{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Solving BPDN$_\\infty$ for quantized Compressed sensing via the cvxopt package\n", "\n", "$\\newcommand{\\eps}{\\varepsilon}$\n", "$\\newcommand{\\bR}{\\mathbb{R}}$\n", "$\\newcommand{\\bZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\1}{{\\rm 1}\\kern-0.24em{\\rm I}}$\n", "$\\newcommand{\\inr}[1]{\\bigl< #1 \\bigr>}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebooks is a simulations support for Section~7 of paper\n", "\n", "> Sjoerd, Dirksen and Guillaume, LecuĂ© and Holger, Rauhut, \"ON THE GAP BETWEEN RIP-PROPERTIES AND SPARSE RECOVERY CONDITIONS\"\n", "\n", "We refer the reader to paper for more details" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "from __future__ import division\n", "import time\n", "%pylab inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Import cvxopt library for solving our optimization problem" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from cvxopt import solvers, matrix, spdiag, log, spmatrix, sparse # writting '%pylab inline' after those lines will cause trouble in the matrix method\n", "solvers.options['show_progress'] = False" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Solving BPDN$_\\infty$ via linear programming\n", "\n", "Given a measurements matrix $A\\in\\bR^{m\\times n}$ and $y=A\\hat x + e$ where $||e||_\\infty\\leq \\eps$, the Basis Pursuit Denoising program BPDN$_\\infty$ is the procedure\n", "\n", "$$\n", "min\\big( ||t||_1: ||At-y||_\\infty\\leq \\eps\\big) \\hspace{2cm} (P).\n", "$$\n", "\n", "This procedure can be recast as a linear program by introducing slack variables $z^+,z^-\\in\\bR^n$: problem~(P) is equivalent to\n", "\n", "> $$\\min_{z^+,z^-\\in\\bR^n} \\sum_{j=1}^n z_i^+ + z_i^-$$\n", "\n", "> subject to $$-\\eps\\leq [A|-A]\\left[\\begin{array}{c} z^+\\\\ z^-\\end{array}\\right]-y\\leq \\eps$$\n", "\n", "> and $$\\left[\\begin{array}{c} z^+\\\\ z^-\\end{array}\\right]\\geq 0$$\n", "\n", "This is a linear program:\n", "\n", "> $$\\min_{\\left[\\begin{array}{c} z^+\\\\ z^-\\end{array}\\right]\\in\\bR^{2n}} \\inr{a,\\left[\\begin{array}{c} z^+\\\\ z^-\\end{array}\\right]}$$\n", "\n", "> subject to $$M \\left[\\begin{array}{c} z^+\\\\ z^-\\end{array}\\right] \\leq b$$\n", "\n", "where\n", "\n", "$$a = \\left[\\begin{array}{c} \\1 \\\\ \\1 \\end{array}\\right],\\hspace{1cm} M = \\left[\\begin{array}{c}[A|-A]\\\\ [-A|A]\\\\ [-I_n|0]\\\\ [0|-I_n] \\end{array}\\right],\\hspace{1cm} b = \\left[\\begin{array}{c}y + \\eps \\1\\\\ -y+\\eps\\1 \\\\ 0 \\\\ 0 \\end{array}\\right]$$\n", "\n", "Solution to (P) is recovered via $t= z^+-z^-$." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### Construction of cvxopt matrices $a,M,b$\n", "Given the measurement matrix $A\\in\\bR^{m\\times n}$, the vector of measures $y\\in\\bR^m$ and a $\\ell_\\infty$ bound $\\eps$ on the noise, we construct cvxopt matrices $a,M,b$ as in the Linear Programming formulation of BPDN$_\\infty$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def cvx_mat(A, y, eps):\n", " '''A, y: numpy array or cvx matrices\n", " eps : positive real number'''\n", " A = matrix(A)\n", " y = matrix(y)\n", " m, n = matrix(A).size\n", " # matrix a\n", " a = matrix(ones(2*n))\n", " # matrix M\n", " I_n = spdiag([1]*n)\n", " z_n = spdiag([0]*n)\n", " M = matrix([[A,-A, -I_n, z_n],[-A, A, z_n, -I_n]])\n", " # matrix b\n", " un_m = matrix(ones(m))\n", " zero_n = matrix(zeros(n))\n", " b = matrix([y + eps*un_m, -y + eps*un_m, zero_n, zero_n])\n", " return a, M, b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Construction of sparse signals in $\\bR^n$ and noisy measurements in $\\bR^m$\n", "We construct signals with sparsity given by *sparsity*, with a randomly chosen support in $\\{1,\\ldots,n\\}$ and with none zero coefficients equal to $1$. \n", "\n", "We construct two types of measures:\n", "\n", "1. measures are obtained by $y_i= \\inr{A_{i,\\cdot},signal} + e$ where $e$ is a variable chosen randomly in $[-\\eps,\\eps]$\n", "2. measures are obtained by quantization; that is $y_i$ is equal to the closest point in $\\eps\\bZ$ of $\\inr{A_{i,\\cdot},signal}$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def signal(n, sparsity):\n", " sel = random.permutation(n)\n", " sel = sel[0:sparsity] # indices of the nonzero elements of xsharp\n", " xsharp = zeros(n)\n", " xsharp[sel] = 1\n", " return xsharp\n", "\n", "def measures(A, signal, eps):\n", " m, n = A.shape\n", " e = random.uniform(-eps, eps, (m,1))\n", " return [sum(a) for a in zip(dot(A, signal), e)]\n", "\n", "def measures_quantized(A, signal, eps):\n", " y = dot(A, signal)\n", " if eps>0:\n", " y_q = [int(ele/eps)*eps for ele in y]\n", " else:\n", " y_q = y\n", " return y_q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### cvxopt linear solver cvx lp " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "####First try exact reconstruction by setting $\\eps=0$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "m , n, sparsity, eps = 15, 50, 3, 0\n", "A, x_hat = randn(m, n), signal(n, sparsity)\n", "y = measures(A, x_hat, eps)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "a, M, b = cvx_mat(A, y, eps)\n", "#print(a, M, b)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sol = solvers.lp(a, M, b)\n", "sol = sol['x']\n", "x_recover = sol[0:n] - sol[n:2*n]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "4.0640307445255899e-08" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "norm(matrix(x_hat) - x_recover,2)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "####Then try reconstruction from noisy measurements (i.e. noise level $\\eps>0$)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "m , n, sparsity, eps = 10, 40, 3, 0.1\n", "A, x_hat = randn(m, n), signal(n, sparsity)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "random noise" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "y = measures(A, x_hat, eps)\n", "a, M, b = cvx_mat(A, y, eps)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.1840669138367335" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = solvers.lp(a, M, b)\n", "sol = sol['x']\n", "x_recover = sol[0:n] - sol[n:2*n]\n", "norm(matrix(x_hat) - x_recover,2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "quantized measurements" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "y_quant = measures_quantized(A, x_hat, eps)\n", "a, M, b = cvx_mat(A, y_quant, eps)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.2310718900162763" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sol = solvers.lp(a, M, b)\n", "sol = sol['x']\n", "x_recover = sol[0:n] - sol[n:2*n]\n", "norm(matrix(x_hat) - x_recover,2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Phase transition diagram for BPDN$_\\infty$\n", "\n", "We construct two types of phase diagram:\n", "\n", "1. One where the number of success is counted. We say that the reconstruction is a success when $||x_{hat}-x_{recover}||_2\\leq 20\\eps + 0.001$ (where *signal = $x_{hat}$*)\n", "2. One where the errors $||x_{hat}-x_{recover}||_2$ are added for every pixel of the phase transition matrix (we don't have to decide wheither it is a succes or a failure)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "####We start with a phase transition diagram where successes are counted; and for random uniform noise" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def dist(x_hat, sol):\n", " n = len(x_hat)\n", " x_recover = sol[0:n] - sol[n:2*n]\n", " return norm(matrix(x_hat) - x_recover,2)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat(n, eps, nbtest):\n", " \"\"\"return a n.n/2 matrix with the number of reconstruction success for every 1\\leq m \\leq n measurements \n", " and sparsity 1\\leq sparsity \\leq n/2\n", " n : ambiant dimension of the signals\n", " eps : infinite norm of the additive noise (= twice the size of cells in CS quantization)\n", " nbtest : number of tests for each pixel\"\"\"\n", " PTM = zeros((n,int(n/2)))\n", " for m in range(1,n+1):#construct one line of the Phase transition matrix for a given number of measurements m\n", " if (m % 20) == 0:\n", " print(\"line number {} done\".format(m))\n", " A = randn(m,n) / sqrt(m)\n", " for sparsity in range(1,min(m+1, int(n/2))+1):\n", " nb_success = 0 \n", " for i in range(nbtest):\n", " x_hat = signal(n, sparsity)\n", " y = measures(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " if dist(x_hat, sol) <= 20*eps+0.001:\n", " nb_success = nb_success + 1\n", " PTM[m-1, sparsity-1] = nb_success\n", " return PTM" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def frontier(mat, nbtest):\n", " \"\"\"construction of the phase transition frontier, i.e. first time the number of success goes below nbtest/2\"\"\"\n", " L = []\n", " n = len(mat)\n", " for s in range(int(n/2)):\n", " m = 0\n", " while mat[m,s]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "titre = \"Gaussian measurements\"\n", "mat_plot(mat, n, nbtest, titre)\n", "#filename = 'noisy_gaussian_{}_eps_{}.png'.format(n, eps)\n", "#plt.savefig(filename,bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "####Now, we plot the phase transition where the reconstruction errors are added.\n", "We explore both random noise and quantized measurements" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat_sum_rand(n, eps, nbtest):\n", " \"\"\"return a n.n/2 matrix with the sum of reconstruction errors at every pixel for every 1\\leq m \\leq n measurements \n", " and sparsity 1\\leq sparsity \\leq n/2\n", " n : ambiant dimension of the signals\n", " eps : infinite norm of the additive noise (= twice the size of cells in CS quantization)\n", " nbtest : number of tests for each pixel\"\"\"\n", " PTM = zeros((n,int(n/2)))\n", " for m in range(1,n+1):#construct one line of the Phase transition matrix for a given number of measurements m\n", " if (m % 20) == 0:\n", " print(\"line number {} done\".format(m))\n", " A = randn(m,n) / sqrt(m)\n", " ind_failure = 0\n", " for sparsity in range(1, int(n/2)+1):\n", " sum_errors = 0 \n", " for i in range(nbtest):\n", " x_hat = signal(n, sparsity)\n", " y = measures(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " sum_errors = sum_errors + dist(x_hat, sol)\n", " PTM[m-1, sparsity-1] = sum_errors\n", " return PTM" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def frontier_sum(mat, eps, nbtest):\n", " \"\"\"construction of the phase transition frontier, i.e. first time the number of success goes below nbtest/2\"\"\"\n", " L = []\n", " n = len(mat)\n", " for s in range(int(n/2)):\n", " m = 0\n", " while mat[m,s]> nbtest*(20*eps+1) and m" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "titre = \"Gaussian measurements -- random uniform noise (level = {})\".format(eps)\n", "mat_plot_sum(mat, n, titre)\n", "#filename = 'Gaussian_random_noise_n_{}_eps_{}.png'.format(n, eps)\n", "#plt.savefig(filename,bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "####now for quantized measurements" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat_sum_quant(n, eps, nbtest):\n", " \"\"\"return a n.n/2 matrix with the sum of reconstruction errors at every pixel for every 1\\leq m \\leq n measurements \n", " and sparsity 1\\leq sparsity \\leq n/2\n", " n : ambiant dimension of the signals\n", " eps : size of bins in CS quantization\n", " nbtest : number of tests for each pixel\"\"\"\n", " PTM = zeros((n,int(n/2)))\n", " for m in range(1,n+1):#construct one line of the Phase transition matrix for a given number of measurements m\n", " if (m % 20) == 0:\n", " print(\"line number {} done\".format(m))\n", " A = randn(m,n) / sqrt(m)\n", " for sparsity in range(1, int(n/2)+1):\n", " sum_errors = 0 \n", " for i in range(nbtest):\n", " x_hat = signal(n, sparsity)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " sum_errors = sum_errors + dist(x_hat, sol)\n", " PTM[m-1, sparsity-1] = sum_errors\n", " return PTM" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "101.018029213 seconds\n" ] } ], "source": [ "n, eps, nbtest = 60, 0.1, 10\n", "start = time.time()\n", "mat = phase_transition_mat_sum_quant(n, eps, nbtest)\n", "print('{} seconds'.format(time.time()-start))" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Uh2zTxLOs6dMO2qEADg24asBVAE8CmklAwzVqTiYVTmYhJNNQaFBxAms0YHT3\n2lYBMQIDoAbtpAFCSzrRmsQ9EgiphSFnUGpRUEBDAVNUADGYgW+/8WO9bDp440Ow56OOwW1pf4F+\nCwCdXqsgAGC3JwE7/c9+GUNzv0tfVen3WPDPfalDrQEbJ4xwj0E8628O9ayfOwLwJR3kp7qf6wgu\nJV8OsD3VcqNz7G8vSeR9AUMLkHLYpPPIwRv5UyKxXBHP1V+8IqXjnxvBZFcg8VoGMmPYI+KS1VMT\ngE4XGN2TCYeq/hGqZKap6rYTt20JJM9k1iw1cT3+piEQKC6hIMsqcNxqhQjgEBIJNGiaaLppuEbg\nRAASZpPIoGnQBKm1x3MXpY6MQJIMXWdy4Dj5K63n0EJzt0EMt3nFiAvINQiYkmyUTLh+0zex+fPf\nh5ajz3wm7sA69E0/O4cAgN2eBHaV5Kp4VmxJtr/tde9LK0kOBew9q3tOD6A/yU3rkItHyW3fs3rk\nhIz68ps6QmgBjHyLWo5Lx6piwVqpMgPomSj0QC3XEvAak1YnXSS0brlkt/4MmaRsmN5ZFyspHnZJ\naFlPyDNpkeO250q9b9PLppG29KpItcsxNwQOAQhNV3YSsHa7coW4gmetduliZcAhgBpuWwyBGzA3\naOqAUDcIVdW1PqSjONRoQoUmTFFRiCRCoe1EJm7atOxWAk3kQ+gAmrSJprsesyP+qqnqyAFAA8L/\nfkO/L2D/jcdhwwnHYHvbApBWQBtLVYR305YAEV0B4BbEbF9h5hOIaF8AHwRwBIArADyLmW+afdtW\nLeQ81u4O+FUdOPdL/pTuaTOU/tr14jDeUaoaeshkUcV7XvzV+mi3F6ecPyUpoG6P10hdI6RlFTvw\nJ0CW2M1a6obMNrnfrQ6YLQIapHQ22ffkqAr3rM7ij94EplQ8S1lgi0qpUeeJF44F7YBodfU2uBlq\nnenr3tDTJXTEUuvfBFQAt+EENETgEG3zTIyGzNBNAV5AjdAJ7fj8Jp0FbiXOTADSCpxxI5fY39BU\nTWeKkqGioUFVNahDjaqaoKqm7YiiUNXdcNLUXwFGRwLUGWoAAWi0bksCMrZnikn77i0XXYabP/+d\nXhYeeeZzsIKl9HTsDA4gRQb973zoy/XkzmgJMICTmHmzuvZaABcy858Q0WvS79fOvpojgdKRU8EC\ntFwn+MtQjj30V6798QhAf0Gs3B4K6Xh7BGDdWofguIfMQWOJIBP+DOCQIgHvQAf+xIhT5jFr8hjT\nCsg17EhVSbSGAAAgAElEQVQ9o9eV0TZvG8ZYy6B3SHH1lk0uJfGY81j3GB3lLLV23QKYB/wtAUi+\nyQijGsASg+xmNHXcIKVdMZMi8FMCRwLajdTbZJA+gVR2OJUjDvFor7XulC4c/eIG0ZQzDV1nrAJ1\nIYG6alBNatSTGtWkQjVJu4WJ6Sgkk4wiAlC/Pt6aiNS5RwTp+ToVGAahZsJPz3o/tNxj4wnY44QH\noo5dzcmv6KYedlnT0HxyZ5mDrG6/AuDE5H4fgEvgkoB93fuiSs9qsW3weYA/ZPwqHd4zVgdrnJ1B\nUidcfbbxknB03FiFk0M1z+3pYKvaueYnZbKMDMjqVoAhAg04NrtLnMjGrZPDih1PIG4J1+qfa7wp\nwOmdx4L7ULLba9btAbwH1p7/un7EyAN/zl9NqlX0sB36WQFoOI3YSYGl8KKZn3s6MCitlon+Z9GL\nK3UrbVaxvHDbeiH3M4qdydwz2UQ9qSUDpgCqGnDTgJlQcVfDD+0hG7k07Wbw0kdgJ5ppM48mALne\njfGPumzZ9DXc+vlv6hzHEWc+t32zL2IG6u72RwjNJ3dWS+AiIqoB/CUzvxfAgcx8Tbp/DYAD86/K\n2QJdqfasxSONEnh77w+JB8oekXi9cjmd7e8SAA9lfk4//Vtftyg2JB5CEdzav36sbREYdwnARGVd\nuwf6jTwLBPo93QgM6PtjzzqrPF6Hcx5IEp8cM37m/LN+6fvaJJMz75SKv/cp6Ph7jc92bR6kSVuI\nLYAlBpYBWmbQGk7X0G2q0iuGBE7r5EcbfwT0dgN2UDs0tFdZ0Gal0gS3FIG2dLcDFGJFpAkcTVEh\ntigaIlAy0xAxuD2ip5QSJv7qNpMRkPeAX//WZEBc45qz/rqXvftuPB73OOG+iOOGZF5A056tvymF\nsBq5M0jgF5n5Z0S0P4ALieh7+iYzMxFltLfzBHJgbUEyV6rn+QKGvo4hgMyBdo4ASv5rVNMA7SWb\nTQfvWq6w6HA8MvDOQ/ec36SemyGDgUPUHGoU2fqDfsZbTskrIiVbfAnYc8mQK5JaPL1g3BrwxY/c\nTODSDGCdJvps9ZEwtMmnnXiWhntOEIeATiL4R+BvQGsZYU0T3WsSMSyld0Jn8ImdvdR29jZ1PKMJ\n3cYqQFtWWOtSMiFSilg6M9ANN23H6TMQ0j6+gcFp5jGn+HCI96N/3O4HIC0DAfX+TN5mBqztNTlu\n3PSv2PL5b/WS/egzn4F1uCP7vu1nWC0BAHcCCTDzz9L5OiL6KIATAFxDRAcx89VEdDCAa/23z1fu\n+wE4GrMtgBKolb7EEiHk3ikB3pDkqqdjxItjjgBy5GGveejp3bfvWwQaQMX41fXf76lF+UaRl/z6\nXV1rF9XtoaOSazyNAeyh6A4VKUsmOtxc2FY37zmPAPR2i3rbRQFM8Uenkx0pJGlkSaA36zjV+jME\nENY2CGtrhLUNaG0TyWC5iUQw6fyOo4ECmiaAp3HoJ6axI7dpEImgAaIlPNbcSYjAEtSMuVHSjtVv\nnj1SJ3F7TsNW7XpEIdX2Bfylll6lWby2xj5LCtEM1P7mGj856wPQcuDGY3HQCfcCYdsM0FuzD4Fx\n7SXfw7WX9OrWc8kuJQEiWg+gYuYtRLQHgFMAvAHAxwG8AMCb0/lc34dTxSf0Sy2QB8EZLczZuseK\nrYGXzp7krtsWQg6MPaT0kCznv37OA/ocKQz5n0EvNYmm66VT70hw2kImNXR9tkHoKJWKQk5yhCPh\n2PB0H/sQOUBd8/yEeS9nprH9ETndciRgD7mn+zpE9HwIYJZAvXDsshN2CYrlSARY5khI6jctp9aA\n7KkrZaFhUJ02WUHsR+CEzywDB7ziT+Y3qx9k3AG9mn+7/2+apQySZSW4XWKiXXSurflHd4Xu7B19\n000H/LZGv3nT5bjx830Af8CZT3fBvosNtdcYhP1POgb7n3RMe//bb+hPNhuSXd0SOBDARynWBCcA\n/hczf5qIvgbgbCJ6EdIQUf/1oS9gSEp2g9zztsppw/b0sbp5upZ0t1WyEukNEaEnFj0t6M8rDvGV\n+EuL5UvbRcLo1/A10Hpik6OUTCXyyBGAbmnYekTuHa9j25ovxtrsrW42PDLv6tq+FKcpunT10tGm\nv42j9d8hAF4CaELpN4GrEM09JH3CBGooDtNUo2oAdKagaUAzTa2BlTQHYEpxGYgGZjctRzebhr1r\nHEccyQJ0qWUgpp24zDO3QB9X9JyiohoT6txeLV+DvQXruMwD0CTAJnAaARXnHHz/rHN6WbH/xuOw\nxwkPxHZV6+9PDPNbAzsiu5QEmPnHAI51rm8GcPKwD7rU2qrWGECFOusdvXfG2L1ctZCR19XTW4O/\nF5aOg3bPQwAl8F8NIWTQ1CUCSlU6UlFLzxPNZoX9iIeyqKSeVXGoBaF1kPslQCfnWunIreRZmlns\nxddz23cYEfxr5559r+SPxM1deZTAEyTzTnRjAnAVYm0aafJWzaBpAq+GgSn39WwIXCMC/koATwm8\nEgmAawJqdHvq2nzyyLV3LfU/tEtXxIxtSYCbHvjLLGFZ8nmCKSaoUZkO2pBGCMloocBxVFT8kqNy\nDWQ8f4Wu/t6db970r7jp89+FlsPOfD5ux/oe2Ht9CzurPwDY7WcMe/Z/Dy1y1RsP4HLtejjnnDtX\nFdNIY/31SMvqaMcyakT14mefKSHjjshQWNx3yrZ8nM6UiCAN0Ssm0dDIXWR+63NOfXGXeNQLwwOb\nscBv37OreHrr+OeIIBfHXGPR21NY+zFkU/fIy5qalgBOLQCacHQHGfePmO8NQCup9l9zt5sX0PZF\ncA1gSsAU4JV4jiSWRg3JEFPEMiR7DLBHABViGKJvw+28A6IGYv6h9Lu18ac1/wNZ005yc78FQMRp\nqGhUK7ZUAhisLKC6xq6yjBtcYfoC9tn4KKw54aHYCoYMH/U6knc2EdwNSEAkhwAlyZX+3P0xYolF\nfnu2CA8sLbDbwerkPOPFdUwVbghJPf9yYYxB5IE8GQIzkXmyZYgQvCyxZg/tj2f6mFkJc86DzPue\nCagUrxIpiGjgt5OzvOJoi5zXUsmBf2bpaZ7QbIsm2YOYEFsAigBI611zbLXoBnGID7SbynB6IenM\nRGp7SJMW6EhIZtcKCZBsKEN21rBeWrpfsWmabpIZ0nIRBEZz223Y8ol/wa2f/iJ4ZYoNv3Qs9nna\niZgcsE+KBgtvdTqBsWXTpbjVjAg69Mznd+nSBi3d4RKL0P72CGA1ZLCbk4BFjTGgVJIhUsiFXwJc\n649FGtu7qW0MUrptC0B/nTl9hkjAQ44SCQxdG0EupJ4lfUZ3r1WBZr3OBTMUvSGQ9LLE1p5zYOiZ\nbEpEQI7b6qnNTQJ8AbHmW2pFZIdAmrjpo0Y/7pbsch3KlgCHOp4tQRK1mN1rkTRoJ5OxygAidPsC\nxAWEIt63S3OqvEpQR8kj1uUpxY3SsE6qGDRpECYNaKlBmNTt7zDp9heIRND1D0TTDrWbxARiTFPt\nm2+7FXdccAlu+8incfunPgfeuk0Uw03/8Glc+dK3Yo+THoG9n/F47PP0E7G0/z4RvglAGhH072f9\nf9Cy78bjsd8J9wbhjhSNMrD7k8hWJ8Q8G8DuIHHuwF/KL+fsfW05Y/LYwwvDu+b9zn3tY9BrNfrq\nNvU8CKnjY925a6V0EHC3BJCuzajugP+Y314UvawfIgFbM9ZR1CRQAryh5RVKumid9NnG14Lvkjnb\n/gPxyxKAbg3YeI6o3WdbBbl0GCz2akZxb8OYNAyTGuh9Btphnb20o7aPIE4mo3bZ5jYpZS8CGeEz\nqeMSEEtpGYhJrUjACUu2h0znZsvt2P6pTdh27iew7cLPAAr4i1JV2HDScdjnmY/DPZ72n7B2/71w\n66Yv47tPfE3vsUd/+Y+x7wn3gTbx2K7hbhHp0CMBe76ENoJtghTkbtYSkLP9ukbH1/FjTBi539Yt\nYm38+tAtAXHb1oH+ckq6lcgh93sMEeTueWSADAHowyMDR52xBKDBNgdAWnItAQvAXu3Ybrs4Uc94\n4Vpg1gBtw/fG5lsSWErXJUytqyUC7besBWRJQPzS8RzaXSxnysqlgfc5ztQ1DQGkGjtVDKSz3iFM\n/GwnjjUENCF2Kjdx5BHa2cWIEBnSiB9ZpjrV/tv1gCq1Z0HoA28DoN5yB7Z98mJsPfcTWLnwM8DW\nrU7EBqSuceumr+LWTV/FlS95K/Z+3LFY+dn1vUcO2PhwHHTCvRCwdYYEZmca9A9tLpLzvLKbk4DI\nUMRKtvcxfs2DSp7b08fTT3+t8tWI21t1lI1bSEGHbQ3KjbnmtfS03/a6dx64Jx2+bVSpc1tvciq1\n78L45RySbPaQaOVUF6nUO3I/RwLW7fUL2KKiddfheODfdnoq0aDqEZWtkesiIodtBdj46rjq9JYW\nhP4tawM15jers1eX0Xq3Hprw2/Tm7ryEOI9gksA5ADKijBCJgBqAa076UpZQOQBcAVxRXGyOKG42\nk/41HGLrI5Xh+tbbsO2Tn8HWj3wC2y68ZFSNPxx+KNY9fSOqDetwx7kXYOVb/+Y/WNe4+aKvz1w+\n5syntZ3QuZaANw/ZDiCVd+aVuwkJjBVdyu3XY8+26jIv6OdIwKKR/m39GbOInbUzDLW9dR9DGBnG\nmPiViEFFD9RPeigV5JWxXOPxcS4pcqA8huc8EigN29Rxbpzr9hl79lojunhYgPTMU8uYJQGRUsew\nzRspmjKcdMXRoaSHZxqyLQQU/Gz9prRMA6WZugQOAFWIk8WkNcmxuwAUcRs1tZ8S91o8qd8ghI4M\nAhAQdyULHEBNBUID3HorVj51IbZ99Hxsv2icqScC/5Ox7umnYu0jHohJYIQwRfX7/xXT7/8At374\nQmz58EXY+s0fFv05cOOxuOcJR4EUAYRUK/AmiO0o4HsySAJE9KcA/ieAOwBcAOBhAH6Hmd+/UzTY\nYbFfmUcAuVqvRQB7HSPOyPwWnTxCGPLXQ6axRDDG7ZGMTgMbnwECkN86ejoLbO2czAOkbpYIwaps\na+S249SC0NBhAc+aliyAeyRjxWsUeqKz0+sH8I5S34AlmiG37kAW0enSIyBudSDPfKTeZyg/KrRr\nBs20qgyZcAAopAq6+SSJIuBTQDSAJJBvNyDT5nBCXAwuhDhQiQiEAGy5Bc1FF2D68Y+h3rRplKmn\nOvxQrDv9l7H+9Cdh7SMejCpwnFuAbWluQRpO+sBDsO8Dz0D4/f+C7d+7Aps/dAluOOezuP2bP57x\n084O9uYHeL/lWX1erQx2DBPR5cz8MCJ6GoDTALwcwOeY+aE7FPKQYkQMvMdeVecSkHn35qk62nB0\n2CX3mN+lZ7z4Wf29geqrIQDvfq514ek4EFc32k5Zm/HC8aME2KUsLXFk6ezVaEsjc4aIYJ746BZI\nuwwDgDXpWEa3NpCdWyB+eyYoDfpe53Gt3DqbAoDA7RpBsgxEXB0UHSFkRhX1ho22IM9pLH809Ujn\nbFynR3XWynXpTFbSTh5TW0p2C80Z5ibElUCn29H807moz/8omosvmgv4N5x+CtY+8oEJ+NXCcWrp\niJ4bTTvDWI47vv9TXPuhf8E1H/0SVq67Bfd79Wm430tPhrc6qHeMXUH0bfT6nd4xLM+cBuAcZr45\nv+rnzpZcjd6zNwTlJvM7wDciW0OpDpeM27umZR6wzF0vkZwH+EMtgRwB5PTJtVxs2uf0Fpuv4z+Z\n+JJ+Xt3L8a9225qvVl+ALjjnEgjbaIidXoqTnXnr+ZPz2yMgz3zijcLRNX8P/HM8rd26qMunICSg\n00f3lbAan19xnAwmS0OvYWBNWg9oDboF4fScgQpAiAQQJ3RRt/JnUAQg6/SEptu0Rc6y41e72bxk\nDiWzUAJ/lEgAADGazTfg9v/ybNSXXYYhqQ4/FOuffio2nH4K1j3ymGjqoRoV3dFNKlOgbxeS85aW\nIDA23P8eOPD1T8ZDX79RXV9B39LvE0FuhVJKGdZl9/zQPIYEzkvLP28F8GIiOiC57wTxIuSBEDBr\n+4ZxW/GqTPKFDJFoCQxL6DKGDMYiR64lkwP9EmJpsUbuIVRWereX2PzOJMHM3IERqg4BsFZBqeKK\n9cNaFt19cE14Q8BO5tqY4adDwzI9U1UurjarSq2E9p4M40w19orb1UGxhtslomlNExeEW+Z+HILY\n4AlxYhXadfhlzR/xP4J8BHvZyrEKUwTZ1pE6IpCJV10e6WGc1JqBrK28vmEzbnjW81B/s79Eg5bq\n8EOw4fQnYc+nPzEBf5NMPLdhgmlvJnEP/Cm/gFxu6eecSccelhCk41hf1++uVsaQwFkA/hTAzcw8\nJaLbADx11SHOJTk7/xixnaPaH13VA2ZbESXxCMAD4FI1zfPTui3CjCWBEhHkwrIiaUTOWb1DUPeU\nfyXwL/FLLgql9+y9IRniRA8Uc0NKNfhbgNfZZm3qQzb+XDbb7Baxn8nY7PY+KVnuQWrsQgBLHJeB\nXtOA1qVlodema8sMLHHSnTvgt7DGshlLVJSoM60I+E/CFJPkjke3gieJbtQvb22nqUMC9Q034sr/\n/JtY+eb3Z6I6OeJg7HX6ydjrGU/E+kc+IG1UViPQ7ahQY0LdekG9paILq4fOrC+UBnJGbbsEL3Xq\n5sggZwa6M9YO+gIzH9cqz3wbEX0OwHGFd3ayjKmdW8khSM5/ec4mqAf6XjieUXkIhD2/tJ/a77F9\nGkMtARuWSKnVxehMPOo5mnHkgxgC8DHHkD9D/nn2fn1foqtnuOaIQL8jv4NzP5d9pVr/0CSsXL/E\n0G84bntN6Uya2GRZ6DUArQGwFkAyC7W7iMnzdoKXMjHpBJbBj+1SDmoZB1m7PxJFRxg9EujFaRYK\np9ffiKs2/ha2f6M/ZHP9SY/AQW96KdYff0zakpgRsDK7R0BaOG5S2C+gtIy0Bm0tGr7j79kMGWo9\n5MB/p5qD0mYvhwBYT0THoSvyewFYP3dIqxKbOCWQzIHgamziQ9dKwO8NIte9djnJtS5KSDKEmvMQ\nUabwaKAnpZfeRH4oat592/0wRh0N1DDnMaBvbe86GXW4Avq2H8CbeZubTOWFQSqM2oQtSz57E7L0\nqBtdlMaQgk6nMUJdpsT1/MXkEgBuAI4bvVADUEOgOsQhnbXMuo3hidmnzca2qHRM2pp3KLUaKKAm\nBlCBOS3D3FRqb98uDFmOug1ToDS56xtuxJVP+i1su7xPAHs84Xgc8bG3oFq/JpJLC9RCAH1gnwzs\nFTBrn4/CqbDGlURtQe+DvyWBOOlLFxea8bv7FCzBzJPZUUotgVMAvBDAoQDeqq5vAfC6uUNalXjV\nlxzQeVWmsaCoxWsJlPzK9ex5gO2JNUSXws6ZmGB+z/ue1SXjdQv4pI50c97oeb+1uqXpDVo8/s/Z\n4r3D+isEoCdI6VEzWm/t/9C6OgLe4v80nVfMM0Odw2MmrcGkk44bjLvXFxDP0b7OHQHILarSujoB\nkBU0meMqnUucSIzbEUBxJi4ws6MXEngnEmiXQiCAOKDmqu0DCAn4I2Ekt7MPQHsNjOaGzbj6lBdj\nuyGA9U84Aff6+NtA65dNxPvTsvT0LG+alge8DEKNoHwJ6lkfmj2kiecUj9anLgy5XyKJeSVLAsz8\nPgDvI6JnMPM5ued2rQyRgAX+sTVkD02MXbuoUyn8HBHYr9Oio/1Cc4Ce079ECJ7+VgpV8xkC8NRx\n8kp7qb0esu4NlWfvXY/3coeXPTZ8b3as7kbS4Xgdvl4nrujdGP+8OoUeIloyOXmtjVzWW+DXcbXP\ngKL1pmEQUVzXf8pq5c5UE+fYCsAUcYtJ2XO44t42je2Cbi0ZdEWmhUmOzZ1u7CELT0QCQAf2cfRQ\n6lPgbjQRX38Dbjj117Fyeb8PYN0THoVDPv52YP2aBK8CniUsGEYDoQ0gQLaM6fYRUC2eon/90T39\no69PQKMIRtoZ/VVF55UxfQLnE9FzARyJru7EzPzGVYW4KskBIpzr3nMl4NN+5Lh5CLVKYXj+ybND\n/nrvjCW3kr2lVC3PFKR2aQgv7S2BprBzvGdlbBS9Z7TaeshjLjyCP+rHhiHAmmvJWKLxRvHkwNkT\nrbs8663/Y1sjtgjnPg/7vD578VTkzhIXuS9r/xPAzEAdCYDTSCKeMKhqgElIZ+6ZtDSJtGWK0Q7x\nbLj/W4CwJQBiNKFGCA1QqchdfwM2b3wBpt/ob9e47gmPwsEfeydo/dq2fh2LS7/WQEB7NyQ4l13A\nur9sgD/uHSbvRd+0oUeIwMuw2SySlkPXpogh6nZKd0+3NiS8+WUMCXwMwE0Avo47bWiolhx425Jt\nqzfe8/ad0m8LbrZaa8P1hqjq+yVUG3v20NB7VsRb08ATBxnMBxqnZfY/mngvYGZlUFD8yHNDQIeu\njYmaVV9Ur9WztgUwwazdvTQSxwI9Zc5el5B+xotDjqC81kqO8HJLVuh+gzFpmftt8yMQEJLqNcca\ne03ACoNDXO6BK6SJZdStA7SE2HnMHciRCqfdNlImfsl2kw0gq3jKewgNmBqEKrZIiOMCcXT99dj8\nlOdh+s1ZAjjkY+9EtX5tC5YRTJHAu1/vrkyCaleVag8d/LI6i0+ArsV3MK59zLUNupZDfKq/bqge\nbdTvHLZEM5+MIYFDmflJq/R/F4hnW5CzV50i9byHMp5YAhjSozHPSvVqDIIA/S99HrAfQkY552r+\nOfuAiSKEADTwJ4RqQT+5NSGAW+DIJkEuuhbYrKqae/XZqxmXauveWHx5z64iWrL0eXEC8lmUIwGr\nrw7bIwLrvxR/L32Hrg11HXH80y7PMEW7VaTY/8nMK6C0q5c25XSduSkYTkTQIBEAQDW6VUEZELNH\nCIhHw6gqxgQNcMN12Pz0M7BiCGD940/AYee+FdX6JXTrYnRR66Az9L5goYM6nbsafUcikQhklFNH\nKRKxDnFmV/bsdwj7RhwJob94dHeeHTHUZtDcMmqIKBE9lJm/saoQdlhszdsrmR4p5PzIiXffIlHu\nORG7HKSErXXUwK/1GkISL3z3KzXnEtAP3U8foYRPHAkAQG+rSArxK25JIIG/VbXEiyUO1NHT4C9m\nHW9Ipw5X8zmhP4XEFhcNwN5MXdvZO8TfnuS+VQvOM30NnF/ieSZdB8i31GdiSRgM6i1Kl4igiS1G\n2QQmvtYAxKCaEeoG1MQD2+4A3XEHaN8N6Qvgdk9eaWVK3Zn15K+WBJKJpEkTtDgO38T11+KGZ56B\nlW/1CWCPxx+PI859SyKAlZi8DgzY8fj9YZ/diKGgauN6DkCrV6+WrkG6n+Fdy0CfO2Lo6KGvV6df\njgRWRwDAOBJ4LIBfI6IfA5Dl9XhXrx00n1iisOJVM0vVI/2VeO6hr14jVTBnTzdLFEOEpcMaI+y4\nS4UmQ36srrXgSuj3FySxnahe1HXSyHMlLpTw7ZIHtXLbcLxadW4Uj71m19e39n6pnQ8Vj7Gi30kj\nbGZ1yhDBEKG2BG10tqas1h9Wff1S++f+iCDWo184jfHndm8ATLeg3nQBVi46F9N/3gRs24pwxBFY\n/pXTsOZpT8bk2IfE/gGmWR2bSGJCPtKSiENFp5h+/au47fzzcft5n0R9TX99/g2PfySO+uibMVkf\nQNiObj6CXYDZA1k56na4qB0Sqt/pm2c6UuiAPKafZG9erCnItgD8UUp2tNJqyGDMAnJHuiozXzF3\naHNIfwE5C0oadEvtcXu9ZJPw3GPtGGMP62/OIJ17H845JwOmnuI1LTlyTAcpnfXcgfZx8mufHhDl\nxvJbMNUcqztNvXH8AbPArmv2SxiuWQ8dXh9Dbo6AjQfMPQJkgbVITKxW7OTWvp5dPE4cDHS7Y5mA\nNdjOxIfVvr2cRgIzQApEKS310G7FmM6hAbZuwfRzn8LKpz6OlX++GNiW70as7n0vrH/aqdjj6adi\n+WEPikE2iOQiZ44ExE2NbV+5FFs+/incet6FmF59nevnno9/BO537h9haY/lCJiUwJxk3L+aBZxZ\njye3obue+DVbC+8bd/pDQ/sdxbMkpH/PAn+VSCm3iBxMuC+jv5prAblR20sS0WMB3JeZ/4aI9gew\ngZl/PDaQ1cjsKqIeCJYAfAjQS3aJsSSAOd1j2uJjSGAsIeRMY2Of9dLaSQu72/fgcFLMRtkbYmmB\nTkedM4dWXfy1i7CtMddKcwa8pLE8LmHYPgRvoTcvq3QyyyYqQgDtwm3creC5hG7EjSYBALKxe9x5\nS53bxdVUgF5+tG7utmiUzdhlq8Yq7spFVRyhQ1tvwcrFn8b2fzoP2y++ePzWi0qWjjoUez/9ZOxz\n+hOw/mH3i9bEeorbv/QN3Pjhi3HjuZ+d2ZHLyt6PPw7HfOyNmKxf7i3tMKEVLGGKJaxgGduxhBUs\nYSURwrSt8ZeAdXViO4r7E9P6pibv6FojEfzL6xKJPJvO27kkQERnAXgEgPsz89FEdCiAs5n5F1eV\nLmMVc/cYFnfvq0G/JOfcQ6A79jwvMI9BwBwZzUsGyPweul6SoXgQugXf1fNk3CU+tLbvXGes9WcM\nSNsWgD40CYg+IrmNWURy/nt9CDaLVdL00kQ6TEWfCQMTjmv2L7Nax597JNCbosGYJQBNAjOtAuoP\n+mo53Zh3EvDLPr0UVtBs+gS2f+QcbN+0aRzwEwEjKp1rjjoYez3mQbj54kux/d9vGHy+2rAOB/3a\nE3HUm16Iyfo10Es8TzDFBCtYTgQgR58IOmCNqdPX0dbnrTsb3V6rod+n0IG6nX0sNf5ZEtDv6D4J\n2yo5jT6z05eSfhqAhyMOEQUzX0VEe44NYMfEfuXy5Ws0sAvFeW5Wv73qI5mzF3ZpCis77qF4iU5a\nSoCbIwEbZokwvbBKkvGLCjqReTcXjO3G0YderkE/r4FUv6/NIZZnS5O2JKySPt74fF1MdLiW0Lw1\n/71WQfubIhH0dKcE+JK2HME96U1thzxS8nNsTRDiAK70SpeUs8MTWSuj/Wo3gG/iPr2TBjRpEJYa\nbFDAX1cAACAASURBVHvTG7D13e/GkEyOOBh7P+Nk7P2sJ2Dd0Ydhy/mfw83nXIxbLvgyeNt2951t\nP/oZrvvRz4r+VhvW4oCnHI+DnvFo7HfqwzFJs4AJt7dg2y39MG1BX4Dfgr+/xo/t3vULszUR+YdH\nAk0P1HMHtbpx0mO2l0F3NM8rY0hgGzM3lKobRLTH3KGsWuQLLQGbRgVb1dJfta3qaULwhpbqZ8aC\nce4ZLeKnXrrarnI65GeJiIZ0gnMuiQZz8x45/pB9Zw61NFfbfW5LDTc49+zz4k8NYDu6pRu8WroV\n289g46P7AKxZy+tzKDb6EhEQICOs2n73GvFHzQBR2nCF0G7GHjgO0Wxr76zuIQF79EKq/wyKo3F6\na/On6CUi0P6FSYPmu5dj61/8RSax0uqczzgZ+zzrCdjjkffHRC3DvOcZv4TDzvhPaG7ZghvP+xKu\n/9A/Y/MFXwdvW8n6J1JtWIsDn/IIHPLMX8CBpz4Mk3VLCVxrEG7H7Lj6uq1Rd2sATdsaf5MKjwBo\nl90d6NtDxBtV5AN4f3x/3xzU/bZDUGUyWiy2hDhtrUJpZJBoPa+MIYEPEdFfAtiHiH4TwH8F8Fdz\nh7QqWU1LwGsReGBrl5LWw1Rgnh1DANb8BPWMFydNQjYe8twQ8Af1nA5Thz1kxsq8Nnh/DuCX89AB\n9HnZXpNDA79NplxtW/ycYpZYvGSyOtvWhu0A9uYdeHMQ9DvZbiApGyqVGS0BUJ3uE9p++Tg+HxEk\nZCXOSRPH60/i0YaVfG4JoAlxchaHNGFLQpYROV2fANEUt7/uNUDTb8VOjjgEG05/IvZ65hOxx/H3\nj+vxY4oKK5hQndwdKIe9Kuz53MfgyOc+GvUtt+Ha876Kqz/0BVx/wWVoFCFUG9bioKcc1wL/0rqJ\nAt5tMzVmPYyy38HagTXAvSdqVNC16BL4iwjAywQy24GcW1LadjZ7oC45Hz+BOE+hWyqi01Dn5I7I\nIAkw858S0SmIC8cdDeD3mPnCHQp1tFjTylhTC2Xc+hl7AL7Jx/M7dw/mun0m9+6QP55YpPLCyJGU\net/bBWxU8M4DOeDPqeUB8DxdIznQz70vYs09tg5g9bDArcHddgTbFoWux1gTkvWbgHZdHeUBAdGW\nzgYEZPKVrM8z4QT8DWi5QZA9AJa4XcNHwok1/gj8cXauEEHXKiBmtVRD7ARe+eDfY/q1r0HLAe/7\nE+z97FNQhbQvADrQlzX5J5YE2loyY3mvJRzx3EfjyOc+Giu33IZrz78Ud1x1Azbc9yAceOpDMVm3\nrAB2qkig718wJJA3zfRStuf2TD8WcD2wFxOTxHOSWhwhLSvnDevsgD8Xuq3ps6PPjsuo0UEAQER7\nIxZzBgBm3rwTwi+Fx8D/Y6+qc+6LL7lX0yHrhVdCM696l/N7LNLlni+hX+4sCKOKj/y2XDIkFtSs\ne0xyyblUoy5lVy4LvSzxhp/maubekM9S7d/ONdDXS8+2z3C3CbtaaE1W27QrZ7Yzb9vO26YjgQkj\nLEkroOkWdmvNQjJ0VIF+E1KrgHqERYgtgUA1cMtmbD7+RDTXd521ezzlcbjXh9/abbROeretKSoS\nU4wmAb9jk2CBrruWs61bm7pdVgHKbx/iffeQnb8/qaxPBHYIan/UUT+eeeC398px0PKrdP7O7Rgm\nov8G4A2IE8X03MyjxgRARBWArwG4kpmfQkT7AvgggCMAXAHgWcx8k/+2Z1axCDMEjCVwl6gQ8rY0\ni24lZMuB/84mgTFVX0ePNirKXVrfR7ttQ0rujalDjAX/3AQuuW+j5enqJUsJgEumm9yzY+oO0spY\nSc/U6v0G6ssTwJc4cDsqB1VaF0f23ZVN2CvZf5e7TdnFbh+armVQNWoFT/TW+wfQ7cQ1s1E7xNrU\nAS81uPl1b+oRAK1dg8Pe9jKsCds6ApDRLc62i7OA7dXY88CrAdizxfvr6lhiwcw1AWdtrhlz6Ilk\ns+Af49onAA/8u3LQFWdNFH5Lpt+C6N5fjYzpE3gVgAczc3mQbl5eBuA7AGRE0WsBXMjMf0JEr0m/\nX+u/au3clgDGgCqM25MhM1Pu/TF6jGkRrAb85/BLg786ZZOplFzarJHjz5L63qHB1htvn5srkJMc\nCXhDUL0afOk5dwKbmGyctPASx3Z1AWjNQKmDFxNuZ97GETl1Gp0Tz2HStOSgx/K36+urNfa7dfhT\noDr92i0ZO3dUR4EOMVYu/TZufe8/9GJy4O8+HxuOuicq2o6gwF+DZH/GrR7eOGsiKZlMcq0BSwqr\nIQAdvlfDL20oM3bDGauDL/1avo2vdefiN6+MIYEfAbhjNZ4T0WEANgL4QwAvT5d/BcCJyf0+AJcg\nSwI930aE6CWERilxa/TyqrpjwhrzzBg/xhKArfIOCWPGbm+9GDrsO163ypholSxxOYD25goMkYBH\nZu2Ye+eQkTu5pSTsZi5tqyQBtiIBAGkNHSjbvdEnxZcDEFfZhEtCVAE0QTTjyJEmiNGSulYp8A/R\nVCQbrHQ7cTXtZitx7l4/E/NdQtz1CTQ1rnnZG3udwWvucygOe9UzsETbZ4DfqynbeznQH08EefAf\nIgJ7T/sjOuqavWfi8baX9Mb9W1206Lq/TvdORzvaadZP6/dqyGAMCbwWwBeJ6IuIg+sAgJn5f4x4\n9+2ILYm91LUDmfma5L4GwIH514fsDraj1jvkGWlVBPR7BL2O2KGWgfcMm0Ou6R7HkhE9V7vPhZ2J\nO+m4prB7gE5ol3km9N2lhpQNPidDBGDt79YMU5osZlsDY7jTmpu8Wr9HBLmN4CccR+S0RKBr2sp+\nLwk1oxulBVkJnI52iWaVLixzBCoCJgSuCE1FQAgIgdEQgdLubkSyKDIhLmvcr9n2FzZLQKF07LLZ\ngCVFP258/3m444v99SOPeueLsX4do8JWeJ2zJQIYA97zHCVgtGYUa16xuvRNPLovozbAL/0RQxvN\nd+amDsX6Kd9d667MmqaG+j76eTiPjCGB9wC4CMA30Z9xVRQiOg3Atcx8KRGd5D3DzBw7gHNynnIf\nDeD++m2likUsDxGsCAF4rQKY3zlSsO168c9bOE6f9bMlvYFZnQpxb5dvYCQjcBfXXjCKCALQTlBK\n4NQDUavC2Fq4Z/fPkYDtE/A6WHMduEOHJYIxwzjtMhOyHn47+YvV7lmsTDL9c7sIW1q+chaWQu8c\nOZraNOSAlgiaEMEeQLv3b2iiPwFN+04ApykAQkYJgKlB4NQygNTyAa/TUWtY33gLrn71u3pZfc+n\nPhoHP/lYVNg2A3oWrOYlAZtCuWs7ThazQzY9nXO1/yGzke4U7oDZKwd9y36X/v007C8f0U/HL1+y\nFV++xJ94N0bGkEDFzC8ffmxGHgPgV4hoI4C1APYiovcDuIaIDmLmq9Nm9tfmvTjN/M4ZoYdEgFne\nXY39zDN823teC0PO+vpQK8MLwwtLEQHJNd0JLOSgSEHvDdy2ABIZBALUxKLe2j9WHc89byvAaw3k\nOm0tYXjvlcLwCKnkZymcRASoOrMMZjpjGzUaRz57ajth48btyXzUxPvtgI6Wuwncrn8cI9Bw4u9U\nnKm3RSWDGgJTamXACHHifu4RQR+OOiIIaHDl778X0+u6cRth7TLu/44X9UwkHsjnzELWnp8He7T6\n9K/3fw+1JvqEY80qs30LY1oydravNRvpZ2xN3ac0XZNHT6+WVHiKCWZbGgENTjwROOnEpdaPd77B\nZnxZxpDAJ9MIoY+jW0p6cIgoM78OaUN6IjoRwCuZ+XlE9CcAXgDgzel87jhVLSCOrabO+5yWUgvA\nTu6S63K2JKAJKGc6ypFTjvgUEXCq3QsRcKrp91ohKi2IEujLgVjr1L97Nnjyk0KrKGdLBJpIPPGS\nwrtuw7NEo0Fb39P6SNZp/yV59BIRdu2gOh1tS4UUKUQ3VwRMAlA1QAhgGeWTyJQRCYATGfQOudem\nI6U+hgSH0nqTvCNC0xBCIDScKhecJhTJoypfYpgBDTUIHFoiQLvhyyw03XrpD3Dtuz/WS/Z7ve7Z\nWD7yEDRpvL4cMplJ17P1b7kWNdX75PrgLm57noVPmiGCgG4NIFbv9WcRlw69l8Dw8g4a8DVx6Rp+\nV6x9ytVPAIRu6L7SnWdbJ4F13LUf42UMCTwn+Ww7b+89Z1ii3R8DOJuIXoQ0RDT/Sg74tdtWVb0j\nVy0cMjJrtcVtEc3bocQiGpmzPXLmIo1cXnpoSbXKFvhTjZOA/nr/CUQUmCCEZHsOHRFUQYF4RodS\nebPJZ4HVZokF+1KW2kng+n2bnGz8yvltWyW2f2BCae9cAFV0x3QCUAVwxaAqbrGIKnTDMtM6PjE7\nFBlQ+nRJgzwpfdJWjQHgSarxM7V9EZzykCkAHEFV0o85Wv8rCmg4wle7BLR09somMNKPwQmehBya\nGj95ydtnOoP3f9VzsT3BodR+I7g37VmA0bues2d74K/NU/oZC/jWvCTXIkHIpi2dH7qG3Qf32cXb\n/Alp2pzU1dqlUMkdawYSV9/opgtkzJeQ7sdiEHc7huQPcwv+/XkIXT7OK2NmDB85v7czfnwWwGeT\nezOAk8e9OQ8JlI6cfcCrrnphAH00sSmtwZ0yz89DBGSeh/NbX9Nqcl/13ivKL+lAppBIICSzhrib\n1D8gwETKfyrX3m0S6edy2eKt1lkq0HpZKW/jeI+v7X2gn7xaHzvhK9X4o52eQYkAYuduJAdO+wC0\nZqD2DFX3SETQmt/67tiaUWRTpQ+bk2mIADSUOqQp7sOb8rLhZAriAKYGDUeo7oFu2suxHSnE6IBf\nyIAYt/3dh2c6gw/6s1diZe1eYExRo2oJQAA1kk2j3BFA9fWcCSdmQbkFgBjLHgFYM46Av64bS7tE\nsrlrlzToRvPMgr5v6orvkglFilOjKnF9tKD2ap8IOpFhuQENmOt0LVGozONIHnZTPlKPEjeOj+Nk\nzGSxPRCHdx7OzL9BRPdDXFb6/LlD22HxQHAI/MeQQu59mLPn9t73ns/FJ0cA9n0v7jD3jde6WsDm\nUZaLZvE6koNm1cgElSUET3JZ0Qy8Z8PI+eddh7mXC0cvhzNFf9OagDjxq0K01begzqZPRUCdZ4uZ\nNVl5fR+iIiWgDwQwR+teag2wmIlSejCHODyUAXBAQ/H5QGIwoQ4aBfRj77ICRWVi2XwTNr/6bb2k\n2eOpJ2H9xl9CnYC8S8quC9O2AKrUDhAQ1S0CSwbw9EB/YTe5pt0W9DT4Q70p2d4VIer97ptoOm20\nn/2ae/wQ+ut2egWL1B2/3dNpHgmranEggTwzAiYxZVmnGaf/TWrxrKIZgHHmoL9BXEb6Men3vwM4\nB8CdQAIaoHIyhhTGmINyZOD5OxRWiYREdKsAyCPTUDztPUd6jRLqzhziuQnxqFPLABSv65YA1Pte\nQ2YeEpCzbQl4/slCJbn7ORnT4Btz2OKhdQkpPRp0wzvbeNEsEVQqTmLCaokEaY4AJ0LgZH5icMoW\nDgIM1HF4y+MBHJr2N4VIFgQARC2kdXMGZk0rctx45jvQXNd1+dHaNTjwHa9qfwvw14m1Ont/rPVr\n0BdSkNaChKLt9p5N314vPVNyy4FeaBVk23l5UnTX5iDr7puBOsroqEKf+zKKBAggblCjQUUBEw5g\nSqGlVl7UfQVTTGKaUpNaAVqX+aZ1jSGB+zDzs4jo2QDAzLfJstK7XnTVzKthA/nWgQf2tjpWIoIh\ncvAIAZl7nt6iu46rh0A2XmMISycNdW79DFNcl16/L9ekX0DbqQFFIOiDob5mo6XVt2ebJU3hqNRZ\nL72QIwWd1NrW740oyvH0kNh3NK8z+oQJ7se5YjUfIbopzUMQEoAs+JYmmJFMNCNqg0FquIE55SfH\nYaqcapDkzKolc1b3Vy7/Dra8+x970dzvdS/E+iP3B6XOYEloMX1IJ68ArhCBQHDl2Ot0TV5Ds3e2\nAD+WKLojAndMLoIs6BBQJYOWfk6PIPIXppvdp9gLt4N8EY8IYJ4IFE07FRrUVKPmCjVVmNIEU55g\nhaaY8HKaoKfJKbXuwABuHCy6WkbtJ0BE69rMI7oP1CihXSveOvtacrXjEgHkDprD7SGap1NOTysl\n+4QOLxfPAkExdUQA6siAkUBD+cmI4C925paDDLHsaAtAqy/HUM3eIxvrn/WblVvG/w8tSWHDGmqB\nWFJzdVEtggT+vd3ClqGIQJFAQDffQPYLELepyQduokkI3AOv2QlGCTTIjHKhBtRM8bOX/GGvM3j5\nPofikFf9KirMjkPX5hkALRzZZwjc1rb1fQ3uudm5djjkGNAXv/VZZ2x8qkLsLK5cP2wndj/sDnj7\nZNS/Phs+VPh9LeVXg5jHzJFEY+0/dvAzpZ6KRAAV98PsJgDOJ2NI4CwAFwA4jIj+HsAvAnjhKsJa\nhYxBFXF7yJIjgrG1eev3QM17UE8rrJ7JVZ9zqDtGv4LOrReqtio117aLwtE9p06OCKyaYkbx/AJm\nQRYj7g0dOnw7+se2CKyftsPa0yFX/KRvoFK1/HbiGbckQIkIZJkIvRlMtwaQXj20iTVGdS1QWlSO\nuqOiBts+dTE2v+W9aK7frLKDe6q3v1em2PbDq3pRu/efvQTr1zKAbT3A0r50WTw71n7s4S3FnJuB\nm6/x54G/9B1aI03//Vhopb4fi24asQMx/kirJrXEjH+5UPtNRxU+G4pQy5BIN18Pfcy1eaVIAhSn\nKN4DwOkAfiFdfhkzX7fK8HaSeF+dXVtgqJZvk6yHfumadku4GsU0sALzZ4MG/1ILIYduduMbaz6C\nua+KDqlnekFTPkolTvakxFM2W0qzer3VPHOcrnXNJZnt8LXJmCMyYDbLcuDfG+WjavlLEfRpmYE1\nTXI3cdnnpaadcBaqBPYJ2NtZv7JOD6kafCKFzh3f2/79H+LKZ74UvDIdkVmzst9TH4XDNj4YwG29\nBLBkEEVqwBEu7d64FfqTnfQQzYkhghwJDBGABd353J0Jp2/v1/HyzUxeq8HTKdd7wIk+oEYHBTSo\nOKbNhKdY4kSS6VxxGsXEjRv3eaRIAmlbyVcz8wdxp3QEj5ESAXjG3pLJBOh/8YIUYkuwA9LFP4sa\nnlvOHsjnrg+1BhrzbFBnTVCiY8DMGP9WTTLJQT53WhE1PB5izEZTzjnwl+zzFpDLrSE0ZNv39JUJ\nX178pI9Bc3suK6Ce84isPRIBTKQlwPFYUsC/3CAs12kDmHjIktFVqBFCXKO/3ZiFEgCQWps/kUFr\n3pEWAjf41u+8adUEENYu4eHveC7W49ZCQoh0NVe9m1d/fZ3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omZME2c0TddEXt1ko6FlS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\nRHZWoFmQ+uOI0BopQ4f+/IqdfHd+mYgUtT3/RkVoV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "titre = \"Gaussian measurements\"\n", "mat_plot_sum(mat, n, titre)\n", "#filename = 'quantized_cs_gaussian_measures_n_{}_eps_{}.png'.format(n, eps)\n", "#plt.savefig(filename,bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Repeat the construction of the frontier *nb_curves* times to \"smooth it\"\n", "\n", "> nb_curves: number of phase transition curves constructed. Those curves are then averaged to \"smooth\" the effect of randomness in phase transition and get a \"stable\" phase transition" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "step 0 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "155.107507944 seconds\n" ] } ], "source": [ "n, eps, nbtest, nb_curves = 40, 0.1, 10, 5\n", "L = zeros(int(n/2))\n", "start = time.time()\n", "for i in range(nb_curves):\n", " if (i % 10) == 0:\n", " print('step {} done'.format(i))\n", " mat = phase_transition_mat_sum_quant(n, eps, nbtest)\n", " F = frontier_sum(mat, eps, nbtest)\n", " L = [sum(a) for a in zip(L,F)] \n", "L_gauss = [i/nb_curves for i in L]\n", "print('{} seconds'.format(time.time()-start))" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#For next use, save the Gaussian phase transition frontier with pickle\n", "#import pickle\n", "#filename = 'L_gauss_n_{}_eps_{}.p'.format(n, eps)\n", "\n", "#Save L_gauss\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(L_gauss, fp)\n", " \n", "#Load L_gauss\n", "#filename = 'L_gauss_100_eps_0.1.p'\n", "#with open(filename, 'rb') as fp:\n", "# L_gauss = pickle.load(fp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Draw the phase transition frontier for quantized CS for Gaussian measurements\n", "(it took 38664.542408 seconds to get it for n, eps, nbtest, nb_curves = 100, 0.1, 15, 40)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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DBDDRYEnAGJOQVq2Ce++FcePcmUBBxx0HY8dC586xjy2WLAkYYxLK5s3w8MPw5JNu6IeC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\nhksuuYTPP/88on3UqlWLpUu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = range(len(L_gauss))\n", "plot(X,L_gauss, linewidth=4, color = 'blue', label=\"Gaussian phase transition\")\n", "titre = \"Quantized CS - Gaussian measurements\"\n", "plt.title(titre)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "plt.legend(loc=4)\n", "#filename = 'gaussian_phase_transition_quantized_cs_{}_eps_{}.png'.format(n, eps)\n", "#plt.savefig(filename,bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Phase transition curves for $\\Psi_\\alpha$ variables" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def mat_exp_power(m, n, alpha):\n", " A = randn(m, n)/ sqrt(m)\n", " return np.multiply(np.power(np.absolute(A),int(2/alpha)), sign(A))" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat_sum_quant_exp_power(n, eps, nbtest, alpha):\n", " PTM = zeros((n,int(n/2)))\n", " for m in range(1,n+1):#construct one line of the Phase transition matrix for a given number of measurements m\n", " if (m % 20) == 0:\n", " print(\"line number {} done\".format(m))\n", " A = mat_exp_power(m, n, alpha)\n", " for sparsity in range(1, int(n/2)+1):\n", " sum_errors = 0 \n", " for i in range(nbtest):\n", " x_hat = signal(n, sparsity)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " sum_errors = sum_errors + dist(x_hat, sol)\n", " PTM[m-1, sparsity-1] = sum_errors\n", " return PTM" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "exp power 1.5 running\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "exp power 1 running\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "exp power 2 running\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "exp power 0.5 running\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n" ] } ], "source": [ "n, eps, nbtest, nb_curves = 50, 0.1, 10, 5\n", "L = zeros(int(n/2))\n", "dict_power_quant_cs = {2: L, 1.5: L, 1: L, 0.5: L}# note that for alpha<0.5 cvxopt solver fails\n", "#dict_power_quant_cs = {2: L, 1.8: L, 1.5: L, 1.3: L, 1: L, 0.8: L, 0.5: L}\n", "for alpha in dict_power_quant_cs.keys():\n", " print('exp power {} running'.format(alpha))\n", " for i in range(nb_curves):\n", " mat = phase_transition_mat_sum_quant_exp_power(n, eps, nbtest, alpha)\n", " F = frontier_sum(mat, eps, nbtest)\n", " dict_power_quant_cs[alpha] = [sum(a) for a in zip(dict_power_quant_cs[alpha], F)] \n", " dict_power_quant_cs[alpha] = [ele/nb_curves for ele in dict_power_quant_cs[alpha]]" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#save the dictionary of phase transitions curves to speed up later investigation\n", "#import pickle\n", "#filename = 'dictionnaries_quantized_cs_power_n_{}_eps_{}.p'.format(n, eps)\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(dict_power_quant_cs, fp)\n", "\n", "#To load the dictionary\n", "#with open(filename, 'rb') as fp:\n", "# dict_power_quant_cs = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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/fN/GvdNOcUcmmRSmE9vdZnYMfhKTPsAtzrlxkUcmkssSnMCnL5rOIT0OiTuM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\npgsVkbjF0Qbe2TlXHNwuBjrHEIM0YNX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = range(int(n/2))\n", "plt.figure(figsize=(8,6))\n", "for key in dict_power_quant_cs.keys():\n", " if key !=2:\n", " L = dict_power_quant_cs[key]\n", " text = 'exp power {}'.format(key)\n", " plot(X, L, label = text)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "plt.title('phase transition curves - quantized CS - exponential moments')\n", "#Gaussian phase transition\n", "#n_gauss = len(L_gauss)\n", "#X_gauss = range(n_gauss)\n", "#plot(X_gauss, L_gauss, 'r--', linewidth=3, label=\"Gaussian phase transition\")\n", "#plot(X, L_gauss[0:int(n/2)], 'r--', linewidth=3, label=\"Gaussian phase transition\")\n", "#plt.legend(loc=4)\n", "#filename = \"phase_transition_curves_quant_cs_n_{}_eps_{}.png\".format(n, eps)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Phase transition curves for Student variables" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def mat_power(m, n, p):\n", " return random.standard_t(p, size=(m, n))" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat_sum_quant_student(n, eps, nbtest, p):\n", " PTM = zeros((n,int(n/2)))\n", " for m in range(1,n+1):#construct one line of the Phase transition matrix for a given number of measurements m\n", " if (m % 20) == 0:\n", " print(\"line number {} done\".format(m))\n", " A = mat_power(m, n, p)\n", " for sparsity in range(1, int(n/2)+1):\n", " sum_errors = 0 \n", " for i in range(nbtest):\n", " x_hat = signal(n, sparsity)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " sum_errors = sum_errors + dist(x_hat, sol)\n", " PTM[m-1, sparsity-1] = sum_errors\n", " return PTM" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "power 20 running\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "power 30 running\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n", "line number 20 done\n", "line number 40 done\n" ] } ], "source": [ "n, eps, nbtest, nb_curves = 40, 0.1, 10, 5\n", "L = zeros(int(n/2))\n", "#dict_quant_cs_student = {30: L, 20: L, 15: L, 10: L, 5: L, 4: L, 3: L, 2: L}\n", "dict_quant_cs_student = {30: L, 20: L}\n", "for p in dict_quant_cs_student.keys():\n", " print('power {} running'.format(p))\n", " for i in range(nb_curves):\n", " mat = phase_transition_mat_sum_quant_student(n, eps, nbtest, p)\n", " F = frontier_sum(mat, eps, nbtest)\n", " dict_quant_cs_student[p] = [sum(a) for a in zip(dict_quant_cs_student[p], F)] \n", " dict_quant_cs_student[p] = [ele/nb_curves for ele in dict_quant_cs_student[p]]" ] }, { "cell_type": "code", "execution_count": 333, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#save the dictionary of phase transitions curves to speed up later investigation\n", "#import pickle\n", "#filename = 'dictionnaries_quantized_cs_student_n_{}_eps_{}.p'.format(n, eps)\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(dict_quant_cs_student, fp)\n", "\n", "#To load the dictionary\n", "#with open(filename, 'rb') as fp:\n", "# dict_quant_cs_student = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": 372, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 372, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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NoJr4efihNfzww888+2xfmjfvxcW4+/DbnUH3i8lEBUbzw+Oluf/+JPo36Ehq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\nEAsURXkPmH59ke5DF0tL+XD5cpYtWYYi4LDFJSK3b+PxgQMpKYGJE2H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i5MiRIiQkRF++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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = range(int(n/2))\n", "plt.figure(figsize=(8,6))\n", "for key in dict_quant_cs_student.keys():\n", " if key != 15:\n", " L = dict_quant_cs_student[key]\n", " text = 'degree {}'.format(key)\n", " plot(X, L, label = text)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "plt.title('phase transition curves - quantized CS - Student variables')\n", "#Gaussian phase transition\n", "#n_gauss = len(L_gauss)\n", "#X_gauss = range(n_gauss)\n", "plot(X, L_gauss[0:int(n/2)], 'r--', linewidth=3, label=\"Gaussian phase transition\")\n", "plt.legend(loc=4)\n", "#filename = \"phase_transition_curves_quant_cs_student_n_{}_eps_{}.png\".format(n, eps)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "#Reconstruction quality of BPDN$_\\infty$ for large $n=1024$\n", "\n", "Construction of phase transition diagrams may take a very long time in high dimensions (large values of $n$). That is the reason why we did not explore values of $n$ larger than $80$ (which is not high-dimensional).\n", "\n", "In this last section, we explore a larger dimension $n=1024$. We consider the same simulation setup as the one in paper \n", " Dequantizing Compressed sensing from L. Jacques, D.K. Hammond and J.M. Fadili:\n", "\n", "1. $$SNR(signal, signal_{reconstruct}) = 20*\\log_{10}\\Big(\\frac{||signal||_2}{||signal-signal_{reconstruct}||}_2\\Big)$$\n", "2. eps : size of bins in CS quantization equal to ||A signal||_\\infty/40\n", "3. $n=1024$, sparsity = 16, nbtest = 500\n", "4. A coefficient is satisfying QC when \n", "$$|(A signal_{reconstruct})_i-y_i|\\leq eps/2$$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def signal_gauss(n, sparsity):\n", " sel = random.permutation(n)\n", " sel = sel[0:sparsity]\n", " x = zeros(n)\n", " x[sel] = randn(sparsity)\n", " return x\n", "\n", "def SNR(x_hat, sol):\n", " n = len(x_hat)\n", " x_recover = sol[0:n] - sol[n:2*n]\n", " return 20*log10(norm(x_hat,2)/norm(matrix(x_hat) - x_recover,2))\n", "\n", "def QC(A, y, sol, eps):\n", " minus_x_recover = sol[n:2*n] - sol[0:n] \n", " pred = dot(A, minus_x_recover)\n", " list_QC = [abs(sum(ele)) <= eps/2 for ele in zip(pred, y)]\n", " return sum(list_QC)/len(y)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def SNR_gauss_quant_cs(n, sparsity, nbtest, list_ratio):\n", " \"\"\"Return a list of the average SNR(x_hat, sol) for different ratio m/sparsity\n", " n : ambiant dimension of the signals\n", " sparsity : sparsity of signal\n", " nbtest : number of tests for point\"\"\"\n", " list_SNR = []\n", " list_SNR_std = []\n", " list_QC = []\n", " list_measures = [ele*sparsity for ele in list_ratio]\n", " for m in list_measures:\n", " print(\"measurement {} running\".format(m))\n", " A = randn(m,n)\n", " sum_snr = 0 \n", " sum_snr_square = 0\n", " sum_QC = 0\n", " for i in range(nbtest):\n", " x_hat = signal_gauss(n, sparsity)\n", " eps = float(max(abs(dot(A,x_hat)))/40)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " sum_snr = sum_snr + SNR(x_hat, sol)\n", " sum_snr_square = sum_snr_square + SNR(x_hat, sol)**2\n", " sum_QC = sum_QC + QC(A, y, sol, eps)\n", " list_SNR.append(sum_snr/nbtest)\n", " list_SNR_std.append(sqrt(sum_snr_square/nbtest-(sum_snr/nbtest)**2))\n", " list_QC.append(sum_QC/nbtest)\n", " return list_SNR, list_SNR_std, list_QC" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n", "3509.82822204 seconds\n" ] } ], "source": [ "n, sparsity, nbtest, list_ratio = 1024, 16, 100, [10, 15 , 20, 25, 30, 35 , 40] \n", "start = time.time()\n", "list_SNR_gauss, list_SNR_std_gauss, list_QC_gauss = SNR_gauss_quant_cs(n, sparsity, nbtest, list_ratio)\n", "print('{} seconds'.format(time.time()-start))" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pickle\n", "#list_SNR_gauss_quant_cs = [list_SNR_gauss, list_SNR_std_gauss, list_QC_gauss]\n", "#filename = 'snr_quant_gauss_n_{}_sparsity_{}_nbtest_{}.p'.format(n, sparsity, nbtest)\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(list_SNR_gauss_quant_cs, fp)\n", "\n", "#To load the list_SNR\n", "#filename = 'snr_quant_gauss_n_1024_sparsity_16_nbtest.p'\n", "with open(filename, 'rb') as fp:\n", " list_SNR_gauss_quant_cs = pickle.load(fp)\n", "list_SNR_gauss = list_SNR_gauss_quant_cs[0] \n", "list_SNR_std_gauss = list_SNR_gauss_quant_cs[1] \n", "list_QC_gauss = list_SNR_gauss_quant_cs[2]" ] }, { "cell_type": "code", "execution_count": 157, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZMjv6iTXGVFjQq7ZEpImqbgq5s0hj35kNo82u2qp8Dhxww5osWwYzZ9rQJsZU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\nTy93Wktj2TJ45hlYuhQkbBV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#plot(list_ratio, list_SNR_gauss, color='blue', marker='*', markersize=15, label='Gaussian measurements')#marker='^', 'o', '8', 'H', '+', 'x'\n", "#plt.legend(loc = 4)\n", "#plt.xlabel('m/s')\n", "#plt.ylabel('SNR (dB)')\n", "#plt.title('Quality of BPDN$\\infty$ - quantized CS - Gaussian measurements')\n", "#filename = 'snr_quant_gauss_n_{}_sparsity_{}.png'.format(n, sparsity)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sFZEBXgcTDA8/DFu2wPvvex2JMcYUrJLXAfhxiar+5jZPfSEi690aygkSExNz\nXsfHxxMfH196EZ6kypVhwgS49Va49lqIivI6ImNMOEpOTiY5ObnE2we9e6yIxACf5HePwmedBGCf\n7z2KopSH8j0KX/fd5/SAmjDB60iMMeVBmbpHUQwnBCwi1UWklvu6BvAnIN+eU+Fg5Ej49FP4+uvc\ny1/3JiBjjPER7F5P04BOQF0gHUgAKgOo6ngRaQB8D9QGsoC9wNnAacBH7m4qAe+q6sh89h8WNQqA\n//s/GD4cVqxwhiVPSVlNp05/Z+HCMbRufY7X4Rljwog9mR2iVOGmm6B9e/jnP6FXrwSSkh6kZ89X\nmDbtSa/DM8aEkeImirJ8M7tcEYHXXoPzz4ebbjrAsmUC1GHZMsjMzKRatWpeh2iMKafKyj0KA0RH\nw+OPw623TictrTsAaWndGT9+useRGWPKM2t68tgLL/ybpKQl1KzpTH2nCt99l8Xhw0/lrBMXN5yG\nDY/n9H37ttKrV3uGDAnLx0uMMUEW0HsUInI+0Au4HIjBeQjuZ2Ah8J6qrjipaE9SOCSKw4cPM2DA\nM8ya1YaMjG6Frh8ZOYOuXVcyYcIwqlSpUgoRGmPCTcAShYh8hjP8xsfAEuA3nG6spwPtgRuBSFW9\n/mSDLqlwSBTZJk6cwdNPp7B582NAfgngELGxzzB8eFv69Ss8oRhjTEECmSjqq2p6IQc7TVW3FzPG\ngAmnRAGQlraJLl3GsWHDqDxlcXFDmTNnIM2b2wiCxpiTE7AH7vJLEiJSV0TEZx3PkkQ4iomJBqrm\nW3boUFViY5uWbkDGGIOfRCEiF4tIsoh8JCLni8hqYDWwXUS6lF6I5Udqaio7dpwFgMgmmjUbjDPa\nOvzyy5lMmpTqZXjGmHLKX/fYscAzwDTgK+CvqtoAuAzI85S0OXnz5i1j9+52REbOoE+ft0lJGUHv\n3lOIiJiJajsGD17G2297HaUxprzxlygqqupcVZ0O/Kaq3wGo6nqc3k8mwBYuXEtMzHuMGSNMnpxA\nzZo1mTIlkTFjICZmGpdcsobhw+Ff/7I5LIwxpcdfovD9KjoY7EAMnHdeNPPm9c/Tq6l//27Mm9ef\nSy+NZtEiZ1yoe++1ObeNMaXDX6+nY8AB9201INOnuJqqej78R7j1eiqqPXvgz3+GU06BadOgRg2v\nIzLGhJJA9nqqqKq13L9KPq9rlYUkUZ7Vru0MSx4VBVdeCTt2eB2RMSac+ev1dKq/v9IM0uRVuTJM\nngzXXAMlQRleAAAcuklEQVQdO0JamtcRGWPClb+awXKc+xQCROM8pQ0QhTOMhz355TERGDECmjSB\nSy+FWbOcYcqNMSaQ/DU9xahqLPAFcIOq1lHVOsD17jJTRtxzjzON6vXXw+zZXkdjjAk3hY4eKyKr\nVfXcwpZ5obzezC7I4sXQrRs8+STcfbfX0RhjyqpgTFz0q4g8AbyD0wx1G7C1hPGZILroIli4ELp0\ngV9+gaeecpqnjDHmZBRl4qJeOHNYz8CZx/o0d5kpg+LiYNEi+Pxz6N8fjhzxOiJjTKgrNFGo6k5V\nfVBV27p/f1PVP4qycxGZKCLpIrKqgPIWIvKtiBwUkSG5yjqLyHoR2SAiQ4t2OgbgtNNg/nz4/Xe4\n4QbYu9friIwxocxf99iJInKhn/KLRGRSIfufBHT2U74TGAS8kGvfFXHGmuoMnA30EpGWhRzL+KhR\nA2bOhKZNoVMn+O03ryMyxoQqfzWKMcAgEUkVkU9EZIKI/Nt9nQrcC4z2t3NV/Zrj3WrzK9+hqkuB\n3A0k7YGNqrpZVY8ASUDXopyQOa5SJRg/Hm65xXnWYv16ryMyxoSiAm9mq+oqoI+IVAXaAk05PhVq\niqoGc/ynRsAvPu+3ABcF8XhhSwSeeAIaN4b4ePjwQ7jkEq+jMsaEkkJ7PanqIeA796+0FLnPa2Ji\nYs7r+Ph44uPjgxBO6OvXD04/HW6+GcaNc2oZxpjyITk5meTk5BJvX+hzFCdLRGKAT1S1lZ91EoB9\nqjrafd8BSFTVzu77YUCWqo7KtZ09R1FMy5fDjTfCP/4BgwZ5HY0xxgsBGxSwlOUOeCkQJyIxIlIF\n6AF8XPphhZ/zz4dvvoHXXoNHHoGsLK8jMsaUdSWqUYhIY1XdUoT1pgGdgLpAOpAAVAZQ1fEi0gD4\nHqgNZAF7gbNVdZ873epLQEXgLVXNM6ue1ShKbudOuOkmiI52Bhesmv9U3caYMFTcGoXfRCEi7YBm\nwFpVXSMiTYB/Ap1VNfqkoz1JlihOTmYm3H477NoFM2ZAZKTXERljSkPAmp5EZATOsB23AB+LyGhg\nIbAWOPNkAzXeq1YNpk+HVq3gssucYT+MMSY3fzPcrQXOV9WD7vwTvwDnqOrmUozPL6tRBIYqjB4N\nr7ziTIjUqsBuB8aYcBDIQQEPZT8roap/iMiGspQkTOCIwMMPQ6NGcNVV8P77cMUVXkdljCkr/NUo\nMnCamrJdBnztvlZVvSnIsRXKahSBN38+9OgBL78MvWzoR2PCUsBuZotIvJ/tVFUXFDO2gLNEERyr\nVjmTIA0a5NQ0bKhyY8JLQHs9lXWWKIJnyxZnXov4eHjpJahY0euIjDGBEsgaxfwCtlEAVb2y+OEF\nliWK4Nq92xnyIyoK3n3X6SVljAl9gUwUF/i8zV6pAzAU2K6qF+TdqnRZogi+Q4eccaL+9z/4+GOo\nU8friIwxJysoTU/u/YongGrACFWdU+IIA8gSRenIynLGhvr4Y5gzB2JjvY7IGHMyAjpntoh0Bh4H\nDuMkiIKao0wYq1ABnnsOmjSBSy+FTz5xxowyxpQP/pqevgfq4cw+9627OGdlVV0e9OgKYTWK0vfR\nRzBwIEydCtde63U0xpiSCOQ9imT3Zb4rqKrnj2RZovDGN9/ArbfCs8869y+MMaHFuseaUrF+vdN9\n9s47nRn07FkLY0JHIAcFvFBETvd531dEPhaRV9yxn0w51qIFfPutM+rsPffA0aNeR2SMCRZ/ExdN\nAA4BiMjlwLPAFGCPW2bKuQYNYMECp+tst26wf7/XERljgsFfoqigqn+4r3sA41X1Q1V9AogLfmgm\nFNSq5fSCqlfPeYp7+3avIzLGBJq/RFFRRCq7r68GfLvG+u1Wa8qXypVh4kTnnkXHjrBhg9cRGWMC\nyd8X/jRggYj8DhzAHTlWROKA3aUQmwkhIvDUU9C4MVx+OcycCRdd5HVUxphAKGwq1IuBBsBcVd3v\nLjsTqGnPUZiCzJ4N/fvDW28583IbY8qWgPV6AlDVb1V1RnaScJelFjVJiMhEEUkXkVV+1nlFRDaI\nSIqItPVZvllEVorIChFZUpTjmbLhhhucmfLuuQfGjSt4vZEjXy+9oIwxJeY3UQTAJKBzQYUich1w\nhqrGAXcDb/gUKxCvqm1VtX1wwzSB1r49/Pe/zhSrjz/uTLfqKyVlNaNGzWTlyjXeBGiMKbKgJgpV\n/RrY5WeVm3C63KKqi4FIEanvU26PcYWw5s1h0SL48kvo2xcOHz5e9uyz08nImMbIkR94F6AxpkiC\nXaMoTCPgF5/3W9xl4NQo5onIUhEZUOqRmYCoVw+++sqZ2+L662HPHjhw4ADLlglQh2XLIDMz0+sw\njTF+lIVurgXVGi5V1V9FpB7whYisd2soJ0hMTMx5HR8fT3x8fFCCNCVXvbozmOADDzg9orp2nU5a\nWncA0tK6M378dAYP7uNxlMaEr+TkZJKTk0u8fdDHehKRGOATVW2VT9k4IFlVk9z364FOqpqea70E\nYJ+qjs613Ho9lXEvvPBvkpKWULNmI1Sdp7i3bMni6NGnctaJixtOw4bHK7f79m2lV6/2DBliFUlj\ngiGg81GUgo+BB4AkEekA7FbVdBGpDlRU1b0iUgP4E/Ckl4Gaknnwwb6sWrWVWbPakJHRLd91Nmx4\nKuchvcjIGXTtKgwa1LcUozTG+BPUGoWITAM6AXWBdCABqAygquPddcbi9IzaD/RX1eUi0gz4yN1N\nJeBdVR2Zz/6tRhEiJk6cwdNPp7B582NAlXzWOERs7DMMH96Wfv3yTyjGmMCwYcZNmZWWtokuXcax\nYcOoPGWRkUNJTh7IeefZPKvGBFtAH7gzJpBiYqKBqvmWZWVVpXPnpkydmveZC2OMtyxRmFKTmprK\njh1nASCyiWbNBiOyyX1/Ji+9lMorr8Bll8GKFV5GaozxZYnClJp585axe3c7IiNn0KfP26SkjKB3\n7ylERMwkI6Mdv/++jMWLnelVO3eG++6DP/4odLfGmCCzRGFKzcKFa4mJeY8xY4TJkxOoWbMmU6Yk\nMmYMxMRMY8GCNVSoAH/9K6xbBxUqQMuWMH48HDvmdfTGlF+WKEypOe+8aObN65+nV1P//t2YN68/\nrVtH5yw79VQYOxbmzoV33nHGjvr229KO2BgD1uvJhABVeO89ePRRuOYaePZZZxpWY0zJWK8nE3ZE\n4PbbYf16OO00aNUKxoyBI0e8jsyY8sFqFCbkrF8PDz4IW7fCq6/ClVd6HZExocUeuDPlgqoz3epD\nDzn3L0aPhiZNvI7KmNBgTU+mXBCBm2+GtWvh7LOhbVv417/g4EGvIzMm/FiiMCGtenVITIQlS+D7\n7+Hcc51pWI0xgWNNTyas/Oc/zv2LM8+El16CM87wOiJjyh5rejLlWufOsGqVMwxIhw7wxBOwf7/X\nURkT2ixRmLBTtSoMHQopKfDTT849jOnTbbBBY0rKmp5M2FuwAAYNcubvfvVVJ3EYU55Z05MxuXTq\nBMuXQ7duzuu//x0yMryOypjQYYnClAuVKjm1ijVrYM8eaNECpkyBrCyvIzOm7LOmJ1MuLVkCDzzg\nJJCxY+H8872OyJjSY01PxhRB+/bw3Xdw111w3XUwcCDs3Ol1VMaUTUFNFCIyUUTSRWSVn3VeEZEN\nIpIiIm19lncWkfVu2dBgxmnKpwoVnESxbh1UruzMfTFunM19YUxuwa5RTAI6F1QoItcBZ6hqHHA3\n8Ia7vCIw1t32bKCXiLQMcqymnIqKcnpDffGFM5z5hRfCokVeR2VM2RHURKGqXwO7/KxyEzDFXXcx\nECkiDYD2wEZV3ayqR4AkoGswYzXmvPOcrrQPPwx/+Qv06QO//eZ1VMZ4z+t7FI2AX3zeb3GXNSxg\nuTFBJQK33eY0R51+ujP3xYsv2twXpnyr5HUAQJHvvOcnMTEx53V8fDzx8fEnGY4xUKsWjBoFd97p\njB315pvwyitw9dVeR2ZM8SUnJ5OcnFzi7YPePVZEYoBPVLVVPmXjgGRVTXLfrwc6AbFAoqp2dpcP\nA7JUdVSu7a17rAk6VZg1y5n74oILnLkvoqML327kyNcZNuy+4AdoTDGFWvfYj4E+ACLSAditqunA\nUiBORGJEpArQw13XmFIn4jzVvXatM4x527YwYoT/uS9SUlYzatRMVq5cU3qBGhMkwe4eOw1YBJwl\nIr+IyJ0ico+I3AOgqp8BP4nIRmA8cJ+7/CjwAPA5sBZ4X1XXBTNWYwpTrRokJMCyZc6QIOecA7Nn\n57/us89OJyNjGiNHflC6QRoTBPZktjEl9Pnnzv2LM85w5r6Ii3OWHzhwgDZtnmPDhkTi4hJISfkH\n1apV8zZYY3yEWtOTMSHr2muduS86dYKLL4bHHnPmvhg3bjppad0BSEvrzvjx0z2O1JiTYzUKY07C\nCy/8m6SkJVSu3Ii0NGdU2lNPzWLbtqdy1omLG07Dhsd/k+3bt5VevdozZMgAL0I2ptg1CksUxpyE\nw4cPM2DAM8ya1YaMjG6Frh8ZOYOuXVcyYcIwqlSpUgoRGpOXNT0ZU4qqVKnClCmJvPiiEhOTCBwu\nYM1DVKqUQHS0cOqpCUyaVIUFC2DbNpt5z5R9VqMwJkDS0jbRpcs4NmwYlafsjDOG8vrrA8nMjGX9\nevjxx+N/hw/DWWc5c2Scddbxv7g4OOUUD06kCOwZkdBW3BpFWXgy25iwEBMTDVTNt0ykKldd1ZQK\nFeCmm04s27nzxMTxzjvOfzdtgoYNjycO30Ry+unO8x1eyH5G5PrrO9G69TneBGFKlSUKYwIkNTWV\nHTvOAkBkE7GxL7Np099QjWX79jNJTU2lRYsWebarUwc6dnT+fB096iSL7BrIsmXO6LY//giZmSfW\nPrITSVyc87xHMB1/RuQVpk17MrgHM2WCJQpjAmTevGXs3n1Bzg3rsWNHcP/9L7g3utvx5ZfL8k0U\nBalUyfnij4uDG288sWzXrhNrIUlJzn9/+gnq18+/KatRo5OvhRw4cIBlywSow7JlkJmZac+IlAN2\nj8KYAOne/TGWLq1EQsL59Ot3vAfUpEkzeeqp5Vx44VE++OCZoMZw9Cj8/DN57oOsX+8843HmmXmb\nss48E6pXL9r+X3xxCo88cgFZWedQocJqRo9ezuDBfYJ6TibwrHusMR4ZMWIcvXpdS/PmsXnK0tI2\nMW3a5zzxxEAPInNkZORNHj/+CBs3Qr16eWshycn/5j//WUKtWsdH+P/11yw2bLBnREKdJQpjTLEc\nOwb/+1/eWsi6dYfZseMZVNuQlWXPiISLlJTVtGnTyhKFMSYw9uyB55+fwbhxKfz++2NAfgngELGx\nzzB8eNsTmtxM2dSrVwJJSU/ZA3fGmMCoXRuefvpmvvuuL3Fx/8x3napVh/PAA/247TZLEmXd8c4I\nxWOJwhhTKH/PiNSpU5VPP21K06bOMOy//lq6sZmi8x2wsjise6wxplD+nhHZv/9MXnstlaysFowd\n68zT0bkzPPCA82yIVw8GlnfZA1bWrHliZ4SsrL7F3pfVKIwxhXKeEWlHZOQM+vR5m5SUEfTuPYWI\niJk5z4icfTa8/rrzkOBFF0G/ftCuHUya5DwgaErXgw/25ZxzGvHDD21YsCCRBQsST+ixVhyWKIwx\nhVq4cC0xMe8xZowweXICNWvWZMqURMaMgZiYaSxYcHzK18hIGDzY6Tn1r3/B9OnQtCkMG+b0rjKl\nI3vAyuefV+rXT6TgASsLZ4nCGFOo886LZt68/nl6NfXv34158/rTunV0nm0qVIAuXeCzz+Cbb5xa\nRdu2cMstMH++jZobTMeOwVdfwd13w7BhN9OwYV/q1cu/M0JRBLV7rIh0Bl4CKgJvquqoXOVRwESg\nGXAQuFNV17hlm4E9wDHgiKq2z2f/1j3WmBCybx9MnQqvvgoVKzr3Me64A2rU8Dqy0JeVBd9+6wzn\nMn06NG4MPXvCX/4CjRodo2XLJ32ansrIA3ciUhH4Ebga2Ap8D/RS1XU+6zwP7FHVp0XkLOA1Vb3a\nLdsEtFPVP/wcwxKFMSFI1fnF++qr8PXX0Lcv3H8/NG/udWShRdUZLDIpCd5/32n269kTevRw5nLP\ntm7dOjp2XM7u3bcjsgnVZmXmOYr2wEZV3ayqR4AkoGuudVoC8wFU9UcgRkTq+ZRbfwljwpAIXHUV\nzJzpfNFVrgwdOsANN8Dnnzu/jk3+VJ252h9/3BkwslcvZ8TgOXOOL/dNEpC3M0JxBTNRNAJ+8Xm/\nxV3mKwW4BUBE2gNNgcZumQLzRGSpiNjAMcaEqZgYGDXKGczw5pth6FBo2dKpbezZ43V0ZUdqKjz9\nNJx7rpNQjxyBDz44cXlBcndGKK5gJoqitAk9C0SKyArgAWAFzj0JgEtVtS3QBbhfRC4LTpjGmLKg\nenW46y5YsQLefNNpkoqJce5jrF/vdXTe2LwZnnsOzj8fOnWC3393PptNm44vL8pzKgV1RiiqYD5w\ntxVo4vO+CU6tIoeq7gXuzH7v3pf4yS371f3vDhGZgdOU9XXugyQmJua8jo+PJz4+PlDxG2M8IAKX\nXeb8bd0K48ZBfDy0bg2DBsF11zk3wsPVr786N6OTkpyRfW+9FV580fk8Snrel17agqlTp5Q4pmDe\nzK6EczP7KuBXYAl5b2ZHAJmqethtXrpEVfuJSHWgoqruFZEawFzgSVWdm+sYdjPbmHLg0CGnmeXV\nV51f1ffd59Q+oqK8jiwwduyADz90ksPKlc50uT17OvdxKlcO/PHK1DDjItKF491j31LVkSJyD4Cq\njheRi4HJOM1Uq4G7VDVDRGKBGe5uKgHvqurIfPZvicKYcmbxYhg7FmbPhu7dnVpGq1ZeR1V8u3fD\njBlOb6XvvnOeOenZE669Fk45JbjHLlOJItgsURhTfqWnw4QJTtNUXJxzL6NbN2cK2bJq3z745BOn\n5pCc7NQYevaE668v3WdJLFEYY8qVI0fgo4+cZqmff4Z774UBA5xZ+8qCzEyn62pSktP199JLnecc\nunaFiAhvYipuorAhPIwxIa1yZeeL97//hY8/hrQ0Zx7wfv1g6dKS7XPkyNdPKqbDh+HTT6F3b2jY\n0Bks8Zpr4KefnOV9+niXJErCahTGmLCzc6fTjfT1150v6kGD4M9/hqLM0JqSsppOnf7OwoVjaN36\nnCIf8+hRpzkpKcl5kLBFC6dZ6c9/hgYNSn4uwWBNT8YY4zp2zLkn8OqrsG6dM0jePffA6acXvI0z\nVeiD9Oz5CtOmPel3/1lZzoCH77/vdGmNjj4+vlKTJn439ZQ1PRljjKtiRecG95dfwhdfODfAzz7b\nGfZi0aK8I9genyq0DsuWQWY+E2mowvffw5AhTmK4/36n1vLNN8eXl+UkURKWKIwx5cI558AbbzhP\nNbdv79wnuOACmDwZDh501vGdKjQtrTvjx08HnOSwciU89pgzjtLttzu9lD7//MTl4cqanowx5dLz\nz/+bCROWsHNnI/budZqjKlbMYvPm47PANW06HKjA9u1OM1ZU1FZuu609o0cPCOkpXu0ehTHGFMHh\nw4cZMOAZZs1qQ0ZG4WMgRUbOoGvXlUyYMIwqRbkrXobZPQpjjCmC7KlCX3xRiYlJpOCpQg8RG5uQ\nM/JqqCeJkrAahTGm3EtL20SXLuPYsGFUnrK4uKHMmTOQ5s1jPYgsOKxGYYwxxRQTEw1ULaC0KrGx\nTUsznDLHEoUxptxLTU1lx46zABDZRLNmg3FmPYDt288kNTXVy/A8Z4nCGFPu5Z4qNCVlBL17TyEi\nYiYZGe348stlXofoKUsUxphyL/dUoTVr1mTKlETGjIGYmGksWLDG6xA9VYYH5DXGmNJx3nnRPPvs\ntXluWPfv343LLz+PadM+9yiyssF6PRljTDljvZ6MMcYElCUKY4wxflmiMMYY41dQE4WIdBaR9SKy\nQUSG5lMeJSIzRCRFRBaLyDlF3dYYY0zpCFqiEJGKwFigM3A20EtEWuZa7TFguaqeB/QBXi7GtmEv\nOTnZ6xCCys4vdIXzuUH4n19xBbNG0R7YqKqbVfUIkAR0zbVOS2A+gKr+CMSIyGlF3Dbshfs/Vju/\n0BXO5wbhf37FFcxE0Qj4xef9FneZrxTgFgARaQ80BRoXcVtjjDGlIJiJoigPODwLRIrICuABYAVw\nrIjbGmOMKQVBe+BORDoAiara2X0/DMhS1bzj+B7fZhPQCji3KNuKiCUUY4wpgeI8cBfMITyWAnEi\nEgP8CvQAevmuICIRQKaqHhaRAcACVd0nIoVuC8U7UWOMMSUTtEShqkdF5AHgc6Ai8JaqrhORe9zy\n8Tg9mia7NYPVwF3+tg1WrMYYYwoW0mM9GWOMCb6QeTJbRCaKSLqIrPJZdqqIfCEiqSIyV0QivYzx\nZBRwfokiskVEVrh/nb2MsaREpImIzBeRNSKyWkQedJeHxfXzc37hcv1OcR+I/UFE1orISHd5uFy/\ngs4vLK4fOM+muefwifu+WNcuZGoUInI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#plot(list_ratio, list_SNR_std_gauss, color='blue', marker='*', markersize=15, label='Gaussian measurements')\n", "#plt.legend(loc = 4)\n", "#plt.xlabel('m/s')\n", "#plt.ylabel('SNR (dB)')\n", "#plt.title('Standard deviation SNR of BPDN$\\infty$')\n", "#plt.legend(loc = 1)\n", "#filename = 'snr_std_quant_gauss_n_{}_sparsity_{}.png'.format(n, sparsity)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "code", "execution_count": 164, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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0YBdwjojszfPYU+RITamn6hJDy5bQqpU73WRJwpjyJ5TRYz9V1etKKJ4CsRpF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\n5QjqAp1F5EiI6wKQkpKS8zw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LY99W1VUi0seb/wZwI9BTRI4A+4BbvdUbAJ9418BXAt5X\n1RnhitUYY0xgZXr0WGOMMeFXZobwEJF3RGSbiCzzmVZbRL4QkTQRmSEicZGMsSgClC9FRDaJyCLv\n0SmSMRaWiDQWka9FZIWILBeRv3vTo+L4BSlftBy/E0RkrogsFpGVIjLYmx4txy9Q+aLi+IHr1+aV\n4TPvdYGOXZmpUXhXRe0D3lXVc7xpzwE7VfU5EekP1FLVxyMZZ2EFKF8ysFdVX4xocEUkIg2ABqq6\nWERigAVAV6AXUXD8gpTvZqLg+AGIyImqekBEKgHfAo8A1xEFxw8Clu9youf4PQS0AWqo6nUF/e0s\nMzUK79LYXXkmXweM8Z6PwX05y6QA5YMo6HSoqltVdbH3fB+wCtenJiqOX5DyQRQcPwBVPeA9rYJr\nc9xFlBw/CFg+iILjJyKNgD8Bb3GsPAU6dmUmUQRQX1W3ec+3AfUjGUyY3C8iS0Tk7bJatfflXQV3\nLjCXKDx+PuX7wZsUFcdPRCqIyGLccfpaVVcQRccvQPkgOo7fcOBR3Hh62Qp07Mp6osjh3RO1bJxH\nC93rQCLQCvgVGBZ88dLNOy3zMfCAqu71nRcNx88r30e48u0jio6fqmapaiugEdBBRC7NM79MHz8/\n5UsiCo6fiFwDbFfVRQSoHYVy7Mp6otjmnR9GRE4Gtkc4nmKlqtvVg6s2ltnBEUWkMi5JjPV640MU\nHT+f8r2XXb5oOn7ZVDUd+A/ufHfUHL9sPuU7L0qOX3vgOhFZD4wHLhORsRTw2JX1RPEpcIf3/A5g\ncpBlyxzvAGa7HlgWaNnSTFyHmLeBlar6ks+sqDh+gcoXRcevbvZpFxGpBlwBLCJ6jp/f8mX/kHrK\n5PFT1SdUtbGqJuL6qX2lqj0o4LErS1c9jQc6AnVx59QGAlOAiUA8sAG4WVV3RyrGovBTvmQgCVft\nVWA90MfnvGKZISIXA7OBpRyr4g4A5hEFxy9A+Z7AjUQQDcfvHFyDZwXvMVZVnxeR2kTH8QtUvneJ\nguOXTUQ6Ag97Vz0V6NiVmURhjDEmMsr6qSdjjDFhZonCGGNMUJYojDHGBGWJwhhjTFCWKIwxxgRl\nicIYY0xQliiMCSMRqSwiCyIdhzFFYYnCmPC6GDdstTFlliUKYwpBRBJE5CcRGSUiq0XkfRG5UkS+\n824Gc763aCdgmohUF5H/eDfHWSYiN0cyfmMKwhKFMYXXDHgBOB04DbhFVS/C3fTmCW+ZJCAVlzA2\nq2or78ZU/y3xaI0pJEsUxhTeelVd4Y0uugKY6U1fDiSIyB+A31X1IG4cqCtEZIiIXKyqeyIUszEF\nZonCmMI75PM8Czjs87wSrhbxXwBVXYO7odEy4BkR+WcJxmlMkViiMCZ8OgHTIGfI8YOq+j7udFXr\nSAZmTEFUinQAxpRheYdeVp+/FYFmqprmTTsHeF5Esmse95RMiMYUnQ0zbkwYiMhFwO2qem+kYzGm\nqCxRGGOMCcraKIwxxgRlicIYY0xQliiMMcYEZYnCGGNMUJYojDHGBGWJwhhjTFCWKIwxxgT1/6JL\nPT/4PPxHAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#plot(list_ratio, list_QC_gauss, color='blue', marker='*', markersize=15, label='Gaussian measurements')\n", "#plt.xlabel('m/s')\n", "#plt.ylabel('Average QC fraction')\n", "#plt.title('QC fraction of BPDN$\\infty$ -- Gaussian measurements')\n", "#plt.legend(loc = 4)\n", "#filename = 'snr_QC_quant_gauss_n_{}_sparsity_{}.png'.format(n, sparsity)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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BRkH2bkRS0rFhjTcUrFmmMaZWxcXF8e9/p3D11UrjxikEb/5gwqVlSzeoSkaG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15, 5))\n", "subplot(131)\n", "plot(list_ratio, list_SNR_gauss, color='blue', marker='*', markersize=15, label='Gaussian measurements')#marker='^', 'o', '8', 'H', '+', 'x'\n", "plt.xlabel('m/s')\n", "plt.ylabel('SNR (dB)')\n", "plt.title('mean SNR')\n", "plt.legend(loc = 4)\n", "subplot(132)\n", "plot(list_ratio, list_SNR_std_gauss, color='blue', marker='*', markersize=15, label='Gaussian measurements')#marker='^', 'o', '8', 'H', '+', 'x'\n", "plt.xlabel('m/s')\n", "plt.ylabel('SNR (dB)')\n", "plt.title('standard deviation SNR')\n", "subplot(133)\n", "plot(list_ratio, list_QC_gauss, color='blue', marker='*', markersize=15, label='Gaussian measurements')\n", "plt.xlabel('m/s')\n", "plt.ylabel('Average QC fraction')\n", "plt.title('Fraction of coefficient satisfying QC')\n", "#filename = 'snr_subplots_quant_gauss_n_{}_sparsity_{}.png'.format(n, sparsity)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "####Histogram of residuals for Gaussian measurements ($m=40*sparsity$)" ] }, { "cell_type": "code", "execution_count": 201, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def SNR_gauss_quant_cs_hist(n, sparsity, nbtest):\n", " \"\"\"Return a list of the (normalized) prediction error (residuals) (A signal_reconstruct-y)_i\n", " n : ambiant dimension of the signals\n", " sparsity : sparsity of signal\n", " nbtest : number of tests for point\"\"\"\n", " m = 40*sparsity\n", " list_residue_avg = zeros(m)\n", " A = randn(m,n)/sqrt(m)\n", " for i in range(nbtest):\n", " x_hat = signal_gauss(n, sparsity)\n", " eps = float(max(abs(dot(A,x_hat)))/40)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " minus_x_recover = sol[n:2*n] - sol[0:n] \n", " pred = dot(A, minus_x_recover)\n", " list_residue = [sum(ele)/eps for ele in zip(pred, y)]\n", " list_residue_avg = list_residue_avg + list_residue\n", " return list_residue_avg" ] }, { "cell_type": "code", "execution_count": 202, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.229198932648 seconds\n" ] } ], "source": [ "n, sparsity, nbtest = 100, 4, 10#1024, 16, 100\n", "start = time.time()\n", "list_hist = SNR_gauss_quant_cs_hist(n, sparsity, nbtest)\n", "print('{} seconds'.format(time.time()-start))" ] }, { "cell_type": "code", "execution_count": 198, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#filename = \"list_hist_gauss_n_{}_sparsity_{}_nbtest_{}.p\".format(n, sparsity, nbtest)\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(list_hist, fp)\n", " \n", "#with open(filename, 'rb') as fp:\n", "# pickleist_hist = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": 203, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 203, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(list_hist)#, bins=100, normed=True)\n", "plt.axvline(x = 1/2)#, 'r--')#, linewidth=4)\n", "plt.axvline(x = -1/2)#, 'r--')#, linewidth=4)\n", "#filename = \"list_hist_gauss_n_{}_sparsity_{}_nbtest_{}.png\".format(n, sparsity, nbtest)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###SNR for exponential power measurements matrices" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def mat_exp_power(m, n, alpha):\n", " A = randn(m, n)/ sqrt(m)\n", " return np.multiply(np.power(np.absolute(A),int(2/alpha)), sign(A))" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def SNR_exp_power_quant_cs(n, sparsity, nbtest, list_ratio, list_exp_power):\n", " \"\"\"Return a list of the average SNR(x_hat, sol) for different ratio m/sparsity\n", " n : ambiant dimension of the signals\n", " sparsity : sparsity of signal\n", " nbtest : number of tests for point\"\"\"\n", " dict_SNR_exp_power = {}\n", " list_measures = [ele*sparsity for ele in list_ratio]\n", " for alpha in list_exp_power:\n", " print(\"----- power {} running\".format(alpha))\n", " list_SNR = []\n", " list_SNR_std = []\n", " list_QC = []\n", " for m in list_measures:\n", " print(\"measurement {} running\".format(m))\n", " A = mat_exp_power(m, n, alpha)\n", " sum_snr = 0 \n", " sum_snr_square = 0\n", " sum_QC = 0\n", " for i in range(nbtest):\n", " x_hat = signal_gauss(n, sparsity)\n", " eps = float(max(abs(dot(A,x_hat)))/40)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " sum_snr = sum_snr + SNR(x_hat, sol)\n", " sum_snr_square = sum_snr_square + SNR(x_hat, sol)**2\n", " sum_QC = sum_QC + QC(A, y, sol, eps)\n", " list_SNR.append(sum_snr/nbtest)\n", " list_SNR_std.append(sqrt(sum_snr_square/nbtest-(sum_snr/nbtest)**2))\n", " list_QC.append(sum_QC/nbtest)\n", " dict_SNR_exp_power[alpha] = [list_SNR, list_SNR_std, list_QC]\n", " return dict_SNR_exp_power" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "----- power 2 running\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n", "----- power 1.5 running\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n", "----- power 1 running\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n", "----- power 0.5 running\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n" ] } ], "source": [ "n, sparsity, nbtest, list_ratio, list_exp_power = 1024, 16, 100, [10, 15 , 20, 25, 30, 35 , 40], [2, 1.5, 1, 0.5]\n", "dict_SNR_exp_power = SNR_exp_power_quant_cs(n, sparsity, nbtest, list_ratio, list_exp_power)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#import pickle\n", "#filename = \"dict_SNR_exp_power_n_{}_sparsity_{}_nbtest_{}.p\".format(n, sparsity, nbtest)\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(dict_SNR_exp_power, fp)\n", "\n", "#with open(filename, 'rb') as fp:\n", "# dict_SNR_exp_power = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AR8eVc1mLUZ/IdrmYtm0bWW43c3v2pEkl3JDy3G76r1vH36KiuK5Fixqwsu5Q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CAAAg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\nEx8fH/r06UObNm2wt7fH19eXs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "marker = ['v', '+', '.', 'o', '*'] \n", "plt.figure(figsize=(15, 5))\n", "subplot(131)\n", "ind = 0\n", "for key in dict_SNR_exp_power.keys():\n", " L = dict_SNR_exp_power[key][0]\n", " text = 'power {}'.format(key)\n", " plot(list_ratio, L, marker = marker[ind], markersize=5, label=text)\n", " ind = ind + 1\n", "plt.xlabel('m/s')\n", "plt.ylabel('SNR (dB)')\n", "plt.title('mean SNR')\n", "plt.legend(loc = 4)\n", "subplot(132)\n", "ind = 0\n", "for key in dict_SNR_exp_power.keys():\n", " L = dict_SNR_exp_power[key][1]\n", " text = 'power {}'.format(key)\n", " plot(list_ratio, L, marker = marker[ind], markersize=5, label=text)\n", " ind+=1\n", "plt.xlabel('m/s')\n", "plt.ylabel('SNR (dB)')\n", "plt.title('standard deviation SNR')\n", "subplot(133)\n", "ind = 0\n", "for key in dict_SNR_exp_power.keys():\n", " L = dict_SNR_exp_power[key][2]\n", " text = 'power {}'.format(key)\n", " plot(list_ratio, L, marker = marker[ind], markersize=5, label=text)\n", " ind+=1\n", "plt.xlabel('m/s')\n", "plt.ylabel('Average QC fraction')\n", "plt.title('Fraction of coefficient satisfying QC')\n", "#filename = 'snr_subplots_quant_exp_power_n_{}_sparsity_{}_nbtest_{}.png'.format(n, sparsity, nbtest)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###SNR for Student measurements matrices " ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def mat_power(m, n, p):\n", " return random.standard_t(p, size=(m, n))" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def SNR_student_quant_cs(n, sparsity, nbtest, list_ratio, list_degrees):\n", " \"\"\"Return a list of the average SNR(x_hat, sol) for different ratio m/sparsity\n", " n : ambiant dimension of the signals\n", " sparsity : sparsity of signal\n", " nbtest : number of tests for each point\"\"\"\n", " dict_SNR_student = {}\n", " list_measures = [ele*sparsity for ele in list_ratio]\n", " start = time.time()\n", " for p in list_degrees:\n", " print(\"---- degree {} running -- {} seconds\".format(p, time.time()-start))\n", " list_SNR = []\n", " list_SNR_std = []\n", " list_QC = []\n", " for m in list_measures:\n", " print(\"measurement {} running\".format(m))\n", " A = mat_power(m, n, p)\n", " sum_snr = 0 \n", " sum_snr_square = 0\n", " sum_QC = 0\n", " for i in range(nbtest):\n", " x_hat = signal_gauss(n, sparsity)\n", " eps = float(max(abs(dot(A,x_hat)))/40)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " sum_snr = sum_snr + SNR(x_hat, sol)\n", " sum_snr_square = sum_snr_square + SNR(x_hat, sol)**2\n", " sum_QC = sum_QC + QC(A, y, sol, eps)\n", " list_SNR.append(sum_snr/nbtest)\n", " list_SNR_std.append(sqrt(sum_snr_square/nbtest-(sum_snr/nbtest)**2))\n", " list_QC.append(sum_QC/nbtest)\n", " dict_SNR_student[p] = [list_SNR, list_SNR_std, list_QC]\n", " return dict_SNR_student" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "---- degree 2 running -- 9.53674316406e-07 seconds\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n", "---- degree 3 running -- 6223.41036606 seconds\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n", "---- degree 5 running -- 12929.707541 seconds\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n", "---- degree 10 running -- 19866.689492 seconds\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n", "---- degree 20 running -- 26878.2539561 seconds\n", "measurement 160 running\n", "measurement 240 running\n", "measurement 320 running\n", "measurement 400 running\n", "measurement 480 running\n", "measurement 560 running\n", "measurement 640 running\n" ] } ], "source": [ "n, sparsity, nbtest, list_ratio, list_degrees = 1024, 16, 200, [10, 15 , 20, 25, 30, 35 , 40], [2, 3, 5, 10, 20]\n", "dict_SNR_student = SNR_student_quant_cs(n, sparsity, nbtest, list_ratio, list_degrees)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#import pickle\n", "#filename = \"dict_SNR_student_n_{}_sparsity_{}_nbtest_{}.p\".format(n, sparsity, nbtest)\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(dict_SNR_student, fp)\n", "\n", "#with open(filename, 'rb') as fp:\n", "# dict_SNR_student = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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iAa7YrtBxUke61O1C57qdS3Tlv7QjUnKdnefsn8M/lv6DyQMm06thL1ebYzAY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\nmrFx48YHfoaMjAx69epFv379DIlbcnIy9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op///vfPPbYY+X2muLKKrTqUEr9FxgAxGut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\nc8WHdNt+hvr169OzZ0/Wr19fYpydO3dm9erV5OfnM3fuXAYNGsSpU6fKo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15, 5))\n", "marker = ['v', '+', '.', 'o', '*'] \n", "subplot(131)\n", "ind = 0\n", "for key in dict_SNR_student.keys():\n", " L = dict_SNR_student[key][0]\n", " text = 'degree {}'.format(key)\n", " plot(list_ratio, L, marker = marker[ind], label=text)\n", " ind+=1\n", "plot(list_ratio, list_SNR_gauss , label='Gaussian measures')\n", "plt.xlabel('m/s')\n", "plt.ylabel('SNR (dB)')\n", "plt.title('mean SNR')\n", "subplot(132)\n", "ind = 0\n", "for key in dict_SNR_student.keys():\n", " L = dict_SNR_student[key][1]\n", " text = 'degree {}'.format(key)\n", " plot(list_ratio, L, marker = marker[ind], label=text)\n", " ind+=1\n", "plot(list_ratio, list_SNR_std_gauss , label='Gaussian measures')\n", "plt.xlabel('m/s')\n", "plt.ylabel('SNR (dB)')\n", "plt.title('standard deviation SNR')\n", "subplot(133)\n", "ind = 0\n", "for key in dict_SNR_student.keys():\n", " L = dict_SNR_student[key][2]\n", " text = 'degree {}'.format(key)\n", " plot(list_ratio, L, marker = marker[ind], label=text)\n", " ind+=1\n", "plot(list_ratio, list_QC_gauss , label='Gaussian measures')\n", "plt.xlabel('m/s')\n", "plt.ylabel('Average QC fraction')\n", "plt.title('Fraction of coefficient satisfying QC')\n", "plt.legend(loc = 4)\n", "filename = 'snr_subplots_quant_student__n_{}_sparsity_{}.png'.format(n, sparsity)\n", "plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###histogram of residuals for Student variables" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def mat_power(m, n, p):\n", " return random.standard_t(p, size=(m, n))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def SNR_student_quant_cs_hist(n, sparsity, nbtest, student_degree):\n", " \"\"\"Return a list of the (normalized) prediction error (residuals) (A signal_reconstruct-y)_i\n", " n : ambiant dimension of the signals\n", " sparsity : sparsity of signal\n", " nbtest : number of tests for point\"\"\"\n", " m = 40*sparsity\n", " list_residue_avg = zeros(m)\n", " A = mat_power(m, n, student_degree)\n", " for i in range(nbtest):\n", " x_hat = signal_gauss(n, sparsity)\n", " eps = float(max(abs(dot(A,x_hat)))/40)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " minus_x_recover = sol[n:2*n] - sol[0:n] \n", " pred = dot(A, minus_x_recover)\n", " list_residue = [sum(ele)/eps for ele in zip(pred, y)]\n", " list_residue_avg = [sum(ele) for ele in zip(list_residue_avg, list_residue)]\n", " return [ele/nbtest for ele in list_residue_avg]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n, sparsity, nbtest, student_degree = 100, 5, 10, 4\n", "start = time.time()\n", "list_student_hist = SNR_student_quant_cs_hist(n, sparsity, nbtest, student_degree)\n", "print('{} seconds'.format(time.time()-start))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#filename = \"list_hist_student_n_{}_sparsity_{}_nbtest_{}_degree_{}.p\".format(n, sparsity, nbtest, student_degree)\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(list_student_hist, fp)\n", " \n", "#with open(filename, 'rb') as fp:\n", "# list_student_hist = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "plt.hist(list_student_hist, bins=40, normed=True)\n", "axvline(x = 1/2, linewidth=4, 'r--')\n", "axvline(x = -1/2, linewidth=4,'r--')\n", "\n", "#filename = \"list_hist_student_n_{}_sparsity_{}_nbtest_{}_degree_{}.png\".format(n, sparsity, nbtest, student_degree)\n", "#plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "#Phase transition diagrams for correlated measurements\n", "In this last section, we consider gaussian vectors with correlated entries as measurements vectors." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def covariance_mat(n, p):\n", " \"\"\"covariance matrix with off-diagonal coefficients equal p and diagonal coefficients equal 0\"\"\"\n", " return (1-p)*identity(n) + p*ones((n,n))\n", "\n", "def mat_gauss_corr(n, m, p):\n", " mean = zeros(n)\n", " cov = covariance_mat(n,p)\n", " return random.multivariate_normal(mean, cov, m)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat_sum_quant_gauss_corr(n, eps, nbtest, p):\n", " PTM = zeros((n,int(n/2)))\n", " for m in range(1,n+1):#construct one line of the Phase transition matrix for a given number of measurements m\n", " if (m % 20) == 0:\n", " print(\"line number {} done\".format(m))\n", " A = mat_gauss_corr(n, m, p)\n", " for sparsity in range(1, int(n/2)+1):\n", " sum_errors = 0 \n", " for i in range(nbtest):\n", " x_hat = signal(n, sparsity)\n", " y = measures_quantized(A, x_hat, eps)\n", " a, M, b = cvx_mat(A, y, eps)\n", " sol = solvers.lp(a, M, b)\n", " sol = sol['x']\n", " sum_errors = sum_errors + dist(x_hat, sol)\n", " PTM[m-1, sparsity-1] = sum_errors\n", " return PTM" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "correlation parameter 0 running\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "correlation parameter 0.05 running\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "correlation parameter 0.2 running\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "correlation parameter 0.1 running\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n", "line number 20 done\n", "line number 40 done\n", "line number 60 done\n", "line number 80 done\n", "line number 100 done\n" ] } ], "source": [ "n, eps, nbtest, nb_curves = 100, 0.1, 10, 10\n", "L = zeros(int(n/2))\n", "dict_gauss_corr_quant_cs = {0: L, 0.05: L, 0.1: L, 0.2: L}# note that for alpha<0.5 cvxopt solver fails\n", "#dict_power_quant_cs = {2: L, 1.8: L, 1.5: L, 1.3: L, 1: L, 0.8: L, 0.5: L}\n", "for p in dict_gauss_corr_quant_cs.keys():\n", " print('correlation parameter {} running'.format(p))\n", " for i in range(nb_curves):\n", " mat = phase_transition_mat_sum_quant_gauss_corr(n, eps, nbtest, p)\n", " F = frontier_sum(mat, eps, nbtest)\n", " dict_gauss_corr_quant_cs[p] = [sum(a) for a in zip(dict_gauss_corr_quant_cs[p], F)] \n", " dict_gauss_corr_quant_cs[p] = [ele/nb_curves for ele in dict_gauss_corr_quant_cs[p]]" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#save the dictionary of phase transitions curves to speed up later investigation\n", "#import pickle\n", "#filename = 'dictionnaries_quantized_cs_gauss_corr_n_{}_eps_{}.p'.format(n, eps)\n", "#with open(filename, 'wb') as fp:\n", "# pickle.dump(dict_gauss_corr_quant_cs, fp)\n", "\n", "#To load the dictionary\n", "#with open(filename, 'rb') as fp:\n", "# dict_gauss_corr_quant_cs = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PBsZi6k7+1Vr3VUpFa60rWe8rTPeOSk5LhBBCCFEAObMIvR6mpbAPph9mWaXUU/bLaHP3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\n2bPZ4uLC0s6dqVGihIOiVkqp3CWrvdAzMxh3s4jUf4CYVC4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = range(int(n/2))\n", "plt.figure(figsize=(8,6))\n", "for key in sort(list(dict_gauss_corr_quant_cs.keys())):\n", " L = dict_gauss_corr_quant_cs[key]\n", " text = 'p = {}'.format(key)\n", " plot(X, L, label = text)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "plt.title('phase transition curves - quantized CS - correlated measurements')\n", "#Gaussian phase transition\n", "#n_gauss = len(L_gauss)\n", "#X_gauss = range(n_gauss)\n", "#plot(X_gauss, L_gauss, 'r--', linewidth=3, label=\"Gaussian phase transition\")\n", "#plot(X, L_gauss[0:int(n/2)], 'r--', linewidth=3, label=\"Gaussian phase transition\")\n", "plt.legend(loc=4)\n", "filename = \"phase_transition_curves_quant_cs_gauss_corr_n_{}_eps_{}.png\".format(n, eps)\n", "plt.savefig(filename, bbox_inches='tight')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }