{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Continuous OT plan estimation with Pytorch\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.8.2.</p></div>\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Author: Remi Flamary <remi.flamary@polytechnique.edu>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 3\n\nimport numpy as np\nimport matplotlib.pyplot as pl\nimport torch\nfrom torch import nn\nimport ot\nimport ot.plot"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Data generation\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "torch.manual_seed(42)\nnp.random.seed(42)\n\nn_source_samples = 1000\nn_target_samples = 1000\ntheta = 2 * np.pi / 20\nnoise_level = 0.1\n\nXs = np.random.randn(n_source_samples, 2) * 0.5\nXt = np.random.randn(n_target_samples, 2) * 2\n\n# one of the target mode changes its variance (no linear mapping)\nXt = Xt + 4"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "nvisu = 300\npl.figure(1, (5, 5))\npl.clf()\npl.scatter(Xs[:nvisu, 0], Xs[:nvisu, 1], marker=\"+\", label=\"Source samples\", alpha=0.5)\npl.scatter(Xt[:nvisu, 0], Xt[:nvisu, 1], marker=\"o\", label=\"Target samples\", alpha=0.5)\npl.legend(loc=0)\nax_bounds = pl.axis()\npl.title(\"Source and target distributions\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Convert data to torch tensors\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "xs = torch.tensor(Xs)\nxt = torch.tensor(Xt)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Estimating deep dual variables for entropic OT\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "torch.manual_seed(42)\n\n# define the MLP model\n\n\nclass Potential(torch.nn.Module):\n    def __init__(self):\n        super(Potential, self).__init__()\n        self.fc1 = nn.Linear(2, 200)\n        self.fc2 = nn.Linear(200, 1)\n        self.relu = torch.nn.ReLU()  # instead of Heaviside step fn\n\n    def forward(self, x):\n        output = self.fc1(x)\n        output = self.relu(output)  # instead of Heaviside step fn\n        output = self.fc2(output)\n        return output.ravel()\n\n\nu = Potential().double()\nv = Potential().double()\n\nreg = 1\n\noptimizer = torch.optim.Adam(list(u.parameters()) + list(v.parameters()), lr=0.005)\n\n# number of iteration\nn_iter = 500\nn_batch = 500\n\n\nlosses = []\n\nfor i in range(n_iter):\n    # generate noise samples\n\n    iperms = torch.randint(0, n_source_samples, (n_batch,))\n    ipermt = torch.randint(0, n_target_samples, (n_batch,))\n\n    xsi = xs[iperms]\n    xti = xt[ipermt]\n\n    # minus because we maximize the dual loss\n    loss = -ot.stochastic.loss_dual_entropic(u(xsi), v(xti), xsi, xti, reg=reg)\n    losses.append(float(loss.detach()))\n\n    if i % 10 == 0:\n        print(\"Iter: {:3d}, loss={}\".format(i, losses[-1]))\n\n    loss.backward()\n    optimizer.step()\n    optimizer.zero_grad()\n\n\npl.figure(2)\npl.plot(losses)\npl.grid()\npl.title(\"Dual objective (negative)\")\npl.xlabel(\"Iterations\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot the density on target for a given source sample\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "nv = 100\nxl = np.linspace(ax_bounds[0], ax_bounds[1], nv)\nyl = np.linspace(ax_bounds[2], ax_bounds[3], nv)\n\nXX, YY = np.meshgrid(xl, yl)\n\nxg = np.concatenate((XX.ravel()[:, None], YY.ravel()[:, None]), axis=1)\n\nwxg = np.exp(-((xg[:, 0] - 4) ** 2 + (xg[:, 1] - 4) ** 2) / (2 * 2))\nwxg = wxg / np.sum(wxg)\n\nxg = torch.tensor(xg)\nwxg = torch.tensor(wxg)\n\n\npl.figure(4, (12, 4))\npl.clf()\npl.subplot(1, 3, 1)\n\niv = 2\nGg = ot.stochastic.plan_dual_entropic(\n    u(xs[iv : iv + 1, :]), v(xg), xs[iv : iv + 1, :], xg, reg=reg, wt=wxg\n)\nGg = Gg.reshape((nv, nv)).detach().numpy()\n\npl.scatter(Xs[:nvisu, 0], Xs[:nvisu, 1], marker=\"+\", zorder=2, alpha=0.05)\npl.scatter(Xt[:nvisu, 0], Xt[:nvisu, 1], marker=\"o\", zorder=2, alpha=0.05)\npl.scatter(\n    Xs[iv : iv + 1, 0],\n    Xs[iv : iv + 1, 1],\n    s=100,\n    marker=\"+\",\n    label=\"Source sample\",\n    zorder=2,\n    alpha=1,\n    color=\"C0\",\n)\npl.pcolormesh(XX, YY, Gg, cmap=\"Greens\", label=\"Density of transported source sample\")\npl.legend(loc=0)\nax_bounds = pl.axis()\npl.title(\"Density of transported source sample\")\n\npl.subplot(1, 3, 2)\n\niv = 3\nGg = ot.stochastic.plan_dual_entropic(\n    u(xs[iv : iv + 1, :]), v(xg), xs[iv : iv + 1, :], xg, reg=reg, wt=wxg\n)\nGg = Gg.reshape((nv, nv)).detach().numpy()\n\npl.scatter(Xs[:nvisu, 0], Xs[:nvisu, 1], marker=\"+\", zorder=2, alpha=0.05)\npl.scatter(Xt[:nvisu, 0], Xt[:nvisu, 1], marker=\"o\", zorder=2, alpha=0.05)\npl.scatter(\n    Xs[iv : iv + 1, 0],\n    Xs[iv : iv + 1, 1],\n    s=100,\n    marker=\"+\",\n    label=\"Source sample\",\n    zorder=2,\n    alpha=1,\n    color=\"C0\",\n)\npl.pcolormesh(XX, YY, Gg, cmap=\"Greens\", label=\"Density of transported source sample\")\npl.legend(loc=0)\nax_bounds = pl.axis()\npl.title(\"Density of transported source sample\")\n\npl.subplot(1, 3, 3)\n\niv = 6\nGg = ot.stochastic.plan_dual_entropic(\n    u(xs[iv : iv + 1, :]), v(xg), xs[iv : iv + 1, :], xg, reg=reg, wt=wxg\n)\nGg = Gg.reshape((nv, nv)).detach().numpy()\n\npl.scatter(Xs[:nvisu, 0], Xs[:nvisu, 1], marker=\"+\", zorder=2, alpha=0.05)\npl.scatter(Xt[:nvisu, 0], Xt[:nvisu, 1], marker=\"o\", zorder=2, alpha=0.05)\npl.scatter(\n    Xs[iv : iv + 1, 0],\n    Xs[iv : iv + 1, 1],\n    s=100,\n    marker=\"+\",\n    label=\"Source sample\",\n    zorder=2,\n    alpha=1,\n    color=\"C0\",\n)\npl.pcolormesh(XX, YY, Gg, cmap=\"Greens\", label=\"Density of transported source sample\")\npl.legend(loc=0)\nax_bounds = pl.axis()\npl.title(\"Density of transported source sample\")"
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