{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# OT between GMM : plan and maps in 1D\n\nIllustration of the GMM plan for\nthe Mixture Wasserstein between two GMM in 1D,\nas well as the two maps T_mean and T_rand.\nT_mean is the barycentric projection of the GMM coupling,\nand T_rand takes a random gaussian image between two components,\naccording to the coupling and the GMMs.\nSee [69] for details.\n.. [69] Delon, J., & Desolneux, A. (2020). A Wasserstein-type distance in the space of Gaussian mixture models. SIAM Journal on Imaging Sciences, 13(2), 936-970.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# Author: Eloi Tanguy <eloi.tanguy@math.cnrs.fr>\n#         Remi Flamary <remi.flamary@polytehnique.edu>\n#         Julie Delon <julie.delon@math.cnrs.fr>\n#\n# License: MIT License\n\n# sphinx_gallery_thumbnail_number = 1\n\nimport numpy as np\nfrom ot.plot import plot1D_mat, rescale_for_imshow_plot\nfrom ot.gmm import gmm_ot_plan_density, gmm_pdf, gmm_ot_apply_map\nimport matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Generate GMMOT plan plot it\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "ks = 2\nkt = 3\nd = 1\neps = 0.1\nm_s = np.array([[1], [2]])\nm_t = np.array([[3], [4.2], [5]])\nC_s = np.array([[[0.05]], [[0.06]]])\nC_t = np.array([[[0.03]], [[0.07]], [[0.04]]])\nw_s = np.array([0.4, 0.6])\nw_t = np.array([0.4, 0.2, 0.4])\n\nn = 500\na_x, b_x = 0, 3\nx = np.linspace(a_x, b_x, n)\na_y, b_y = 2, 6\ny = np.linspace(a_y, b_y, n)\nplan_density = gmm_ot_plan_density(\n    x[:, None], y[:, None], m_s, m_t, C_s, C_t, w_s, w_t, plan=None, atol=2e-2\n)\n\na = gmm_pdf(x[:, None], m_s, C_s, w_s)\nb = gmm_pdf(y[:, None], m_t, C_t, w_t)\nplt.figure(figsize=(8, 8))\nplot1D_mat(\n    a,\n    b,\n    plan_density,\n    title=\"GMM OT plan\",\n    plot_style=\"xy\",\n    a_label=\"Source distribution\",\n    b_label=\"Target distribution\",\n)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Generate GMMOT maps and plot them over plan\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "plt.figure(figsize=(8, 8))\nax_s, ax_t, ax_M = plot1D_mat(\n    a,\n    b,\n    plan_density,\n    plot_style=\"xy\",\n    title=\"GMM OT plan with T_mean and T_rand maps\",\n    a_label=\"Source distribution\",\n    b_label=\"Target distribution\",\n)\nT_mean = gmm_ot_apply_map(x[:, None], m_s, m_t, C_s, C_t, w_s, w_t, method=\"bary\")[:, 0]\nx_rescaled, T_mean_rescaled = rescale_for_imshow_plot(x, T_mean, n, a_y=a_y, b_y=b_y)\n\nax_M.plot(\n    x_rescaled, T_mean_rescaled, label=\"T_mean\", alpha=0.5, linewidth=5, color=\"aqua\"\n)\n\nT_rand = gmm_ot_apply_map(\n    x[:, None], m_s, m_t, C_s, C_t, w_s, w_t, method=\"rand\", seed=0\n)[:, 0]\nx_rescaled, T_rand_rescaled = rescale_for_imshow_plot(x, T_rand, n, a_y=a_y, b_y=b_y)\n\nax_M.scatter(\n    x_rescaled, T_rand_rescaled, label=\"T_rand\", alpha=0.5, s=20, color=\"orange\"\n)\n\nax_M.legend(loc=\"upper left\", fontsize=13)"
      ]
    }
  ],
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    "kernelspec": {
      "display_name": "Python 3",
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      "name": "python3"
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    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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