{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "TlR5Yep_5tmZ" }, "source": [ "# Optimal transport between Gaussian mixture models (GMM-OT)\n", "\n", "This notebook presents simple experiments using a transportation distance between GMM defined by restricting the set of possible coupling measures to Gaussian mixtures. In the following, we denote by $GMM_{d}(\\infty)$ the set of probability distributions which can be written as finite Gaussian mixture models on $\\mathbb{R}^d$.\n", "\n", "Let $\\mu_0$ and $\\mu_1$ be two Gaussian mixtures on $\\mathbb{R}^d$, we define \n", " $$MW_2^2(\\mu_0,\\mu_1) := \\inf_{\\gamma \\in \\Pi(\\mu_0,\\mu_1) \\cap GMM_{2d}(\\infty)} \\int_{\\mathbb{R}^d\\times\\mathbb{R}^d} \\|y_0-y_1\\|^2d\\gamma(y_0,y_1).$$\n", "The problem is well defined since $\\Pi(\\mu_0,\\mu_1) \\cap GMM_{2d}(\\infty)$ contains at least the product measure $\\mu_0 \\otimes \\mu_1$.\n", "We can show that $MW_2$ defines a distance, and this distance is obvisouly larger than the Wasserstein distance since it has the same definition with a smaller set of constraints. \n", "\n", "Moreover, if $\\mu_0 =\\sum_{k=1}^{K_0} \\pi_0^k \\mu_0^k$ and $\\mu_1= \\sum_{k=1}^{K_1} \\pi_1^k \\mu_1^k$, it can be shown that\n", " $$\n", " MW_2^2(\\mu_0,\\mu_1) = \\min_{w \\in \\Pi(\\pi_0,\\pi_1)} \\sum_{k,l}w_{kl} W_2^2(\\mu_0^k,\\mu_1^l), $$\n", "where $\\Pi(\\pi_0,\\pi_1)$ is the subset of the discrete probability distributions with marginals $\\pi_0$ and $\\pi_1$, *i.e.*\n", "\n", "$$\\Pi(\\pi_0,\\pi_1) = \\{w \\in \\mathcal{M}_{K_0,K_1}(\\mathbb{R}^+);\\;\\forall k,\\sum_j w_{kj} = \\pi_0^k \\text{ and }\\forall j,\\;\\sum_k w_{kj} = \\pi_1^j\\;\\}.$$\n", "\n", "See the following references for more information:\n", "\n", "[Delon, Desolneux, *A Wasserstein-type distance in the space of Gaussian Mixture Models*, 2019.](https://hal.archives-ouvertes.fr/hal-02178204)\n", "\n", "[Chen, Georgiou, Tannenbaum, *Optimal transport for Gaussian mixture models*, 23rd International Symposium on Mathematical Theory of Networks and Systems, 2018](http://mtns2018.ust.hk/media/files/0122.pdf)\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "3czpqOIO8cSh" }, "source": [ "**Authors:**\n", "* [Julie Delon](https://github.com/judelo)" ] }, { "cell_type": "markdown", "metadata": { "id": "FZsUezHh8qX2" }, "source": [ "## Importing packages\n", "\n", "Below is a list of packages required in the notebook:\n", "\n", "- `numpy` \n", "- `matplotlib` (display of images and graphics)\n", "- `scipy.linalg` (algebra functions)\n", "- `scipy.stats` (probability density functions)\n", "- `ipywidgets` (interactive widgets)\n", "- `ot` and `ot.plot` (Optimal Transport library https://github.com/rflamary/POT)\n", "\n", "In order to use the Optimal Transport library we must first install it using PIP. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "U4pCdl7pCQeV", "outputId": "b589082a-c345-4fe7-bc69-cb454b5bb56f", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", "Collecting POT\n", " Downloading POT-0.8.2-cp37-cp37m-manylinux_2_12_x86_64.manylinux2010_x86_64.whl (664 kB)\n", "\u001b[K |████████████████████████████████| 664 kB 4.3 MB/s \n", "\u001b[?25hRequirement already satisfied: numpy>=1.16 in /usr/local/lib/python3.7/dist-packages (from POT) (1.21.6)\n", "Requirement already satisfied: scipy>=1.0 in /usr/local/lib/python3.7/dist-packages (from POT) (1.7.3)\n", "Installing collected packages: POT\n", "Successfully installed POT-0.8.2\n" ] } ], "source": [ "!pip install POT" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "LbVrJ7Rh5tmb" }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.linalg as spl\n", "import scipy.stats as sps\n", "%matplotlib inline\n", "\n", "import ot \n", "import ot.plot\n", "import os\n", "\n", "from ipywidgets import interact, interactive, fixed, interact_manual" ] }, { "cell_type": "markdown", "metadata": { "id": "fJt4Espw5tmd" }, "source": [ "To import the solutions, execute the following cell. If you are using a Windows system, comment the `os.system` line, download the file by hand, and place it in the same folder as the notebook." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "tNC_vTPpEKfd" }, "outputs": [], "source": [ "#os.system(\"wget -nc https://raw.githubusercontent.com/storimaging/Notebooks/main/ContrastAndColor/Solutions/GMM_OT_introduction.py\")\n", "#from GMM_OT_introduction import *" ] }, { "cell_type": "markdown", "metadata": { "id": "iufl8SIC5tmf" }, "source": [ "## Optimal Transport between Gaussian Mixture Models in 1D\n", "\n", "We start with simple 1D experiments, with \n", "$$\\mu_0 = 0.3 \\mathcal{N}(0.2,0.0009)+ 0.7\\mathcal{N}(0.4,0.0016),$$\n", "$$\\mu_1 = 0.6 \\mathcal{N}(0.6,0.0036)+ 0.4\\mathcal{N}(0.8,0.0049).$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "ywEDzRIT5tmf", "outputId": "ffa4b717-ada9-4fd2-f66c-be8d3536966e" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "# first GMM\n", "d=1 # space dimension\n", "pi0 = np.array([.3,.7]) \n", "m0 = np.array([[.2,.4]]).T\n", "#S0 = np.array([[[.03]],[[.04]]])\n", "S0 = np.array([[[.0009]],[[.0016]]])\n", "\n", "K0 = pi0.shape[0]\n", "\n", "# second GMM\n", "pi1 = np.array([.6,.4]) \n", "m1 = np.array([[.6,.8]]).T \n", "#S1 = np.array([[[.06]],[[.07]]])\n", "S1 = np.array([[[.0036]],[[.0049]]])\n", "K1 = pi1.shape[0]\n", "\n", "# GMM densities\n", "n = 100\n", "x = np.linspace(0,1,num=n)\n", "gmm0 = densite_theorique(m0,S0,pi0,x)\n", "gmm0 = gmm0/gmm0.sum()\n", "gmm1 = densite_theorique(m1,S1,pi1,x)\n", "gmm1 = gmm1/gmm1.sum()\n", "\n", "# display densities\n", "plt.plot(x,gmm0,'b',label='mu_0')\n", "plt.plot(x,gmm1,'r',label='mu_1')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "id": "m4fALiNe5tmg" }, "source": [ "## Transportation maps \n", "\n", "We can compute the traditionnal Wasserstein map between $\\mu_0$ and $\\mu_1$ thanks to the function `ot.emd` of the POT library.\n", "\n", "### For $W_2$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 369 }, "id": "gflX0Cse5tmh", "outputId": "31ae07d3-6698-43f8-9037-1bb8ebeaed7c" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\n", "M /= M.max()\n", "G0 = ot.emd(gmm0, gmm1, M)\n", "plt.figure(3, figsize=(5, 5))\n", "ot.plot.plot1D_mat(gmm0, gmm1, G0, 'OT matrix G0')" ] }, { "cell_type": "markdown", "metadata": { "id": "aclPwnGU5tmi" }, "source": [ "### For $MW_2$ \n", "\n", "Now we compute the $MW_2$-map. We start by computing the $K_0\\times K_1$ cost matrix between all the Gaussian components of the two mixtures." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "1pIveL_L5tmi", "outputId": "f6d52262-f960-4382-c8cf-9f22f260312f" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[0.3, 0. ],\n", " [0.3, 0.4]])" ] }, "metadata": {}, "execution_count": 6 } ], "source": [ "wstar,dist = MW2(pi0,pi1,m0,m1,S0,S1)\n", "wstar" ] }, { "cell_type": "markdown", "metadata": { "id": "70pOhzG05tmj" }, "source": [ "An optimal transport plan between $\\mu_0$ and $\\mu_1$ for $MW_2$ is given by\n", "$$ \\gamma (x,y) = \\sum_{k,l} w_{k,l}^\\ast g_{m_0^k,\\Sigma_0^k}(x)\n", "\\delta_{y=T_{k,l}(x)},$$\n", "where $T_{k,l}$ is the $W_2$-optimal map between $\\mu_0^k$ and $\\mu_1^l$ and $w_{k,l}^\\ast$ is a solution of the linear program $\\inf_{w \\in \\Pi(\\pi_0,\\pi_1)} \\sum_{k,l}w_{kl} W_2^2(\\mu_0^k,\\mu_1^l).$\n", "\n", "Moreover, if $(X,Y)$ is distributed according to the law $\\gamma$, then \n", "$$ T_{mean}(x) := \\mathbb{E}_\\gamma (Y | X=x) = \\frac{\\sum_{k,l}\n", "w_{k,l}^\\ast g_{m_0^k,\\Sigma_0^k}(x) T_{k,l}(x)}{\\sum_{k} \\pi^k_{0} g_{m_0^k,\\Sigma_0^k}(x)} .$$\n", "\n", "In the following, we compute and display these two maps on a regular grid." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 297 }, "id": "o0q9bFu25tmj", "outputId": "f110fa44-532f-478b-d063-c35047d0152c", "scrolled": true }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "n = 100\n", "x = np.linspace(0,1,num=n).reshape(n,1)\n", "\n", "Tmap,Tmean = MW2_map(pi0,pi1,m0,m1,S0,S1,wstar,x)\n", "plt.figure(3, figsize=(4, 4))\n", "ot.plot.plot1D_mat(gmm0, gmm1, Tmap*10, 'Tmap')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 297 }, "id": "DFIyyKhN5tmk", "outputId": "772a2fbf-1c51-4d58-e7e5-6d0b5b9908e3" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "plt.figure(3, figsize=(4, 4))\n", "ot.plot.plot1D_mat(gmm0, gmm1, Tmean, 'Tmean')" ] }, { "cell_type": "markdown", "metadata": { "id": "0UgCRqeQ5tml" }, "source": [ "## Interpolation \n", "\n", "### Interpolation for $MW_2$\n", "\n", "We now compute the interpolation between the two distributions for $MW_2$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 315, "referenced_widgets": [ "a1e1ea4edcea4cea9745e6c02ec0481f", "55c1729488a04236adf0fe7507651490", "9d849576ff3242f49522c7c07273ab8f", "67df7d9ab06842c9b4d08e4c9b3f8496", "feb641b4be0c44a8856e0c750d758252", "40b047f0367244e78216ae310f7001a7", "606c444cde0d49fcabbeb6a3a5eaaba0" ] }, "id": "QPdEb3VL5tml", "outputId": "6d9f6690-326b-4a86-d22a-7096cd5cec91" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "interactive(children=(FloatSlider(value=0.5, description='t', max=1.0, step=0.05), Output()), _dom_classes=('w…" ], "application/vnd.jupyter.widget-view+json": { "version_major": 2, "version_minor": 0, "model_id": "a1e1ea4edcea4cea9745e6c02ec0481f" } }, "metadata": {} }, { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 9 } ], "source": [ "def barygmmot(t):\n", "# Barycenters for MW2\n", " pit = wstar.reshape(K0*K1,1)\n", " mt = ((1-t)*m0+t*m1.T).reshape(K0*K1,1)\n", " St = (((1-t) + t*np.sqrt(S1.T/S0))**2*S0).reshape(K0*K1,1,1)\n", " gmmt = densite_theorique(mt,St,pit,x)\n", " gmmt = gmmt/gmmt.sum()\n", " plt.plot(x,gmmt)\n", " plt.plot(x,gmm0,'r')\n", " plt.plot(x,gmm1,'k')\n", " plt.show()\n", "\n", "interact(barygmmot,t=(0.0,1.0,0.05))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "rTkCdcUq5tmm", "outputId": "5d9066fc-ce9c-4d4e-b9e4-565de4dd3644" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "pit = wstar.reshape(K0*K1,1)\n", "for t in [0.2,0.5,.8]:\n", " mt = ((1-t)*m0+t*m1.T).reshape(K0*K1,1)\n", " St = (((1-t) + t*np.sqrt(S1.T/S0))**2*S0).reshape(K0*K1,1,1)\n", " gmmt = densite_theorique(mt,St,pit,x)\n", " gmmt = gmmt/gmmt.sum()\n", " plt.plot(x,gmmt,label='t=%.2f' %t)\n", " \n", "plt.plot(x,gmm0,'b:',label='mu_0')\n", "plt.plot(x,gmm1,'r:',label='mu_1')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": { "id": "RDHZAzH15tmn" }, "source": [ "### Interpolation for $W_2$\n", "\n", "We now compute the interpolation between the two distributions for $W_2$, thanks to the function `ot.barycenter`of the POT library." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 315, "referenced_widgets": [ "a85c1b52c27e4ed6adc24967220de316", "0309010444ba4289aec8771af64ef203", "52f31e777cee4d2da74ad789b02929f9", "0df533aa22b04867b18fb55ba946685e", "9913355ae2f949d8b2f47837b0d4620d", "9d5535d1694946ea813613c159705aec", "6073661f40b841dda8250b56fb29bc11" ] }, "id": "fdeMAAVK5tmn", "outputId": "d05d7b93-ce1e-404e-e517-b6eeb31bc236" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "interactive(children=(FloatSlider(value=0.5, description='t', max=1.0, step=0.001), Output()), _dom_classes=('…" ], "application/vnd.jupyter.widget-view+json": { "version_major": 2, "version_minor": 0, "model_id": "a85c1b52c27e4ed6adc24967220de316" } }, "metadata": {} }, { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 11 } ], "source": [ "# Barycenters for OT\n", "M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\n", "M /= M.max()\n", "G0 = ot.emd(gmm0, gmm1, M)\n", "A = np.vstack((gmm0, gmm1)).T\n", "\n", "def baryot(t):\n", " weights = np.array([1 - t, t])\n", " reg = 5*1e-4\n", " ott = ot.barycenter(A, M, reg, weights)\n", " plt.plot(x,ott)\n", " plt.plot(x,gmm0,'r')\n", " plt.plot(x,gmm1,'k')\n", " plt.show()\n", "\n", "interact(baryot,t=(0.0,1.0,0.001))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "1cErR1UG5tmo", "outputId": "aa1cebee-5beb-4a18-da3b-156a445defdc" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "A = np.vstack((gmm0, gmm1)).T\n", "for t in [0.2,0.5,0.8]:\n", " weights = np.array([1 - t, t])\n", " reg = 1e-3\n", " ott = ot.barycenter(A, M, reg, weights)\n", " plt.plot(x,ott,label='t=%.2f' %t)\n", "plt.plot(x,gmm0,'b:',label='mu_0')\n", "plt.plot(x,gmm1,'r:',label='mu_1')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "SUsPCRG15tmp" }, "source": [ "## Optimal Transport between Gaussian Mixture Models in 2D\n", "\n", "In the second part of this notebook, we illustrate the use of the distance $MW_2$ for two dimensional Gaussian mixtures. We use the following simple mixtures:\n", "$$\\mu_0 = 0.5 \\mathcal{N}\\left(\n", " \\begin{pmatrix}\n", " 0.3\\\\0.3\n", " \\end{pmatrix}\n", ",0.01 I_2\\right)+ 0.5 \\mathcal{N}\\left(\n", " \\begin{pmatrix}\n", " 0.7\\\\0.4\n", " \\end{pmatrix}\n", ",0.01 I_2\\right),$$\n", "and\n", "$$\\mu_1 = 0.45 \\mathcal{N}\\left(\n", " \\begin{pmatrix}\n", " 0.5\\\\0.6\n", " \\end{pmatrix}\n", ",0.01 I_2\\right)+ 0.55 \\mathcal{N}\\left(\n", " \\begin{pmatrix}\n", " 0.4\\\\0.25\n", " \\end{pmatrix}\n", ",0.01 I_2\\right),$$\n", "where $I_2$ is the $2\\times 2$ identity matrix." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 269 }, "id": "Y8t9FvXW5tmq", "outputId": "2f607a87-bbba-4dac-fdaa-9837106d04d6" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "d = 2 #space dimension\n", "\n", "# 2D Gaussian mixtures\n", "K0,K1 = 2,2\n", "pi0 = np.array([[0.5,0.5]])\n", "m0 = np.array([[0.3,0.3],[0.7,0.4]])\n", "S0 = np.array([[[ .01, 0],[0, .01]],[[ 0.01, 0],[0, 0.01]]])\n", "pi1 = np.array([[0.45,0.55]])\n", "m1 = np.array([[0.5,0.6],[0.4,0.25]])\n", "S1 = np.array([[[ .01, 0],[0, .01]],[[ 0.01, 0],[0, 0.01]]])\n", "\n", "# display\n", "n=50 \n", "x = np.linspace(0, 1,num=n)\n", "y = np.linspace(0, 1,num=n)\n", "X, Y = np.meshgrid(x, y)\n", "XX = np.array([X.ravel(), Y.ravel()]).T\n", "Z = densite_theorique2d(m0,S0,pi0,XX)\n", "Z = Z.reshape(X.shape)\n", "Z2 = densite_theorique2d(m1,S1,pi1,XX,)\n", "Z2 = Z2.reshape(X.shape)\n", "CS = plt.contour(X, Y, Z,8,cmap='plasma')\n", "CS = plt.contour(X, Y, Z2,8,cmap='viridis')\n", "plt.axis('equal'); " ] }, { "cell_type": "markdown", "metadata": { "id": "rDJ4VaOA5tmr" }, "source": [ "### Interpolation for $MW_2$ \n", "We compute the $K_0\\times K_1$ cost matrix between the Gaussian members of the mixtures." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "VWli-frQ5tms", "outputId": "92c853d0-66b2-4c40-d7f9-fb2c561c172c" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([[0. , 0.5 ],\n", " [0.45, 0.05]])" ] }, "metadata": {}, "execution_count": 14 } ], "source": [ "wstar,dist = MW2(np.ravel(pi0),np.ravel(pi1),m0.reshape(K0,d),m1.reshape(K1,d),S0.reshape(K0,d,d),S1.reshape(K1,d,d))\n", "wstar" ] }, { "cell_type": "markdown", "metadata": { "id": "GvBibcKA5tmt" }, "source": [ "Now we can compute and display the barycenters between $\\mu_0$ and $\\mu_1$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 269 }, "id": "RveuK6Lf5tmu", "outputId": "8cf6001f-ef49-41ed-818c-d2f7de5d656e" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "def barygmmot2d(t):\n", "# Barycenters for G\\MW2 in 2d\n", " pit = wstar.reshape(K0*K1,1).T\n", " mt = np.zeros((K0*K1,2))\n", " St = np.zeros((K0*K1,2,2))\n", " for k in range(K0):\n", " for l in range(K1):\n", " mt[k*K1+l,:] = (1-t)*m0[k,:]+t*m1[l,:]\n", " Sigma1demi = spl.sqrtm(S1[l,:,:])\n", " C = Sigma1demi@spl.inv(spl.sqrtm(Sigma1demi@S0[k,:,:]@Sigma1demi))@Sigma1demi\n", " St[k*K1+l,:,:] = ((1-t)*np.eye(2)+t*C)@S0[k,:,:]@((1-t)*np.eye(2)+t*C)\n", " \n", " # contour plot\n", " Z = densite_theorique2d(mt,St,pit,XX)\n", " Z = Z.reshape(X.shape)\n", " CS = plt.contour(X, Y, Z,8)\n", " plt.axis('equal')\n", "\n", " \n", "barygmmot2d(0.5)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 319, "referenced_widgets": [ "c7cf85782ba8428084f05a4a3cc7b72e", "27fd0c42be184726ae134a56b9f342a8", "d1770c9c929647139c276d0c4911e4e3", "b54c53d40893449c83daa52e2a637fc4", "d3026851c3cc4be4a308be822e04e166", "7591b2b3b04f434585c1f86c38aa6bec", "618148cd6433426eb9e21ca3239df670" ] }, "id": "z5D6jZDK5tmv", "outputId": "62f4bbab-fc19-400d-f776-d968e1db2a3f" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "interactive(children=(FloatSlider(value=0.5, description='t', max=1.0, step=0.05), Output()), _dom_classes=('w…" ], "application/vnd.jupyter.widget-view+json": { "version_major": 2, "version_minor": 0, "model_id": "c7cf85782ba8428084f05a4a3cc7b72e" } }, "metadata": {} }, { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 16 } ], "source": [ "# interactive display \n", "interact(barygmmot2d,t=(0.0,1.0,0.05))" ] }, { "cell_type": "markdown", "metadata": { "id": "PlVqsBrR5tmw" }, "source": [ "### Interpolation for $W_2$\n", "\n", "In the following we display the same barycenters but this time for the $W_2$ distance. The computation between two steps is not instantaneous and can take a few seconds." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "3bGHUNXc5tmx", "outputId": "d9f46021-04ec-4933-cb5a-9eeb0faa4f8b", "colab": { "base_uri": "https://localhost:8080/", "height": 326 } }, "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "/usr/local/lib/python3.7/dist-packages/ot/bregman.py:1533: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.\n", " warnings.warn(\"Sinkhorn did not converge. You might want to \"\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "M = ot.dist(XX.reshape((n**2, 2)), XX.reshape((n**2, 2)))\n", "gmm0 = densite_theorique2d(m0,S0,pi0,XX)\n", "gmm1 = densite_theorique2d(m1,S1,pi1,XX)\n", "A = []\n", "A.append(gmm0)\n", "A.append(gmm1)\n", "A = np.array(A).T\n", "\n", "def baryot(t):\n", " # Barycenters for W2 in 2d\n", " weights = np.array([1 - t, t])\n", " reg = 1e-3\n", " ott = ot.bregman.barycenter(A, M, reg, weights)\n", " # contour plot\n", " Z = ott.reshape(X.shape)\n", " CS = plt.contour(X, Y, Z, 8)\n", " plt.axis('equal')\n", "\n", "\n", "baryot(0.5)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 287 }, "id": "oOlC6mPX5tmx", "outputId": "0d494eee-5828-47c9-834e-3ab6c176692c" }, "outputs": [ { "data": { "image/png": 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\n", 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HH5GYmOghCw3+SrlCr6qFwGRgGbAHmK+qu0TkRRFxjALOwvLJJwNPAr8IwTS4iJwc2LkTxo6FiAhr2+jREBICH3/sXdsqihH6y5gzZw579+7l+eefJzAwsNz2U6dOpVGjRvz+979H/e1pzuBRnPLRq+oSVW2nqm1U9SX7tudUdaF9PVdVx6hqW1XtraoppZzjeVX9u2vNr4Fs3Qo2G/Tq9fO2+vVhxAiYNw+KirxnW0XwxKxYB/XqQViY5SryUQoKCnjhhRfo1q0bd955p1PH1K1bl2nTprF+/Xo+/fRTN1to8GfMzFh/w/GY3rPn5dsnTLBS8a5a5XmbKkN2NhQUeEboRazEaT4s9LNnz+bgwYO8+OKLBAQ4/2/54IMP0rVrV6ZOnUqRv/zIGzyOEXp/IykJmje3il4XZ+RIK6e7v7hvPBVD78CHhb6oqIhp06bRq1cvbr311godGxgYyJ///GdSUlJYunSpmyw0+DtG6P2NxMRf9ubBck2MHAn+MpHGCP0lVq9ezeHDh/nDH/6AVCIv/6hRo2jSpAlvv/22G6wzVAeM0PsTZ87AgQOX++eL07275b45dcqzdlUGh9C7Mxd9cZo3t4TeBwctP/roIyIjI7mtkjOcg4ODefjhh/nmm28uS5dgMDgwQu9PbNliLUvr0QN06mQtd/lBtgmH0Jd0QbmLZs2surHZ2Z65npOcP3+ezz77jDFjxhAeHl7p8zz88MMEBATw7rvvutA6Q3XBCL0/caWBWAf+JvRRURAa6pnrOZ4cfMx988UXX5CTk8N9991XpfM0b96cUaNG8f7775Obm+si6wzVBSP0/kRSErRuDQ0alL6/RQsrtt4fhD493XKneArHtXwsZcBHH31EXFwc/fr1q/K5Hn30UbKysliwYIELLDNUJ4zQ+xOJiVf2z4MVRtixo38I/dGjnhV6H+zRp6ens3LlSu69994KhVReiUGDBtGuXTszKGv4BUbo/YXMTEhNvbLbxkGnTrB7d9ltfIG0NM8KfUyMlS7Ch3r0H3/8MarKvffe65LzBQQE8Mgjj7Bhwwb27dvnknMaqgdG6P2FpCRrWVaPHiyhP3nS5wYdLyM31/rh8qTQBwdD48Ze69EXFtlIzjjPNzuO85/1h3ht6R5en/lvmrXvyteHlffXHWL70TNVTmUwfvx4RIS5c+e6yHJDdcCZfPQGXyApyXLNXHNN2e2KD8jecIP77aoMjogbTwo9eDSW/tiZiyQePsXm1NNsOXKa/SfPk19ou7S/6NRRso4k0/Tmx/jXqgOXoj5bRdfmtm5NufvaFjSuG1bh6zZt2pSBAwcyZ84c/vKXv1QqLt9Q/TBC7y8kJkKHDlCnTtnt/EHoHe4TTwt98+bWPAQ3oKpsOXKGlXtO8u2ek+w/aZVgqBUSSPfYekzs25L2MXVp37gOzeqH8+8ZbzAF2PjuFJo1a052Tj6r9p7kq23HeGvVAWZvOMwbd3XnxvaNKmzL3XffzUMPPcTmzZvpWZ6rz1AjMELvL2zb5pxwN29upULw5QFZbwl9s2awZo1LT3n2YgGfb0njo42ppGTmEBQg9G7VgLE9Y+nTOooOMXUICvylh3TRokV0796d2Fir1EPDOqHc1asFd/VqQXLGeSbP2cIDHyQyeWBbnhjSjsAA53vmd955J4899hhz5swxQm8AjND7BxcvWlEqHTqU39YfIm8cQu+pWbEOmjWzZhfn5FS5qtVPuQX8vzUH+WD9YS4WFHF1i3r8fUw3burYmMjwsgu1Z2Vl8f333/PMM8+Uur9towi+eKwfz321k3+tSiYlM4cZd1/ttBumfv36jBgxgnnz5vH66687lfLYUL0xQu8POKa1t23rXPtOnWBhydowPkRamlVCsDw3lKtxPEGkp1uFWypBQZGNuZuO8ObKA5zKyWdU96Y83L81nZtFOn2OJUuWYLPZykx5EB4SyOtjutGqYW1eW7qPzgmRPHqj8zWB7777br788ksSEhIYNGiQ08cZqicm6sYfcPiVKyL0mZnWyxfxdGilgyrG0u87cY473l7Pc1/tol3jCBb9z/VMH3d1hUQe4Ouvv6ZJkyZcU97AOvDogDaM7NqE15ft5bsDzv89R44cSUREBHP8sZawweUYofcHkpOtZUWEHnzXfeNtoa9gLH1hkY2Zq5O59V/rOH4ml7cnXMPch/tUWOAB8vPzWbZsGSNHjnRqkpSI8NrorsQ3qsPjc7eSdvqCU9cJDw/nzjvvZMGCBeTl5VXYTkP1wgi9P5CcDNHRVqUkZ+jY0Voaob+cSvToj2RfYOy7G3h92T6GdGzE8t/fwIguTSodtpiQkMC5c+cqlKmyVkgQ79zbg0Kb8sS8bU7H2o8bN46zZ8+yYsWKStlqqD4YH70/cOCA8715sATNVyNvCgqsVMouEHpVJWF/JnN+OEJocCAxdUNpEhnOkKsa0yKq1i8PiIiwxgacEHpV5fMt6fxl4S5EYPq47ozqXvXB44ULFxIeHs7gwYMrdFyr6Nr8acRVTP18B0t3nuDmLk3KPWbw4MHUq1eP+fPnM3LkyMqabKgGOCX0IjIcmA4EAv+nqn8rsT8UmA30ALKBu1T1sIj0Bt5zNAOeV9UvXGV8jSE5uWIx8SKW+8YXhf74cSsnfBWFfsPBbP6xfB9JqadpXDeU8OBAVvyUS26BjWmLdzO0YwwP9W9Fj5b1L+99N2tWruvm+NmLvLBwN0t3naB3qwb8c2w3mtcv5YejgqgqX3/9NUOGDKlUSuIxPZrz/rpDvLp0L4OvakxIUNkP5CEhIdxxxx189tln5OXlEeqpTKEGn6Nc142IBAIzgZuBjsB4EelYotkk4LSqtgXeAF61b98J9FTV7sBw4F0RMU8RFSE31wqtjI+v2HG+mvPGBTH0X25NZ/y/N3L09AWm3d6Z754axJo/DmTPi8NZP2UQvxnQhg0p2Yx+ZwOj39nA6n0ZP7s7HAVISqGwyMb/fZfCkH8ksHpfBk8P78Dch/u4ROQBdu/eTWpqaoXLBToICgxg6ogOHM6+wNxNR5w6ZsyYMfz000/GfVPDcUZ0ewPJqpoCICLzgFFAcRUZBTxvX18AzBARUdXiI0dhgO+V9/F1Dh2yesAVcd2A9cOQlQVnz1ruCl+hikJ/4OQ5pn6+g96tGjD7wd6EBf8cIy4iNKsXzlPDOzB5UFs+TUrj3YSDPPCfRDo3q8u4Xi24PboxETt3Xm7S6Qss2JzGgs1ppJ2+yI3tG/LXUZ2JbeAagXewfPlyAIYNG1bpcwxs34i+raOY/u0B7rimGXXDyo7ZN+4bAzgn9M2Ao8XepwHXXqmNqhaKyFkgCsgSkWuB94GWwL2qWljyAiLyCPAIQIsWLSp6D9WbioZWOmhjj7lOSYGrr3atTVWhCkJ/Ib+Qxz7eQq2QQP41/urLRL4ktUKCmHhdHON7t+DLrem8s/Ygz365k1OH8vnt8RNMfGcd5wrhXF4hh7JyUIV+baN4bmRHburY2C05YpYvX06HDh2q9B0XEf404ipunbGOd9Yc5KnhZU+iCwkJ4fbbb+fzzz837psajNujblT1B1XtBPQCporILzI1qep7qtpTVXs2bNjQ3Sb5FxUNrXTQurW1PHjQtfZUlbQ0a1ZqBZ8yVJVnv9xJcuZ5po+72umEXyFBAYztFcu3Tw7g2z8MoEe/LgSqjfBTWUTWCqFDTB2eGNyO754ayMcP9WFopxi3iHxubi4JCQncdNNNVT5Xl+aR3NatKR9+f5hzuQXlth87dqxx39RwnBH6dCC22Pvm9m2ltrH74COxBmUvoap7gPNA58oaWyNJTrYqSl2pqtSVKN6j9yUcoZUVFNOVezL4fEs6jw+K5/r46ApfVkRo0zCCfgO6AfDvQTHMfrA3b0/owe+GxLvcTVOS77//nosXLzJ06FCXnO+h/q3IyS9iweby5wQUd98YaibOCH0iEC8irUQkBBgHlJxfvxCYaF8fDaxSVbUfEwQgIi2BDsBhl1heU6hoaKWDunWt2Htf7NFX0G2jqry9JpnYBuH8z6BKfBbFKZ4GwYMsX76c4OBgbrzxRpecr2vzelzToh6zN6Ris5U99OVw33z11Vdm8lQNpVyht/vUJwPLgD3AfFXdJSIviohj1scsIEpEkoEngSn27dcD20VkG/AF8JiqZrn6Jqo1ycmVE3qw3De+2qOvAEmpp9l65AwP929daibICuGlkoLLly/nuuuuIyIiwmXnnHhdHIeyckhwIjWCw32zbNkyl13f4D849V+jqktUtZ2qtlHVl+zbnlPVhfb1XFUdo6ptVbW3I0JHVT9S1U6q2l1Vr1HVL913K9WQvDw4cqTioZUO2rTxrR59UZFVdKSCQv9uwkHq1wpmTI/Y8huXR3Q0hIR4tKRgRkYGW7dudZnbxsHNnZvQqE4oH6w/XG7bIUOG0KBBA+bNm+dSGwz+gUmB4MscPgw2W9V69EeOWLNRfYGTJy2xr4DQHzh5jpV7Mph4XRzhIS5Ityvi1KQpV7Jy5UoAlwt9SFAAE65tScL+TFIyz5fZNjg4mNGjR/PVV1+Rk5PjUjsMvo8Rel+msqGVDtq0sYT1iHOTa9xOJUIr31ubQlhwAPf1jXOdHXFxVqF1D7F8+XKioqK42g1hrndf24LgQGH2hvLvZ9y4cVy4cIHFixe73A6Db2OE3pepbGilA0fkja+4byoo9Cd/yuXLbemM7RlLg9ohrrMjLs56WvIAqsry5csZMmSIWwqANKwTysiuTflscxq5BUVltr3hhhuIiYkx7psaiBF6XyY52cpYGRVVueMdsfS+MiBbQaGfn3iUgiJl0vWtXGtHXJw1VuCBCJRdu3Zx/Phxl8TPX4nRPZpzLq+QFbtPltkuMDCQsWPHsmTJEs6ePes2ewy+hxF6X8YRWlnZCTxNm0JoqG/16ENDnf7h+vrHY/SOa0DLqKqV/fsFcXHW0gMuLYd/3p1C36d1FDF1w/hia/mRROPGjSMvL4+vvvrKbfYYfA8j9L5MVUIrAQICrF69rwj90aPWQKgTP1z7Tpxj/8nz3Nqt/HS8FcYh9B5w36xcuZL4+Hi3pvYIDBBGXd2UhP2ZZJ0v+ymlT58+tGzZkk8++cRt9hh8DyP0vkpBgTVgWBWhB9+KpT98+GeRLYevtx8jMECcyrteYTwk9AUFBSQkJDBkyBC3XgfgzqubU2RTFm0/VmY7EeGuu+5i+fLlZGWZKS01BSP0vsqRI1bETBvnC0KXiiOW3smqRG7l0CFoVb6/XVVZuP0Y17WJIjrCDUm4mjaFoCC3C/2mTZs4f/68R4S+fUwdOjap65T7ZsKECRQWFjJ37ly322XwDYzQ+yoOd4tjQLWytG4N589bKYu9yYULVhy9E/fzY9pZjpy6wK3dmrrHlqAgiI11u9CvXLkSEXFZ2oPyuPOaZmxPO8vBcmLqu3btSo8ePZg1a5bTZQkN/o0Rel/FIfSu6NEXP5+3OHTIWjrRo/96+zGCA4VhnWLcZ48HQixXrlxJjx49aFDRhHSV5LZuTQkQ+GJL+b36SZMmsX37drZs2eIBywzexgi9r5KSYkWoNKmij9rXhL6cHr3Npiz68TgD2jUiMrzsohpVws1Cf/78eTZu3OgRt42DRnXD6Nc2mi+2ppfbUx8/fjxhYWHMmjXLQ9YZvIkRel/l4EFLFAOq+CdyDDx6e0DWcf1yevRJqac58VMut3V3k9vGgZtj6deuXUthYaFHhR5gVPdmpJ+5yLajZ8psV69ePX71q18xZ84cLl686CHrDN7CCL2vkpJSdbcNQHi4FdLoCz362rWhnMIy3+w8TmhQAIM7NHKvPW6OpV+5ciVhYWH069fPLee/Ejd1bExwoLBkx/Fy206aNImzZ8/y+eefe8Ay5zlz5gw//vij+QFyIUbofRHVn3v0rsAXslg6Im7KiKFXVVbtzeC6NlHUDnVzDXk3h1iuXLmSfv36ERbmXCUsVxEZHsz1baNZsuNEue6bAQMG0Lp1a6+7b1SVpUuXMnr0aFq3bk39+vXp1q0bderUoVu3bjzyyCPs37/fqzb6O0bofZHMTCtSxhU9evCNWPqUlHLdNilZOaRmX2DQVY3db48bhf7kyZPs2LHD424bByO6NE9478kAACAASURBVCH9zEV+TCs7zUFAQAAPPPAAq1evJtmRV8nDJCYmMnjwYG6++WY2btxIr169eOWVV5gzZw5TpkyhadOmzJ07ly5duvDMM8+YzJuVxAi9L+IQZVcJfZs2lj/6wgXXnK+iqFo9+nKeUFbtyQBgkLvdNuDWWPpvv/0WwGtCP7RjDEEBzrlvHnzwQYKDg3njjTc8YNnPFBQU8MQTT9C7d2927tzJv/71L1JSUvjkk0+YMmUK48ePZ9q0aXzzzTccOHCAcePG8fLLL9OxY0eSkpI8amt1wAi9L+KqGHoHjtm13urVZ2VZTyjl9Oi/3XuSDjF1aFYv3P02uTGW3p1piZ0hslYw/dpGs3jH8XLdN02bNmXixInMmjWLEydOeMS+rKwshg0bxvTp03n88cc5ePAgkydPJiSk9AylMTExfPjhh3z33XcEBAQwePBgNm7c6BFbqwtG6H0Rh9A7EXPuFI4KVY789p7GidDKsxcLSDp82jO9eQduCLFUVVasWMHgwYPdkpbYWW7p0oS00xfZmf5TuW2feuopCgoKePPNN91u165du+jVqxfff/89H374IdOnT6dOnTpOHXv99dezdu1aGjZsyNChQ1m3bp2bra0+GKH3RVJSrEgZVw3kOVxAXvLDOjNZ6rsDmRTalMFX+bfQ7969m2PHjrm8mlRFGdqpMUEBwmIn3Dfx8fGMGTOGt99+m9OnT7vNpq1btzJgwADy8vJYu3Yt9913X4XPERsbS0JCAk2bNmX48OGmZ+8kTgm9iAwXkX0ikiwiU0rZHyoin9j3/yAicfbtN4nIZhHZYV8Ocq351ZSDB13nnwcrp310tPeE3okY+lV7MqhfK5jusfU9ZBRuiaVfvnw54N60xM5Qr1YI17WNZokT7huAqVOncu7cOWbOnOkWexITExk0aBC1a9fmu+++o3fv3pU+V7NmzVizZg2NGzdmzJgxZGaWXxy9plOu0ItIIDATuBnoCIwXkY4lmk0CTqtqW+AN4FX79izgVlXtAkwEPnKV4dUaVws9WH56b/boGzWy4uhLocimrN6XwY3tGxEYUMnc+5XBDbH0K1asoH379m5NS+wsIzrHcOTUBXYfL999061bN0aMGMH06dNdHtnimCFcv359EhISaOOC73ZMTAwLFiwgMzOTCRMmUFRUdnWtmo4zPfreQLKqpqhqPjAPGFWizSjgQ/v6AmCwiIiqblVVR97UXUC4iLghHWE14sIFOH7cdQOxDuLjveejLye0ctvRM5y+UOBZ/zy4PMQyLy+PNWvWeL037+Cmjo0JEFi207lB1j/96U9kZWXx2muvucyGH374gaFDh9KoUSMSEhKIczJNtTNcffXVzJgxgxUrVvDXv/7VZeetjjgj9M2Ao8Xep9m3ldpGVQuBs0DJMkK/Araoqvvrt/kzDn+2O3r0R4+CN2YblhNauWrvSQIDhBviy54163JcLPTr16/n4sWLXvfPO4iKCKV3qwZ846TQ9+vXj3vuuYeXX36Z7du3V/n6mzZtuiTyq1evJjY2tsrnLMmkSZOYOHEiL7744qVqXoZf4pHBWBHphOXO+fUV9j8iIkkiklTj/W2uylpZEkeIpeOHxFMUFlqukTJ69An7M+nRoj6RtdyYxKw0XBxLv2LFCoKCgjyWltgZhneK4UDGeZIzyk5d7ODNN98kKiqKBx54gIKCgkpfNykpiaFDhxIVFcXq1atp7mSd4IoiIrz99tu0b9+ehx56iPPnnbvPmoYzQp8OFP8pbm7fVmobEQkCIoFs+/vmwBfAfapa6jx8VX1PVXuqas+G5eRCqfY4Bi5d7bpxCL2n/fRpaZbYX+F+Ms/lsTP9Jwa098Lf3RFL76Ifv+XLl9O3b1+nwwU9wbDOVqrnZbuc69VHRUXx9ttvs3XrVl5//fVKXXPlypUMGjSI+vXru60nX5xatWrx73//m9TUVJ577jm3XstfcUboE4F4EWklIiHAOGBhiTYLsQZbAUYDq1RVRaQesBiYoqrrXWV0tebgQahb1+kC2k7jEHpP++nLCa387oD1BDegnZd+4Nu0ccmPX2ZmJlu3bvUZt42DJpHhdI+tx1In3TcAd955J2PHjuWFF15g69atFbre3LlzGTFiBC1btmTdunW0bNmyoiZXiuuvv55HH32U6dOns2nTJo9c058oV+jtPvfJwDJgDzBfVXeJyIsicpu92SwgSkSSgScBRwjmZKAt8JyIbLO/PDzi5mc4kpk5UUC7QjRoYL083aMv5wklYX8m0REhdGxS14NGFaNDB9i7t8qlFleuXImq+sxAbHGGd45hR/pZ0k47nwJjxowZNGzYkIEDB5KQkFBu+8LCQl5++WXuvvtu+vbty3fffUezZiWH8tzLK6+8QkxMDA899FCV3E7VEad89Kq6RFXbqWobVX3Jvu05VV1oX89V1TGq2lZVe6tqin37NFWtrardi70y3Hc71QBXpScuDW+EWB46BIGBUIqPtsimrN2fyQ3xDQnwZFhlca66Cs6dg/TyqzKVxeLFi4mOjqZnz54uMsx1DO/kcN+cdPqYhg0bsn79epo2bcrQoUP59NNPr9h269at9OnTh2eeeYa77rqLZcuWUa9evSrbXVEiIyN5++232bFjB//4xz88fn1fxsyM9SWKipxK/lVpvCX0LVpY/vAS7Ew/y+kLBd7xzzvoaJ8SsmdPpU9RVFTE0qVLGT58uFfTHlyJuOjadIip43SYpQOH+6VXr17cddddjB07ltmzZ5ORkcHhw4f5+OOPefDBB+nVqxdpaWnMnz+fuXPnejw1c3FGjRrFqFGjmDZtGsePlz8ruKZghN6XSE2F/Hxo394952/b1oqAcVNVpVI5cOCKTygJ+zMRgevbRnvOnpJcdZW13L270qfYtGkT2dnZ3HLLLS4yyvUM7xxDYuopMs7lVui4Bg0asGLFCv7nf/6H7777jokTJ9K4cWNatWrFPffcw4IFC3jooYfYs2cPY8aMQVztcqwEf//738nPz+dPf/qTt03xGYzQ+xKOXmWHDu45f9u2YLN5LsTSZrMEtFOnUncn7M+ka7NIoiK8OIeuUSOoX79KPfrFixcTGBjIsGHDXGiYa7m5cxNUnZ88VZzw8HCmT59Oeno6SUlJvPzyy8yYMYOtW7dy+vRp3nnnHerX92DqinJo27YtTzzxBB988AGJiYneNscnMELvSzjExtHLdDWOLJaect+kpkJOTqlCf+ZCPluPnGZAey+PzYtYn3cVhf66667zKbErSbvGEbRpWJslOyqfijggIIAePXowdepUfvvb39K9e3efdFUBPPvsszRq1IgnnnjCqVw/1R0j9L7E3r1WD7NBA/ec39Mhlrt2WcvOnX+xa11yFjb1Ylhlcaog9Onp6Wzbts2n3TZgTSy6pUsTfjiUTdb56j85vW7durz88st8//33zJs3z9vmeB0j9L7Enj3u682DFZsfGem5Hv3OndaylB79mn2Z1A0LolvzSM/YUhZXXWWVb8zOrvChS5YsAfB5oQcY0bUJNqVCMfX+zP3330/37t2ZOnUqeZ4cl/JBjND7CqqW0LvLPw+Wm8KTkTc7d1ozT+teHiNvsylr9mVwQ7uGBAX6wFfQ8eNaiV794sWLadGiBZ2uMA7hS7RvXIfW0bX5ZmfNiEYJDAzk9ddfJzU11W3pl/0FH/gvMwCQkQGnT7u3Rw+Wn96TQl+K22ZH+lmyzud7Plvllaik0Ofl5bFy5UpGjBjhE9Em5SEijOjShA0Hs8muAe4bsOr2Dhs2jGnTprm1qIqvY4TeV9i711q6W+jbtrWSeOXnu/c6hYXWPZUi9Kv2ZiDiI/55gJYtITy8wkKfkJBATk6OX7htHIzoYrlvKjJ5yt959dVXOXPmDK+88oq3TfEaRuh9BXdH3Dho394Ke3T3gOzBg1a8fikujdX7MugeW8+7YZXFCQiwPpcKCv2XX35JrVq1GDTIfwqnXdWkDq2ia7PEiRKD1YVu3bpx33338dZbb3HEhUVm/Akj9L7Cnj1WBSY3pXO9RNeu1vLHH917HcdAbIkefca5XH5MO8sgb4dVlqSCkTdFRUV8/vnn3HLLLdSqVcuNhrkWEeHmzjFsSMnmVI6bn+p8CEdhkmeffdbLlngHI/S+gmMg1t2+3g4drHQE7hb6Xbt+jlEvxpp9VrbKgb7in3dw1VVW3L+T+czXrVvHyZMnGT16tJsNcz0juzalyKZOFQ6vLsTGxvK73/2O//73vy4pquJvGKH3Ffbudb/bBiAkxLqOJ3r0rVtDid7u6r0ZNK4bSqemXspWeSUcn/2+fU41X7BgAWFhYYwYMcKNRrmHq5rUoX3jOny5tWqJ3PyNKVOmUK9ePZ5++mlvm+JxjND7AufPW2X+PCH0YLlvPCH0Jdw2+YU2vjuQxcD2jXwvSqUCkTc2m43PPvuMESNGEBER4WbDXI+IcPvVzdicepoj2c6nLvZ36tevzzPPPMOyZcv49ttvvW2ORzFC7wt4KuLGQdeuVuWnU6fcc/68PNi//xcDsUmHT3E+r9D33DZghZ0GBjol9N9//z3Hjx/3S7eNg1HdmwLw1baa1av/7W9/S4sWLXjqqaew2WzeNsdjGKH3BdydzKwkjgHZHTvcc/79+62UyyV69Kv2ZhASGODdbJVXIiTEyrLphNB/+umnhIaGMnLkSA8Y5h6a1gunT+sGfLEtvUblggkLC2PatGls2bKFTz75xNvmeAwj9L7A3r3WAKkjF427cXfkTSkRN6rKst0n6NMmitqhv8xN7xN07gzbtpXZxOG2GT58uE/Vhq0Md1zdjJTMHHakn/W2KR5lwoQJdOvWjalTp5KbW7G0zf6KEXpfYM8eS+SDgz1zvSZNIDravUIfGAjt2l3atOvYTxw9dZFbusS455quoG9fK4XzyStPJtq4cSPp6emMGTPGg4a5h+GdmxASFMAXNWxQNiAggL///e+kpqby1ltvedscj2CE3hdwdzKzkoi4d0B21y5L5EN/nhC1ZMdxAgOEmzr6uNADbNhwxSZz5871e7eNg8jwYIZc1Yivtx+jsKjm+KvBSo0wcuRIXnrpJTIyqn91UyP03qagwMo94yn/vIOuXa2ed1GR68+9ZQt06XLpraqyZMdxrmsTRYPaIa6/nqvo0cN6qrqC0Ofm5vLxxx9zxx13EBnpA1k3XcDt3ZuRdT6ftQcyvW2Kx3n99dfJycnh+eef97YpbscpoReR4SKyT0SSRWRKKftDReQT+/4fRCTOvj1KRFaLyHkRmeFa06sJu3ZZeWGKCaNH6NoVLlywipG7ktRUK1T0+usvbdpz/ByHsy9wc+cmrr2WqwkLg2uuge+/L3X3F198wenTp5k0aZKHDXMfAzs0omGdUD7eWPNSA3To0IFHH32U9957j91VKCXpD5Qr9CISCMwEbgY6AuNFpGOJZpOA06raFngDeNW+PRf4M/C/LrO4uuHoPfbp49nrumtAdu1aa3nDDZc2fbPzOAECQzs1du213EHfvpCUVGrSt1mzZhEXF+dXuW3KIzgwgHG9Ylm1L4O00zUnpt7BX/7yFyIiIvjDH/5QraOPnOnR9waSVTVFVfOBecCoEm1GAR/a1xcAg0VEVDVHVddhCb6hNDZuhMaNIS7Os9ft2NFK5uVqoU9IgHr1Lj2hqFpT7fu0jiLaV5KYlcV110FuLpSYJn/o0CG+/fZbHnjgAQICqpfHc1zvFggwb9NRb5vicaKjo/nLX/7C0qVLWbhwobfNcRvOfGObAcW/AWn2baW2UdVC4CwQ5awRIvKIiCSJSFJmZg3zFW7YYPXmPT1TNDzcGjB1R4++f3/rRwTYf/I8KZk53NzFx902DhwDsiXcN//5z38QEe6//37P2+RmmtULZ1CHRsxLPEp+Yc0alAWYPHkynTt35ne/+x0XLlTPpxqf6Jqo6nuq2lNVezZs6CM5yj1BVpaVLtghLp7G1ZE3x49b91PMbbNkx3FEYJg/uG3Ayh4aG3vZgGxRURH/+c9/GDp0KC1atPCice5jQp+WZJ3PY/numlFmsDjBwcHMnDmT1NTUapuz3hmhTwdii71vbt9WahsRCQIigYoX4Kxp/PCDtfSm0KekwLlzrjnfd99ZS7vQqyoLtx+jd1wDGtUJc801PEHfvpcJ/YoVK0hLS6tWg7AluSG+Ic3rh9fIQVmAG264gXvuuYfXXnuNA+6u1eAFnBH6RCBeRFqJSAgwDijpzFoITLSvjwZWaXUe2XAVGzZYE4t69PDO9R3X3bjRNedLSLBy6l9zjXXalFMcysrhrl6x5RzoY1x3HRw5AulWf2bGjBlER0dz2223edkw9xEYINx9bQs2pGSTnOGiH34/4/XXXycsLIzJkydXu4HZcoXe7nOfDCwD9gDzVXWXiLwoIo5v/iwgSkSSgSeBSyGYInIY+Cdwv4iklRKxU3PZsAG6dbPE0Rv072/Fja9Y4ZrzrV0L/fpZ6RyAuZuOUDcsiBH+4p93UGzi1I8//sjixYt5/PHHCQ31g8HkKjC2ZyyhQQG8t9bFIbd+QkxMDC+99BLLly/nww8/LP8AP8IpH72qLlHVdqraRlVfsm97TlUX2tdzVXWMqrZV1d6qmlLs2DhVbaCqEaraXFWrd8CqsxQVwaZN3nPbgPUD06+fa4Q+O9uagGV325zKyWfpzhPceU1zwoIDq35+T9K9uxVTv2EDf/vb34iIiGDy5MnetsrtREeEMr53Cz7fks7RU9VzULI8HnvsMW644QaeeOIJ0tOrT2oInxiMrZHs2mXlofd0/HxJbrrJSuRVRn4Xp1i3zloOGADA51vSyC+yMb63Hw5ehoRAz56kfPstn3zyCb/+9a+pX7++t63yCL8e0JoAEd5JOOhtU7xCQEAA77//Pvn5+Tz88MPVxoVjhN5bOPzi3uzRAwwdai2rWohh7Vort02vXqgqczYd4ZoW9Wgf46cZHgcP5vXt2wkKCuLJJ5/0tjUeo0lkOKN7NufTpDROnK2Z01/atGnD3/72N7755ptq48IxQu8tNmywMki2bu1dO66+Gho0qLr7JiHBejoJDWXToVOkZOb4Z2/ezomBA/kPMLFnT5o2beptczzKowPaUKRaY3v1YMXW9+/fn9/97nccPOj/n4MRem+xYYPVm/d2Sb3AQBg82BL6yj6mJifD5s0wfDgAczYdoU5YECO7+q9A/v3rrykA/piX521TPE5sg1rccXUz5m46Qsa5mtmrDwgIYPbs2QQEBDBmzBi/z1tvhN4bnDplFaH2ttvGwdChViihE9WVSuWDD6yZsPfey+GsHBb9eJzRPZoTHuJng7B29u/fz1tvvcW93bsTv3mzVXaxhvHbgW0ptClvrKh+MeXOEhcXx+zZs9m6dSu///3vvW1OlTBC7w0cOTV8JTnWTTdZy8q4b4qKLKEfPhyaNeOtbw8QFCA8OqCNS030FKrK448/Tnh4OH+bYU+4umCBd43yAq2ia3P/dXHMSzzCtqNnvG2O17j11lt56qmneOedd5gzZ463zak0Rui9wccfW/VJe/f2tiUWLVtaxbErI/QrVlhPAw88QHLGOb7cls7E6+JoVNePZsIW46uvvmLZsmW88MILxPTrZ4Va1qDaosV5Ykg8DSNCefbLHRTZqkf0SWV46aWX6N+/Pw8//DBJSUneNqdSGKH3NMeOWREuEyZ43z9fnKFDYc2aUtPzlsn770NUFNx6K2+sPEBYcCC/vsHLA8yV5MKFCzzxxBN07tz557j5u+6yIqRSU71rnBeoExbMn0d2ZGf6T3z8Q827fwdBQUHMnz+fRo0accstt/jl4KwRek8zb5416DlhgrctuZxhwyAnB5Yscf6Y7Gz46iu45x72nMpj8Y/HebBfK6L8IR1xKbz00kukpqYyY8YMguyzexk71lp++qn3DPMiI7s24fq20by+bB+Z52rewLSDmJgYli5dSlFREcOGDfO78oNG6D3Nxx9Dr16XFc72CW6+2XIn/fWvzkffzJljPQE88AD/WL6fOmFBPNzfP3vzy5cv55VXXmHixIkMsE/6Aqzw1549Ye7cykcl+TEiwgujOpFXYOOPC7Zjq8EunPbt27No0SKOHTvGLbfcwtmzZ71tktMYofcke/ZY9VR9rTcPVn6aP//Zss+ZAgw2G/zf/8E11/CVRrNyz0kevbENkbWC3W+ri0lNTWX8+PF06tSJmTNn/rLBpEnW57J4seeN8wHaNIzgzyOvYs2+TN5cud/b5niVPn36MH/+fLZv386NN97IyarOKPcQRug9yccfW3Hr48Z525LSmTAB2raF558vv/f61lvw44+ceug3PPvlTnq0rM8jftibz83NZfTo0RQWFvL5559Tu7QEc5MmWU9gTz1l1fetgdzTpyWjezTnrVXJrNjtH+LmLkaOHMnChQvZt28f/fv3J9UPxm+M0HsKVUvohwyxSgf6Io5e/bZtlu/9SuzYAVOmoLfexm+kE6rwxtjuBAX619epqKiIX//61yQlJTF79mzi4+NLbxgcDK++aj2RzZrlWSN9BBFh2u2d6dIskic/2cbBzPPeNsmrDB8+nBUrVpCZmUm/fv1ITEz0tkllo6o+9erRo4dWSxYuVAXV2bO9bUnZFBSoxserdu+uarP9cv/Fi6pduqg2bqyzvtioLZ9epJ8mHfW8nVUkPz9fx48fr4C++OKL5R9gs6lef71qo0aqP/3kfgN9lKOncvTqF5drr2krdN+Jmvs5ONi+fbu2aNFCg4OD9c0331Rbaf8zHgJI0ivoqteFveSrWgr9mTOqzZqpduqkmpvrbWvKZ/Zs66tx772qp079vL2oSPXxx1VB17/1obaaskgf++9mr365K8PFixf11ltvVUBfeeUV5w/cuNH6XJ5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