJCqmBZMKtWrZ4l/SPNqtWqZwHm7021epb0D51Vq1bPknMkeFatWD1L+keYVatWzwrq75+1OmVGDUSeVatWzwJMZ9XK1bOAMLNqC6pnAabfl1FtIRpHnEkTERE5FIM0ERGRQzHdTSlHy9QAw+KvANXUt+p91NK/5tS3avUsIDGpb9XqWdI/QupbuXoWYJr6Vq2eBUROfatWz5InQvs7cTEZYJ76Vq2eBZimvlWrZ0l/3Vh9/49Vq2cBjk99cyZNRETkUAzSREREDsV0N6UczQ2ESxWrpr6t2EJU+oemvmPbQjS4XXfuIz/NsW0hKlfVjzC4f0xbiAI2p76j30JUzhF96juWLUSBKFLfTr+PGgiMJYYtRKU5Quo7li1Egcip7xi2EJVz6N5CpNR3FFuIxhNn0kRERA7FIE1ERORQTHdTyvG6g//6dHbqW716VnD7kXMoV8+Sq+pHGNrX2tS3avUsIFzqW616lpyj5tS3avUsIEzqO0W3EJXmCKlv1epZgGnqW7V6lpxD9xYUU9/xxJk0ERGRQzFIExERORTT3ZRyNLcWlDY2PKs7dkbqW716FpCY1Lda9SwgcupbeZ9vwDT1rVo9S8aqG5dZelW1ehZgmvpOh+pZ0myS+latngWYpr7Vq2cBEVPfMVbPshpn0kRERA7FIE1ERORQTHdTypG9uwPSL/Wtts93uLOplrgMaU9A6lu5xCUQOfWtWuIy+DpHUr3KJS7lQnAExdS3aolLIEzqW7nEJRAp9R3VPt9xxJk0ERGRQzFIExERORTT3ZRygtPdeqqpb9USl3KdRKe+a1/iMtzZLE99q+7zDZinvlVLXAIRU9/KJS4B89S3aolLIOlT36olLuUyJqlv1RKXwdcxSX3HXOLSYpxJExERORSDNBERkUMx3U2px60hmgRgLKlv1RXfIa81SX2rlrgM365W4hIwf2+qJS6lf82pb0tKXAIJSX2rlrgEwqS+VUtcBvX3p5adkvYGIqe+VUtcAqapb+USl0AUqe8o9vmOI86kiYiIHIozaUo9QQvHrJlV1/4+6pDX+mfpatWzpH/orFp1C1Eg8bNq1epZcg6TPsrVs4CIs2rF6lnS32RWrVo9S54I7e/ExWSA+axatXoWYDqrVq2eJf11YzWdVUfeQjSeOJMmIiJyKAZpIiIih2K6m1KOq4aFY+qpb2u3ENW/VvU+aukfmvq2onoWEEh9q1fPktGY9z+ycExxC1Hpn+DUt2r1LMA09a1aPUuaTVLfTr+PGgiMRbV6VnB//0cRatWzgChS31FsIRpPnEkTERE5FIM0ERGRQzHdTSnHlelFuES1Xiypb6dXz5L+oau7rUh9q1fPkqvqRxjc34rqWdL/yL3MitWzgGhS34rVswDT1Ldq9SwgTOo7RbcQleYIqW/V6llA5NR3VFuIxg9n0kRERA7FIE1ERORQTHdTynG7vUGJqNqnvlWrZwGJT32rV88CEp36Vq6eBZimvpW3EAWiSH2rVc+Sc5ikV1WrZwGmqe90qJ4lzSapb9XqWUDE1Hd0W4jGD2fSREREDsUgTURE5FBMd1PKcWca05lMffv6qqa+1fb5Dnc231V9IzHv67zUt2r1LBmrbly+9Kpq9azg6xxJ9SpXz5ILwREUU9+q1bOAyKnvqPb5jiPOpImIiByKQZqIiMihmO6mlFOnzmGE+9Zm6tvXN5bUd+1LXAa/0nzUFqS+Vff5BiKmvpVLXAKmqW/lEpeAeepbtcQlkPSpb9USl3KZCKnvaPb5jiPOpImIiBwqpiBdXV2Nu+++G6WlpcjNzUXLli1x//33G/4S0TQN99xzD5o0aYLc3Fz07dsX69evt3zgREREqS6mdPfDDz+M5557DtOnT0e7du2wfPlyXHXVVSgoKMCNN94IAHjkkUfw5JNPYvr06SgtLcXdd9+Nfv36Yc2aNcjJyYnLmyDSq+MO3lO39qlv9RKXwa8OTX2rlriU64SmvlVLXIZvVytxCUROfauWuJT20NS3JSUuAfPUt2qJS8A09a1a4hIIk/pWLXEZ1D8pU9+qJS6ByKnvKPb5jqeYgvSXX36JAQMGoH///gCAFi1a4PXXX8fSpUsByBt8/PHHcdddd2HAgAEAgH/9618oKirC3LlzMWjQIIuHT0RElLpiCtI9e/bElClTsG7dOhx//PFYvXo1Fi1ahMceewwAsGnTJpSVlaFv377+1xQUFKBbt25YvHixaZCuqKhARUWF/98ej0f1vRABALIya6pO47xZtepispDX+s+nVj1L+ofOqlW3EAUiz6pVq2dJ/9BZtWr1LDlHgmfVitWzpL/JrFq1epY8YdrfP2t1yowaMJ9Vq1bPAiLOqqPZQjSeYgrS48ePh8fjQZs2beB2u1FdXY0HH3wQQ4cOBQCUlZUBAIqKigyvKyoq8j8XbPLkyZg4caLK2ImIiFJaTEn1N998EzNmzMDMmTPx9ddfY/r06fj73/+O6dOnKw9gwoQJKC8v9z+2bt2qfC4iIqJUEtNM+q9//SvGjx/vT1t36NABmzdvxuTJkzFs2DAUFxcDAHbu3IkmTZr4X7dz50506tTJ9JzZ2dnIzs5WHD5RqOyQhWPhRJ/6Vr2PGogm9V37+6j1r1W9j1r6h6a+raieBSQm9a26haj0j5D6Vq6eBZimvlWrZwGmqW/V6lnSHCH17cTFZEBgLKrVs4L7m6S+o9pCNI5iusqBAweQETQwt9sN75GBl5aWori4GAsWLPA/7/F4sGTJEvTo0cOC4RIREaWPmGbS559/Ph588EE0a9YM7dq1w8qVK/HYY4/h6quvBgC4XC6MHTsWDzzwAFq3bu2/Batp06a48MIL4zF+IiKilBVTkH7qqadw99134y9/+Qt27dqFpk2b4rrrrsM999zj73Pbbbdh//79GDlyJPbs2YPTTjsNH330Ee+RpoTJdseYJwYQOfVd+y1EgXCpb+dtISr9Q1d3W536Vq+eJaMJ7m9F9Szpn4jUt2L1LMA09a1aPQuIIvWd7PdRA+qp72i2EI0jl6Y55b+y8Hg8KCgoQHl5OfLz8+0eDjnMvn1AXp4cHzgA5OYan/d4PLhkxb2oqA4E3YrqwC/OysOB4ypde1VVoH/14cAPc3X1kc+kdW1ate6H+rDuWNfuOhzmWNcno9rXhjB9A+36YKb/xW14rcn5DK+r1gVpk9eFO3eG7nWGc+vbDa8z729oP/JLMuNwaFvwMQzn0x97Q/tXh/klGq5d/+tPH3i9Juc2nC/MOQzn0wVpfbv/fNWhbUBQoDDu5mg2Pv81wwVpvXDXgb7Z5LVh+jomSOu5zP8wNHzWbmiO0D/M8y7ddT4+8GrUw4sV9+4mIiJyKFbBopSTm1lVyzOE/lhYXT0L0KeTw73SGalv9epZQKTUt3r1LLmqfpShfa1NfatWzwLCpb7VqmfJOUxS36rVs4DIqe9U2kIUiC31HcUWovHEmTQREZFDMUgTERE5FNPdlHJyap3u1ot/6lu1ehbA1LfuFf6RmPetfepbeZ9vwDT1rVo9S8aqG5cvza1aPSv4Oiap75StngVETn1Hsc93PHEmTURE5FAM0kRERA7FdDelnHruyjictfYlLmtq90m/1LfaPt/hzqZa4jKkPQGpb+USl4Bp6lu5xCUQMfWtXOJSLgRHUEx9R7XPdxxxJk1ERORQDNJEREQOxXQ3pZxct5Wru804O/WtWuJSrhOa+lYtcVlTu3637dC2oHPHkPpWLXEp7RFS36r7fAPmqW/VEpeAaepbtcQlEEXqW7XEJZD0qe+o9vmOI86kiYiIHIpBmoiIyKGY7qaUUy+zIoFXq33qW73EZfCrXUf66q5sQepbtcSl9I+U+lYrcQmYvzfVEpfSv+bUtyUlLoH4pb4VS1xK/wipb9USl0H9/allp6S9gcip72j2+Y4jzqSJiIgcijNpSjl1Mypt+s52yqy69vdR61+reh+19K95Vq26hSiQ+Fm1avUsOYdJH+XqWYDprFq1ehYQeVatWj1Lngjt78TFZID5rDqKLUTjiTNpIiIih2KQJiIiciimuynl5LkPGRscnvpWvY8aCJf6dt4WotI/NPVtRfUsIJD6Vq+eJaMx739k4ZjiFqLSPxGpb8XqWUDE1Ldq9SxpNkl9O/0+aiAwlii2EI0nzqSJiIgcikGaiIjIoZjuppRTPzjdrefI1HfttxAF9Cumw73Sealv9epZwe1HzqFcPUuuqh9hcH8rqmdJ/yPbeCpWzwLCpb7VqmfJOWpOfatWzwLCpL5TbQvROOJMmoiIyKEYpImIiByK6W5KOfkZB6Pr6JDUt1OqZwGJT32rV88CEp36Vq6eBZimvpW3EAVMU9+q1bNkrLpxmaW+VatnAaap75SrnhVHnEkTERE5FIM0ERGRQzHdTSmnboZCFSymvo/01109KVPfavt8hzub76q+kZj3dUbqW7l6FhA59a1aPSv4OkfS2crVs+RCcIQEjYMzaSIiIodikCYiInIoprsp5eRn1LCZSTQS/lNR+xKXNbX7qKa+VUtcynUSnfqufYnL4Feaj9qC1LfqPt+AeepbtcQlEDH1rVziEjBPfauWuAScmfqOI86kiYiIHIpBmoiIyKGY7qaUk1fbdLdeEqa+1UtcBr/adaSv7soWp75VS1yGb1crcQlETn2rlriU9tDUtyUlLoGEpL5VS1wCYVLfqiUug/r7U98pnPbmTJqIiMihGKSJiIgciuluSjl5GVXWn9Qhm50AdqS+a7/ZSchr/al0tRKX0j809a26zzcQOfWtWuJS+oemvlVLXMo5TPool7gEIqa+FUtcSn+T1LdqiUt5IrR/Cq/45kyaiIjIoTiTppST59KAeMymfRw+q1a9jxoIN6u2dgtR/WtV76OW/qGzaiuqZwGJmVWrbiEq/RM8q1atngWYzqpVq2dJs8msOoXvo+ZMmoiIyKEYpImIiByK6W5KOXkZmYBXl6NMu9R37bcQBfSLscK90hnVs6R/6MIxq1Pf6tWzZDTB/a2oniX9j9zLrFg9C4gm9a1YPQswTX2rVs8CwqS+U3gLUc6kiYiIHIpBmoiIyKGY7qaUUz8jB4Bua9A0S307pXoWkPjUt3r1LCBS6lu9epZcVT/K0L61T30rbyEKRJH6VqueJecwSX2rVs8CTFPfqVw9izNpIiIih2KQJiIiciimuynluJtsQHl5OfLz8wEA+TaPh4hIleOCtO8zCY/HY/NIyIkOHQKuukqO9+8HqoI+YvZ932hJ9JkTEVE4Ls1hv83+97//oaSkxO5hUJLbunUrjj32WLuHQURUK44L0l6vF9u3b0deXh5cLvPNBYjC0TQNe/fuRdOmTZGRwSUXRJTcHBekiYiISHCqQURE5FAM0kRERA7FIE1ERORQDNJEREQOxSBNRETkUAzSREREDsUgTURE5FD/D1DslFzuwEyGAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Baselines: KL and quadratically regularized OT"
      ],
      "metadata": {
        "id": "YOej1aDeBHjH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### KL-regularized OT"
      ],
      "metadata": {
        "id": "6L49Gm4G9nUP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "lambd = 2e-3\n",
        "Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl')\n",
        "\n",
        "pl.figure(3, figsize=(5, 5))\n",
        "ot.plot.plot1D_mat(a, b, Gsm, 'KL regularized OT')\n",
        "\n",
        "pl.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "id": "Mc3-iyxw9qyu",
        "outputId": "fdab07b3-c3cd-4faf-c778-32d16a51ff10"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Quadratically regularized OT"
      ],
      "metadata": {
        "id": "eBY3Y5_o9vtO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lambd = 1e-1\n",
        "Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2')\n",
        "\n",
        "pl.figure(4, figsize=(5, 5))\n",
        "ot.plot.plot1D_mat(a, b, Gsm, 'Quadratically regularized OT')\n",
        "\n",
        "pl.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "id": "4yalCP7s7pSw",
        "outputId": "4e950c7f-b344-4168-ad86-5858988b7d2a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Sparsity-constrained optimal transport, implemented by POT\n",
        "\n",
        "The implementation is based on the [Python Optimal Transport (POT)](https://github.com/PythonOT/POT) library. This implementation is compatible with different backends such as NumPy and PyTorch."
      ],
      "metadata": {
        "id": "tbayHsLHBMj1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import jax.numpy as jnp"
      ],
      "metadata": {
        "id": "bOOoy1WgCqCr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "lambd = 1e-1\n",
        "max_nz = 2  # two non-zero entries are permitted per column of the OT plan\n",
        "\n",
        "\n",
        "# use the numpy in sparsity-constrained OT\n",
        "Gsc_np = ot.smooth.smooth_ot_dual(\n",
        "    a, b, M, lambd, reg_type='sparsity_constrained', max_nz=max_nz)\n",
        "\n",
        "\n",
        "# use the pytorch in sparsity-constrained OT\n",
        "Gsc_torch = ot.smooth.smooth_ot_dual(\n",
        "    torch.from_numpy(a),\n",
        "    torch.from_numpy(b),\n",
        "    torch.from_numpy(M),\n",
        "    lambd, reg_type='sparsity_constrained', max_nz=max_nz)\n",
        "  \n",
        "np.testing.assert_allclose(Gsc_torch.detach().numpy(), Gsc_np)\n",
        "\n",
        "pl.figure(5, figsize=(5, 5))\n",
        "ot.plot.plot1D_mat(a, b, Gsc_np, 'Sparsity contrained OT matrix; k=2')\n",
        "\n",
        "pl.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "id": "6w-g7L_v97Lm",
        "outputId": "de943983-8ea0-45ac-d185-bacb5ccf9d3a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Sparsity-constrained optimal transport, implemented with JAXopt\n",
        "\n",
        "The implementation of sparsity-constrained OT is based on JAX. It uses the [JAXopt](https://jaxopt.github.io/stable/index.html) library.\n",
        "\n"
      ],
      "metadata": {
        "id": "rd0qV-cY_XWL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install git+https://github.com/google/jaxopt -q\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1gaHJLdD_eYQ",
        "outputId": "a5425511-43df-4eb1-8059-6abe3e5cc6b1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"Projection with k-sparse constraints.\"\"\"\n",
        "from typing import Callable, Any\n",
        "import jax\n",
        "import jax.numpy as jnp\n",
        "import jaxopt\n",
        "from jaxopt._src.projection import projection_sparse_simplex, projection_transport, _make_semi_dual #, _regularized_transport_semi_dual\n",
        "\n",
        "\n",
        "\n",
        "def _max_l2_top_k(x, k, marginal_b=1.0, gamma=1.0):\n",
        "  scale = gamma * marginal_b\n",
        "  p = jaxopt.projection.projection_sparse_simplex(x / scale, k)\n",
        "  p = jax.lax.stop_gradient(p)\n",
        "  z = jnp.dot(p, x) - 0.5 * scale * jnp.dot(p, p)\n",
        "  return z\n",
        "\n",
        "_max_l2_top_k_grad = jax.grad(_max_l2_top_k)\n",
        "\n",
        "\n",
        "def _regularized_transport_semi_dual(cost_matrix,\n",
        "                           marginals_a,\n",
        "                           marginals_b,\n",
        "                           make_solver,\n",
        "                           max_vmap,\n",
        "                           max_grad_vmap,\n",
        "                           gamma=1.0):\n",
        "\n",
        "  r\"\"\"Regularized transport in the semi-dual formulation.\n",
        "\n",
        "  Args:\n",
        "    cost_matrix: The cost matrix of size (m, n).\n",
        "    marginals_a: The marginals of size (m,)\n",
        "    marginals_b: The marginals of size (n,)\n",
        "    make_solver: A function that makes the optimization algorithm\n",
        "    max_vmap:  A function that computes the regularized max on columns of\n",
        "      its matrix-valued input\n",
        "    max_grad_vmap:  A function that computes gradient of regularized max\n",
        "      on columns of its matrix-valued input\n",
        "    gamma: A parameter that controls the strength of regularization.\n",
        "\n",
        "  Returns:\n",
        "    The optimized plan. See the text under Eqn. (10) of\n",
        "      https://arxiv.org/abs/1710.06276\n",
        "  \"\"\"\n",
        "  size_a, size_b = cost_matrix.shape\n",
        "\n",
        "  if len(marginals_a.shape) >= 2:\n",
        "    raise ValueError(\"marginals_a should be a vector.\")\n",
        "\n",
        "  if len(marginals_b.shape) >= 2:\n",
        "    raise ValueError(\"marginals_b should be a vector.\")\n",
        "\n",
        "  if size_a != marginals_a.shape[0] or size_b != marginals_b.shape[0]:\n",
        "    raise ValueError(\"cost_matrix and marginals must have matching shapes.\")\n",
        "\n",
        "  if make_solver is None:\n",
        "    make_solver = lambda fun: jaxopt.LBFGS(fun=fun, tol=1e-3, maxiter=500,\n",
        "                                    linesearch=\"zoom\")\n",
        "\n",
        "  semi_dual = _make_semi_dual(max_vmap, gamma=gamma)\n",
        "  solver = make_solver(semi_dual)\n",
        "  alpha_init = jnp.zeros(size_a)\n",
        "\n",
        "  # Optimal dual potentials.\n",
        "  alpha = solver.run(alpha_init,\n",
        "                     cost_matrix=cost_matrix,\n",
        "                     marginals_a=marginals_a,\n",
        "                     marginals_b=marginals_b).params\n",
        "\n",
        "  # Optimal primal transportation plan.\n",
        "  X = alpha[:, jnp.newaxis] - cost_matrix\n",
        "  P = max_grad_vmap(X, marginals_b, gamma).T * marginals_b\n",
        "\n",
        "  return P, alpha\n",
        "\n",
        "\n",
        "def k_sparse_projection_transport(sim_matrix: jnp.ndarray,\n",
        "                                  marginals_a: jnp.ndarray,\n",
        "                                  marginals_b: jnp.ndarray,\n",
        "                                  k: int,\n",
        "                                  row_k_sparse: bool = False,\n",
        "                                  make_solver: Callable[..., Any] = None,\n",
        "                                  gamma=1.0,\n",
        "                                  return_alpha=False):\n",
        "  r\"\"\"Projection onto the transportation polytope with k-sparse constraints.\n",
        "\n",
        "  Args:\n",
        "    sim_matrix: similarity matrix, shape=(size_a, size_b).\n",
        "    marginals_a: marginals a, shape=(size_a,).\n",
        "    marginals_b: marginals b, shape=(size_b,).\n",
        "    k: number of nonzeros that each row (if row_k_sparse is True) or\n",
        "    column (if row_k_sparse is False) can have at most.\n",
        "    row_k_sparse: if True, each row of transportation plan has at most k\n",
        "      nonzeros; else, each column of transportation plan has at most k\n",
        "      nonzeros.\n",
        "    make_solver: a function of the form make_solver(fun),\n",
        "      for creating an iterative solver to minimize fun.\n",
        "    gamma: a parameter that controls the strength of squared l2 regularization.\n",
        "  Returns:\n",
        "    plan: transportation matrix, shape=(size_a, size_b).\n",
        "  References:\n",
        "    Liu, T., Puigcerver, J., & Blondel, M. (2023).\n",
        "    Sparsity-constrained optimal transport. \n",
        "    Proceedings of the Eleventh International Conference on Learning \n",
        "      Representations (ICLR).\n",
        "  \"\"\"\n",
        "\n",
        "  def maxop(x, marginal_b, gamma):\n",
        "    return _max_l2_top_k(x, k=k, marginal_b=marginal_b, gamma=gamma)\n",
        "\n",
        "  maxop_vmap = jax.vmap(maxop, in_axes=(1, 0, None))\n",
        "  max_grad_vmap = jax.vmap(jax.grad(maxop), in_axes=(1, 0, None))\n",
        "\n",
        "  if row_k_sparse:\n",
        "    # enforce sparsity constraint rowwise:\n",
        "    marginals_a, marginals_b = marginals_b, marginals_a\n",
        "    sim_matrix = sim_matrix.T\n",
        "\n",
        "  plan, alpha = _regularized_transport_semi_dual(\n",
        "      cost_matrix=-sim_matrix,  # pylint: disable=protected-access\n",
        "      marginals_a=marginals_a,\n",
        "      marginals_b=marginals_b,\n",
        "      make_solver=make_solver,\n",
        "      max_vmap=maxop_vmap,\n",
        "      max_grad_vmap=max_grad_vmap,\n",
        "      gamma=gamma)\n",
        "  if row_k_sparse:\n",
        "    plan = plan.T\n",
        "\n",
        "  if return_alpha:\n",
        "    return plan, alpha\n",
        "  else:\n",
        "    return plan"
      ],
      "metadata": {
        "id": "ouWYKUMD_Yc6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "sparsity_constrained_plan = k_sparse_projection_transport(-M, a, b, k=2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GwauPN89_-db",
        "outputId": "2af25cc8-fe47-4250-9636-5131d7062568"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:jax._src.xla_bridge:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pl.figure(6, figsize=(5, 5))\n",
        "ot.plot.plot1D_mat(a, b, sparsity_constrained_plan, 'Sparsity contrained OT matrix; k=2')\n",
        "\n",
        "pl.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "id": "TWrUAJ5mAf8y",
        "outputId": "5d8e7f4e-c2f3-45e0-ec45-32a4713b0c49"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# More applications\n",
        "\n",
        "See the [vmoe](https://github.com/google-research/vmoe/tree/main/vmoe/projects/sparsity_constrained_ot) repo for more demos of sparsity-constrained OT, including its applications in 2D samples, color transfer, and vision mixture-of-experts.\n",
        "\n",
        "\n",
        "If you find these implementations helpful, consider citing our paper:\n",
        "\n",
        "\n",
        "> Liu, T., Puigcerver, J., & Blondel, M. (2023). [Sparsity-constrained optimal transport](https://openreview.net/forum?id=yHY9NbQJ5BP). \n",
        "Proceedings of the Eleventh International Conference on Learning Representations (ICLR)."
      ],
      "metadata": {
        "id": "DodVD2I4GaED"
      }
    }
  ]
}