{ "metadata": { "name": "", "signature": "sha256:e01831efa84095a87a681a09f08c8991bbe439e010c2bc4cd3559dc4d3bf0bde" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pylab as pl\n", "import ot" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Data generation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "n=20 # nb samples\n", "\n", "mu_s=np.array([0,0])\n", "cov_s=np.array([[1,0],[0,1]])\n", "\n", "mu_t=np.array([4,4])\n", "cov_t=np.array([[1,-.8],[-.8,1]])\n", "\n", "xs=ot.datasets.get_2D_samples_gauss(n,mu_s,cov_s)\n", "xt=ot.datasets.get_2D_samples_gauss(n,mu_t,cov_t)\n", "\n", "a,b = ot.unif(n),ot.unif(n) # uniform distribution on samples\n", "\n", "# loss matrix\n", "M=ot.dist(xs,xt)\n", "M/=M.max()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot dataset" ] }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure(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.legend(loc=0)\n", "pl.title('Source and traget distributions')\n", "\n", "pl.figure(2)\n", "pl.imshow(M,interpolation='nearest')\n", "pl.title('Cost matrix M')\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Cd5pZEcGPw4Pu/mQE7YqISIJ0BqiISBbTGaAiIgVEyVxEJA8omYuI5AElcxGR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\nXEQkDyiZi4jkASVzEZE88P8B8sPqteLhUE0AAAAASUVORK5CYII=\n", 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solve OT" ] }, { "cell_type": "code", "collapsed": false, "input": [ "G0=ot.emd(a,b,M)\n", "\n", "\n", "pl.figure(3)\n", "pl.imshow(G0,interpolation='nearest')\n", "pl.title('Cost matrix M')\n", "\n", "pl.figure(4)\n", "ot.plot.plot2D_samples_mat(xs,xt,G0,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.legend(loc=0)\n", "pl.title('OT matrix')\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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wd24wcMtRdH//MKrvPYS17ziXQuT1z8hgFmpYGLs32TXWjz461DN/7jmvxu2n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\n/XWSd0EBCSs62rHnqe6VuXkzf2evOqIabW3Ad75DmWbbNv7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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solve OT with entropic regularization" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# reg term\n", "lambd=5e-3\n", "\n", "Gs=ot.sinkhorn(a,b,M,lambd)\n", "\n", "pl.figure(5)\n", "pl.imshow(Gs,interpolation='nearest')\n", "pl.title('OT matrix sinkhorn')\n", "\n", "pl.figure(6)\n", "ot.plot.plot2D_samples_mat(xs,xt,Gs,color=[.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.legend(loc=0)\n", "pl.title('OT matrix Sinkhorn with samples')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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5eXmorKxEJBLBddddh0gkMq5rFVcNA/CLX/wCmzZtQn9/P2644YaUcnHct7a2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