{
  "cells": [
    {
      "cell_type": "markdown",
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      "source": [
        "\n# Sliced Wasserstein Distance on 2D distributions\n\n<div class=\"alert alert-info\"><h4>Note</h4><p>Example added in release: 0.8.0.</p></div>\n\nThis example illustrates the computation of the sliced Wasserstein Distance as\nproposed in [31].\n\n[31] Bonneel, Nicolas, et al. \"Sliced and radon wasserstein barycenters of\nmeasures.\" Journal of Mathematical Imaging and Vision 51.1 (2015): 22-45\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
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      "source": [
        "# Author: Adrien Corenflos <adrien.corenflos@aalto.fi>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 2\n\nimport matplotlib.pylab as pl\nimport numpy as np\n\nimport ot"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Generate data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "n = 200  # nb samples\n\nmu_s = np.array([0, 0])\ncov_s = np.array([[1, 0], [0, 1]])\n\nmu_t = np.array([4, 4])\ncov_t = np.array([[1, -0.8], [-0.8, 1]])\n\nxs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)\nxt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)\n\na, b = np.ones((n,)) / n, np.ones((n,)) / n  # uniform distribution on samples"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(1)\npl.plot(xs[:, 0], xs[:, 1], \"+b\", label=\"Source samples\")\npl.plot(xt[:, 0], xt[:, 1], \"xr\", label=\"Target samples\")\npl.legend(loc=0)\npl.title(\"Source and target distributions\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Sliced Wasserstein distance for different seeds and number of projections\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "n_seed = 20\nn_projections_arr = np.logspace(0, 3, 10, dtype=int)\nres = np.empty((n_seed, 10))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "for seed in range(n_seed):\n    for i, n_projections in enumerate(n_projections_arr):\n        res[seed, i] = ot.sliced_wasserstein_distance(\n            xs, xt, a, b, n_projections, seed=seed\n        )\n\nres_mean = np.mean(res, axis=0)\nres_std = np.std(res, axis=0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot Sliced Wasserstein Distance\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "pl.figure(2)\npl.plot(n_projections_arr, res_mean, label=\"SWD\")\npl.fill_between(\n    n_projections_arr, res_mean - 2 * res_std, res_mean + 2 * res_std, alpha=0.5\n)\n\npl.legend()\npl.xscale(\"log\")\n\npl.xlabel(\"Number of projections\")\npl.ylabel(\"Distance\")\npl.title(\"Sliced Wasserstein Distance with 95% confidence interval\")\n\npl.show()"
      ]
    }
  ],
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