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Diffstat (limited to 'docs/source/auto_examples/plot_optim_OTreg.ipynb')
| -rw-r--r-- | docs/source/auto_examples/plot_optim_OTreg.ipynb | 76 |
1 files changed, 38 insertions, 38 deletions
diff --git a/docs/source/auto_examples/plot_optim_OTreg.ipynb b/docs/source/auto_examples/plot_optim_OTreg.ipynb index 02bf175..107c299 100644 --- a/docs/source/auto_examples/plot_optim_OTreg.ipynb +++ b/docs/source/auto_examples/plot_optim_OTreg.ipynb @@ -1,6 +1,7 @@ { "cells": [ { + "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false @@ -8,17 +9,17 @@ "outputs": [], "source": [ "%matplotlib inline" - ], - "cell_type": "code" + ] }, { + "cell_type": "markdown", "metadata": {}, "source": [ "\n# Regularized OT with generic solver\n\n\nIllustrates the use of the generic solver for regularized OT with\nuser-designed regularization term. It uses Conditional gradient as in [6] and\ngeneralized Conditional Gradient as proposed in [5][7].\n\n\n[5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, Optimal Transport for\nDomain Adaptation, in IEEE Transactions on Pattern Analysis and Machine\nIntelligence , vol.PP, no.99, pp.1-1.\n\n[6] Ferradans, S., Papadakis, N., Peyr\u00e9, G., & Aujol, J. F. (2014).\nRegularized discrete optimal transport. SIAM Journal on Imaging Sciences,\n7(3), 1853-1882.\n\n[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized\nconditional gradient: analysis of convergence and applications.\narXiv preprint arXiv:1510.06567.\n\n\n\n\n" - ], - "cell_type": "markdown" + ] }, { + "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false @@ -26,35 +27,35 @@ "outputs": [], "source": [ "import numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" - ], - "cell_type": "code" + ] }, { + "cell_type": "markdown", "metadata": {}, "source": [ "Generate data\n-------------\n\n" - ], - "cell_type": "markdown" + ] }, { + "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\na = ot.datasets.get_1D_gauss(n, m=20, s=5) # m= mean, s= std\nb = ot.datasets.get_1D_gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" - ], - "cell_type": "code" + "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\nb = ot.datasets.make_1D_gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" + ] }, { + "cell_type": "markdown", "metadata": {}, "source": [ "Solve EMD\n---------\n\n" - ], - "cell_type": "markdown" + ] }, { + "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false @@ -62,17 +63,17 @@ "outputs": [], "source": [ "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')" - ], - "cell_type": "code" + ] }, { + "cell_type": "markdown", "metadata": {}, "source": [ "Solve EMD with Frobenius norm regularization\n--------------------------------------------\n\n" - ], - "cell_type": "markdown" + ] }, { + "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false @@ -80,17 +81,17 @@ "outputs": [], "source": [ "#%% Example with Frobenius norm regularization\n\n\ndef f(G):\n return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n return G\n\n\nreg = 1e-1\n\nGl2 = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(3)\not.plot.plot1D_mat(a, b, Gl2, 'OT matrix Frob. reg')" - ], - "cell_type": "code" + ] }, { + "cell_type": "markdown", "metadata": {}, "source": [ "Solve EMD with entropic regularization\n--------------------------------------\n\n" - ], - "cell_type": "markdown" + ] }, { + "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false @@ -98,17 +99,17 @@ "outputs": [], "source": [ "#%% Example with entropic regularization\n\n\ndef f(G):\n return np.sum(G * np.log(G))\n\n\ndef df(G):\n return np.log(G) + 1.\n\n\nreg = 1e-3\n\nGe = ot.optim.cg(a, b, M, reg, f, df, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Ge, 'OT matrix Entrop. reg')" - ], - "cell_type": "code" + ] }, { + "cell_type": "markdown", "metadata": {}, "source": [ "Solve EMD with Frobenius norm + entropic regularization\n-------------------------------------------------------\n\n" - ], - "cell_type": "markdown" + ] }, { + "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false @@ -116,29 +117,28 @@ "outputs": [], "source": [ "#%% Example with Frobenius norm + entropic regularization with gcg\n\n\ndef f(G):\n return 0.5 * np.sum(G**2)\n\n\ndef df(G):\n return G\n\n\nreg1 = 1e-3\nreg2 = 1e-1\n\nGel2 = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True)\n\npl.figure(5, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gel2, 'OT entropic + matrix Frob. reg')\npl.show()" - ], - "cell_type": "code" + ] } ], "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, "language_info": { - "name": "python", "codemirror_mode": { "name": "ipython", "version": 3 }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", "nbconvert_exporter": "python", - "version": "3.5.2", "pygments_lexer": "ipython3", - "file_extension": ".py", - "mimetype": "text/x-python" - }, - "kernelspec": { - "display_name": "Python 3", - "name": "python3", - "language": "python" + "version": "3.6.5" } }, - "nbformat_minor": 0, - "nbformat": 4 + "nbformat": 4, + "nbformat_minor": 0 }
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