{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Gromov-Wasserstein example\n\n\nThis example is designed to show how to use the Gromov-Wassertsein distance\ncomputation in POT.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Author: Erwan Vautier <erwan.vautier@gmail.com>\n#         Nicolas Courty <ncourty@irisa.fr>\n#\n# License: MIT License\n\nimport scipy as sp\nimport numpy as np\nimport matplotlib.pylab as pl\nfrom mpl_toolkits.mplot3d import Axes3D  # noqa\nimport ot"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Sample two Gaussian distributions (2D and 3D)\n---------------------------------------------\n\nThe Gromov-Wasserstein distance allows to compute distances with samples that\ndo not belong to the same metric space. For demonstration purpose, we sample\ntwo Gaussian distributions in 2- and 3-dimensional spaces.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "n_samples = 30  # nb samples\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([4, 4, 4])\ncov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n\n\nxs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)\nP = sp.linalg.sqrtm(cov_t)\nxt = np.random.randn(n_samples, 3).dot(P) + mu_t"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plotting the distributions\n--------------------------\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "fig = pl.figure()\nax1 = fig.add_subplot(121)\nax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\nax2 = fig.add_subplot(122, projection='3d')\nax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')\npl.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Compute distance kernels, normalize them and then display\n---------------------------------------------------------\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "C1 = sp.spatial.distance.cdist(xs, xs)\nC2 = sp.spatial.distance.cdist(xt, xt)\n\nC1 /= C1.max()\nC2 /= C2.max()\n\npl.figure()\npl.subplot(121)\npl.imshow(C1)\npl.subplot(122)\npl.imshow(C2)\npl.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Compute Gromov-Wasserstein plans and distance\n---------------------------------------------\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "p = ot.unif(n_samples)\nq = ot.unif(n_samples)\n\ngw0, log0 = ot.gromov.gromov_wasserstein(\n    C1, C2, p, q, 'square_loss', verbose=True, log=True)\n\ngw, log = ot.gromov.entropic_gromov_wasserstein(\n    C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)\n\n\nprint('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))\nprint('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))\n\n\npl.figure(1, (10, 5))\n\npl.subplot(1, 2, 1)\npl.imshow(gw0, cmap='jet')\npl.title('Gromov Wasserstein')\n\npl.subplot(1, 2, 2)\npl.imshow(gw, cmap='jet')\npl.title('Entropic Gromov Wasserstein')\n\npl.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
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      },
      "file_extension": ".py",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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