{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Dual OT solvers for entropic and quadratic regularized OT 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\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(1)\n\nn_source_samples = 100\nn_target_samples = 100\ntheta = 2 * np.pi / 20\nnoise_level = 0.1\n\nXs, ys = ot.datasets.make_data_classif(\"gaussrot\", n_source_samples, nz=noise_level)\nXt, yt = ot.datasets.make_data_classif(\n    \"gaussrot\", n_target_samples, theta=theta, nz=noise_level\n)\n\n# one of the target mode changes its variance (no linear mapping)\nXt[yt == 2] *= 3\nXt = Xt + 4"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(1, (10, 5))\npl.clf()\npl.scatter(Xs[:, 0], Xs[:, 1], marker=\"+\", label=\"Source samples\")\npl.scatter(Xt[:, 0], Xt[:, 1], marker=\"o\", label=\"Target samples\")\npl.legend(loc=0)\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 dual variables for entropic OT\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "u = torch.randn(n_source_samples, requires_grad=True)\nv = torch.randn(n_source_samples, requires_grad=True)\n\nreg = 0.5\n\noptimizer = torch.optim.Adam([u, v], lr=1)\n\n# number of iteration\nn_iter = 200\n\n\nlosses = []\n\nfor i in range(n_iter):\n    # generate noise samples\n\n    # minus because we maximize the dual loss\n    loss = -ot.stochastic.loss_dual_entropic(u, v, xs, xt, 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\")\n\nGe = ot.stochastic.plan_dual_entropic(u, v, xs, xt, reg=reg)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot the estimated entropic OT plan\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(3, (10, 5))\npl.clf()\not.plot.plot2D_samples_mat(Xs, Xt, Ge.detach().numpy(), alpha=0.1)\npl.scatter(Xs[:, 0], Xs[:, 1], marker=\"+\", label=\"Source samples\", zorder=2)\npl.scatter(Xt[:, 0], Xt[:, 1], marker=\"o\", label=\"Target samples\", zorder=2)\npl.legend(loc=0)\npl.title(\"Source and target distributions\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Estimating dual variables for quadratic OT\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "u = torch.randn(n_source_samples, requires_grad=True)\nv = torch.randn(n_source_samples, requires_grad=True)\n\nreg = 0.01\n\noptimizer = torch.optim.Adam([u, v], lr=1)\n\n# number of iteration\nn_iter = 200\n\n\nlosses = []\n\n\nfor i in range(n_iter):\n    # generate noise samples\n\n    # minus because we maximize the dual loss\n    loss = -ot.stochastic.loss_dual_quadratic(u, v, xs, xt, 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(4)\npl.plot(losses)\npl.grid()\npl.title(\"Dual objective (negative)\")\npl.xlabel(\"Iterations\")\n\nGq = ot.stochastic.plan_dual_quadratic(u, v, xs, xt, reg=reg)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot the estimated quadratic OT plan\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(5, (10, 5))\npl.clf()\not.plot.plot2D_samples_mat(Xs, Xt, Gq.detach().numpy(), alpha=0.1)\npl.scatter(Xs[:, 0], Xs[:, 1], marker=\"+\", label=\"Source samples\", zorder=2)\npl.scatter(Xt[:, 0], Xt[:, 1], marker=\"o\", label=\"Target samples\", zorder=2)\npl.legend(loc=0)\npl.title(\"OT plan with quadratic regularization\")"
      ]
    }
  ],
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