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      "execution_count": null, 
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        "%matplotlib inline"
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      "source": [
        "\n# 2D Optimal transport for different metrics\n\n\nStole the figure idea from Fig. 1 and 2 in\nhttps://arxiv.org/pdf/1706.07650.pdf\n\n\n\n"
      ], 
      "cell_type": "markdown", 
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      "cell_type": "code", 
      "source": [
        "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n\n#%% parameters and data generation\n\nfor data in range(2):\n\n    if data:\n        n = 20  # nb samples\n        xs = np.zeros((n, 2))\n        xs[:, 0] = np.arange(n) + 1\n        xs[:, 1] = (np.arange(n) + 1) * -0.001  # to make it strictly convex...\n\n        xt = np.zeros((n, 2))\n        xt[:, 1] = np.arange(n) + 1\n    else:\n\n        n = 50  # nb samples\n        xtot = np.zeros((n + 1, 2))\n        xtot[:, 0] = np.cos(\n            (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)\n        xtot[:, 1] = np.sin(\n            (np.arange(n + 1) + 1.0) * 0.9 / (n + 2) * 2 * np.pi)\n\n        xs = xtot[:n, :]\n        xt = xtot[1:, :]\n\n    a, b = ot.unif(n), ot.unif(n)  # uniform distribution on samples\n\n    # loss matrix\n    M1 = ot.dist(xs, xt, metric='euclidean')\n    M1 /= M1.max()\n\n    # loss matrix\n    M2 = ot.dist(xs, xt, metric='sqeuclidean')\n    M2 /= M2.max()\n\n    # loss matrix\n    Mp = np.sqrt(ot.dist(xs, xt, metric='euclidean'))\n    Mp /= Mp.max()\n\n    #%% plot samples\n\n    pl.figure(1 + 3 * data, figsize=(7, 3))\n    pl.clf()\n    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n    pl.axis('equal')\n    pl.title('Source and traget distributions')\n\n    pl.figure(2 + 3 * data, figsize=(7, 3))\n\n    pl.subplot(1, 3, 1)\n    pl.imshow(M1, interpolation='nearest')\n    pl.title('Euclidean cost')\n\n    pl.subplot(1, 3, 2)\n    pl.imshow(M2, interpolation='nearest')\n    pl.title('Squared Euclidean cost')\n\n    pl.subplot(1, 3, 3)\n    pl.imshow(Mp, interpolation='nearest')\n    pl.title('Sqrt Euclidean cost')\n    pl.tight_layout()\n\n    #%% EMD\n    G1 = ot.emd(a, b, M1)\n    G2 = ot.emd(a, b, M2)\n    Gp = ot.emd(a, b, Mp)\n\n    pl.figure(3 + 3 * data, figsize=(7, 3))\n\n    pl.subplot(1, 3, 1)\n    ot.plot.plot2D_samples_mat(xs, xt, G1, c=[.5, .5, 1])\n    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n    pl.axis('equal')\n    # pl.legend(loc=0)\n    pl.title('OT Euclidean')\n\n    pl.subplot(1, 3, 2)\n    ot.plot.plot2D_samples_mat(xs, xt, G2, c=[.5, .5, 1])\n    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n    pl.axis('equal')\n    # pl.legend(loc=0)\n    pl.title('OT squared Euclidean')\n\n    pl.subplot(1, 3, 3)\n    ot.plot.plot2D_samples_mat(xs, xt, Gp, c=[.5, .5, 1])\n    pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n    pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n    pl.axis('equal')\n    # pl.legend(loc=0)\n    pl.title('OT sqrt Euclidean')\n    pl.tight_layout()\n\npl.show()"
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