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diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb b/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb deleted file mode 100644 index e59cdc2..0000000 --- a/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb +++ /dev/null @@ -1,126 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n# 1D Wasserstein barycenter demo for Unbalanced distributions\n\n\nThis example illustrates the computation of regularized Wassersyein Barycenter\nas proposed in [10] for Unbalanced inputs.\n\n\n[10] Chizat, L., Peyr\u00e9, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.\n\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Author: Hicham Janati <hicham.janati@inria.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate data\n-------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n\n# make unbalanced dists\na2 *= 3.\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Plot data\n---------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Barycenter computation\n----------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# non weighted barycenter computation\n\nweight = 0.5 # 0<=weight<=1\nweights = np.array([1 - weight, weight])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nalpha = 1.\n\nbary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Barycentric interpolation\n-------------------------\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# barycenter interpolation\n\nn_weight = 11\nweight_list = np.linspace(0, 1, n_weight)\n\n\nB_l2 = np.zeros((n, n_weight))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_weight):\n weight = weight_list[i]\n weights = np.array([1 - weight, weight])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights)\n\n\n# plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = weight_list\nfor i, z in enumerate(zs):\n ys = B_l2[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel(r'$\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with l2')\npl.tight_layout()\n\npl.figure(4)\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = weight_list\nfor i, z in enumerate(zs):\n ys = B_wass[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel(r'$\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with Wasserstein')\npl.tight_layout()\n\npl.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.8" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}
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