{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true, "deletable": true, "editable": true }, "source": [ "Optimal Transport with Linear Programming\n", "=========================================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This numerical tours details how to solve the discrete optimal transport\n", "problem (in the case of measures that are sums of Diracs) using linear\n", "programming." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from __future__ import division\n", "\n", "import numpy as np\n", "import scipy as scp\n", "import pylab as pyl\n", "import matplotlib.pyplot as plt\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Optimal Transport of Discrete Distribution\n", "------------------------------------------\n", "We consider two dicretes distributions\n", "$$ \\forall k=0,1, \\quad \\mu_k = \\sum_{i=1}^{n_k} p_{k,i} \\de_{x_{k,i}} $$\n", "where $n_0,n_1$ are the number of points, $\\de_x$ is the Dirac at\n", "location $x \\in \\RR^d$, and $ X_k = ( x_{k,i} )_{i=1}^{n_k} \\subset \\RR^d$ for $k=0,1$\n", "are two point clouds.\n", "\n", "\n", "We define the set of couplings between $\\mu_0,\\mu_1$ as\n", "\n", "$$ \\Pp = \\enscond{ (\\ga_{i,j})_{i,j} \\in (\\RR^+)^{n_0 \\times n_1} }{\n", " \\forall i, \\sum_j \\ga_{i,j} = p_{0,i}, \\:\n", " \\forall j, \\sum_i \\ga_{i,j} = p_{1,j} } $$\n", "\n", "\n", "The Kantorovitch formulation of the optimal transport reads\n", "\n", "$$ \\ga^\\star \\in \\uargmin{\\ga \\in \\Pp} \\sum_{i,j} \\ga_{i,j} C_{i,j} $$\n", "where $C_{i,j} \\geq 0$ is the cost of moving some mass from $x_{0,i}$\n", "to $x_{1,j}$.\n", "\n", "\n", "The optimal coupling $\\ga^\\star$ can be shown to be a sparse matrix\n", "with less than $n_0+n_1-1$ non zero entries. An entry $\\ga_{i,j}^\\star \\neq 0$\n", "should be understood as a link between $x_{0,i}$\n", "and $x_{1,j}$ where an amount of mass equal to $\\ga_{i,j}^\\star$ is transfered.\n", "\n", "\n", "In the following, we concentrate on the $L^2$ Wasserstein distance.\n", "$$ C_{i,j}=\\norm{x_{0,i}-x_{1,j}}^2. $$\n", "\n", "\n", "The $L^2$ Wasserstein distance is then defined as\n", "$$ W_2(\\mu_0,\\mu_1)^2 = \\sum_{i,j} \\ga_{i,j}^\\star C_{i,j}. $$\n", "\n", "\n", "The coupling constraint\n", "$$\n", " \\forall i, \\sum_j \\ga_{i,j} = p_{0,i}, \\:\n", " \\forall j, \\sum_i \\ga_{i,j} = p_{1,j}\n", "$$\n", "can be expressed in matrix form as\n", "$$ \\Sigma(n_0,n_1) \\ga = [p_0;p_1] $$\n", "where $ \\Sigma(n_0,n_1) \\in \\RR^{ (n_0+n_1) \\times (n_0 n_1) } $." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from scipy import sparse\n", "\n", "Rows = lambda n0,n1: sparse.coo_matrix((np.ones(n0*n1), \n", " (np.ravel(np.tile(np.arange(0,n0),(n1,1)),order='C'),\n", " np.arange(0,n0*n1))))\n", "Cols = lambda n0,n1: sparse.coo_matrix((np.ones(n0*n1), \n", " (np.ravel(np.tile(np.arange(0,n1),(n0,1)),order='F'),\n", " np.arange(0,n0*n1))))\n", "Sigma = lambda n0,n1: sparse.vstack((Rows(n0,n1),Cols(n0,n1)))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# plot the constraint matrix." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We use a simplex algorithm to compute the optimal transport coupling\n", "$\\ga^\\star$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from nt_toolbox.perform_linprog import *\n", "maxit = 1e4\n", "tol = 1e-9\n", "otransp = lambda C,p0,p1: np.reshape(perform_linprog(Sigma(len(p0),len(p1)).toarray(),np.vstack((p0,p1)),C,maxit,tol),(n0,n1),order=\"F\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Dimensions $n_0, n_1$ of the clouds." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n0 = 60\n", "n1 = 80" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute a first point cloud $X_0$ that is Gaussian, and a second point cloud $X_1$ that is Gaussian mixture." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from numpy import random\n", "gauss = lambda q,a,c: a*random.randn(2, q) + np.transpose(np.tile(c, (q,1)))\n", "X0 = random.randn(2,n0)*.3\n", "X1 = np.hstack((gauss(int(n1/2),.5,[0,1.6]),np.hstack((gauss(int(n1/4),.3,[-1,-1]),gauss(int(n1/4),.3,[1,-1])))))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Density weights $p_0, p_1$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "normalize = lambda a: a/np.sum(a)\n", "p0 = normalize(random.rand(n0, 1))\n", "p1 = normalize(random.rand(n1, 1))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Shortcut for display." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "myplot = lambda x,y,ms,col: plt.scatter(x,y, s=ms*20, edgecolors=\"k\", c=col, linewidths=2)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the point clouds.\n", "The size of each dot is proportional to its probability density weight." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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3LBVavdHd9633+ERKkQKv24Ht+hKtGI4mKspDRFvPErMsNxK/l4mfzd9SAFZ7\nZvZ74PBViMSrxUq45mNgE7IB2OXufkS7ez4KfONcItmrVOeS1ijhUXf/ZhmXShNR8CXdiircS3dg\nZpcD31mcKDO/XpFznyP6AX0UT69w98PrPb6eJCXXTwAWeJXiM17tvQasEYfTgSGZJHwzWwt4eVC6\ncbH+me1NAYaQzQFbq32LL2kNrV5qQqSNFEBtB3x4P7GkWKi341doE3htp8BLmkXK8TqsL50HXqT3\n7yI7y3uYma1Qz/H1QAcBC2xNeYEX6fyt4rAfkUufcQjphXICL4g8mgNyTw8t83JpEgq+pNtx9xeJ\niiM3zoVZdxB/We2cHu8gm+N1IzHj9WKHNxNpvCMB24fOA6+M9YC949DS9VI7B0Ms+1Yi77rTzKxX\nOv4qVNZ5AmCb3OFKFd5CupiWHaVbS0n4BzNvV5ur3f1/XTk2kfZSOYkPgEWeJpfjVYqnga/H4URg\nSZWhqA0zmwoM+IzY7FCuSUQ3h+Ri4DjgYeCbDwHDK7jnQ8AWcfh3dy+lfIw0md5dPQCRekoBVrcu\nHyHdypLAIktSXuBFOv9LwP+iHMWXiN63UoVUuX4AxL/cKtFuWfFYYvJ9KnTecaIjUwoeSivRsqOI\nSPMYCJXNsFjb6yqNFSRP6sLwOVQe5WR6aeXtvD6GaKtVds/VjPtyh29VeAvpYgq+RESax1SIpapy\nedvrNCNSO+Mglvoq8WB6XBHoE4c7E5Vw+CO54KxUU4Brc0+vrHBY0sUUfImINI8PgIkfAM+UeeEz\nQEpinJg7lBq4GqKmWiUy1x1ONk9rPmIp87EpwOVl3u9yspH1oyoz0boUfImINImUJH8VlP/DPu/8\nK5VsX1PXADPuJ+p2leM1oqRNps5EXt+7QcB5EC2D7i7xfncDP8o9Pb/M4UgTUfAlItJcLgP8euAb\nwFBgmfS4I9Hapn1k9Szw5zj0dL3USCqM+gnACKJyfSk+JloMQXThXjhzkzAltQY6ZzbRMuhcOl4r\nnpLez2stdLZaC7U2lZoQEWkSZtYbOAk4Dejf0XlLE9vmTiLqpuyIKtzXi5mtCvzDiMh2ZWA0pfd2\nXItoCjkdWBaYBXOB5d39HTObj9iNfRLkCqhuQ64uzn1EjldeYHYWcIq7z63V9yiNp+BLRKQJmNkA\n4BZSj+WhRIHOLcn9IH6AWF58PV0zhGjRkGbC1NuxDszsQuC4/YBXiC7ZEJXrjybyuDL/fx4k/v+k\n7hmsRfwjBiZkAAAgAElEQVRPWRr4JfDTeHmcu6/Y7jN2A04ANi0ylEeB8zXj1T0o+BIR6WJpxusO\nYPvFiJmO7YjyEe05cA+xlJW3jHUFcIxyvWrPzP4HLPECsWPxJKJN2fQi1/QjZrDOAgYTQdn2ZBug\nf+buC3fwWWsSLYNWIhfTvUXk8Sm5vhtR8CUi0gkzG0r8QHzL3V/v7PwK7n8K8JvFgMeAVUq45g1g\nE7IB2I/d/Yxaj6unS+2AZhuRa5VJkv6UyML/NbkAuC8RnB1BBF4LE1tOLwd+RTbwyujt7nPqOnhp\nagq+REQ6YGaLAtcD2+a9fC+wn7t/Uviqsj+jDzAeWPou0ppjie4GdojD94g8otm1GJMEMxsMTBpI\n4WT4OcDxRM8giDpeWxC7Gj8hZrwyU5HHEttYp8XTBd290gL30g0o+BIR6YCZ3QNsO5Dom/gU2aKY\n97h7OXFSsc8YAYwaCvyDwkuNHXFgVWIWDBjh7qNrMSYJHc185XMix+t3wF+JbPqM+YiKqscAm5Mt\nsgqa+erxFHyJiBSQlhr/ORD4J1Hu4R1gNbIB2Kq1WII0szuBHX4LfLeC638LfC8O73L3Hasdj7SV\nn/M1rJNz3wGeJ2bJBgHrEjscIXalrhOHH7r7l+oxVmkdqvMlIlLYShAzXsukF5ZNz/Pfr4EVIXY1\nViLvuhVqMBaZ15+htOJpywLfIjZDfItc4AVwae7wxtoNTVqVgi8RkcLeglhqfCe98E56nv9+DQyE\nyjthDyp4KDV0KcCfqKznJsBnROJg/v2kZ1PwJSJSQFpSvHcqsdS4NW2WHO+p4a7HqVB5J+wpBQ+l\nVtL/5wenEbsbK/Ebson2D7j7G7UZmbQyBV8iIh3bD7hnKpFUnQm8gG/X8DP+DVFAtRJ5142rwVhK\nYmaLmdnJZvaSmb2XHk9Ou0O7o18Cc84mEuvLcTFwdhzOIapOiCjhXqQZmZkBGxM71wcDk4md60+4\n/tA2XD3rfLXabkczW5eocrF4gbc/ArZ39+frPY5GM7PvEGW7OAn4MbBQkfM/I2a8zs69dLi7X1G/\nEUorUfAl0mTMbHfgZ0R3kvZeBk5XSYHuo5XqfJnZYkSMuPgmwCnEb9KxwBnA43HaR8RO0JrUQWsm\nKQC7FOjVn5j+PJL4NehFTG2NTSdcT3apcQ5wlAIvyafgS6SJmNkPSP9YXhzYl+gLNwG4gWzzZICT\n3P2cxo9Q6iFT4X5RIoBp1gr3ZnYycOYmwEO0qVvFLGA48EQ8Pdndz6r3eLqCmQ0nGp9nN5oa0QV9\nGjEbmecB4Ffu/nCjxietQcGXSJNIM163GtET7rvA/HnvzwAuAn5I9i94FdXsJlJvx9uBHSro7XgX\nsGsjqtub2UvA2mOAQgXFxhBFRYGX3f1r9R5PV0pL0UcC+wBL5L31IVFO4rJ6tKKS7kHBl0gTSDle\nLwFrnQ38oMi5ZxMBGLEEOUw5YN2DmQ0AbiatJA4FjiKmVzIdlh8ALiGb4wUReO3p7p83aIzvAUu/\nTdsaVhnvAMvF4QR3H9KIMTWDVAl/APC5KtdLKRR8iTQBM9sEeGxx4gfY/EXOnUEU/fw4nm7i7k/U\ne3zSGGkG7CSiFeDSRU59j9h4d3Yj+zlq5kukNnp39QBEBIhdjexL8cCL9P6+RFsZYmJEwVc3kQKp\nM8zsHCKOOZSoXJ+Z/BoHXAnc0UVNtG8E1j4D2IZ5c77yks5uaOiouoE087kHsDJReHcq8CYwqlEz\nm9I4Cr5EmsNgKD7VkS/vvMF1GIt0MXefBYxOX03BzAYTKWezHoc+w4ndjmsT699nkP1XwEdEgCgl\nMLMViRTPg4AFC5xyoZldA1zk7v9u4NCkjhR8iTSHyRC7GkuRd97kOoxFJMvMvkKkGe5P5DUBEWjt\nPO/pXwCHdscyE/VgZrsQvSP7AWxEbLTIFPa7B3gyArLvAYeb2d7ufkcXDVdqSDlfIk1AOV/SjMzs\nm8BfgIUhSkkcSayD3gGMAv4HzATy1sU+JXZfPtrQwbaYFHjdBsy3B1G0dViB814kirWOiqdzgd0U\ngLU+BV8iTaCeux1TEve2xM/MccC9XZQvJC3EzDYF7gfm34Eof7J6kfNfI35f3hVPZwBbKwArLC01\nvgL0O4XoGVmss4ETwdmZ8XQ6sKaWIFubejuKNIEUQP0C4gfY2cRPr3wz0usn5146vYTAayjwT2Ij\n2m/T4z/T6yIFpaXG24H5DyVmuYoFXqT37yB2CBCTt7en+8i8vgv0G0nngRfp/d8Q2fjEEuWxdRyb\nNIBmvkSaSPsK9/vQtsL9x7lTO61wn2a8XgdWXBHYipjGSN2X3yJawMxO5/Yl7bBy95m1+46kFZnZ\npcCROxABVa8yrp0N7Ep2BuxSdz+61uPrCmk34iBgSjW7D9N93gMWfBEopx7HC8C6cTgJGKJdkK1L\nwZdIk0mV7n9KbCRrr+Tejma2IzBmRaLfXKb9yZpkA7CdiZ+rRwNbE//AdiJGuwQYo4KRPU/a1TgB\nGPAasFoF93gNWCMOpxJBQktuDDGzgcB+RL3b/D+PL5NaOLr71DLveSBwzUZUViNmI+CpODzQ3a+t\n4BbSBLTsKNJkUmA1jGjd91PgnPS4CZHjVWr5gRUgZrz6pxf6p+fJWUQy9TbzgS0EzBcB2Dbp9THp\nh4/0LAcAA4ZTWeAFsQS5WRwOJHZJthwz24xoeH4ZsPb8RA+htBlm7fT6+LQpoRwrQ+xqrERe4/WV\nK7yFNAEFXyJNyMMT7v5Ldz8pPT5RZiuhcRDTWNPSC9PS82TVxYDziMJMn6bH84DF4v3tgFtS6xTp\nOfaB2NVYjaNyh/tWeauGS4HXfcCiGxBL/pOInZ2TgOuBDeLURYH7ywzABkLlBfoGFTyUVqPgS6T7\nuhd4axyx1HhEevxPenMx4HHgBGCR9Noi6fnjtAnAdmrUgKUpLAXZ3KKKrZM7XLLKWzVUmu29Fej7\nHWJpcB9y5V8yHSaeAL4TL/UFRpcxSzwVKi/QN6XgobQaBV8i3VRKpt+ZFIBdTjbXaxrE1vWO1i1W\nJqqXJ0d1cJp0TwOh+mmVFp6h2Y8043UpHW826JXez5sBK3WG702IAqqVuLvdfaQ1KeFepJtLux63\nAVYE/gv8ZT6wj8jNeBUykdhxOTeS8BfQLsiewczGAV/5F7BSFff5F9ngfpy7r1j9yBoj0zz8ekqL\npq4Hvh2HJTUTz9/t+AKFC6t2pN1ux6XdfVqx86V5aeZLpJtz99nufpe7XwQ8BthgigdepPfTlIWR\nZkOkR3gf4Pkqb/JC7vCDKm/VMCkwWnt+YESJ1+xBrDsCa6fri0rlIa6BqN1V6vSH06Zx+dUKvFqb\ngi+RnmUq4JOJma1iJpJNKvF0nfQMN0Js5avGpbnDG6q8VSMNgmimWKzFV775adMNu9Ql1ouA6aOA\nU+k8AMtUuE8thqYDF5f4OdKkFHyJ9CBp6fD+ucAfOzn3GqKRHHCflhx7lGuBzx8G/lHhDV4DHonD\nqcB1tRhUg0yBWNNr32GiIzPS+fnXdya1BtobmHsGsCfRw7GQF9P7qbXQXGBvtRZqfQq+RHqeSyCW\nPDrK2H2TNkscl3ZwmnRDqSDqdQAnAeVW2Z1NtvcowHWtVGA1LQm+PIPY7liKUURjcSLnq+SK86k5\n9m6kGbB1iAKqpwPnp8eN0utpxmsa8C011e4elHAv0sOkul1jgO0WI3Y1HkTkeE0kZrzOINvK6B5g\nJ1W671lST8bngYUPBX5PaS2GZhP1wa6Mp58C67r7f4pc0nTM7Ajgsg2IchLFvu85wMbAM/H0CHe/\nvILPW5Ho1XgwbVYwsyYBVwMXa8ar+1DwJdIDpZpEt5AKbc9HalpHdqkRIvAaWW77FOkezGxToibv\n/DsQ7RCKNdd+lWj6nno6zgC2dvdH6zvK2kt/NsYDi36HjstNzCECzT/E00+A5av5s5KS9UcQm0Qz\nfxzfBG5VD8fuR8GXSA+VZsB2Iup4bUOut+N9xM8c9Xbs4VIAdjuwMETLoKOIpbBMdPA88Zvl77nL\nPgV2bcXAKyNVrL8f6LsB8D0iKpqfiCpHAb8lO+M1kwg0/17oXiKFKPgSEcysL1FOYqqS6yVfWoI8\niejRWKzkSCa5/uxWW2osJAVgo4kCqvQl1gQnkc3xgpjx2l2Bl5RLwZeIiHTKzAYTAdi+RMugzOTX\nB0St0T+1UnJ9KdIS5L7A0UQz7YyXiY0rN2hZXiqh4EtERKQTKSdrEDBFOVhSLQVfPYiZrQccSnQN\nGUgsE7wFXOnuz3Xl2ERERHoKBV/dnJkZsBdwIrB+kVOfAc4Dbnb9phAREakbBV/dWNrNdgFRQ4aF\ngUOArYDBwGRiO8/VxPak5CLgBO1yExERqQ8FX91UmvH6LXBsX2JK6xCgX4FzpxEB2Ilkd/FcBHxP\nM2AiIiK1p+CrmzKzvYA/9yWKHm5ZwjUPADuQDcD2dveb6jU+ERGRnkq9HbuvEyFmvEoJvEjnnZt7\nekLNRyQiIiKa+eqO0q7GZxcG3gX6l3HtNGAZsjlg67n787Uen4iISE+mma/u6VCIHK9yAi/S+Qe3\nu4+IiIjUjoKv7mkliF2Nldi63X1ERESkdhR8dU8DIcpJVGJQwUMRERGpBQVf3dNUiDpelZhS8FBE\nRERqQcFX9/QWwN8qvPj+dvcRERGR2tFux26o2t2OQ4DP4ql2O4qIiNSYZr66odQk+5lPicr15biK\nbOD1tAIvERGR2tPMVzelCvfS7MxsMeDbwMrEJpGpwJvAn9z9464cm4hIPSn46qZSb8cLge9mejse\nTOElyGnEjNf3yQZevwWOV2/HjpnZAGBDcj3Kn3b3z7t2VK3BzIYRHRT2BOYvcMoM4GbgfHd/sZFj\nExFpBAVf3ZiZ9QLOB74LsDARgG1N1JCYAtxHLE1+lrvsIuAEd5/T2NG2BjNbjohTD6JtNY9JwB+B\nc9397S4YWksws0OAy4FeRsy0bksugr0HuBtIfyvNBo5w96u6YqwiIvWi4KubSzNgexK9HjcocurT\nRKB2s2a8CksbGe4GFgNYh2jF9C7wQu60j4HtU96d5EmB15UARwI/BL5S4Lz/AGcBl+VeOsTdy01f\nFBFpWgq+epAUPBxCVK7PTH69BVyp5Pri0ozX88BiWxPBwdfy3n+JCCZSmY6PgXU1A5aTlhqfBXpd\nAHyvhGsuBI6Pw9nABlqCFDNbCDgAGE7u77CHgWvd/bOOrxRpLgq+REpgZhcCx20N3An0KXDOLGBH\nsgHYhe5+fKPG1+zM7Fpg/yOBS8u47kjg93F4rbsfWPuRSSswsz7AGcBRdJy6egnwY3ef1cixiVRC\nwZdIJ1Jy/QRg8Iu0nfFq7yVgWBxOAoYoCT+7q/E9g77/pvBSY0fGEdO0Hkn4y2gXZM+TAq/RwE4Q\nO7cPAJYEPgCuJXZqJ2OA3RWASbNTnS+Rzm0IDF6H4oEX6f0UfC1I8Ry7nuTbQN8dKC/wAlgB2D4O\n5wf2q+mopFWcAey0KPA40bnjAGCb9Pi39Pqice5OwG+6YpAi5VDwJdK5wRDJ9aXIO2/BOoylFa0M\nsauxEnnXrVyDsUgLSTleRwHcAWzcwXkbp/eTo81Mf/akqSn4EuncZIhdjaXIO29SHcbSigZC27oc\n5ci7blANxiKt5QCg/5Z0HHhlbAxsEYf903UiTUvBl0jnngYmv0DkdBXzYvoiAq9n6jqq1jEVUgRb\ngbzrptRgLNJahkPpkVTeeZvXfigitaPgS6QTKWn+GohyEh1l8s4CTs49vUbJ9llvAtxb4cV5171Z\ng7FIaxkEkVxfirzzNEsqTU3Bl0hpzgU+vp8oJ9F+Buwl2pSZ+Jjo6CThT8CMu4gCquUYR1S1JXY7\nXl/TUUkrmAKxq7EUeedpllSamoIvkRKkgqnbkwKwYUSF+13S4zDaBF7bq8BqTioPcbMTxWnLcRbZ\nVkM31arMhIXhZnaBmV2THoenbhDSXB6GKCdRirzzHqr9UERqR3W+RMqQKt2fSPR2zN9RNYlYmjxP\ngde8UoX7Z4DeXVnh3szWIXpwrlHg7VeBA1RJv3mk3Y7vAf0fp3jS/RPAJnE4DVja3bXhRZqWgi+R\nCqTCqxsQAdgk4BnleBWX39vxCCJ/boUC540jZrx+n3upJr0dU+D1CDBwSXJ9tt4CriK7ZDUV2Mzd\nXyh8F2k0MzsH+P6idFxu4gliFvqTeHqOu5/UqPGJVELBl4g0jJkdDFwO9DZiHXdbopzEZOCe9JX+\nVpoNHF6jwMuAscAaI4HriKqtGTOA/YFb4umrwFpqMN8c2le434J5K9w/mDtdFe6lJSj4EpGGSkuQ\nxwN70TYGypgB3ARcUKslQDMbDjy0JDC+yIcuT3YGbLi7P1KLz5bqpQDsN8DRFO7t+DnRNlS9HaUl\nKPgSkS6Rej7uR1SuH0TsUHsTuL7WPRzN7ALgez8Gfl3kvB8TvWxQY/SmlCrXH0DU8cr8nnmIaLyu\nHC9pGb27egAi0jOlAOvCBn3cQhA5XsXkvb9QHcciFUoB1kXpS6RlqdSEiPQEn0Ek1xeT9/5ndRyL\niPRwCr5EpCf4C8SuxhkdnDADyMvsv63uIxKRHks5XyLS8sxsFWAo0cR7KvC6u7+R9752O4pI01Dw\nJSItycz6ArsRO+C+WeCUvwOXALe5+8y0y/LvpDpfB5Or83U1bep8fVOFVkWknhR8iUjLSZ0G7iRb\nqX4gsBm5imGPEHEUEDNZO7r726VUuCd20B1J1JXKFNEdA1zq7v+uyzckIj2Kgi8RaSkp8HoCGAIr\nAt8Hvk1UHsiYQvTzPoeomc97wMYpADNipmw3YlfjZ0SO19+BXwCnAYX6PDrwK+BnXb0kaWa9gQHA\n5+4+uyvHIiLlU/AlIi0jLTU+D6wRnfzGULwqxKfAzsDjEDNb67r7zA7ufTrwE+hFBHPfAb4C/Ae4\nggjm5gD80t1/WovvpxxmtgCwJ3AU8PW8t54iCoze7O5fVHjv1YmOS18llzf3L+Aqd3+tmnGLyLwU\nfIlIyzCzvYA/x4zXc8wbeH1KNCj6FFgY2C69vh5pBmwvd7+5wH1XAt6EXga3ArsW+PTbgRHAHAe+\n2sglSDPbkJidWyq9Qi5Gyv4d/j7wLXd/poz77kxMHW5W5LSHiYbxfy1z2CLSAZWaEJFWcnQ8fJ+2\ngddkIk1rCLAvcEx6HAKckrss76CdIwGLGa9CgRfp9W8T53FkZcMvXwq8HgSWgrWJ3uRTie95anq+\nFvE+D5nZBiXc08zsTKJX9WYRyB1FtFD8W3o8kljZZDhwh5mdkZZsRaRKmvkSkZaQykm8HoHCBHI5\nXpOJbjMvpOebA6sAbxCdZyCClreIFoAMzS9Dke79elz0GLGc2ZHHgW8AvOHuQ6v8ljqVlhrHAUtF\nJ6argT4FzpxF7N+8HmIGbIViS5Bmdgbwo1hi/Q0RaA0ucOZk4DKi8dIcgDPd/ZRKvx8RCZr5EpFW\nkYKdzWibXP9DIvBaCXiFmCS6ND2+kl5/GVgkc8EqBe69YDx8pZMhLN/u/Lrbk+yMV0eBF+n1q8mb\nARvZ0Q3TUmMKvP5C/PoVCrxIr/8wndcL4EfpehGpgoIvEWkVA+MhP1D4FLg2Hd/GvBUk1iBXrH5C\n5sVBzCs1Zf5PJ0MY3+78ujsqHo6j48Aro086D+h4eRXgxHj4DVFNoxQ7kdeS/MQSLxKRDij4EpFW\nkQp3Tc576R5gOrHUWKh0F+n14aRlM4g6FO2NiYcrOhlC9v26J5+nchJfjxSzvUu8ah9SlYyvp+vb\n33N1YHjEseWmreVywMxstTIvFpE8Cr5EpKbMbAEz29bM9k6PC9To1q/HwyPk4qdP02OhlcR8bd5/\no8AJlwEe5SRu7+AetxONifB0ftlSovsGZnaVmb1gZm+mx6sKJMoPiIeBQP8SP6F/7rK8gzyHxMP+\ndLzU2JEF03UAHFrmxSKSR8GXiNSEmc1vZr8C3iWmpG5Mj++Y2a/MbP6iN+hESpL/e0yA/Sm9unB6\nLBRP5cu+/8/2yfbp3m8Bv4rZsRHAQURy/Xvp8SBgd2AuwK8KlZkws15mtpqZjTSzA9PjambWK72/\nKfAs8DSRHT+MqKs1LD1/2syeS+dB2h0Q3++0Tr6/jGm5y/IO8nw1HrYu8X7tbZM5WKnCG4gIMM+0\ntIhIuVJgNQbYKl5ZE1gV+CfwymLAqcCGZraTu8+o4qMuAb4Zlev3Jup49SN2Nb5K4aXHV4hSVQCc\nVeTeP4uHOafBHy26EM3j/3LnhbSUdwyxHbHglkEzexLYEugdif+HEsHcwsTs3WiiZMTEdYEHzGxf\ndx9lZk+Bfx3+THbSqqgbSXW/nuqg8n2BvLlyDJrnQETKp5kvEamFnwBbwZeIQOdl4Kb0+BDxOlul\n86pxG/BqVF/YmchvOiC9tVu81car6XUAJgI3dHRjDz8lZofOIaa9MrV4ZgFHuPuPMq2F0vLqWcBY\nIjF+MCwH7JLGtAvxnMHAtkBvWIcoeXEWUaR+lfR4FjFh+F2IzPkb0gzYpfHxF6YhFDML+G3myVVm\ntpyZDU5jHWhmXyVtWWybN1eOQulyIlIu1fkSkaqknK53gUUj8CpULP1hIimej4FlK22Dkz4vr7fj\nCsTGvuuIQA8iuT5T5+vhzGWzgLXd/Z9lftYgor7EeHefkvf6osDdwPrxb9jvEIHT6gXu8ipwMZGs\nPzcu4W5g0Q4+9TjgIog2St+g5DpfB5FiyxlAXyIydaLu1xK0Wek4iphELNdRpHS3V9x9rQpuICIo\n+BKRKpnZtsA9UWPqJTruSb02sQTItu5+X5WfuRxwJ9l1xgHEct4E8nY1ZkwENnX3f1TzmXmfvQDR\nhHv9iMv+DGxYwpVPEbsRx8el/B0otBdhOrAMMWw2IH5BHwL6x6/xcek+/YkcrxuJGa+xeffoDSwJ\nfABkVh8XARYngtKBxMReOcuPk4iOAZ+T/jOoqxuMi7QqLTuKSLVS1vtQCgdepNezBeEX6eCkkrn7\n28C6wF7AIxELvEO7wOufRCL7UrUKvJLTyQZej1Fa4AWxvPgYcd2ztEsdy9OPvPyuI1Ovxs2B9yPA\nOowIngalx8PIBV4GnBan8k56PC29PpGY7RpOJPGXu2HzMvJy+AfQeeExEemAZr5EpCpdMfNVYAyr\nEGuNg4jEpDcK7WqsweesDoyF+eaLlc9SA698T5FrYfQKUKhk1lPARgAvuPu66bMXICrXH01Ecvkn\n9wPWjkDrlwXudxpRJHVH4AgiHy1T4b6UQqtjgG/Rrlbagpr5EqmMgi8RqUqjc766kpldAhwVAUxF\npb6SI4DLiTjqdwXef53YLcq/3H3lAuPoTcw+fU6sP34GvS1muhYrcL+Pia5Dc+JUzgDOpPPejpOI\n7/PUdO0apE0NV7j74aV9ryLSnoIvEalaqu91auxq/DMRgGXyvR8hykL8D+DX7n5aV42zHCmo3B1Y\nj1jf+5yImvpFAFIoub5UrxLlOAYTy4G92r0/78xXkXEuB/w38sTeKXLmMkSe13+BZYlm2Wem9wYQ\nBVS3ITd5eC9RTy2z1JgNvGYC67j7a518kyLSAQVfIi3MzJYmcp8GEok8z7v7hOJX1WUcBep8DSVm\ncF7JnPY3oNo6X3VnZgsBPyKKcRWYRkqxTtWWI4Klf5BmufKcRFS74Cp3L1pNPpWTKHPmKzPL9Vfg\nPPJ2hXZmJrCfu48q9QIRmZcS7kVakJkNN7NbgbeBO4gaA3cAb5vZKDMb3sjxpIAq03354wi4biEF\nXh8Dv6KKwMvMhprZMWZ2Snoc2vlVFX3OMkRJ+5OBxeBrxLLcZcQOQ4jXamFYemxfm2w6cFXmSadr\nm+4+GbgvdjVe2MFZFxDv70Db5cWdiY2UrxGJ+3FLYivmK+SmvaYQtTLWUeAlUj1VuBdpIWY2HzEl\nckK80pvYvbYoEeM80gtmjwBGmNn5wA/cfW4jxpYCq9PSEuQ3iV2NE4G/V5rjZWabAT8Ftijw3oPA\n6e7+SOWjbnO/hYi1ttUiCf4PRF57ZgPBAkRZh4Vq8XFEr0SYt3XQyaQyE8+7+7Ml3uwGYNuIfR04\nnpgB+5gIvH6TTjuxg8tXI2KrB4FxBhzq7m+ZmRG7GmcpuV6kdhR8ibSWFHj1Bk4hEqWXznt7AjFZ\ncgYw+wTiJ/H3GznAFGhVvZvRzA4gpoB6RU757kSdqfeIdjzTtgA2M7ND3P3aaj+PWGpMgddj5PpG\nZmSaW39Wg4+CSGbPv+90IvC6CGJ574Qybpamz5wIwP6PyL/7H7k6X+dTIIZtJ9s1aDBE1f80FhGp\nIeV8ibSItJT4UExE/JXoWNORe4lVwNkAm7v7wzUaw4JEdNKPiBb+4e6Til9V0edsBjwA9Ir8p1PJ\nzRRBBC6/Bs6GSGTaspoZsJRc/w6wWJSQ2KjAWf8gkuxrnfN1I1HM/irSjFfZeVWpddCbkde1DnAX\nEYgZsdR4Ip0HXgArEgX1+WpqNi4idaDgS6RFmNkoYES0Rzy9hCt+Sqr5NMrdR1bxuYsTVT8PZN7M\ncIhipn8kksM/qvRz2n3mA8AWEXgV64WdTUx/wN23quLz9gWujzys5ylcq2wOsZI6mUiHKtTEu1SZ\n3Y7zeB44wd0fLeduZjYQmAjz9YngaWFihm4hSq9iP55o1+QzgUXdfWo5YxCR0inhXqQFpF2N34rl\nxqNKvOpIUmbBbun6cj/TzOwI4qf5mcCq0TJwGFGzaxjxnFXT++PM7IiUJ1SxlEy/RSzHndrJ2aeS\nlu22rDIJf714GEnHVfp7Ef0VIXo1VuOizMEk4AVi2msDd1+v3MALIAVKo6J35OVEwLUc5bUPupzU\nR3xUfuBlZkPMbBcz2zc9Dil3fCLSloIvkdawLtArkuuXKvGSpYm8d3oBvzOzK83sXDP7RmcBUiod\ncQuRQDYwljjvJDa9vUAkZr+Qnt9JWgIdmM6/JV1fqS3jYXfaLjUWslA6L/+6igyMh846Hx1D/LV5\nBd1TjM0AACAASURBVFGLqxJPEcn8zAU2dvd13f3QMpLrO5I6Zf8BKHd/wxfAlW3uY2abm9loYo31\nduD69PhfM7vVzDavcrwiPZaCL5HWkIKDRcu45GViFQuI3jCHEMk/jwIvmdnaha5Kgdn1wIgIfm4C\n7iFyh/q2O7tvev2edN6CxHVcX8UMWJquKXWCJTupV840T3tppmdiJ6etTuxfmEuUnnivzI95L103\nF+CcGvecfBx4GT4kWlqWusl1LnAQcR0vA0+a2XlEhL0b9O4FWxOFcrcmnrM78KCZnZd24IpIGfSH\nRqQ1pODgkxJPfxnYlFjVWoLYRXdFelwCohHjo+0DsFTn6hZgRCT270iUEislyNiTKNaZDcAqbT8z\nOR5KDWyyNWUnV/h5AM/Fw82kpbciUl9txgPfoPQZsKfS+eOheGftiqSdiQcCU6LLwH50PgP2BbAv\nETgzJV2fdtT2SUN8m9i8emN6fDu93oc4L3Y9iEgZ3F1f+tJXk38R0zuzobfDBAcv8jXXYS0HHEY4\nTG/3/nSH3dP72U7YWwK3xmfg8371Stf8Ld2/2Of/OXPdFGCxCr7XoXF9f4fPOvmsT9N5ODC0il/f\nBYCP4j5PdPKZ7vCxw6rpc+dzOMLhlQ7OfcXh8HQeDjwDLFLH3yubE4GowxIOP3YY325M4x1OcVg8\nM6bJ6brN43kfh/s6+TW4N52HEztqu/zPib701SpfXT4AfelLX6V9AaPiB91POvmh+KjnfvC2D7wy\nX9PT+zhR0iEd93YY6XCuw+XpcWR6PXPOSIdpRT5/rsM2mfN/WOH3msZ0Uiff6w8yn/O3Gvz6nhn3\nWs1hYief+4nD0Mxnz8392izrsIvD/ulx2bxfN+YQBbgWaMDvlbVTYJ0XIK7gsHZ6nC9/XC8Ba6fr\nRsdrP+vk+898/TRzj1u7+s+HvvTVSl9dPgB96UtfpX0R2fYpELqnyA/EE9MPxJM7+cH5w7wfwIMd\nfuEdz6q9l94fnM7/ZicB2J2Ze79W4fe6WW4W7gceM1z59/80P/CaDWxWg1/fhYgaECkAe9znneWb\nm15fLfPZrwIbAr8j1ni9wNek9P5qDf79YsAmRP7ezHZjmkF0zd6EXMmhIREgljK7mvmakH4/MhsY\n0tV/RvSlr1b5Up0vkRaSEqE7qXC/IzGZcQV5/foKuIJIy+oPPE1pdateAbYn8rFGErlChfLqZxLV\n0mcCLOjRf7AshSvcL018j6NJbXnmAAe7+3Xl3r+Dz1yG2D2werzyNSKXbWHgUyIn7KXM6W8RvXu+\nSIP5JxGErEoMeBoRnL3p7nNqMb5KpTpgSxKbEiYDH3i7Ol5mtgtweyTVl9OgYGuiZzq7uPtfazNi\nke5N7YVEWssPAIfZJ0YB1TOISaJFiWT8h4l4BCI2KCbz/khKLxi6JhGbbELk5R9B4QoPfYn45UWI\nivhl12Vw92vN7L/AT2DaljFR08YDwC+9Rr0d02e+a2bfIHYmHAYvLZYXbGV8QZTvWIl5C359TvRZ\nvNjdx9ZqXNVKgVZnvyEq2FHb5vxBxc4SkRzNfIm0oNRq6FhgN9rsWu5F7HJ8mNjV+F8il7y9L4Av\nE+UFHiOCqXL8Avg5samxoy44m6dxsKW7P1jmB7SRCqhuSW7m5gF3f72E675M9Mz5t7uX1RMo1Sob\nQdRYW4iYBhtGdqpvhfTSQkQ1+ZdIrXkglvYuBE519/ads5uSZr5EGkfBl0gLM7OngA2jhNduRF+/\npYigYCyxVHc9bQOwL4gyBKOJSalX6biqe0cmEMGbEwFeoZpc65BmvjZy9+zMl5mtT6yXfo2YbZlK\nRC6XefWFRjOfMRi4mrwKrMQ3fHC5S6CpvdK9wLAIbo8k4t5CBfVfJybDLiPNQL4IbOs1artUT6ly\n/X+jjtfblFbM932ikv7sOcBy7j6hkwtEBAVfIi0rFbecCfSKyaD8VZ9Mna8pxAzYQcQq2VvANcSM\nVx+i3FTBWqsl2JNYejyHKDyab96cr7ScdwExk9SR54Hj08CWIdYvpwIfuvuMUkdmZrcCu0fQuQ5R\njf8LgNHuPqKM+/QnpgaHxa/fjWQ7ERX1HFGU9N8ArwEPEdOLg4j/KY8QweYbpY6lEVJF+92ijtfP\nS7jiZ6Q+o2X9uor0dAq+RFpUCgw+jwBjeoEzXgYOIGbACjmOWBmr1LlECtrxwPnt3ruLSPznH+6+\nupmNIHKh+kYLn0OISan/Z++8w+Sojr39nl0FkISEyEEgshDBXMAiCUzOQQQJTDJCgAGRDZ9twMA1\nYLBNumByBpOFyNGARBYSmGgyEiiRDAhFUNit74+qnu4dTdydsDNb7/Oc7enu06dPd8/M1tSp86so\nkP0BNL3NtGwnm4e68K4SkX9nqwSpocYv9L68hxpNn6LxanMBVil0CDKEcJle4BpoYoDlCjnM+Ag1\n1GbnqvQIMFREsl54JbGUQaPUMH8M2ClH7X8BewDzAbYTkdHl76Hj1AeucO84tcvPQJMuZmbYHUk9\nvYR6poahw2UR67bx9JGnLf3cUbgTALeZx8sMrxOAKago+ubo0N3mwBYsbKSsAPSzJV3QnDlvhBDG\n5EmivbouNkKNJoA1STjcVi/g4ggh/AI4SYca76E4w2saOpFhNjrx8SjgReBj1Ol1JLAowF7ACyGE\n3iGERUMIS4cQFi3iRCXFDKjL1KDaA/VsfZVW6yvbnjK8LnXDy3GKpNpaF168eGl9Qf+jC1xToC7T\n1Qmtp0sKPCZbudjaOTlte0uFe3QMTuCEDLpZInCrQLBjeovqlH2SVucT27541PYPaCxZpntiwWiL\nJNr5RKBrdGzfAu/t9Vr/uFbcm73sXGsLTMxSZ6LAGlGfZsXPBUHHh/8frcgQUIL3VAPq1rS+dBLY\nQeAAWyYFd7kEaKj258CLl1orVe+AFy9eWl/QLM2iop9z8xgEcyUhDiqqVJ+rfr4yxNq5OLHtTYFe\n0TmORpMgCiwhmUVZ35VYbX2QwMw855yZMGz4gSwphdBUSWaAbZE0vApSYkdleMwg+rDI+/Khnatb\nDsOrSVQdPtUv0VQ9S0oiZY+gbs0/V8PAQaerZko5tQCd4uophbx4aWWpege8ePHS+oIOx03Sf4r7\n5zDA5iaMJaZScJ7IbGWq6PGNAlNEPVr3JA2v+9EplDfp+mlZ2lnT6u8lsKDAc89PGmBjstyXnrEB\nliojgZ4F3tdf6DGrteLenGznOzKH4XWY1QkCuwk8lrj+Bba+m8QeQW6plocJncq6J5qBe09ghWq/\n7714qfXiMV+OU8OIyDxgb2CWqq9vCFyDzn7EltfY9hFoPfYAHlYHxg2tPPMN6PF7oYH9u6Cz+6aD\nGjkHi4igchK0VHyIeAMNhO+NxtI3FnjuTlZ/cYDNQggLzZ4UkRmis+9WQfXBVhGR/aRwmYmEwn2x\nRJqvhya2zULtp9OBzYDbgO7oxITH0ckJ0fU32vrjtr876HTVc1rRmTYjIlNF5FERucuWLifhOG3E\nZzs6Th0QQtgIeAhYKd7aFZvdFzEZGCQib4UQtgeeVQfRKxSucA86g3BL1LDrhBphgFoYpwHXm+FF\nCOFjYC3NvJMeIz8MNUh+h4YOFcvvsFmWN4lI1jxKIYSV0Qj3DYl1xd4CbhSRSVmOOQK4Uft4U5H9\nWhMN2foYdf5dgRpbyYkJATWsdimgvaeA3QCZi+ZP/L7IDjmO085wz5fj1AEi8iY6te9ANAi/yQyv\nJlv/NbCGiLxlh4wCRqgBtQsqtFoI71n9yIG0AOADNB3PqiJynbT8RWf5A9OVFOaiMwhBRUtbQ+q4\ng0yNvgUhhLVCCA8BnwNnoR6/bWx5FvB5COHBEMJaGRo3VfofW9GvaBbofejo5ZWo4TUQ2Nn27Uph\nhhdWbxdQa/rwVnTIcZx2hhtfjlMniMg8EblHRLZGhZq6A51FZGsRudeGKKO6AhwGvKghYAPRuO50\nWYGIL23/lvaad9Gkkr1EZF0R+buIfJfhQEuM+EDa5m9RbbIVUE9Ra1gLU2FfFFg6uSeEsDmaT3IQ\ndG5Qm/R+NB3k/eh65wZ0yPY1q5/k/RbdL4qtbXkWGi9/gLXzMnF6xeFFtpmqf3QrOuQ4TjvDhx0d\npwNjmlK3oaJU6DDiPsCmxGLsY4EHSQwvjgAOE5FMyq7p7Q8Axqmw6hRM2wodhlwH1fHKm6IxB/2A\nT7DGJlrnNweOABZRra+RaOhXOt8Av0V1TpkGbCYin4QQlkWtwle0wy+hRmehPE3s1ToLNVoDamx2\nQ+3inyg8xg3Ugbkopqt1CXC7tKPE3Y7jFIcbX45TZ4QQVkIj4SP5+EdEZHKO+gHYDjgW9QRlsgqa\n0Jiya4BRkuOLw9rbFJWZWAwdH1wJjgP+gRoik9GcgCugnrfWsgLmrbseNSB7L1ynNzpadzywatq+\nBWju7EdAUxrNIXZdJdgG9T7tjRpPuTgBHWo8AE1HFOXN/C+a6mlJIJOTMB9LouoaKe5D1fHzGsGO\n47Qv3PhynDrBPDZXod6fZEhBM+q6Ok5EvsnTxopofFgfYtfXFOAeEclpJYUQOqGz8o4j6zTB7VAb\nrgtqFP2Eeq5aM/T4Cer5SrIJ6nXqicalPYnaVKCjsPehwesRApxHy4mE3VAjLbr8z0mFgLE88Hvg\nJDInI5+FGoQz0aHGZN7MUnm+fgvcEfXpPjS5Zn/iyQQfAm/kMpAdx6kubnw5Th1ghtcrwOo6dDgI\nNUw+Bh7GhgzHAwPzGWAFnm9F1LO1HmoVLED1EUz2YSnUBlwS+B61/SJvT2fUyTYBzR/Y5tmOqEfq\nTDInvX4duAA1+hrR+7E7sSFzq9VbF/VuHYIabxEzUGPnalKhYAxFnW3pXrBb0BmSA9EYr3TWQB/D\nY9aHQnkMldiK8lSOBX6FJS7PxDvW4TtFJGdyScdxqkC1hca8ePHS9oJGkQtsKDApTdRzkm1X8dM2\nnCOgFtVoWoqXppX+AvdKy1RCPwvcLqrgnl6/t+RXtk8vMyVONfQbyZy2KFmaBf6f1e8uMF5gqK13\nExhRYBsjrD4Ch2c45o+277wsbfzd9u9W5PXuasddJPCBwCqJ+7e0wIECx9hy6eT9/RzoX+33pxcv\nXloW93w5To1jMV5f6Oy9CeiIYTqTgdWABc1obsMpRZ6jD6qsapHk3VDvzv8QD/G9jTrfoiG6XeyQ\nZH8+tuO+Bw2QXxZYREPURqJeu3wsQEVbH0WHLr8n8xBgOmLHPYTGcD1v1/EsGqNfKGOAHdDrvAw4\nObHvEFQA9nLgxAzHfofej3kUr/PVBbV7d0dD+X6BKnzsh6pQRMxF7+Xf0EmpTEM9nh8WcnWO45Qf\nl5pwnNpnL6BBF5kML1Dt1b3QegwqpvEQwnqoHP0uauxcjspN/Audybc2Ggu1FTr0NxRVn38KHQZM\naoj1Ix4qZBoqfDpNA973IyULlpVZxIYX6NBfIYYXVu8Mex2p0N9GcYYXVv82e306er2D0Ht/p23P\nFlC/FGowCTAYvUe5eMrqCXAKmuFnGmqAjbH1dImzrrZ9DBbf1ht4IoTQPd+VOY5TIartevPixUvb\nCvAnQOCMPENXp0dDUX8qou0+wNd63LYS54L8VOBUGzLMNPS4uEAfe72swOREP34SWCqquylqzfwQ\nH3eKwMdpff/Yti+eOEf/IofuorK6Hb9uAUON2UqztExSnl4aBI4SeDvDsem5HXcVeFRa5nZ81LZH\nuR0HCVxjr38hMLvAfs4WWD/q11HVfq968eJFSyE+fsdx2jcmH/9xnmqp/SuGEE4jnh33MfCUiMxP\n1jbJiBuAZWFbdJisK2rrXYD+Pwf1bm1BPDvwFeDfxOrw3wBH2fEBWAQNkL8RYBMR+UcIYQvgFvhx\nM/WMXYZ606I2W4i/TgH6pKTJiibSKxtO4V6zdIIdf3xi21pALzS/5SforbsB9Vzdhg5xgjofbwb6\nokODT1rpTHy9qUfRrAc8TRzA/4dEW/noZvUPARgeQrhRRCT3MY7jlJ1qW39evHhpW0HHFJugsywc\nbB+VN8wbkzVQfipwNrBcot19dF9vUY9Xs8Awq98oGrA+Lsv5xtn+xsQ5Rib2/yHafkbatWyMWmVz\n0vo3x7ZvDFyq2y5uhcfqa2uvm8D0Vnq9ojJd4uD7l9P2fShwokAP279FFm/Vf0WD8NdIfx6fonky\nVwTujbcvLTp5oZh+/iwJT+OAar9fvXjxIh7z5Ti1jqiA6oPqLRmEBtcnuR8d3Wu29X5okPjZtuwH\nKk71Z+CDEMJWVtEixs9BvVBnox6bbmjM1S2o2kQmBtj+R4i9NL9L7E/lhk5mm0ZE/i2aJLs3alSu\nY8veInKkiPybVGDYDIonUtlYlZZyEq2hJ7Fy/qu0lH1YG42NG4d2/1U0m1M6S6E21q+jDT8B64nI\nmiJysYhMFZEDUHcjGui/UBrLPHQFdkx2rOIEpat5Ux2nw+PGl+PUB8cB4+EtdFbjfmhw+dbo8FwT\nKnD6HKrBeRlqa11m68/afnoDz4QQ9gG2UcNpKJqT8C+oTtb9aGLoQtjN6jeikxtfQfMdPhRVGJfp\nKBGZKyJTRORDW85N7Lbx03zB6pmIAvoXy1mrcKJ2fo865Sam7e+PDhn2QO/DO2n730ENr/NBPVMH\nicj7LIwNLfdqZT9ThmapLjwvIYTOIYQhIYTR6BTMn4G5IYTRtj1fqgDHqVvc+HKcOkBUOHUgMFLl\nJB4ALgRetBpHobMTt2PhOKcAbG/7jwR1ldyu+wai//CvRW2DQync8IrY1Y4DFWMfgc0GfIssxlce\nHgSm6aFvFHnoF7acmatSEUTt9EFndW4BTEqr0x9NbwR6fy9Hja1IquM+UMNkXxF5iMyY1Ti9lf1M\neQlLdeE5CSFsgAa+3YfqenQ2QdrOtn4f8InVc5wOhxtfjlMniMg3IjIYHQs7HnVzoQbXNeRPZ9OI\nGlnbgbpqUOPgJ3S4EdTB1hqG2/IpErpYV4tI0cHfIjIHHdNEvXGFNiHAP+3157Ru2DLJDGJjbhSa\nfPtLVAYiXXn+WFu+gV7/WehQJDPQhJe/yGF4gbonUQ/l3BzVMjEXeCZaKTqLeQihIYTQL4QwwJY5\n/2+YQfUisIoOaV+JOu7m2fJKbKh7FeBFN8CcDkm1g868ePFS+oJ6GKYCAs8VGaD9bCLw+39FVd0R\n+GUbA9Q3TgaUPw50asP1rYp6g0SV6wtRpz8tOneTLq9q4/Vcae1tY+vTBFazbfdmqL9mdP470Omi\nQ4EeBV5vQFVsBe4ssp93ROd9C0spV+A5ewL/D82HlHx249FAtZ5Z3nefa719JPvkgJ9tf0qFv3O1\nPzNevFSyuOfLceqTXYAV1MOwbZGHbkecsPod4gD+LQo8/js0V+PBqLDrwba+YVThA2B/EVmQ8fAC\nEJHPgQOAJrgIFV59PUvt123/xWh9/q7br6Zwr9lCPbDjIfbqLQ6cStx2Oql4rX+IyBkicquI5FOV\n1bOJJE74N+IsAvmYY/W1U9ZOXkIIfdFx3b8Dq8FyaEzbcug6FwHjrF6SvUl5vO4m++SArsBdJDxg\nRQn/Ok6t48aX49QnZj3tSvFaVoE47c1/KDxIfTI6o68P6hi5C50VeZet3xJVfEpKkOxZRB5H/2nP\n1gD+Taycgxpa56CzLjfBAvxno9bg2cDXmiR7ZCvPPhK1IZdH7Y2IQ9AR2xdYWHctFa+VMe7KZgQu\nEUJY2ZbpD+5O4AtNGbQ/+Q2wOehki/dAhzdfzFk97kdPdJZAP1gfTeo9BR0ynYI+0/XQ/Txt9SPM\nEj2B/LMyFyGhkzY8R0XHqTvc+HKc+sRitlorpxAd9zlxrFiuWO33UDmL29HYnt3QOLGHbLkbsdQF\nR4QQ1m9lx1pgBtj6qGttmnq5zkVHy87FAvKn2f71ReQJUTFZcwcdhqbhKYYxwG/s9e+xQHKjJzrD\nFFqGV32ISncxh7QpkSGEXiGEE1Fr7nvb/z0q+3FiCKGXXets9EZO01HbzVF7LD0GbK5t3wwVtk11\n7OUQQjZtkCRHkzK8XkJj2KL3QCOwByr4uj5aj9/adQR0FgHq7SyEQ6IXW7oMhdOhqPa4pxcvXkpf\nUFeTwMmtjGc6KRHjM9SW2WK+Jgksb3W2Fhifpd54258Sde1T4mteFP2v/2dUiPXPtr5ohroBdcWJ\nCqWOkMLixkYILGrXcHiWYw60/f9MbDshuu7r0vqxI2oc2v7uommZuidjrKYBOyaO6U8qrioSXj1Q\n4GhbLpU4dhWBBwR2irb9F1g5xz1sIBXj9Wie+/Fo1OZ4O66rrncu8r3WKWqna7U/N168VKpUvQNe\nvHgpfQH21H9o/QowKtJLs8BaiX/gi0ucUzGTov1vbN82kl99/aekAXZble9RZ9QtZ/1ZRzSIPl35\nfrptT+ZyPFxgXpZr3N3qPGTrH0isdM8GifPviCrjCmwlmgEganOewP0CW0bHzQd2SBzbHdUPeTth\npCXKBgLXC8xKtJcywC7PcU/6aZ3lJM41ma0ssHoImlspoG5P0ckHhbzXpkXHz6OIyQBevNR6qXoH\nvHjxUvpCaWY7TkG1ISROkj00re5/BbqKJoDO5vFKL+OtPj8DS1bgXiyNxnotnWFfQLUfvowNl25m\naG1qyyiFEKIevssku0E7PWFofWSG10rR8SMS5+0Ve7xOEE22nam9Jkl4zaYBvdL6H+XnFE2cfruo\ngZypf29F7UwnyyxLNEhOdGZqIc9yo6jNAXb8aF2/ssDj/xEdP6ranxkvXipZqt4BL168lKeggeUC\n20l+L0ZUFlh9BBWj6gN8HRsfjQJPJOpfbNt3K7D9qOwanePUMt+DpdGcQmLLhQwwq9cZjU4fndmT\ntK3okGM2b1dUrrL6A8xoSnm8PgWWSJzvRN2+ZQ7DKypNkvCAnZDW7+1baSxtl+U+tNrzZccP0fV+\nUpgXtF90/OBqf168eKlk8YB7x6lfrgemqQDoMajKQi6arN4o9DiuF5EpaELBb+I6g4En7Zg3bTm4\nyK4NiV5sVOSBxbI5sIy9XsbWF0JE5ovICBHZFlgWjdhHbc9P0HsymJbB9en8iMb1gwb+/4N4pihr\noAH0m1lguamunkz+eU8NwEnRyvC0wPSecT8LIVUvW56iT4EJam8/maVKxJNoPSag+adAZ1h8oTM9\nD0Sdm5n4GTgImxH6BfBwvp47Tj3hxpfj1Cki8jUqxTAXbgR2QkXvJb0mqpy+E1qPucAg0ZRFiMh/\ngF+SSqY4Bw0pO5xYA2yJInvXO3pR7lyDY4Bv7fW3mKx8LkTkW+AGQHTkdRhqWOViGnpPJtj6osTJ\nshuBDUCNulForNfaGra1V4GXMQitz9qooFiEyfRPKbCdVL2MeYpEpBlNcwCcnq2abT89WrnGjkN0\nJune2q8H0QwJVxLfvx9t/X/Q/cwA9rbjHKfjUG3XmxcvXspbgF8BP5AaQusnOpvxLFsmg+v5Adgq\nSzsB2IcWM+2icnORw443R8e+V4Hrj2K+lirimNVIDbMiqlx/lWQOxr9KYmX7pQWekTjQva9tf1bi\niQl8q8s+Rd6zFaPjV070swdqCQm8nef4/DFf1mZPVCdDYH3RWY3REOQCgUcE1ova+ojMSvcbLPw+\n6SQt1/kcTatU9c+IFy+VLkEk/Vew4zj1RghhWVS/6WhghQxVpgLXoUON3+Rpqx/wv8B+pMbhdkO1\npwplNxLDWoeJyO1FHFx2LN/g2xoC1RkVmwW1dbZG7ZMZqJhqNLS4HnoPVk60tL4dOxR1pm2CZvkB\n9WRNI/dQZsR81Fs4GzR2bFqir1cAJ6jn8rEs7c1H9bn+BXCFiJyUoVIKU643oVVQZfsV0HkJX0fV\nPgZ2FpGJC7cAIYTOqMtuOJr4srN15GVUrf9hcY+X00Fx48txOhD2D3EXVBpgMVQ59RPgScmT7ieE\n0BUdkhoab12OVDgYn6EOo3xMQEOgGoEFoHFGa4sNXbUHQgirAeOhL3p7HkLthRcy1N4atS/2Brqk\n7VsF1UxdHDVa7kaHa/kZWATuR23YfNyPxcl9BKwjiS/uEMLKwL+BpdQA+zs2zGm8DfwBM7y+AzYW\nkUn5zmjK9b9F49OSD3Y8mqn9BhEpKDu5xal1AeaJ/9NxHDe+HMfJjxlejwE7aFqYQ9D/yRuhKvG3\no0bIU+j+bPyM2n4vWBsvYHFjO4nIM+Xqf7GEELoBP0DoqrbGqrbnY9T+mYnarmsT58FMJzIywUZY\ngdXtuGjyw5boPcgVftuM3tuXAU4UkX9k6O8A1JW4pG7ZCA2un0I8KYLvgN1EJFsSzIyEEBrsQnqh\nQ5aftSdD2XFqEQ+4dxynEK4FdtCY8THoEFo0UfF8dEjqBdSwmpCxAd0eGV4rABeSSC+zfVl63UpE\nZA5wnxpN1yX29ENH0g6xZTbDCztOiCcjzEQD8XtEFaarQXUyidRLaTTb/pdBo9UzDs+aQbURcAUw\nQw2uRzDDa4Zt37hYw8vabhaRT0TkdVu64eU4bcQ9X47j5MRivD5Sj9YYdKZaOu8BOwNfESfmHoLG\nKU0DRpDSa2UFe70+KsdwIsDVInJcWS+kSEIImwFjYCl06LBbEUfPQWO/vieOlVrI87UbaiF1Ug/Y\nyei8gCg06mHgcszwWgDsKiLPFtDvHmhwWeSpGicis3IfVRuEEBZBH0gkLvudiGTTs3CcdkunanfA\ncZx2zzG6OITMhheoITUW+BNwLzoClq4T1RU4APgLsd7UV9HOXFm7q8VY4N/w3cY6tHovhQ0WNKOJ\nt79HhyU/QkcD10RjvpoAXheRJ0MIuwIj4OXF1cjqjsaH/YgF12MrQwoxvADM0BpV0BXWABYvth0a\nWDeIOMs3QFMI4WE0IG+Ux5M5tYIPOzqOk5UQQhcsQjylC5qVlYDb0ImTF6PeL1BPzl9t+23EhtcC\n4J/Rwc+VqMslw/6RDwVmaMD7AahHKxdzgP2BkeiMyChO/QjUZrgiqni1neNZNCr/ROAjNbimITHf\nowAAIABJREFUYobXR7Z9lUINr3ojhHAw8CEqRLdvAzQuj84WWR5o0Ju6r+3/0Oo7TrvHhx0dx8lK\nCGFVYIIaTJPzVc9AH9SY+By1MZJcixl07W62Y5IQwq+AR4Ge6sE6AnUGrpqo9Tl6PTehHq9eqLfs\nCnSA4T/ABVjI1jfAqiLyU9p5Aur2imah/thRPTl2Ly4A/giwIqqRciRqdEV8icoCX2evjb8CZ3TU\ne+fUBm58OY6TlRDC+sC7sC6x1lUxrAt8oE2wvm1bgP7LPB4bgmt3Ol/phBDWA24FNrYtaExXZCdN\nIs4csDbq8XrC1g9H5R7eAvgJzav4WkU6XqOEEC4E/hj5Cn9L7hiZBWgurRNJzSP9q4icnuMQx6kq\nbnw5TgfApAj2IY6Af7CQmW+l83wdC/RHY7zuSLZ1noic3YqGK455YzZBY48OooU9ENBZjV1p4YMh\nkEjn9A2aSscNrxzY0OEdjai62h5FHPsYqrZmBtghInJnqfvnOKXAjS/HqWNCCOsAt6BGQzrjgKEi\n8mGO47ugRsPiquNZTB7sf6MpITPyKXB+OTxeIYROwO7oSNUGxDPj3kFHqB7PJyhbwDm6oRc3FP1/\n3zuxewEtHTWvozFe96YPNTotMQP3I2Ctq1Art1iuBmza7MdAfx9+dNojbnw5Tp1ihtfLQG/1yhyK\nzrj7FI09mob92VJEPsjRzmXAyRpxc0MRPTgSjYFiJCp/H43RPQc8V44YrxDCEOASNPo/G5OBU0Vk\nRInO2RW9sdH1fYq6u3oAs0RkXinO0xEIIWwPPLsi8AWtm46/AM1LYP7H7UWkbmZ+OvWDG1+OU6eE\nEMYCm6gT6B4S4p6oI+jXWD7GcSKyaY52EjpfrwIbFnD2t4AtUEV7+onIJ625hmIIIZwE/J+urYH6\nTfYhlm54EPWLfBYdcrKIXF7ufjmFE0IYCex7LnBWG9o5FzhHX44UkcFt75njlBY3vhynDrEYr3Hq\n8ZpIS8MrYhYaND4NYJNcMWAhhFuAoapw/xTZ9b5ADa9dsZyPt4rI4a24hKIwj9d9unYxcAqZlXSa\ngcuA06IN+0cesBDC8sAw1LqMvFhvATeLyFcLt+WUEhNQndUAjVNoOauxWL5EXZ/NGv7Vw4VYa5cQ\nwpqozluUzf45Efks91HtH9f5cpz6ZB9dHEpmwwvbfmha/awcAzyrBtXm6JDim2lV3rTtW2CG17Ok\nBFrLh8V4XaJrFwOnkv2rrcH2XxxtuCSEsEYI4V50yuL5aKbrnWx5PjAphHCvTT5wysdSQOOytM3w\nAs0psIy+bCSV79KpJUIIA0MIT6OZ7a9FM8ZfC3waQngqhDCwqh1sI258OU59YgHga+aptlZa/cyI\nyFx04tmtOpR4E6q60AeVk+hj6zdhQ423AHvYceVmd2AlvdZTCjzkFCzp9UrAG8D+0NhJ9TrvRNX5\n70TXGzvpfsaGEDYucd+dmB6gLsdSsFjGl04tEEI4EHge2GkRNEDiVFsuolV2Bp63ejWJG1+OU59M\n08WneaqlQrGm5WtQRObaEGI/dOzuR5WR+ABd8qNt7yciwypkeIHOakTlLAr9SmtA7SkAeul3+Rfo\n3ICDUHX+g2z9C9QRxtLAkyGE1XDKwSwoXZ6pmRlfOu0d82jdDnQ6Cf1muRv1Vd9t6ydp1U7A7bXq\nAfOYL8epQ1oR8zVARN4o8hxd0BGeKD7qy2rM7AshTNV+ZFLRz8Ue6ISDnVEB+8456s4H9gSeBrhP\nRA5oVWedrHjMlwNgQ407JWbPZORkNO088LSI7JKjarvEPV+OU4dY8Pw4+AF11s9KqzETzVU4DXS2\nY1GGl51jnoh8ISLv2bJakgpmWS5exCFfoYZUI6q2n8vwwvbfaPXZN4SwXLGddHJjBtLDzeidbgs3\nolMrgIfc8KodLLh+p0WAfMrLZxEPQdpxNYUbX45TvwwFpql3Z2XUWX+VLfti6W+mWb1axizLH4s4\n5GZUEWoQcaLvfPQB9gId7hhWxMmcwrkaVAm3tSq48+34ZHtOzbAdqGrxEnkqLol+eo1ty9ajMuHG\nVxUwFWfHKSumXL8lME5trCvQfIpXEHm8gIG5FO5rhHd08WARh7xly/2KPFVKMqoYqX+ncEYBH09F\nczW2hhtICax+DIwuSa+cStETNJF6ISTq9SpDX8qKG18VICgDQwh3hRCmA80hhOm2PtCNMadciMgH\nJqC6CXAhOlX7QlTXa9M6MLwg5ei4htRgU15m2DLf7+t0UpNCfQZdGbBUQOeBJsl+rMjjH7PjjPM8\ntVDNMQNs+k4BJOpNL0NfyoobX2XGgpJvR9O8HIhZ9rY80LbfbvUcpyyIyOsicoaIHGvLvEm1a4jH\ngck6s/OyAg/52pY/FHmq1KRQn0FXJiwZ9l+b0OGnq8k/BLnA6iWSav/Vk2rXJKNAE6rn+2R+Dzyc\ndlwt4cZXGTGP1k3AId2BM4EJ6JfDBFvvrlUPAW50D5jjFI8lyT5V105D9VazecCabf97tj6yyLPd\nH71IV5h1SssZmAF2HDqH9VxSw4kpvgT+jEYwHkfK8LrQjndqDBH5FPjXz+jzzsV5mKKgznasOcV7\nl5ooI6Y/8nJ3NPBgQIY6r6ORgrN1dUsReaVS/XOcemLh3I7HsnBux2tI5HZshsYG1fEqJOh+Cvpv\nvnkBsJKIfJ3nAKeNhBAORie29QP1FixDrG3yLS3M7I/RoUb3eNUw9n/zeUzn62xaBgd8jxpeJjOx\nANimFv9vuvFVRkIIdwEHnonmKMnGmcAF+vIuETm4/D1znPrEcjxegso8ZWMy6ikbDOyvAqqPkV/n\naw/gX+A6XxXFRgS2RTOl743pfRhN6CjV1cBoj/GqD0y5/nag0yLorMYV0Rivh0l5vBYAh4rIPdXp\nZdtw46uMWHB9zwlArqRwnwMmmT1DRGpu1objtCcs1+NuaF7JXxA7St5FJxw8LiJNlqtxLLC0Cq3e\nSGYP2BTgCMzw+i+wqYh8Xu7rcBbGhFiXJH6m37uOV31iHrCz0A9nOk8B59eixyvCja8yYb/WmkF/\nmuUKrmtChYOMBv/15jiVwXI1PgksrQ6VvVCHWG80uP5+9Ld2M6jhtauI/Ls6vXWcjocJqG6LyklM\nB0bVYoxXOm58lRH3fDlO+8dyNV6IZtHulKHKAuAB4I/u8XIcpxRk+qJxAEsfcgQqB7E8msJkFpqX\n5G7gRhH5Jk8zjwMH3kTumK9EKo1iZW0cp6KEEEK9eWZFZAJwgH3mh6ECqtGw1pvAzR5c7zhOKXHP\nVxohhPXRGPh9yR+BOxK4QETey1TBZzs6tY4Nn2+BzuTfjdj1/wSaq+jVejPGHMdxyo3rfCUIIewJ\nvAYc0ACd90aj+r4FfrLlU+h0mwY1zH4NvBZC2CNLk68Cd8xGDawz0SHGZlueSQvD659W33HaBSb8\neyuxQHA0JN6LWCD4VhcIdhzHKQ73fBlmeD0ENByCSj/km6t+BnCHrjYDg0RkoWFD+8d0I3Bojub+\nCRwpIvNa03fHyUUIYW00vVA0dD5ORD7Kc0xADa/fqBTwSegofF9gIqodfDn20+F2YKh7wBzHcQrD\njS9SQ42vAd3+gEbeFiI1L8DpwN90dQ6wWaYhyMTQzXBULKgnmsPqMVSfxodunJJi77n90OHCbTJU\neR4dNhyZ6b0XDZmr4TUKtd3SGQdshxlgPmTuOI5TIG58ASGEe4ADDkF/wheT40dQl5ZJKt8jIgcW\ncL52F7QcQugB7ICKCf8APCsis6rbK6c1mLf1ZsAEe7uj4VpLovrQT5Aa7Na37rB0r2skEKz+3b/k\nONsZ6M8VFwh2HMcplA5vfNkMp0kN0PkLcg81ZmMSKiXRrEH4KxUwC7LdEELohv53PQKd4RUxEx1b\nOlNE5lSjb07xmMfrDuAgNbouAIYS53MHdbreihpOs0ENsEOTPwhCCD8CvWA8KSGUjEwAVgeYLiKL\nl+o6HMdxykkIoTMqnn8QKqAfhWVMBe4CHhaR+WU7vxtf4Uzg/L3RzG+tZW9SGdbPFJEL2t6z8mOG\n1zPokCibAWsDH6FjsMarwI5ugNUGIYTBwAg1vLLNsY1oMdd2sIiMtDZSAsEqcdWY+XAgTSLYBYKd\nDoV9VgYA+wO/BNYBFkXnaH0AvIGmoxpXtU46LQghLAUcD/wWlZHKxlfA9cCVIvJdyfvR0b8rQwj/\nAdZ9isw5DArlaWAXffkfEVm/7T0rPyGEy4CTV0I1M5L/pl9HA4Ym6+plIvK7SvfPKZ4QwmhgGw2G\nP7GAI65Ag+kZLSLbJdpxz1eCEEIjsDtwNLAB8a/kd4DrsJRF1ethx8ZSSq1LHE/7vogsKPM5twIu\nRY2ufLwB/E5EXipnn9ojIYSlgSHowFL0uZkMjBCR/1a4L+ugcRd9AfoDx6IPMBL2ewO4BvgwPmwi\nmtniQ0qJiHToggbByLcg0obyjYZ/CfBdta+pwOteHc1PKuOyXNO4+JqmAz2q3WcveZ9pf31e3QWm\nF/jW/dHqI8Daibbu0m1n5Dn+9OjYO6t9/WW8r4PtC1hylImo97Dq/e1IBQ1kPBtNwJl8HlPQvIBL\nluGcnYDLUO+wLAHyO5DHQaaAzLDl47Z9ibhPzaix1qna960CzyWgds2HqHs802dmLjrTf3PMEVTm\nPq2DxjPLAJDRIM1ZvtiaQUZZPevrD0D/kvan2g+p2sXeAPJTG42vOYk3VLWvKc/1bg7ch44nyWZ5\nrmvT+Lr2rnbfveR9tr/RZzWkyLfvkOgZH5poa2BsyI3NctzYpOE2sNrXX6Z7elL8z2INgUsEJgj8\nYMtLbHvqc3JStfvcUQqwJiqZKID0BRloy8Tz+BxYs4Tn7IQm/JRGkLPsuz/f/4Y/WX3r0/31bICh\njqQfMhlcy4McB7IHSGi57xagSxn7tBTwBSC7g8wu8MtxttW3Pn4BLFWyPlX7QVW70IE8X8AJ0a+1\n6I0/NM91HRZf17Bq999L3uc7XJ/VMUW+fY+OnvHwRFsBuC02wE4XGC+wwJanJw2v2yrxy7UK93Nw\n/M/hIoGmLPevyfanPivuASv/s1kyMrw2BnmW2IvRbOsbtzTASuIBQz1XsjjIK0X+j3jFjrM+XVrt\ne1im5/LL6If9siCng9xky2Xt2hcDeQvkc9veLb4nT5XLAAP+F5BNijC8kgZYwgN2Tsn6VO2HVe0C\n/AeQp9pofD0VP5z3qn1NWa7z+OifwykgN9pr93zVTyml58va6xIbYFnLbeX8xVrFe9mITmQ2w6qQ\n+5gywCYCjdW+hnou6FCjbAwyK8sDmdXSADurBOfcCmhubIXhlTTAzAPWDGxV7ftY4mcSIo/XYJCf\n0679J9sOyPrExvLrIEvHz+mWUv+QQ7PRfAk61Nia5zYq7t9UoHNJ+lXtB1btgmb5kb3baHwNih/O\nGdW+pgzXuHnk8brB+jsT/QUCBcV8zcJjvtp9QSerSilivhJtBnQI8k7gR6v3o60PrEePl133Xnqt\na0h2j1d6aRJYPbqXe1b7Guq1oEN/U0A9XLkeyjPxd9gUWjnUhyoJ/RWNx5az2vi/4k9xn16v9r0s\n8XM5NvJ4pRteSQMs8oC9mNj+Oi08YJuXuF+DAelP9hivfKUZZO24f/uVpF/VfmDVLsBywLwGkEmt\nfDATQRr0ocwDlq32NWW4xvsij1ey3yfbm2mlDAbYONtub7aPq30NXgp+1qP1mV1e4Nv38ugZjyqw\n/bo0tjJc5+N6Xy4p8uvg4uh+Pl7ta6jXgs42lb4F/DNtokUM2AZFnmcx4J7ohyto8Hy+GK98ZQ5I\n77hPA6p9P0v4XD4EHUrMdf1/JB6BybQd+GeJ+/UAIFe08bldHvfvgVL0q8Mn1haRr4EHmlHJSSn2\neDvORJFGSjsTWA0hrADs0wicmrbvL6jA12Q0ecxmqBznZrY+Oa66Wgghlx6K0364ShdnoIIhuXjd\n6iWPy43Yt1kHYANd7FPkYan6vyhhX5yW9AToQ/5sJA2oembyuEIIISyG/pA5oAuEdWz7UFTEqy0s\nau0YB7SxuXZBCGEZYC2ANfLUjfZPS9t+NKnnub/JU5SKFaEwPZBcJI5foY1NAbjxZfwFmHMHmqux\n0P8uYvUttdAcVE68vfEboNPetPgSAiBSWD0F/VYaiwbwjLX1U9CxF9TNf1hFeuu0lZHAnSqcui2q\n4zU9rcp0254SWL0D/XXoxPTQRbHSZan6i+Wq5bSJGRBrS+SiGQ3SSR5XIDcAG6+OKqVGlsD2RTSQ\ni0Q7bbUJ2guDMXviReAYNFfdZrY8hvin4Ge27J3WwCpoEjQ01nRICfvWA9r+gVws48vW0yl/lfpH\nRN4LIRwAPPw3aJiKWmMr5zhmEuozMMOrGThAMiTVbgesCbBTlp3d0Ok75wLPotGSS6AfmB6ovO8j\nWjXfDxqnHSAiEkIYpmuzD1alhDPQr7UobedCuR2P6EAerUKZBfTS8Lb0fxO5+DF6MbPkPXIi3gem\nToQVR5HbIBqFzn5AbbD3C2k8hLAqsH8XVDw7MsAg5Q5tM4l21sleq6ZIZea7LcPO51Al4o2Ija9M\nPuXN0PF+1LFZKmZB2z+QMzO+bD3u+TJE5DE0z9OcO9AIy73RD9+3aK6Ib219b9uf8HgNsuPbIz0g\nv7+9B3pdw2xpP/uTJv7qpe+aUw5Ek2Qfiv4aHa2G1gj0628EZniNtv2HSlpSbQdQ5XqKTzqWqv9u\nCfviJBBVrr8e4A8kfkakMRv4Y7x6nRSueH80EA4g/tL7yZYFj1vmIdFOwaOYIYTlQwjrtrcQkET2\nB0B/4p2G6ka8asvTbPubqPtxSXQWWDql9i4ZU0GV69tC4vgv29iUUu0gvfZWgPWBu9HgeclR5qEq\n4OtXu895rucmQK5rZZDhdfH1NgHbVvt6vLTqPbA2aowNt+VCsxq9LHTPfLZjYfepC7AncJQtKyI7\nQprO1zO01Pl6hhYyExMoQucLtRnkX4mHG0khTGlj0HZUJsd9+7aA/uyNjuYl//+8SDuQ/0HDtK4C\npAvI1WSfkDDH9nexaziOhSdMnBdf3wUl7KPPdqylAiyLjte8B3yHKuF/Z+tn0A5nNWa5jj8Csl8r\n33T7tvzA/wiskbg/JwB/B6625Qm1cl+8lPQ9VnczIFGdL0sp5DpfWe7RYcA3aUbBN8BhFTr/Qgr3\nW7CQwv0EilS4t+94eSfxcLe29h4vkfH1WNy/5/P05dzoWrqZAZGQZBDg3Cq/Bw4EpCuqhVXItY9K\nGGB3pe1LqMkPL2EfXefLS+ULOjNjfiPF/2qbjAoCdgLZOX7zPUxuz2DkEdyy0H/K6Pj+cDNqhwN9\nqn3fvOR8XiuiitEfo6MIzbb82LavWO0+lug6XeE++705LLre9UCG2TJxDw6rUD+WRHM4pud2nAz8\niVYo25PB83Wqtfu7Ehlfp8T9vDhHP/bGvoMvQnNGii0vokW6oqp5wNA4erm6yOu/yvo+ILHtc1KZ\nV+YCS5e4n/8bnc8V7r1UrKCBKAvpquQrkQ7Y/iDvphlZDSB7gVwIcqUt9yKldxaVO4CuOfq1DBqE\ntCDti3MBqk22TLXvXb0VdDreCaiS9AhbHg8sXsCxG6J56dKfV3pZYPU2rPb1luB+JXI7ri6q4zVe\n4HtbXiyJoUYBTqx2nytwT7piHq9LaTncd0l8H76mgpkP0MljG6Aq9BvQhtyJqKCqHJr4LhxL5XW+\nsKHGi7K08/e4jReq9D4Y0Np7krwHkcZkuXS+rK+e29FL5Qvwf9E/hxsKfNNdnzCyXgDZwda7g5yJ\nCstmOm6i7e8ev2GfyWSAmeH1KahnbR/78O1j63bsp+U2wNDhpfVQybP1qNPhImB5dPr87CwG02w0\niHn5LMfvh8YdC3QSTUn0nMA0gfm2fM62d4ra/AnYt9rXXoJ7N5jUEGTWMpEO4PGy+7EnqKcrPYam\nGWTd+J7sUe2+tvL6VgWau4B8lriuX9p1VULh3j6v0o3Y45VeZtBiCHK5KtynawE5rZX3IfImHk15\nFe4T/e2PpT8agA4lZosBawZ5jhYerx+A/iXtT7Xf6F7KX1DprtQ/ipPRIcVMb7rJxB4vUFXgg+31\nsiBvFvjBepM4jQTqAQtpfboPkP9hYUNuom23Y+8r0z3pjQ5zpv9TnWjbe1f7uZXwWtcmlacQ2R7k\nGpB7bbl9y+ufRFpAvhlepvI9TODLPI9/qtVD7LiSBKhW+R42mtHxODqk9aMtH7ftdWm0Z7kXR4EO\nNWZ6Axwev5eOqnZf23CN9wCyGsindl0vosNibcnt+DItcjtumeP864LGeOVqLxEEvm4V7tGz0Pq8\nyFE+5E0ob27HtD73xzxg2P273J7nu7a8vOV9FatfUsNLxI2vDlGif7z/S2pMXRrRYPrr0KDH61Cv\nUxRH0ADyD5CXiD1ehRpeSQMs4QHbMtGfPsCCTuT2oJkHbAEljiFCZ5CPjz5cfdAE431afuDGA6tX\n+9mV4FqXj57/5iAfZbnfH9r+hAG2vB2/ISmP1zkCzQU+/maBs6P2fqIOhiC9pN5Tde35smtcDFUX\nkC4gh4A8bUtAFqd4A+xlO87uzaV5zp/R89VkRst5aBhJ57i9jB7rMt+j1wB5tcj7EJVXEv9r7Bqe\npAJD1egQ5Dlo8LzkKFOtXsmGGlv0o9pvci/lL5ir9TuQMWgMV6csb7hOtn+MfUAOtO1ntvIDdkbc\n9p2J/gwHNfZyHbtPfOyxJbwXvSPDa0P7ImtK+2JLeN3GU+MeMHSoUTYnf5zDbFoYYNfb8ffr+rAi\nDK+oNAscHrU3otr3wkvJ3lOpmK9LaB8xX2W6zoVyOyZLIzqEmC/eaY7VSwTI308BMWkkYr5+suVq\n2Q2F8aic1iIVvD8l8XxZuaXS7xd0FuR+aHaP11AR3tdsfT9KNKsx6/mr/Qb3Uv5ingz53N70C1Bv\n1yB0FuNgkCPQoPkvEx+Or9FfVg1k91DlK1+wcNJxLI3mH/Mc+4f4g3lGCe/FGZHhlSuWImGAnV7t\n59eGa10cFQHO6vFKLx/F1z0bddEv0Biuqa15/HZco2g7rFDte+KlZO+tw6J/nOuhQ43VmO1YoWtd\nFbgQnQX5ni3HRUZZb9QL9RgatjHdlo/Z9kRwfTOaUKSgyQDYbMcGkFUS97YvGmd1ARo31bflfX8Z\nWKJC96UkMV/ohLC6k6vJe/+q3QEvFXjIFvN1N+rqTf/11A/kkwwfjits/16t/HBFZa/4XCdYf6ri\n+SKh3ZTv19qT8blrVrMJndUo2xf5vLaLr/0JXQ5py+MXGBy1d06174mXkr6/DkM9XMnvk6/ryfDK\nc/1bYVILBZTXga1acY6/RG30AXkU/fGc/IAtAHmEFmETL1MBDxglmu0I/LLaz7IaxdML1TEhhH4h\nhN2AT0DV8AaiqoOrAEcAfVFxpj1RCfskk22ZKQ1EMWwWv4zydT0CND2KuuQyMQl4VF82kUov2Wb6\nAyv3AXbMU3EnUp1dGQ1Yr0U2Ap2qVwyJjLYDdXFMG7txbPTiwDY25LQjROQ29POxJ/BbW65s2+se\nEXlJRAYAmwCXAC8A/0VzCf7X1i8BNhGRASLyUitOMw30u+hVYA/0F2SSaCbIq6S+swai8jElJ4Sw\nXgjhTyGES4Cdgfd/AG4tsp1bsAvTGZ9tzfxTk3hi7TokhLAEOsNw10z7VwH+A3RHx5bWRQ2ws4AL\nEvVm2bLU2eBFZEoI4YEFMGQQqtqaTGI+CU2yaYnYHhCRqW3sQkRP0C+ofL86GlAl0Sm62qtE5680\nPUBzqhVDIo10N11s1MZubBi9aFc56Zy2I5oXtL3mta0IIvI66tkqKSGEBnSUgGtIZK7OwkpoqpG9\ndPXYEMKlItJcor6sDtwIbJNp/8noL9RtC2hrNHBKvHpZmztXo7jnqz5pYXgtB5yN+q8BtkcNL2y5\nvb2+EDXAxNaj5NplygZ/PPDZ2+jUw33RPEj72vrbWuczSvsLbgaoQZXvG6kZy8aqTC9hHyrJLNDZ\nFsUwLX5pP856ZK5YMCnze7EQQmhjY47TUdgRWHUVsvyKzsBu6GgGsBr5HfwFYYbXK8A2PVCdkYts\nGf0fmQfsghp/P2VqxLZfbfXm6aar0AkNHRI3vuqMEEI/7LPaAFyOepL+DGxsdZ5FPV7Y8rnoWOB8\ndG4txL+0xrSxT6/FL6dEL0TkW9Q9PmIBND0I/A2NvFygQ40jgIFWr1R8CEyagiq/5uJfcWcnAR+V\nsA+V5E3QqVXFMCJ++bMuZmWuWDApm3umWLCI4zh5GQAaNpA+1JiNRlqEGfyyRP24EVh2W/TL8Hp0\nWuX1aGjKNlZpHnAcOmJwGvA0OhT6tK2vaPsThtdJHfn7wI2v+mMo6IfwAeBEdD4twA5APzSCfF00\n5mtdW++H/tNtAM4D7kUHmxrQMYVssVn5mEhqTGI+KqyaQkS+FZH90R9rw4EzbdlXRPYvseGFiDQB\n14F62bJ59GYCp8er19pxtcg/gZ+eQ4eVC+EjYJS+nEPK/nyzjd14K3rxVRsbcpyORKvCBhL12xox\nQghhPczjNZIWIQlg6w8Qe8CA/0xDA912QX9d72LrUYwXcBA6+apWv1dLghtfdYQN6QwGnc88KG1/\nIxrEHhlgNxMbXo+iwiaXWt0j0MzYzVaub2Wfric1xDdCRL7JVEdEporINSJygS1LFeOViWuACW8D\nvwKeivtHs63/itSw5wR0OnVNIiI/AncCHI5aU7mYAwyLV++Mjm37LbgmenF3GxtynI5Eq8IGEvXb\nGjECKnfBgSxseEX0psVMmnvRCQjXoYMsY215HTrxYBMRubsje7wigt+D+iGEsDXw/HKop6pzlnpN\n6FDjeDS+antit/Y81A31ta7+jI7A7dUdeIlE6HQBvIkaMjbEuZWIvFzE4WXDYhj+hcZF0Ad1iU8l\nMS6qhtdOIjK+8j0sHSGE5dEvwJU2R2cZ9ctQ7yPU8LIh5knoJNUGYCJ0alQzfYVW9OASOZn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (10,7))\n", "plt.axis(\"off\")\n", "\n", "for i in range(len(p0)):\n", " myplot(X0[0,i], X0[1,i], p0[i]*len(p0)*10, 'b')\n", " \n", "for i in range(len(p1)):\n", " myplot(X1[0,i], X1[1,i], p1[i]*len(p1)*10, 'r')\n", " \n", "plt.xlim(np.min(X1[0,:])-.1,np.max(X1[0,:])+.1)\n", "plt.ylim(np.min(X1[1,:])-.1,np.max(X1[1,:])+.1)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the weight matrix $ (C_{i,j})_{i,j}. $" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "C = np.transpose(np.tile(np.transpose(np.sum(X0**2,0)),(n1,1))) + np.tile(np.sum(X1**2,0),(n0,1)) - 2*np.dot(np.transpose(X0),X1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the optimal transport plan." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "gamma = otransp(C, p0, p1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Check that the number of non-zero entries in $\\ga^\\star$ is $n_0+n_1-1$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of non-zero: 139 (n0 + n1-1 = 139)\n" ] } ], "source": [ "print(\"Number of non-zero: %d (n0 + n1-1 = %d)\" %(len(gamma[gamma>0]), n0 + n1-1))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Check that the solution satifies the constraints $\\ga \\in \\Cc$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Constraints deviation (should be 0): 0.00, 0.00\n" ] } ], "source": [ "from numpy import linalg\n", "print(\"Constraints deviation (should be 0): %.2f, %.2f\" %(linalg.norm(np.sum(gamma,1)-np.ravel(p0)),linalg.norm(np.transpose(np.sum(gamma, 0))-np.ravel(p1))))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Displacement Interpolation\n", "--------------------------\n", "For any $t \\in [0,1]$, one can define a distribution $\\mu_t$ such\n", "that $t \\mapsto \\mu_t$ defines a geodesic for the Wasserstein metric.\n", "\n", "\n", "Since the $W_2$ distance is a geodesic distance, this geodesic path solves the\n", "following variational problem\n", "\n", "$$ \\mu_t = \\uargmin{\\mu} (1-t)W_2(\\mu_0,\\mu)^2 + t W_2(\\mu_1,\\mu)^2. $$\n", "This can be understood as a generalization of the usual Euclidean\n", "barycenter to barycenter of distribution. Indeed, in the case that\n", "$\\mu_k = \\de_{x_k}$, one has $\\mu_t=\\de_{x_t}$ where $ x_t =\n", "(1-t)x_0+t x_1 $.\n", "\n", "\n", "Once the optimal coupling $\\ga^\\star$ has been computed, the\n", "interpolated distribution is obtained as\n", "\n", "$$ \\mu_t = \\sum_{i,j} \\ga^\\star_{i,j} \\de_{(1-t)x_{0,i} + t x_{1,j}}. $$\n", "\n", "\n", "Find the $i,j$ with non-zero $\\ga_{i,j}^\\star$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "I,J = np.nonzero(gamma)\n", "gammaij = gamma[I,J]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the evolution of $\\mu_t$ for a varying value of $t \\in [0,1]$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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72aZty92GvHHKYB8zwfUm+rkJrjfYx9QZpMkC833DLJ/R19lecIm9nFcecas3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\nKH2XJin9sjNRl7N7Nv4yUs5mlydpBQXbMedAL2M87ZN5ZK5EozVa5V7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htGx8sBkhhFHS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adwJaN8PadWWcV8XuI+gOecc2e19e8hOHYe8Dt8Iajdem+G0khnCAWsS2g1k04G6WRRR3VstiyX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xVE5Og4QQ7sKZ/fCwplsyx+J4Clugd8cYz2qlaxqO3+4uCamekuvQm5Kg2x5zcLhiS+jwGOO1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize =(15,10))\n", "tlist = np.linspace(0, 1, 6)\n", "\n", "for i in range(len(tlist)):\n", " t = tlist[i]\n", " Xt = (1-t)*X0[:,I] + t*X1[:,J]\n", " plt.subplot(2,3,i+1)\n", " plt.axis(\"off\")\n", " for j in range(len(gammaij)):\n", " myplot(Xt[0,j],Xt[1,j],gammaij[j]*len(gammaij)*6,[t,0,1-t])\n", " \n", " plt.title(\"t = %.1f\" %t) \n", " plt.xlim(np.min(X1[0,:])-.1,np.max(X1[0,:])+.1)\n", " plt.ylim(np.min(X1[1,:])-.1,np.max(X1[1,:])+.1)\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Optimal Assignement\n", "-------------------\n", "In the case where the weights $p_{0,i}=1/n, p_{1,i}=1/n$ (where $n_0=n_1=n$) are\n", "constants, one can show that the optimal transport coupling is actually a\n", "permutation matrix. This properties comes from the fact that\n", "the extremal point of the polytope $\\Cc$ are permutation matrices.\n", "\n", "\n", "This means that there exists an optimal permutation $ \\si^\\star \\in \\Sigma_n $ such\n", "that\n", "\n", "$$ \\ga^\\star_{i,j} = \\choice{\n", " 1 \\qifq j=\\si^\\star(i), \\\\\n", " 0 \\quad\\text{otherwise}.\n", " } $$\n", " \n", "where $\\Si_n$ is the set of permutation (bijections) of\n", "$\\{1,\\ldots,n\\}$.\n", "\n", "\n", "This permutation thus solves the so-called optimal assignement problem\n", "\n", "$$ \\si^\\star \\in \\uargmin{\\si \\in \\Sigma_n}\n", " \\sum_{i} C_{i,\\si(j)}. $$\n", "\n", "\n", "Same number of points." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "n0 = 40\n", "n1 = n0" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute points clouds." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "X0 = random.randn(2,n0)*.3\n", "X1 = np.hstack((gauss(int(n1/2),.5,[0,1.6]),np.hstack((gauss(int(n1/4),.3,[-1,-1]),gauss(int(n1/4),.3,[1,-1])))))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Constant distributions." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "p0 = np.ones([n0,1])/n0\n", "p1 = np.ones([n1,1])/n1" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Compute the weight matrix $ (C_{i,j})_{i,j}. $" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "C = np.transpose(np.tile(np.transpose(np.sum(X0**2,0)),(n1,1))) + np.tile(np.sum(X1**2,0),(n0,1)) - 2*np.dot(np.transpose(X0),X1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the coulds." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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NffjoxIMwH3WekOeRTnjciF8/WvexVnhOzoeffTWFd1JIpzzeSeE74rn6TIZt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\nSUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (10,7))\n", "plt.axis('off')\n", "\n", "myplot(X0[0,:],X0[1,:],10,'b')\n", "myplot(X1[0,:],X1[1,:],10,'r')\n", " \n", "plt.xlim(np.min(X1[0,:])-.1,np.max(X1[0,:])+.1)\n", "plt.ylim(np.min(X1[1,:])-.1,np.max(X1[1,:])+.1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Solve the optimal transport." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "gamma = otransp(C, p0, p1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Show that $\\ga$ is a binary permutation matrix." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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VwN5ueS9w1YzqmLqqOlJV3+yWnwEOAucz5XOySh1TVT3PdncXulsBlwN3d+uncT5WqmNd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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (5,5))\n", "plt.imshow(gamma);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display the optimal assignement." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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yTcHGck7A0sZO8OUpmIuFUixbHtmci/n8ZVWdVeexui7j0Ys674EZIRNrPMzp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\nYirc13cfAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "I,J = np.nonzero(gamma)\n", "\n", "plt.figure(figsize = (10,7))\n", "plt.axis('off')\n", "\n", "for k in range(len(I)):\n", " h = plt.plot(np.hstack((X0[0,I[k]],X1[0,J[k]])),np.hstack(([X0[1,I[k]], X1[1,J[k]]])),'k', lw = 2)\n", "\n", "myplot(X0[0,:], X0[1,:], 10, 'b')\n", "myplot(X1[0,:], X1[1,:], 10, 'r')\n", "\n", "plt.xlim(np.min(X1[0,:])-.1,np.max(X1[0,:])+.1)\n", "plt.ylim(np.min(X1[1,:])-.1,np.max(X1[1,:])+.1)\n", "plt.show()" ] }, { "cell_type": "raw", "metadata": { "deletable": true, "editable": true }, "source": [ "" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.4.5" } }, "nbformat": 4, "nbformat_minor": 0 }