{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Performance of Sparse Recovery Using L1 Minimization\n", "====================================================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tour explores theoritical garantees for the performance of recovery\n", "using $\\ell^1$ minimization." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: Method definition macroexpand(Module, Any) in module Compat at C:\\Users\\Ayman\\.julia\\v0.5\\Compat\\src\\Compat.jl:1491 overwritten in module MacroTools at C:\\Users\\Ayman\\.julia\\v0.5\\MacroTools\\src\\utils.jl:64.\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\constants.jl:1\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\constants.jl:1\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\constants.jl:7\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\constants.jl:7\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\constants.jl:12\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near In[1]:4\n", "\u001b[1m\u001b[31mWARNING: readall is deprecated, use readstring instead.\u001b[0m\n", " in depwarn(::String, ::Symbol) at .\\deprecated.jl:64\n", " in readall(::IOStream, ::Vararg{IOStream,N}) at .\\deprecated.jl:30\n", " in #parse_file#6(::Array{Any,1}, ::Function, ::String) at C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\files.jl:63\n", " in parse_file(::String) at C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\files.jl:61\n", " in #arequire#10(::Symbol, ::Array{String,1}, ::Function, ::String) at C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\Autoreload.jl:65\n", " in arequire(::String) at C:\\Users\\Ayman\\.julia\\v0.5\\Autoreload\\src\\Autoreload.jl:47\n", " in include_string(::String, ::String) at .\\loading.jl:441\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\execute_request.jl:157\n", " in eventloop(::ZMQ.Socket) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\eventloop.jl:8\n", " in (::IJulia.##13#19)() at .\\task.jl:360\n", "while loading In[1], in expression starting on line 4\n", "WARNING: replacing module NtToolBox\n" ] } ], "source": [ "using PyPlot\n", "using NtToolBox\n", "using Autoreload\n", "arequire(\"NtToolBox\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sparse $\\ell^1$ Recovery\n", "--------------------------\n", "We consider the inverse problem of estimating an unknown signal $x_0 \\in\n", "\\RR^N$ from noisy measurements $y=\\Phi x_0 + w \\in \\RR^P$ where $\\Phi \\in \\RR^{P \\times N}$\n", "is a measurement matrix with $P \\leq N$, and $w$ is some noise.\n", "\n", "\n", "This tour is focused on recovery using $\\ell^1$ minimization\n", "$$ x^\\star \\in \\uargmin{x \\in \\RR^N} \\frac{1}{2}\\norm{y-\\Phi x}^2 + \\la \\normu{x}. $$\n", "\n", "\n", "Where there is no noise, we consider the problem $ \\Pp(y) $\n", "$$ x^\\star \\in \\uargmin{\\Phi x = y} \\normu{x}. $$\n", "\n", "\n", "We are not concerned here about the actual way to solve this convex\n", "problem (see the other numerical tours on sparse regularization) but\n", "rather on the theoritical analysis of wether $x^\\star$ is close to\n", "$x_0$.\n", "\n", "\n", "More precisely, we consider the following three key properties\n", "\n", "\n", "* *Noiseless identifiability*: $x_0$ is the unique solution of $\n", "\\Pp(y) $ for $y=\\Phi x_0$.\n", "* *Robustess to small noise*: one has $\\norm{x^\\star - x_0} =\n", "O(\\norm{w})$ for $y=\\Phi x_0+w$ if $\\norm{w}$ is smaller than\n", "an arbitrary small constant that depends on $x_0$ if $\\la$ is well chosen according to $\\norm{w}$.\n", "* *Robustess to bounded noise:* same as above, but $\\norm{w}$ can be\n", "arbitrary.\n", "\n", "\n", "\n", "\n", "Note that noise robustness implies identifiability, but the converse\n", "is not true in general.\n", "\n", "\n", "Coherence Criteria\n", "------------------\n", "The simplest criteria for identifiality are based on the coherence of the\n", "matrix $\\Phi$ and depends only on the sparsity $\\norm{x_0}_0$ of the\n", "original signal. This criteria is thus not very precise and gives very pessimistic\n", "bounds.\n", "\n", "\n", "The coherence of the matrix $\\Phi = ( \\phi_i )_{i=1}^N \\in \\RR^{P \\times\n", "N}$ with unit norm colum $\\norm{\\phi_i}=1$ is\n", "$$ \\mu(\\Phi) = \\umax{i \\neq j} \\abs{\\dotp{\\phi_i}{\\phi_j}}. $$\n", "\n", "\n", "\n", "Compute the correlation matrix (remove the diagonal of 1's)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\kernel.jl:31\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\kernel.jl:31\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\kernel.jl:31\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\kernel.jl:31\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\kernel.jl:31\n", "WARNING: Base.UTF8String is deprecated, use String instead.\n", " likely near C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\kernel.jl:31\n" ] } ], "source": [ "remove_diag = C -> C - diagm(diag(C))\n", "Correlation = Phi -> remove_diag(abs(Phi'*Phi));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the coherence $\\mu(\\Phi)$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mu = Phi -> maximum(Correlation(Phi));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The condition\n", "$$ \\normz{x_0} < \\frac{1}{2}\\pa{1 + \\frac{1}{\\mu(\\Phi)}} $$\n", "implies that $x_0$ is identifiable, and also implies to robustess to small and bounded noise.\n", "\n", "\n", "Equivalently, this condition can be written as $\\text{Coh}(\\normz{x_0})<1$\n", "where\n", "$$ \\text{Coh}(k) = \\frac{k \\mu(\\Phi)}{ 1 - (k-1)\\mu(\\Phi) } $$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Coh = (Phi, k) -> (k*mu(Phi))/(1 - (k - 1)*mu(Phi));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate a matrix with random unit columns in $\\RR^P$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "normalize = Phi -> Phi ./ repeat(sqrt(sum(Phi.^2, 1)), inner = [size(Phi)[1], 1]);\n", "\n", "\n", "PhiRand = (P, N) -> normalize(randn(P, N))\n", "Phi = PhiRand(250, 1000);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the coherence and the maximum possible sparsity to ensure\n", "recovery using the coherence bound." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coherence: 0.29\n", "Sparsity max: 2\n" ] } ], "source": [ "c = mu(Phi)\n", "println(@sprintf(\"Coherence: %.2f\", c))\n", "println(@sprintf(\"Sparsity max: %d\", floor(1/2*(1 + 1/c))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 1__\n", "\n", "Display how the average coherence of a random matrix\n", "decays with the redundancy $\\eta = P/N$ of\n", "the matrix $\\Phi$. Can you derive an empirical law between\n", "$P$ and the maximal sparsity?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo1.jl\")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Support and Sign-based Criteria\n", "-------------------------------\n", "In the following we will consider the support\n", "$$ \\text{supp}(x_0) = \\enscond{i}{x_0(i) \\neq 0} $$\n", "of the vector $x_0$. The co-support is its complementary $I^c$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "supp = s -> find(abs(s) .> 1e-5)\n", "cosupp = s -> find(abs(s) .< 1e-5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given some support $ I \\subset \\{0,\\ldots,N-1\\} $, we will denote as\n", "$ \\Phi = (\\phi_m)_{m \\in I} \\in \\RR^{N \\times \\abs{I}}$ the\n", "sub-matrix extracted from $\\Phi$ using the columns indexed by $I$.\n", "\n", "\n", "J.J. Fuchs introduces a criteria $F$ for identifiability that depends on the\n", "sign of $x_0$.\n", "\n", "\n", "J.J. Fuchs. _Recovery of exact sparse representations in the presence of\n", "bounded noise._ IEEE Trans. Inform. Theory, 51(10), p. 3601-3608, 2005\n", "\n", "\n", "Under the condition that $\\Phi_I$ has full rank, the $F$ measure\n", "of a sign vector $s \\in \\{+1,0,-1\\}^N$ with $\\text{supp}(s)=I$ reads\n", "$$ \\text{F}(s) = \\norm{ \\Psi_I s_I }_\\infty\n", " \\qwhereq \\Psi_I = \\Phi_{I^c}^* \\Phi_I^{+,*} $$\n", "where $ A^+ = (A^* A)^{-1} A^* $ is the pseudo inverse of a\n", "matrix $A$.\n", "\n", "\n", "The condition\n", "$$ \\text{F}(\\text{sign}(x_0))<1 $$\n", "implies that $x_0$ is identifiable, and also implies to robustess to\n", "small noise. It does not however imply robustess to a bounded noise.\n", "\n", "\n", "Compute $\\Psi_I$ matrix." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "PsiI = (Phi,I) -> Phi[:, setdiff(1:size(Phi)[2], I)]' * pinv(Phi[:,I])';" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute $\\text{F}(s)$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "F = (Phi, s) -> norm(PsiI(Phi, supp(s))*s[supp(s)], Inf);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Exact Recovery Criterion (ERC) of a support $I$,\n", "introduced by Tropp in\n", "\n", "\n", "J. A. Tropp. _Just relax: Convex programming methods for identifying\n", "sparse signals._ IEEE Trans. Inform. Theory, vol. 52, num. 3, pp. 1030-1051, Mar. 2006.\n", "\n", "\n", "Under the condition that $\\Phi_I$ has full rank, this condition reads\n", "$$ \\text{ERC}(I) = \\norm{\\Psi_{I}}_{\\infty,\\infty}\n", " = \\umax{j \\in I^c} \\norm{ \\Phi_I^+ \\phi_j }_1. $$\n", "where $\\norm{A}_{\\infty,\\infty}$ is the $\\ell^\\infty-\\ell^\\infty$\n", "operator norm of a matrix $A$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "erc =(Phi, I) -> norm(PsiI(Phi,I), Inf);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The condition\n", "$$ \\text{ERC}(\\text{supp}(x_0))<1 $$\n", "implies that $x_0$ is identifiable, and also implies to robustess to\n", "small and bounded noise.\n", "\n", "\n", "One can prove that the ERC is the maximum of the F criterion for all signs of the given\n", "support\n", "$$ \\text{ERC}(I) = \\umax{ s, \\text{supp}(s) \\subset I } \\text{F}(s). $$\n", "\n", "\n", "The weak-ERC is an approximation of the ERC using only the correlation\n", "matrix\n", "$$ \\text{w-ERC}(I) = \\frac{\n", " \\umax{j \\in I^c} \\sum_{i \\in I} \\abs{\\dotp{\\phi_i}{\\phi_j}}\n", " }{\n", " 1-\\umax{j \\in I} \\sum_{i \\neq j \\in I} \\abs{\\dotp{\\phi_i}{\\phi_j}}\n", " }$$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "g = (C, I) -> sum(C[:,I], 2)\n", "werc_g = (g, I, J) -> maximum(g[J]) / (1 - maximum(g[I]))\n", "werc = (Phi, I) -> werc_g(g(Correlation(Phi), I), I, setdiff(1:size(Phi)[2], I) );" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One has, if $\\text{w-ERC}(I)>0$, for $ I = \\text{supp}(s) $,\n", "$$ \\text{F}(s) \\leq \\text{ERC}(I) \\leq \\text{w-ERC}(I) \\leq\n", " \\text{Coh}(\\abs{I}). $$\n", "\n", "\n", "This shows in particular that the condition\n", "$$ \\text{w-ERC}(\\text{supp}(x_0))<1 $$\n", "implies identifiability and robustess to small and bounded noise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 2__\n", "\n", "Show that this inequality holds on a given matrix.\n", "What can you conclude about the sharpness of these criteria ?" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N = 2000, P = 1990, |I| = 6\n", "F(s) = 0.20\n", "ERC(I) = 0.24\n", "w-ERC(s) = 0.28\n", "Coh(|s|) = 1.55\n" ] } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo2.jl\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N = 2000, P = 1990, |I| = 6\n", "F(s) = 0.19\n", "ERC(I) = 0.23\n", "w-ERC(s) = 0.28\n", "Coh(|s|) = 1.54\n" ] } ], "source": [ "## Insert your code here.\n", "\n", "N = 2000\n", "P = N - 10\n", "Phi = PhiRand(N, P)\n", "s = zeros(N)\n", "s[1:6] = 1\n", "I = supp(s)\n", "k = length(I)\n", "\n", "println(@sprintf(\"N = %d, P = %d, |I| = %d\", N, P, k))\n", "println(@sprintf(\"F(s) = %.2f\", F(Phi, s)))\n", "println(@sprintf(\"ERC(I) = %.2f\", erc(Phi, I)))\n", "println(@sprintf(\"w-ERC(s) = %.2f\", werc(Phi, I)))\n", "println(@sprintf(\"Coh(|s|) = %.2f\", Coh(Phi, k)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 3__\n", "\n", "For a given matrix $\\Phi$ generated using PhiRand, draw as a function of the sparsity $k$\n", "the probability that a random sign vector $s$ of sparsity\n", "$\\norm{s}_0=k$ satisfies the conditions $\\text{F}(x_0)<1$,\n", "$\\text{ERC}(x_0)<1$ and $\\text{w-ERC}(x_0)<1$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Insert your code here.\n", "\n", "N = 600\n", "P = Int(N/2)\n", "Phi = PhiRand(P, N)\n", "klist = Array{Int64,1}(round(linspace(1, P/7., 20)))\n", "ntrials = 60\n", "proba = zeros(length(klist), 3)\n", "\n", "for i in 1:length(klist)\n", " proba[i, 1:3] = 0\n", " k = Int(klist[i])\n", " for j in 1:ntrials\n", " s = zeros(N)\n", " I = randperm(N)\n", " I = I[1:k]\n", " l = randn(k, 1)\n", " s[I] = l./abs(l)\n", " proba[i, 1] = proba[i, 1] + (F(Phi, s) .< 1)\n", " proba[i, 2] = proba[i, 2] + (erc(Phi, I) .< 1)\n", " proba[i, 3] = proba[i, 3] + (werc(Phi, I) .> 0).*(werc(Phi, I) .< 1)\n", " end\n", "end\n", " \n", "figure(figsize = (8, 5))\n", "plot(klist, proba/ntrials, linewidth = 2)\n", "xlabel(\"k\")\n", "legend([\"F <1\", \"ERC <1\", \"w-ERC <1\"])\n", "title(@sprintf(\"N = %d, P = %d\", N, P))\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Restricted Isometry Criteria\n", "----------------------------\n", "The restricted isometry constants $\\de_k^1,\\de_k^2$ of a matrix $\\Phi$ are the\n", "smallest $\\de^1,\\de^2$ that satisfy\n", "$$ \\forall x \\in \\RR^N, \\quad \\norm{x}_0 \\leq k \\qarrq\n", " (1-\\de^1)\\norm{x}^2 \\leq \\norm{\\Phi x}^2 \\leq (1+\\de^2)\\norm{x}^2. $$\n", "\n", "\n", "E. Candes shows in\n", "\n", "\n", "E. J. Cand s. _The restricted isometry property and its implications for\n", "compressed sensing_. Compte Rendus de l'Academie des Sciences, Paris, Serie I, 346 589-592\n", "\n", "\n", "that if\n", "$$ \\de_{2k} \\leq \\sqrt{2}-1 ,$$\n", "then $\\norm{x_0} \\leq k$ implies identifiability as well as robustness to small and bounded noise.\n", "\n", "\n", "The stability constant $\\la^1(A), \\la^2(A)$ of a matrix\n", "$A = \\Phi_I$ extracted from $\\Phi$ is the smallest $\\tilde \\la_1,\\tilde \\la_2$ such that\n", "$$ \\forall \\al \\in \\RR^{\\abs{I}}, \\quad\n", " (1-\\tilde\\la_1)\\norm{\\al}^2 \\leq \\norm{A \\al}^2 \\leq (1+\\tilde \\la_2)\\norm{\\al}^2. $$\n", "\n", "\n", "These constants $\\la^1(A), \\la^2(A)$ are easily computed from the\n", "largest and smallest eigenvalues of $A^* A \\in \\RR^{\\abs{I} \\times \\abs{I}}$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "minmax = v -> (1 - minimum(v), maximum(v) - 1)\n", "ric = A -> minmax(eig(A'*A)[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The restricted isometry constant of $\\Phi$ are computed as the largest\n", "stability constants of extracted matrices\n", "$$ \\de^\\ell_k = \\umax{ \\abs{I}=k } \\la^\\ell( \\Phi_I ). $$\n", "\n", "\n", "The eigenvalues of $\\Phi$ are essentially contained in the\n", "interval $ [a,b] $ where $a=(1-\\sqrt{\\be})^2$ and $b=(1+\\sqrt{\\be})^2$\n", "with $\\beta = k/P$\n", "More precisely, as $k=\\be P$ tends to infinity, the distribution of the\n", "eigenvalues tends to the Marcenko-Pastur law\n", "$ f_\\be(\\la) = \\frac{1}{2\\pi \\be \\la}\\sqrt{ (\\la-b)^+ (a-\\la)^+ }. $" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 4__\n", "\n", "Display, for an increasing value of $k$ the histogram of repartition\n", "of the eigenvalues $A^* A$ where $A$ is a Gaussian matrix of size $(P,k)$ and\n", "variance $1/P$. For this, accumulate the eigenvalues for many\n", "realizations of $A$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[1m\u001b[31mWARNING: hist(...) and hist!(...) are deprecated. Use fit(Histogram,...) in StatsBase.jl instead.\u001b[0m\n", " in depwarn(::String, ::Symbol) at .\\deprecated.jl:64\n", " in #hist!#996(::Bool, ::Function, ::Array{Int64,1}, ::Array{Any,1}, ::LinSpace{Float64}) at .\\deprecated.jl:629\n", " in hist(::Array{Any,1}, ::LinSpace{Float64}) at .\\deprecated.jl:644\n", " in macro expansion; at C:\\Users\\Ayman\\Desktop\\gpeyre\\numerical-tours\\julia\\NtSolutions\\sparsity_6_l1_recovery\\exo4.jl:22 [inlined]\n", " in anonymous at .\\:?\n", " in include_from_node1(::String) at .\\loading.jl:488\n", " in include_string(::String, ::String) at .\\loading.jl:441\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\execute_request.jl:157\n", " in eventloop(::ZMQ.Socket) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\eventloop.jl:8\n", " in (::IJulia.##13#19)() at .\\task.jl:360\n", "while loading C:\\Users\\Ayman\\Desktop\\gpeyre\\numerical-tours\\julia\\NtSolutions\\sparsity_6_l1_recovery\\exo4.jl, in expression starting on line 11\n", "\u001b[1m\u001b[31mWARNING: hist(...) and hist!(...) are deprecated. Use fit(Histogram,...) in StatsBase.jl instead.\u001b[0m\n", " in depwarn(::String, ::Symbol) at .\\deprecated.jl:64\n", " in #hist!#996(::Bool, ::Function, ::Array{Int64,1}, ::Array{Any,1}, ::LinSpace{Float64}) at .\\deprecated.jl:629\n", " in hist(::Array{Any,1}, ::LinSpace{Float64}) at .\\deprecated.jl:644\n", " in macro expansion; at C:\\Users\\Ayman\\Desktop\\gpeyre\\numerical-tours\\julia\\NtSolutions\\sparsity_6_l1_recovery\\exo4.jl:22 [inlined]\n", " in anonymous at .\\:?\n", " in include_from_node1(::String) at .\\loading.jl:488\n", " in include_string(::String, ::String) at .\\loading.jl:441\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\execute_request.jl:157\n", " in eventloop(::ZMQ.Socket) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\eventloop.jl:8\n", " in (::IJulia.##13#19)() at .\\task.jl:360\n", "while loading C:\\Users\\Ayman\\Desktop\\gpeyre\\numerical-tours\\julia\\NtSolutions\\sparsity_6_l1_recovery\\exo4.jl, in expression starting on line 11\n" ] }, { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "\u001b[1m\u001b[31mWARNING: hist(...) and hist!(...) are deprecated. Use fit(Histogram,...) in StatsBase.jl instead.\u001b[0m\n", " in depwarn(::String, ::Symbol) at .\\deprecated.jl:64\n", " in #hist!#996(::Bool, ::Function, ::Array{Int64,1}, ::Array{Any,1}, ::LinSpace{Float64}) at .\\deprecated.jl:629\n", " in hist(::Array{Any,1}, ::LinSpace{Float64}) at .\\deprecated.jl:644\n", " in macro expansion; at C:\\Users\\Ayman\\Desktop\\gpeyre\\numerical-tours\\julia\\NtSolutions\\sparsity_6_l1_recovery\\exo4.jl:22 [inlined]\n", " in anonymous at .\\:?\n", " in include_from_node1(::String) at .\\loading.jl:488\n", " in include_string(::String, ::String) at .\\loading.jl:441\n", " in execute_request(::ZMQ.Socket, ::IJulia.Msg) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\execute_request.jl:157\n", " in eventloop(::ZMQ.Socket) at C:\\Users\\Ayman\\.julia\\v0.5\\IJulia\\src\\eventloop.jl:8\n", " in (::IJulia.##13#19)() at .\\task.jl:360\n", "while loading C:\\Users\\Ayman\\Desktop\\gpeyre\\numerical-tours\\julia\\NtSolutions\\sparsity_6_l1_recovery\\exo4.jl, in expression starting on line 11\n" ] } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo4.jl\")\n", "\n", "# klist = [10, 30, 50]\n", "# P = 200\n", "# ntrials = 200\n", "# tmin = 0\n", "# tmax = 2.5\n", "# q = 50\n", "# t = linspace(tmin, tmax, q)\n", "# t1 = linspace(tmin, tmax, 1000)\n", "# dt = (tmax - tmin)/q\n", "\n", "# for j in 1 : length(klist)\n", "# k = klist[j]\n", " \n", "# # simulation \n", "# v = []\n", "# for i in 1 : ntrials\n", "# v = [v; svd(randn(P, k)./sqrt(P))[2].^2]\n", "# end\n", " \n", "# figure(figsize = (10, 10))\n", "# subplot(length(klist), 1, j)\n", "# h = hist(v, t)[2]\n", "# h = h/sum(h)/dt\n", "# h = [h; 0]\n", "# bar(t[1 : end], h, width = 1/20, color = \"darkblue\", edgecolor = \"black\")\n", " \n", "# # theoritical law\n", "# beta = k/P\n", "# a = (1 - sqrt(beta))^2\n", "# b = (1 + sqrt(beta))^2\n", "# z = sqrt(max(t1 - a, zeros(length(t1))).*max(b - t1, zeros(length(t1))))./(2*pi.*beta.*t1)\n", " \n", "# plot(t1, z, \"r\", linewidth = 3)\n", "# xlim(tmin, tmax)\n", "# ylim(0, maximum(h)*1.05)\n", "# title(@sprintf(\"P = %d, k = %d\", P, k))\n", " \n", "# show()\n", "# end" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 5__\n", "\n", "Estimate numerically lower bound on $\\de_k^1,\\de_k^2$ by Monte-Carlo\n", "sampling of sub-matrices." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YRURExAlUl8HhDbYA+v2HYKlxPCZkqO3s5+hrIGI0uLj0fJ3dzCnDaFiAOVuJduR1CwsLKS8vt2t77rnnALjmmmsA2LNnT+MlfBEREXECtZVwZKNtHdDDG6Gu0vGYwBgYc7UtgEaPd8oA2pxThtH2Xio3U1JSEqtWreKZZ57h8ssvZ8OGDSxZsoTVq1cTEhIC2MLoZZddRklJCQsWLOCyyy7j9ttvN7lyERER6ZC6avh+k20ppkMfQE2Z4zH+kTB6ri2Axkzs1YvUdzWnDKN9wfz580lLS+Ovf/0rDz/8MGPHjuXtt9/m0ksvbTzmwIED+Pj4cMkll/DII48wa9YsEysWERGRdrPUwrFPbZfgD/wHqosdj/EdaFuCafQ1EDcFXN16vs5ewMUwjFbWCOhdSkpKCAoKori4mMDAQLu+qqoqjh07xtChQ/H29japwq5XWVlJdHQ0Q4YMYe3atYwePbrbXstZ30MREZEeZbXAj1tsZ0D3vweVBY7HeAfByCtsE5GGXABuznNe8FR57VSc5x1wMt999x3nnnsumZmZuLvrP5OIiEivZLVC+pf1AfRdKMt1PMYzAEZcagugwy4Cd8+er7MXU8rppfbs2cP555/PnDlzmDdvHp9++in+/v5mlyUiIiKGAZnf2ALovnegJNPxGA9fGD7HFkDPnAkePj1fZx+hMNpL7dmzp3F70Lvuuotbb72VN954w+yyRERE+ifDgJy9TfvBF6U6HuPmBWfNsi3FNPxi8PTr+Tr7IN0zKnoPRURETub4wfoA+hac+N6x39UDzphuC6BnXwre7b9X0tnonlERERGRrnDiB9vZz31vw/H9jv0urjB0mi2AjrgcfAf0fI1ORGFUREREpCitKYBmf9vKAS4Qd55tMfqRV4F/WI+X6KwURkVERKR/KsmCfettATTj69aPiZlkOwM6ai4ERvVsff2EwqiIiIj0H2V5sH+9bRZ86hdAK1NnouJts+BHz4XgwT1eYn+jMCoiIiLO78QPsOlROPBvMKyO/eGjbWdAR18NA8/o+fr6MYVRERERcV7l+fDp/8COF8BaZ9838CzbGdAx10DY2ebUJwqjIiIi4oRqK2H7atiyHKpLmtr9wmH8fFsAjRgDLi7m1SiAwqiIiIg4E6sV9qyDzY9BSUZTu4cvTLkXptwDXtrRsDdRGBURERHn8MPH8OFDtp2SGri4wvgFcNHvISDSvNrkpBRGRUREpG/L3QcfLoXvP7JvP2s2zPojhI80py5pF4VRERER6ZtKsuHjP8HuV+1nyEeeA7Mfg2HTzKtN2k1hVERERPqW6lLY+lfYthJqK5rag2Jh+kMw9lpwdTWvPukQhdFeLD09nQULFnD8+HHc3d156KGHuPbaa80uS0RExByWOvjmJfjkcSjPa2r3CoLzkyHpTvDwNq8+6RSF0V7M3d2d5cuXEx8fT05ODgkJCVx66aX4+fmZXZqIiEjPMQw49AF89DDkH25qd3WHibfBBb8Bv4Hm1SenRWG0F4uKiiIqyrYPbmRkJKGhoRQUFCiMiohI/5G5EzYuhdQt9u2jroIZD2u3JCegGypMlpOTw7x584iMjMTT05Po6Gieeuoph+N27tyJxWIhNjbWhCpFRER6WGEqvPlzWDPdPojGJsHPP4TrXlYQdRI6M2qyO+64g9raWj766CNCQkLIzc2lqKjI7piCggIWLlzImjVrTKpSRESkh1QWwmdPwVfPgaWmqX3AMJj5KIy8QrsmORmFUZNVV1eTmprKtm3bmDlzJhMmTHDonzt3LosXL2bKlCkmVSkiItLN6qrhqzXw2TKoanZSxncgTFsMibeAm4d59Um3URg1UV1dHRdffDEXXXQRQUFBrFy5ksOHD/Paa6/h7++PYRjcfPPNTJ8+nQULFphdroiISNczDNj3Nnz0KBSlNrW7e8PkX8LUX4F3kHn1SbfTPaMmuu+++4iNjWXcuHEMGTKEp556ij179vC3v/0NgK1bt7Ju3TrWr19PfHw88fHx7N27t41nFRER6SN+3Gq7J/TNW5sFURcYdwPcsxNmPqIg2g8455nRv0+DsuM9/7r+4XDHp+06dPfu3axdu5bly5fbtQcFBZGdnQ3A1KlTsVqtrQ0XERHpu/KPwIcPw6H37duHXWjbvjNqnBlViUmcM4yWHYfSLLOrOKW33nqL4cOH4+HRdP9LeXk5hw8f5t577wXg3Xff5eOPP3YIrCIiIn1SWZ5twfqd/wTD0tQePgpm/T84c4YmJ/VDzhlG/cN7/esWFhZSXl5u1/bcc88BcM011wCwZ88exo3Tvw5FRKSPq6mAbatg63KoKWtq94+E6Q9C/I3g6mZefWIq5wyj7bxUbqakpCRWrVrFM888w+WXX86GDRtYsmQJq1evJiQkBLCF0csuu4ySkhIWLFjAZZddxu23325y5SIiIu1ktcC3r8Pmx6A0u6nd0x/Ouw/OvRs8tZFLf+ecYbQPmD9/Pmlpafz1r3/l4YcfZuzYsbz99ttceumljcccOHAAHx8fLrnkEh555BFmzZplYsUiIiId8P1Htp2Tju9ranNxg4Sb4MIl5l3FlF7HxTAMw+wi2lJSUkJQUBDFxcUEBgba9VVVVXHs2DGGDh2Kt7e3SRV2vcrKSqKjoxkyZAhr165l9OjR3fZazvoeioiICXL2wsaH4OjH9u1nX2qbHR92thlVSQ84VV47lU4t7bRq1SqGDBmCt7c3SUlJfPXVV6c8vrq6mgcffJC4uDi8vLwYMmQIL7zwQmdeut/47rvvOPfcc7Farbi76wS2iIj0csWZ8M4vIeV8+yAaPQFufh9ueF1BVFrV4ZSzbt06kpOTSUlJISkpieXLlzNnzhwOHTpEeHjrp9yvu+46cnNzef755znzzDPJzs7WkkVt2LNnD+effz5z5sxh3rx5fPrpp/j7+5tdloiIiL2qEtjyDGxfDXVVTe3Bg2HGwzD6GnDVsuZych0Oo08//TS33XYbt9xyCwApKSm8//77vPDCCyxevNjh+A0bNvDpp59y9OhRBgwYAMCQIUNO+RrV1dVUV1c3Pi4pKelomX3enj17GrcHveuuu7j11lt54403zC5LRETExlJrW6Lpk8eh4kRTu3cQXPAbmHQ7uHuZVp70HR36p0pNTQ07d+5k5syZTU/g6srMmTPZtm1bq2Pee+89EhMTefLJJxk0aBDDhw/ngQceoLKy8qSv8/jjjxMUFNT4FRsb25EyncKzzz7LFVdcAcDPf/5zBVEREekdDAMO/BtWT4b/PtAURN084dxFcO9umHKPgqi0W4fOjObn52OxWIiIiLBrj4iI4ODBg62OOXr0KFu2bMHb25t33nmH/Px87rrrLk6cOMGLL77Y6pglS5aQnJzc+LikpKRfBlIREZFeJf1r+PAhSGtxAmrMT2DGUggZYkpZ0rd1+8wYq9WKi4sLr776KkFBtv1ln376aX7605+yevVqfHx8HMZ4eXnh5aV/UYmIiPQKBUfho0dh/3r79sFTYPZjEJNgTl3iFDoURkNDQ3FzcyM3N9euPTc3l8jIyFbHREVFMWjQoMYgCjBy5EgMwyAjI4OzzjqrE2WLiIhIt6sogM+WwVdrwFrb1D7wLJj1qG25Jm3fKaepQ/eMenp6kpCQwKZNmxrbrFYrmzZt4txzz211zHnnnUdWVhZlZU3bfx0+fBhXV1diYmI6WbaIiIh0m9oq2PosPBtvmyXfEET9wuCyv8Bd22DEZQqi0iU6vNZCcnIya9as4aWXXuLAgQP88pe/pLy8vHF2/ZIlS1i4cGHj8fPmzWPgwIHccsst7N+/n88++4zf/OY33Hrrra1eohcRERGTWK2w5w1YORE+XArVxbZ2dx/bDPl7d8HEX4Cbh7l1ilPp8D2j119/PXl5eSxdupScnBzi4+PZsGFD46Sm7Oxs0tLSGo/39/fnww8/5J577iExMZGBAwdy3XXX8dhjj3XdbyEiIiKn59hntp2Tsnc3a3SB+Bth+oMQGG1aaeLctB2o6D0UEemvqooh7zB8/hQc3mDfd8YMmPVHiBxjTm3S53R2O1DtMykiIuKMDMM2Aak4DYrSoCgditNt34vSbO1VxY7jIsbC7D/CGdN7vmbplxRGRURE+iKrFcpy6wNmWtP35qGztrz9zxc4CKb/Ac65Hlzduq9ukRYURkVERHojSx2UZjU7k9kQNut/Ls4AS03nntvV3RY+gwdDUCxEj4cJC8BDE4ul5ymMioiImKGu2hYoG4Nmuv3PJZlgWDr33O7eEBTTFDaDYyFosO1xcCwEROnsp/QaCqMmW7VqFcuWLSMnJ4dx48axYsUKJk2a1Oa4rVu3Mm3aNMaMGcPu3U0zH/ft28fSpUvZuXMnqampPPPMM9x///3d+SuIiEhrasqbXTJPbfZz/aX0spzOP7env33QbPy5PnD6hWkNUOkzFEZNtG7dOpKTk0lJSSEpKYnly5czZ84cDh06RHh4+EnHFRUVsXDhQmbMmOGwG1ZFRQXDhg3j2muv5Ve/+lV3/woiIv1XZVErZzXTmn6uLOj8c/uE2AfMxqAZa/vZJ0RhU5yGwqiJnn76aW677bbGDQNSUlJ4//33eeGFF1i8ePFJx915553MmzcPNzc31q+33yd44sSJTJw4EeCUzyEiIqdgGFCef4qZ6OlQXdL55/ePOPlZzaAY8Arout9FpJdz3jD69NO2r7ZMmADvvWffduWV8M03bY9NTrZ9dUJNTQ07d+5kyZIljW2urq7MnDmTbdu2nXTciy++yNGjR1m7dq02DhAR6WoFR2HbatsuRNWtLHvUHi6utslBjfdqNj+rWR82PbSms0gD5w2jJSWQmdn2cbGxjm15ee0bW9L5fxXn5+djsVgad65qEBERwcGDB1sdc+TIERYvXsznn3+Ou7vz/qcTEelxGTvgi7/CgX+DYT31sa4eTZODGicGNTvDGRit7TJFOsB5E01gIAwa1PZxYWGtt7VnbAd2FzhdFouFefPm8eijjzJ8+PAee10REadltcLhD+CLFZDW4oqUhx/Endvi8nn9z/4R4OpqTs0iTsh5w+hpXEJ3uGzfDUJDQ3Fzc3OYgJSbm0tkZKTD8aWlpezYsYNdu3axaNEiAKxWK4Zh4O7uzsaNG5k+XbtliIi0qbYSvv0XbFsJJ7637/OPgKQ7IOEW8B1gTn0i/YzzhtFeztPTk4SEBDZt2sTcuXMBW7jctGlTY9hsLjAwkL1799q1rV69ms2bN/Pmm28ydOjQHqlbRKTPKj8BX/8DvnoOKvLt+0LPhin3wDnXgbuXOfWJ9FMKoyZKTk7mpptuIjExkUmTJrF8+XLKy8sbZ9cvWbKEzMxMXn75ZVxdXRkzZozd+PDwcLy9ve3aa2pq2L9/f+PPmZmZ7N69G39/f84888ye++VERHqLEz/A9tWw61Woq7TvG3I+TLkXzpypS+8iJlEYNdH1119PXl4eS5cuJScnh/j4eDZs2NA4qSk7O5u0tLQOPWdWVhbjx49vfPzUU0/x1FNPMW3aND755JOuLF9EpHdL/6p+UtJ/AKOp3cUNRs+1nQmNHn/S4SLSM1wMwzDaPsxcJSUlBAUFUVxcTGCLSUNVVVUcO3aMoUOH4u2tpTI6Q++hiDgNqwUO1U9KSt9u3+fhBwk3QdKdEBJnTn0iTuxUee1UdGZURET6vtpK2P0abFsFBT/Y9/lH2iYlJd5i27lIRHoVhVEREem7yvObTUo6Yd8XNtJ2KX7sTzUpSaQXUxgVEZG+58QPtqWZdr8GdVX2fUMvaJqUpP3bRXo9hVEREek70r60TUo6+D4Ok5LGXAPnLoLoeNPKE5GOc5ow2gfmYfVaeu9EpFezWuDQf2HrXyHjK/s+T3+YcBNMvtO2O5KI9Dl9Pox6eNj2/62oqMDHx8fkavqmiooKoOm9FBHpFWoq4NuGSUlH7fv8I20BNOEW8Ak2pz4R6RJ9Poy6ubkRHBzM8ePHAfD19cVF9wi1i2EYVFRUcPz4cYKDg3FzczO7JBERKMuDr9fAV2ugssBZhyhxAAAgAElEQVS+L3yUbVLSmJ+Cu6c59YlIl+rzYRRo3Mu9IZBKxwQHBze+hyIipsn/3jYp6dvXW5mUNA3OuxfOmKFJSSJOxinCqIuLC1FRUYSHh1NbW2t2OX2Kh4eHzoiKiHkMA9K22xapP/RfHCcl/QSmLIKocaaVKCLdyynCaAM3NzcFKxGRvsBqgYP/sYXQjK/t+zz9IeFm205JwbGmlCciPcepwqiIiPRyNRWw+1XbpKTCY/Z9AdG2SUkTbtKkJJF+RGFURES6X9lx24Skr//RyqSk0fWTkn6iSUki/ZDCqIiIdJ/8I7ZL8d/+CyzV9n3DLrKF0DOma1KSSD+mMCoiIl3LMCBtW7NJSc24utdPSroHIseaU5+I9CoKoyIi0jWsFjjwni2EZu607/MMgMSbbZOSgmJMKU9EeieFUREROT015bDrVdsaoUWp9n0B0TD5l5BwE3gHmVOfiPRqCqMiItI5Zcfhq+fqJyUV2vdFjLVdih99tSYlicgpKYyKiEjH5B2q3ylpneOkpDOm20LosIs0KUlE2kVhVERE2mYYkPoFfPFXOLzBvs/VHcZeC+cugsgx5tQnIn2WwqiIiJycpQ72r7ctUp/1jX2fV2DTTklBg0wpT0T6PoVRERFxVFUCu16B7X+D4nT7vsAY26SkCQvBO9Cc+kTEaSiMiohIk+IM+DIFdr4E1SX2fZFjYcq9tklJbh7m1CciTkdhVEREIGu3bVLSvnfAWmffd9Zs2/2gQy/QpCQR6XIKoyIi/ZXVCkc22kLoj5/b97l5wbjrYfLdED7CnPpEpF9QGBUR6W9qK217xW9fDfmH7ft8B8LEX9i+/MPNqU9E+pVOhdFVq1axbNkycnJyGDduHCtWrGDSpEmtHvvJJ59w0UUXObRnZ2cTGRnZmZcXEZHOKMuzLVD/9T+gIt++b+CZcO7dMO4G8PAxpz4R6ZQ6i5Xs4ioyCitJL6wgo7CSjPrvpVV1fHDf+WaXeEodDqPr1q0jOTmZlJQUkpKSWL58OXPmzOHQoUOEh5/8X9GHDh0iMLBp1uWpjhURkS6Udxi2r4LdrzsuUh93nu1+0OEXg6urOfWJyClZrAY5JVVkFFS0Gjizi6uwWI2Tji+rrsPfq/deDO9wZU8//TS33XYbt9xyCwApKSm8//77vPDCCyxevPik48LDwwkODm7Xa1RXV1Nd3fSBWVJScoqjRUTEgWHAj1ts94O2XKTexQ1Gz7WF0EETzKlPRBpZrQbHS6vrQ2YFGQXNA2clWUWV1J0ibJ7KAD9P8kurnSeM1tTUsHPnTpYsWdLY5urqysyZM9m2bdspx8bHx1NdXc2YMWN45JFHOO+880567OOPP86jjz7akdJERATAUgv71sO2FZD9rX2fZwAk3ARJd0DwYHPqE+mHrFaD/LJq0pudzcworCC9wPY9q6iKGou1U88d7OtBTIgPMcG+xA7wISbEl5gQH2IH+DIo2Ae/XhxCG3Sowvz8fCwWCxEREXbtERERHDx4sNUxUVFRpKSkkJiYSHV1Nf/4xz+48MIL+fLLL5kwofV/kS9ZsoTk5OTGxyUlJcTGxnakVBGR/qWq2LY26Jd/h5IM+77AGJh8Z/0i9UHm1CfixAzDIL+spjFoNj+rmVFQQUZRJTV1nQubAd7uxNYHzJgQ+8AZE+JDgHffX/O32+Py2Wefzdlnn934eMqUKfzwww8888wzvPLKK62O8fLywsvLq7tLExHp+4rSYHsKfPMy1JTa90XFw5R7YNRVWqRe5DQYhkFBeU1TwCyssA+chRVU1XYubPp5uhE7wNcuYDYPnUE+zv9nt0NhNDQ0FDc3N3Jzc+3ac3NzOzQzftKkSWzZsqUjLy0iIs1l7oQvVsL+d8Gw2PcNv9gWQuPO0yL1Iu1gGAbFlbWNl82bAmfT44oaS9tP1AofDzf7y+ctznIG+Xjg0s//nHYojHp6epKQkMCmTZuYO3cuAFarlU2bNrFo0aJ2P8/u3buJiorqWKUiIv2d1WqbjLRtJaRute9z94ZxP7MtUh823Jz6RHqx4spau/s0m5/VzCispKy6ru0naYWXu2vjPZqNIbPZWc4Bfp79Pmy2pcOX6ZOTk7nppptITExk0qRJLF++nPLy8sbZ9UuWLCEzM5OXX34ZgOXLlzN06FBGjx5NVVUV//jHP9i8eTMbN27s2t9ERMRZ1VTAt6/bFqk/8b19n28oTLrNtki9X6g59Yn0Ag1hs2XIbPi5tKpzYdPT3ZWYYB8GOQRO2/dQf4XN09XhMHr99deTl5fH0qVLycnJIT4+ng0bNjROasrOziYtLa3x+JqaGn7961+TmZmJr68v55xzDh999FGrC+GLiEgzZcfhqzW2ReorC+z7QofbFqk/53otUi9OzzAMSirrHNbXbPg5s7CS0k6e2fRwc2FQsP0s9Ob3bob5e+HqqrDZnVwMw+jcwlU9qKSkhKCgIIqLi+0WzhcRcUrHD9ouxe95w3GR+iHn2+4HPXOWFqkXp9GdYdPd1YXoYJ/GgDmofgmkhtAZHuCNm8Jml+hsXuv9i0+JiPQHhgHHPrVNSvr+Q/s+V3cYfY3tTGh0vDn1iZyG7g6bgxrOZAb7Nv1cf6YzIlBhs7dTGBURMVNdDex723YmNGevfZ9XICTcbFukPijGlPJE2qO7L6M3ntkMrr+E3mx2us5s9n0KoyIiZqgsgp3/tC1SX5pl3xc02LZI/fgF4K1bk8R8CpvSnRRGRUR6UuGPtkXqd70CNWX2fdETYMoiGHkVuOnjWXpOwzqbrQXNhp87u/SRwqa0RZ92IiI9IWMHfLECDrwHRvOdWlzg7EttIXTwuVqkXrpFdZ2FnOIqMosqyS6qIru4kqziKrLqH2cWnV7YbD4bfVCwwqZ0jMKoiEh3sVrg0H9tk5LSt9v3uftA/DyYfBeEnmlOfeIULFaD46VVZBXVh8viSrIaAmf99/yymk4/f8uw2XxyUEyIL2EBXgqbcloURkVEulpNOex+zbZIfcFR+z6/cJh0OyTeCn4DzalP+oyGPdGzG85i1n/PKq4iu6iSrKJKckursVg7v0qjp5srUcHedrsGNQ+b4QFaZ1O6l8KoiEhXKc2Br56DHS9AZaF9X9gIOHcRjL0WPLzNqU96nbLqOlu4rA+a2UWVZNafzWwIntV11raf6CRcXSA8wJvoYG+ign2IDvImKsiH6GAfW1uQDwP9PBU2xVQKoyIipyt3P2xbBXvfAEuLy6FDp9UvUj9T94P2Mw33adpdPm92n2ZWcWWnt6hsMMDPk6j6gDmoPnBGBXkzKNiHqGAfwgO88HDT5gjSuymMioh0hmHA0Y9t94P+sMm+z9UdxvzUtkh91Dnm1Cfdqvl9mrZ7M5vuz2w4o3k692kC+Hm6EV0fKqODvG0/N/seFeSDj6dbF/1GIuZRGBUR6Yi6GvjuTduZ0Nzv7Pu8gyDhFtsi9YHR5tQnXaK4opb0woqm+zQbJgPVP84pqTrt+zQjg2yXz6ODfIgKbji72fRzoLc7LjqbLv2AwqiISHtUFMDOF+HL56Asx74vOM42K378fPDyN6c+OS2GYXA4t4wP9+fw4f5cvs0o7vRzNdynGRVsO4vZdJ9mw1lN3acp0pzCqIjIqRQche1/g11robbCvm9Qou1+0BGXa5H6PshiNdiZWsjGfTl8eCCX1BMVbQ/C/j7NpoDZ9D0i0Fv3aYp0gD49RURak/YlbFsBB993XKR+xGW2EBqbpElJfUxljYXPj+SxcX8umw8ep6C89fs6R0YFMi4miKj6S+iDdJ+mSLdRGBURaWC1wMH/2CYlZXxl3+fhC/E3wuRfwsAzzKlPOuVEWTWbDh7nw/25fH4kj6pax6WS3FxdSBo6gFmjIpg5MoLYAb4mVCrSPymMiohUl8HuV22L1Bf+aN/nH9G0SL3vAFPKk477Mb+cD/fn8uH+XHakFtDaXCNfTzemDQ9j9ugILjo7nGBfz54vVEQURkWkHyvJhq/+blukvqrFhJXwUfWL1P8U3L3MqU/azWo12JtZzMb6CUiHc8taPS7U34tZo8KZNSqCKWeE4u2hS+4iZlMYFZH+J+c72LYS9r4J1lr7vjOm29YHPWOG7gft5WrqrGw7eqJxBnxuSXWrx50R5sesUZHMGhXB+NhgzWIX6WUURkWkfzAM+H6TbVLS0U/s+1w9bNt0nns3RI4xpTxpn5KqWj6uv//z00N5lFY77mDk4gLjY4OZPdoWQM8I03JbIr2ZwqiIOLe6atjzhm2R+rwD9n3ewbZ7QSfdDoFR5tQnbcourmy8/3P70RPUWhxvAPV0d2XqmaHMGhXBjJHhhAd4m1CpiHSGwqiIOKeKAtjxPHy1Bspy7ftChsDku2H8jeDpZ0p5cnKGYXAot5QP9+WycX8uezNbX4A+yMeDGSNs939eMDwMPy/9lSbSF+lProg4lxM/2GbF73oV6irt+2KTbJOSRlwGrpq40pvUWazsSC1sPAOaVtD6AvSDgn2YPTqCWaMimDhkgBaXF3ECCqMi0vcZBqRtt01KOvg+0OwyrosrjLwCzr0HYieaVqI4qqip4/Mj+Wzcl8vmg7kUVtS2etzo6EBmjYpg9qhIRkYFaL92ESejMCoivZ9h2C67F6dBURoUpdu+F6c3/Vzd4lKuh59tr/jJv4QBQ82pWxzkl1Wz+cBxNu7P4fMj+VTXtb4A/eRhA5g1MoKZoyKICdEC9CLOTGFURMxnGFB2vD5cprYIm/Xhs7a8fc8VEFW/SP0t4BPSvXVLuxzLL29cfmlHaiFGKwvQ+3m6ceHZtvs/Lzo7nCBfj54vVERMoTAqIt3PaoHSnGYBs2XgTAdL62tEtsnVA4IGwYBhMPY6GPMTcNdOOmayWg32ZBazcZ8tgB453voC9GEBXswcGcHs0RGcO2ygFqAX6acURkXk9FlqoSSzlTOa9T8XZ4DVcT3IdnH3hqBYCI6t/z646SsoFgIiNRmpF6ius7DthxNs3J/LR/tzOV7a+j8uzgz3r7//M4JxMVqAXkQURkWkPeqqbYGyecBsfu9maRYYjvf+tYuHX324jG0KmM0Dp1+YdkLqpYora/nk0HE21i9AX3aSBegnDA5h9ijbDPhhWoBeRFpQGBURqKmwP5vZMnCW5XT+ub2DIGjwyQOnT4jCZh+SVWS/AH2dtfUF6M8/M5TZoyOYPiKCsAAvEyoVkb5CYVSkP6gqaf3yeUPYrMjv/HP7DnQMmI0/x9rCqPRZBeU1fJNayM60Qj4/ksd3mSWtHhfs68H0EeHMHhXJBcND8fXUXy8i0j76tBBxRscP2tbczN5tC5xVre9g0y7+kS3u14yF4Lim+zi1g5HTMAyDH/LK2ZlawM7UQnakFnI07+SrGMSE+DB7VGT9AvQhuGsBehHpBIVREWeSsxc+Wwb738Nu4feTcXGFgOhWLp/XB87AQeChPb6dVWWNhT0ZRexILWw8+1l0koXnG4wZFNgYQEdEagF6ETl9CqMiziBrF3y6DA69b9/u6m4LlC1noDeEz8BB4Kb1HPuL3JIq2xnPH23Bc19mcav3fDbwcHNhzKAgEgaHkDgkhAlxIYQH6B8nItK1FEZF+rL0r+GzJ+HIRvt2v3A4715IvFWX0fspi9XgYE4J39Rfbt+ZWkhGYeUpx4T4epAQN4CEOFv4HDsoSGt/iki3UxgV6Yt+3GoLoUc/sW8PiIap98OEheDhY0ppYo7Sqlp2pRWxsz547korpLzGcsoxZ4b7kzA4hIQhISTGhTA01E+X3UWkxymMnszTT9u+2jJhArz3nn3blVfCN9+0PTY52fbVoLQURo5sX33vvgsJCU2P//MfuPPOtsf5+8PBg/Ztv/kNvP5622Mvuwz+/nf7tsREyGnHsj9PPgnz5jU9PnQIZsxoexzA119DVFTT4+eegz/+se1xw4fD5s32bTfeCJ9+2vbY226Dhx+2b4uJaXscwNq1cOGFTY8/+QTmz2/f2IwM+8ePPgpr1jQ9tlRDdZlt3c/mzgqElL/Y9mJ3r19GZ/p0OHy47ddcuhRuv73pcXY2TJzYvno3bYKzz256/Npr8Nvftj0uMhJ27LBvu+MOeP/91o9v7oYbYNky+7YRI6Cs9V1+7KSkwOWXNz3euROuuqrtcQAHDkBAQNNjEz8jDGxnPmstVmosVmrqDOqsVs4y4CzgZ8BtP3mI7yLPbBx68Y9f86f/W42nmyse7q54urnS6nrz+ozo258RJzNtGrz6qn2bPiMcOclnxCmP6YUURk+mpAQyM9s+LjbWsS0vr31jS1oskWIY7RsHUFNj/7iysn1jm/9BaVBY2L6xBQWObTk57RtbUWH/uK6u/b+rpcXZnbKy9o0NamVJofz89o0tbmX2eXvrra52fNzesa3V0Z6xAyfCxJ/bt+Xmtm9syw9oi6X99da1WOS8oqLzv2tBQfvGFhY6tmVl2T6E21LZ4jJ1TU376225oXoPfkbU1FnZl1XMnv1p3JSZiQu2D2934GTnvyO8XYgbG8WEONtZz9FflOG+Lq/t19RnhHN+RuS3snybPiMc9dHPCLsaWo5reUwvpDB6MoGBMGhQ28eFhbXe1p6xgYH2j11c2jcOwLPF3ts+Pu0b69/K7ichIe0bO2CAY1tkZNvjAHx97R+7u7f/d3Vrcc+av3/7xkZEOLaFhrZvbGt/SbW3Xi8vx8ftHducYUDtcQj2tG232ZyrO3gFNF2KDwt3HB8R0fpfmC21/H/Cza399bq3+Ajx9W3f2Nb+vxkwoH1jQ0Ic26Kj23fWw6dFdPP0bP/v2vLydTd+RlgNqLFY+SKripSUbXybUUR1nRW/6gpm+w9spTbwcHXFw93FdubTzZV//GIKLokTmo7x89NnREt9/TOioY72jA0NdWzTZ4SjPvIZYfcaLWtoOa7lMb2Qi2G0jPK9T0lJCUFBQRQXFxPYB95UkdNitcKB9+CzpyB3r31f2Ei44AEYfbX2Y3cSHV3bE8Dfy53xg4NJrJ9sFD84GH8vnVsQEXN1Nq916tNr1apVLFu2jJycHMaNG8eKFSuYNGlSm+O2bt3KtGnTGDNmDLt37+7MS4s4L6sF9r1jC6F5B+z7IsbCtN/AiCvAVQuL92WdWdszdoAPiXEDGi+5D48IwK3VGz5FRPqeDofRdevWkZycTEpKCklJSSxfvpw5c+Zw6NAhwsNbuVRYr6ioiIULFzJjxgxyc3NPq2gRp2Kpg73/C58/BSe+t++LngDTfgvDL9b+7X1UZ9b2HB0dRGJcCAn1X+GBWttTRJxXhy/TJyUlMXHiRFauXAmA1WolNjaWe+65h8WLF5903M9+9jPOOuss3NzcWL9+fYfOjOoyvTiluhr49nXY8jQU/mjfF5sEF/wWzpyhENqHWKwGh3JK2Zla0MG1PUMa1/c8J0Zre4pI39Qjl+lramrYuXMnS5YsaWxzdXVl5syZbNu27aTjXnzxRY4ePcratWt57LHH2nyd6upqqpvNNizpAzPBRNqtrhp2vQJblkNxun1f3FTbmdChFyiE9gGlVbXsTi9ix4+FfJNWyK60Isqq6045pvnanglxIQzT2p4i0s91KIzm5+djsViIaDEDMSIigoMt16Wrd+TIERYvXsznn3+Oe8tZdSfx+OOP8+ijj3akNJHer7YSdr4EW5dDabZ937CLbCE0boo5tUmbDMMgo7CyfpJRATtTiziUU8Iprrjj7eHKuJjgxh2NxseGEOLnefIBIiL9ULdOv7RYLMybN49HH32U4cOHt3vckiVLSG62QGtJSQmxra3DJdIXVJfBjhfgixVQfty+76zZtsvxse1cQFp6TMPang07Gu1MLeR4afUpx4QHeJE4xHbJPTEuhJFRgXi6a8KZiMipdCiMhoaG4ubm5jABKTc3l8hW1gQrLS1lx44d7Nq1i0WLFgG2e0wNw8Dd3Z2NGzcyffp0h3FeXl54tVyHTaSvqSqBr9fAFyuhssVi4GdfZpsdHz3enNrEQWF5jS10phWy88fCxrU9T8bVBUZEBjae9ZwwOISYEB9dchcR6aAOhVFPT08SEhLYtGkTc+fOBWzhctOmTY1hs7nAwED27rVfJ3H16tVs3ryZN998k6FDh55G6SK9VGUhfPl32P43qCpq1uECo66CC34DkWNMK09Ob23PhLgQEuMGMC42iABvjx6qWETEeXX4Mn1ycjI33XQTiYmJTJo0ieXLl1NeXs4tt9wC2C6xZ2Zm8vLLL+Pq6sqYMfZ/6YaHh+Pt7e3QLtLnVRTAtlXw1XNQ3WzSnYsrjPkJnP8AhI8wr75+rKrWwrfpWttTRKQ36nAYvf7668nLy2Pp0qXk5OQQHx/Phg0bGic1ZWdnk5aW1uWFivRaZXmwbQV89Q+obXZ2zcUNxv0MpiZD6Jnm1dcPHS+palxaaUeq1vYUEenNtB2oSGeVZMMXf4UdL0Jds7UkXT0gfh5M/RUM0K0oPSGzqJLNB3Ibw2d71/acUH/JXWt7ioicvh7dDlSkXyvOsK0R+s3LYGk2u9rNEyYshPPuh2Ct/tDdrFaDT4/k8er2VDYfPH7KJZbOCPNr3Mc9YYjW9hQR6U0URkXaq/BH+Pxp2P0aWJvdb+juDYm3wpR7ITDKtPL6ixNl1byxI4PXvkolvcDxDKiXuyvjYoMbL7lPGKy1PUVEejOFUZG2nPgBPv8LfPsvMCxN7R5+MPHnMOUe8A83r75+wDAMdqQWsnZ7Kh/szaHGYr/kUlSQN9dPjOXCs8MZpbU9RUT6FIVRkZPJOwSfPQXfvQlGs/DjGQBJd8Dku8BvoHn19QOlVbWs35XJ2u1pHMotdei/YHgY85MGM31EOO5uCqAiIn2RwqhISznfwWfLYP+7QLMbEb2DbAE06Q7wCTGtvP5gf1YJa79M5d1dmZTXWOz6Qnw9uC4xlnlJg4kb6GdShSIi0lUURkUaZO22hdCD/7Fv9xkA594Nk24Hb63m0F2qai188F02a7ensTO10KE/IS6E+ZMHc8mYKM18FxFxIgqjIulfw2dPwpGN9u1+YbZJSYm3gpe/ObX1A6knynntyzTe2JFOYYuF6P083Zg7fhA3JsUxKlr/EBARcUYKo9J/pX4Bnz4JRz+2bw+IgvPugwk3gaevObU5uTqLlc0Hj7P2yzQ+O5zn0D8iMoAbJ8cxNz5aW26KiDg5hVHpXwwDjn1mC6GpW+z7gmJh6v0QPx88tPtOdzheUsW/vk7n9a/SyC6usuvzdHPlkrGRLJgcR0JciNYBFRHpJxRGpf/I/AY2LIH07fbtIUNsW3aOuwHctR5lVzMMg20/nGDtl6ls3JfrsC1n7AAf5k2K47rEGAb6e5lUpYiImEVhVJxfXY1tYtLnf7FfJ3TgmXD+AzD2WnDTH4WuVlxRy5vfZPDql6kczSu363N1gekjwrlxchzTzgrD1VVnQUVE+iv9DSzOLXcfvHMH5Oxtags9G6b9FkZfDa6ald3Vvk0vYu32VP69J4uqWvvF6UP9vfjZxFhuSBrMoGAfkyoUEZHeRGFUnJOlDr54Fj5+vGnrTld3uOC3cH4yuGlSTFeqrLHw3re2xen3ZhY79E8eNoD5k+OYPSpSuyOJiIgdhVFxPnmHYf2dkLmzqS1sJFydAtHx5tXlhL4/Xsra7Wm89U0GpVV1dn0B3u78ZEIM8ycP5szwAJMqFBGR3k5hVJyH1Qpf/g02/RHq6mdqu7jalmm6cAm4a3JMV6ips7Jxfw5rt6ey/WiBQ//YQUHMnzyYK8ZF4+upjxgRETk1/U0hzqHgGLx7N6RubWobeCbMTYHYiebV5UQyiyp5/cs0/vV1Ovll1XZ9Xu6uXDkumvmT4xgXG2xShSIi0hcpjErfZhiw4wXY+BDUNpuxnfRLmLFUi9afJqvV4NMjeby6PZXNB4/TYlUmhoX5cWNSHD+dEEOQr+7DFRGRjlMYlb6rOAPeuwd+2NzUFjwYrloNQ883ry4ncKKsmjd2ZPDaV6mkF1Ta9bm7ujB7dATzk+I494yBWpxeREROi8Ko9D2GAd/+Cz74HVQ3m7mdcDPMfgy8NFmmMwzDYEdqIWu3p/LB3hxqLPbLMkUFeXPDpMH8bGIs4YHaoUpERLqGwqj0LaW58J/74dB/m9oCouHKFXDWTPPq6sNKq2pZvyuTV79M42BOqUP/BcPDmJ80mOkjwnF307JMIiLStRRGpe/Y9w78Jxkqm83gPudncMkT4BNiXl191P6sEtZ+mcq7uzIpr7HY9YX4enBdYizzkgYTN9DPpApFRKQ/UBiV3q+iAN7/Nex7u6nNLwwuXw4jLzevrj6oqtbCB99ls3Z7GjtTCx36E+JCmD95MJeMicLbQ7tTiYhI91MYld7t0Afw3r1QfrypbeSVcPkz4BdqXl19TOqJcl77Mo03dqRTWFFr1+fn6cbc8YO4MSmOUdGBJlUoIiL9lcKo9E5VxbBhCex+tanNOxgu+wuM+QloBneb6ixWNh88ztov0/jscJ5D/4jIAG6cHMfc+GgCvLUsk4iImENhVHqfHzbDu4ugJLOp7aw5cMWzEBhlXl19xKGcUt7elcG7u7LIKamy6/N0c+WSsZEsmBxHQlyIlmUSERHTKYxK71FdBh8uhR3PN7V5BtgmKMXfqLOhp3C8pIp3d2fx9q5MDmSXOPTHDvBh3qQ4rkuMYaC/tkUVEZHeQ2FUeocft8K7d0Hhj01tQ6fBVSttC9mLg4qaOv5vXw5vf5PJ1u/zHXZHcnd14cKzw7lx8mCmnRWGq6vCvIiI9D4Ko2Ku2krY/BhsWwXUpykPX5j1R0j8ObhqXcvmLFaDL37I551vMtmwL4eKFksyAcTHBnPNhEFcNjZKZ0FFRKTXUxgV82TshPV3Qv7hprbYyTB3NQw8w7y6eqH9WSW8syuDd3dncby02qE/doAPV8cPYu74QQwL8zehQhERkc5RGJWeV1cDn/4PbHkajPotJ3UN6dwAACAASURBVN28YMZDMPkucNX6lgA5xVW8uzuTd3ZltrozUqC3O5edE801EwaRqMlIIiLSRymMSs/K2Qvv3Am53zW1RY+HuSkQPsK8unqJsuo6/u+7HN7ZlcnWH/IxWtwH6uHmwkVnh3P1+EFcNCJcC9OLiEifpzAqPcNSB1ufgU/+B6z1i667usO0xTD1fnDrv+tc1lmsbPk+n3d2ZbJxXy6VtY73gU4YHMzVE2K4fGwUIX6eJlQpIiLSPRRGpfvlHbKdDc36pqktfDRcnQJR55hXl4kMw2BfVgnv7MrkvW+zyGvlPtC4gb7MjR/E1eMHMSRU+8OLiIhzUhiV7mO1wPbVsOn/gaU+bLm4wtRfwbTfgXv/m+mdXVzJ+l1ZvLMrg8O5ZQ79QT4eXH5OFNdMGMSEwboPVEREnJ/CqHSPgqOw/i5I29bUNvAs29nQmETz6jJBaVUtH3yXw/pdmWw7esLhPlBPN1emjwjn6gmDuPDsMLzcdR+oiIj0Hwqj0rWsVtsOSh8uhdqK+kYX2yz5GQ+Bh4+p5fWUOouVz4/k8/auTD7cn0NVrdXhmMS4EK6uXw802Ff3gYqISP+kMCpdpygd3lsERz9paguOg7l/gyHnmVZWTzEMg+8yS3h7Vwb//jaL/LIah2OGDPTl6vExXD1+EIMH+ppQpYiISO+iMCqnzzBg96uwYQlUN9sXPfFWmPX/wMu5F2HPLKpk/S7beqDfH3e8DzTE14MrxkUzd/wgxscG6z5QERGRZhRG5fSU5sC/74PDG5raAgfBlSvgzBnm1dXNSqpq+WBvNm9/k8mXxwoc+j3dXZk5Mpyrx8cwbXgYnu7a1lRERKQ1CqPSOYYB370F/30AKgub2sfNg4sfB59g82rrJrUWK58dzuPtXZl8tD+X6jrH+0AnDRnA1RMGcenYKIJ8+u/aqSIiIu3VqTC6atUqli1bRk5ODuPGjWPFihVMmjSp1WO3bNnC7373Ow4ePEhFRQVxcXHccccd/OpXvzqtwsVE5Sfg/WTYv76pzS8crngWRlxqXl3dwDAMvs0o5p1vMvj3nmwKyh3vAx0W6sfV4237wscO0H2gIiIiHdHhMLpu3TqSk5NJSUkhKSmJ5cuXM2fOHA4dOkR4eLjD8X5+fixatIhzzjkHPz8/tmzZwh133IGfnx+33357l/wS0oMO/Af+cz+U5zW1jb4aLv0L+A00r64ull5QYbsPdHcmR/PKHfoH+HlyZf19oONignQfqIiISCe5GEbLVQ9PLSkpiYkT/3979x4dRZmve/zp3ENIGjCQAAmEi4ByCfeQeAsQBDajMLgVHLdERlzqoDMMs7fCOjOgZ/Y5jHscR+fIVmdGQFQQFAVH3CBELg6iSAIKCBEwAkIuoJJOAuTS/Z4/Ih0CSUhD0tXd+X7W6rUqlbeKXxUv7WNVvW8N0/PPPy9JcrlcSkxM1KOPPqo5c+Y0ah+TJ09WVFSUXn311Ua1dzgcstvtKi4uVkxMjCfloqmcPS39z+PSF2/UrItsK034k9TvDuvqakLFZyv1/p58vZNzXDu+qfs50DHXx2nyoM66uVd7hQbzHCgAAOddaV7z6MpoRUWFsrOzNXfuXPe6oKAgZWRkaPv27Q1sWWPXrl36+OOP9Z//+Z/1tikvL1d5ec3rER0OR71t4QWHNkprHpVKTtSs6zW++rZ8dJx1dTWBiiqXNucWafXu49q4v0gVdTwHmtKtnSYP7qzx/TsqJoLnQAEAaEoehdFTp07J6XQqLq52AImLi9OBAwca3DYhIUEnT55UVVWVnnjiCc2YMaPetgsWLNCTTz7pSWloDuUl0ge/lbKX1KwLj5HGPyUl3y356a1pY4x2HTutd3KO670vTuiHM5WXtOnRPkqTBydo4sBOSmjLc6AAADQXr42m/+ijj1RaWqpPPvlEc+bMUc+ePXX33XfX2Xbu3LmaPXu2+2eHw6HExERvlQpJ+uaf0uqHpdNHa9Z1HylNfF6yJ1hX1xUwxqjAcU4HCkq0++hpvfv5CeWduvQ50NjWYbotuZMmD0pQv84xPAcKAIAXeBRGY2NjFRwcrMLCwlrrCwsLFR8f3+C23bp1kyT1799fhYWFeuKJJ+oNo+Hh4QoPD/ekNDSVijNS1v+WPn2hZl1olHTr76snsffxgFZ8tlJfFZboQEGJcgsc+qqgVAcKHHKcq6qzfXhIkG7tG6/JgzrrxmtjeQ4UAAAv8yiMhoWFaciQIcrKytKkSZMkVQ9gysrK0iOPPNLo/bhcrlrPhMJHHPtMWv2Q9N2hmnVd0qRJC6V23a2rqw7lVU4dLipTbqFDuQWlyi1wKLegRCeKz112W5tNGtHtGv10cGeN7xevaJ4DBQDAMh7fpp89e7YyMzM1dOhQDR8+XM8++6zKyso0ffp0SdW32I8fP66lS5dKqp6TtEuXLurTp48kaevWrXr66af1y1/+sgkPA1elqlzavEDa9pxkfhzAExwuZcyXUh6Wgqy7WuhyGX37w1kdKHBccMWzRHmnylTlatxEEPExEeodH60+8dHqHR+tEd2vUac2kc1cOQAAaAyPw+iUKVN08uRJzZs3TwUFBRo4cKDWrVvnHtSUn5+vo0drnjN0uVyaO3eu8vLyFBISoh49euipp57Sgw8+2HRHgStXuE9aNUMq+rJmXech0qQXpfa9vFrKd6Xlyi0oUW5hdeA8UFCig4UlKqtwNmr76PAQ9f4xcFYHzxj1jouWvRVXPgEA8FUezzNqBeYZbSYVZ6S/DJRKf3wGOChUSp8j3TBLCm6+sW1nK5w6WFRzlfN88DxV2rhHN0KDberRvrU7cPaJj1av+Gh1skcw6AgAAIt4ZZ5RBJh979QE0fbXSXf8TYrv32S7r3K6dOT7M+6wef65ziPfn1Fj/xcosV2kesfFuG+x946PVrfYKAYaAQAQIAijLdnORTXLt/+/Kw6ixhgVlZS7A+f5K54Hi0rrnES+Lu2iwtQ7ruYWe6/4aPWKi1brcLooAACBjP/St1T5n0vHd1Yvx/WTEoY2arOSc5W1BhIdKCjRV4UlOl3HxPF1iQgNUq+4aHfwPP9p3zqcW+wAALRAhNGWaufimuWh0y+ZP7SiyqWvT5VecIu9+nP89NlG7T7IJiXFRlVf5YyrGVDUpV0rBQcROgEAQDXCaEtUXiLteVOSZEKjdCLxNu3/slC5P17x/KqgRIdPljZ66qS4mPAfR663dg8o6tmhtSJCg5vzKAAAQAAgjLZEe96UKkolSf+MHKl7n93ZqM1a/zh1Us2Vzurb7W2jwpqzWgAAEMAIoy2NMdJnNQOX/nAy7ZIm56dO6hUXXWuy+M5tInmuEwAANCnCaEtzPFsq3CNJ+ibiOu07lyRJumNwgm7uFas+8THqFhulsBCmTgIAAM2PMNrSXDCd04ulN0mSrokK0/+d3E/hITzjCQAAvIvLXy3J2R+kvaskSeeCW2tN1QhJ0t3DuxBEAQCAJQijLcnnK6Sqc5Kk1eZmnVWEgoNsumdEF4sLAwAALRVhtKUwptYt+pfPpkuSxvaNU0d7pEVFAQCAlo4w2lIc+Vg6lStJ2hfaVwdNgiQpMzXJwqIAAEBLRxhtKS64KvrXslskSX3iozW8WzurKgIAACCMtghlp6Qv11QvBtu1zjVckpSZlsS8oQAAwFKE0ZZg9+uSq1KStLzyJpUrTDERIZo4sJPFhQEAgJaOMBroXC5p52L3j69VjpQkTRmWqFZhTDMLAACsRRgNdHmbpR/yJEk7bAP0jekom026d0SSpWUBAABIhNHAd8HApUXloyRJo3p3UJdrWllVEQAAgBthNJA58qUD70uSfghqp42uwZKkaWlJFhYFAABQgzAayHa9KhmnJOm1iptVpRB1j43STT1jLS4MAACgGmE0ULmcUvYr1Yuy6Y2q6oFL01K7KiiI6ZwAAIBvIIwGqoMbJMe3kqStZpCOq72iwoJ1x5AEiwsDAACoQRgNVBcMXFpaWT1w6Y4hCYqOCLWqIgAAgEsQRgPR6aPSwQ8kSYW2WG12DZRUfYseAADAlxBGA1H2K5KMJOm1inS5FKQbe8aqZ4doa+sCAAC4CGE00Dgrq0fRS3IqSCucNQOXAAAAfA1hNNDkvi+VFkqSPnAOUZHaqnObSI2+Ls7iwgAAAC5FGA00Fwxcet2ZIUm6N7WrgpnOCQAA+CDCaCD57rD09WZJ0lETp22uvgoPCdKUoYnW1gUAAFAPwmggyV7sXnytapSMgjRpYGe1jQqzsCgAAID6EUYDReU5adfrkqQKhegt5y2SpGlpDFwCAAC+izAaKPb/Qzr7vSTpf5zD9b1iNCyprfp2sltcGAAAQP0Io4HiwoFLVaMlSdNSkywqBgAAoHEIo4GgaL909GNJ0kFXZ+0wfdQhOlzj+sVbXBgAAEDDCKOBYGfNwKXXnaMl2XRPSleFBvPXCwAAfBtpxd9VnJE+f0OSdE6hett5o0KDbbo7hemcAACA7yOM+rt9b0vlxZKkf1SlyqHWmtC/ozpER1hcGAAAwOURRv1dHW9cmpaWZFExAAAAniGM+rMTu6Xj2ZKkfa6u2m16aECCXYMS21hcGAAAQONcURhduHChkpKSFBERoZSUFO3YsaPetm+//bbGjBmj9u3bKyYmRqmpqVq/fv0VF4wLZF84cClDkk3TUpNks/EeegAA4B88DqMrVqzQ7NmzNX/+fOXk5Cg5OVljx45VUVFRne23bt2qMWPG6P3331d2drZGjhyp2267Tbt27brq4lu0cw7pizclSaUmQmucaWoXFaafDOhocWEAAACNZzPGGE82SElJ0bBhw/T8889LklwulxITE/Xoo49qzpw5jdpH3759NWXKFM2bN69R7R0Oh+x2u4qLixUTE+NJuYHrs79La38jqXqS+/9Vdb9+kd5Dj43rY3FhAACgJbrSvObRldGKigplZ2crIyOjZgdBQcrIyND27dsbtQ+Xy6WSkhK1a9eu3jbl5eVyOBy1PriAMdLOJe4flzlHK8gm/dsI3kMPAAD8i0dh9NSpU3I6nYqLi6u1Pi4uTgUFBY3ax9NPP63S0lLddddd9bZZsGCB7Ha7+5OYyJyZtXy7UyrcI0na5eqpfSZJt14fr05tIi0uDAAAwDNeHU2/bNkyPfnkk1q5cqU6dOhQb7u5c+equLjY/Tl27JgXq/QDtaZzqn4PfSbTOQEAAD8U4knj2NhYBQcHq7CwsNb6wsJCxcc3/B70N954QzNmzNCbb75Z6zZ/XcLDwxUeHu5JaS3Hme+rJ7qXVGxa6T3nCPWOi9aI7vU/9gAAAOCrPLoyGhYWpiFDhigrK8u9zuVyKSsrS6mpqfVut3z5ck2fPl3Lly/XhAkTrrxaVL/6s+qcJGmV82adU7impXVlOicAAOCXPLoyKkmzZ89WZmamhg4dquHDh+vZZ59VWVmZpk+fLqn6Fvvx48e1dOlSSdW35jMzM/Xcc88pJSXF/WxpZGSk7HZ7Ex5KC2DMJbfooyNC9NNBnS0sCgAA4Mp5HEanTJmikydPat68eSooKNDAgQO1bt0696Cm/Px8HT161N3+r3/9q6qqqjRz5kzNnDnTvT4zM1NLliy5+iNoSY5sk747KEn61NVHh01n3T80Ua3CPP5rBAAA8AkezzNqBeYZ/dFbP5f2rpIk/bLiEf3DpGnTb9KVFBtlcWEAAKCl88o8o7BQ6Unpy3clSd+ZaK1zDVN6r/YEUQAA4NcIo/5i92uSq1KS9KYzXRUKZTonAADg9wij/sDlkrKXuH9c5hylbrFRuvna9tbVBAAA0AQIo/7g603SD99IkrY6++uoidO9I7oqKIjpnAAAgH8jjPqDi6ZzahUWrH8dmmBhQQAAAE2DMOrrHCek3P+RJBWaNspyDdbkwZ0VExFqcWEAAABXjzDq63JelYxTkvSGc6SqFKLM1CRrawIAAGgihFFf5qyScl6pXjQ2ragaqbQe1+jauGiLCwMAAGgahFFfdvADyXFckvSha5BOKJbpnAAAQEAhjPqy7MXuxWXO0ercJlKj+3SwsCAAAICmRRj1VT8ckQ5ukCR9a2K1xZWsfxvRVSHB/JUBAIDAQbLxVTmvSDKSpOVVoxQaEqKpwxKtrQkAAKCJEUZ9UVVF9Sh6SZUmWCudt+j25E5qGxVmcWEAAABNizDqi3LXSmVFkqQPXEN0Um0ZuAQAAAISYdQX7aw9cGlI17bq19luYUEAAADNgzDqa04dkvK2SJLyXHH62NWXq6IAACBgEUZ9zUXTOcVGR2pc33gLCwIAAGg+hFFfUnlO2v26JKnchOgt5826J6WLwkL4awIAAIGJlONLvlwjnf1BkvS+K0WlwXb9LKWLxUUBAAA0H8KoL9m5yL34etVoje/XUR2iIywsCAAAoHmFWF0AflT4pXTsE0nSV67O2ml6axUDlwAAQIDjyqivuGDg0uvODPXrbNfgLm0sLAgAAKD5EUZ9QUWZ9PkbkqSzJkzvOG9UZmqSbDabxYUBAAA0L8KoL9i7Sip3SJLedaYpuFUb3ZbcyeKiAAAAmh9h1BdcOHDJOVpTh3dRRGiwhQUBAAB4B2HUaid2VX8k7XElaa+66x6mcwIAAC0EYdRqF72Hfsz18Upo28rCggAAALyHMGqlc8XSnrckSSUmUu8603gPPQAAaFEIo1b6YqVUWSZJWu28QZ3j2iu1+zUWFwUAAOA9hFGrGHPJLfppTOcEAABaGMKoVY7tkIr2SZKyXdfq2/Ae+umgzhYXBQAA4F2EUatc+MalqtG6c0iiosJ5OysAAGhZSD9WOPO9zN63ZZN02kRprWuE1qV2tboqAAAAr+PKqBU+Xy6bs1yStMp5s1J7d1a32CiLiwIAAPA+wqi3GVPrjUvLnKOUmZpkXT0AAAAWIox62zcfSd8dkiRtd14vZ7trdUuv9hYXBQAAYA3CqLdd9B76e1OTFBTEdE4AAKBlIox6U2mRzP73JEmnTIy2Bo/Qvw5JsLgoAAAA6xBGvWnXa7K5KiVJbzpv0W2Du8oeGWpxUQAAANYhjHqLyyWTfeEbl0ZpGgOXAABAC3dFYXThwoVKSkpSRESEUlJStGPHjnrb5ufn62c/+5l69eqloKAgzZo164qL9WuHP5Tt9FFJ0hbnACV0u16946MtLgoAAMBaHofRFStWaPbs2Zo/f75ycnKUnJyssWPHqqioqM725eXlat++vX77298qOTn5qgv2WxcNXMpMY5J7AAAAj8PoM888owceeEDTp0/X9ddfrxdffFGtWrXSokWL6myflJSk5557TtOmTZPdbr/qgv1S8XGZr9ZJkgpMW+1vnaaM6+IsLgoAAMB6HoXRiooKZWdnKyMjo2YHQUHKyMjQ9u3bm6yo8vJyORyOWh+/tutV2YxTkrTCOVJ3p3VXSDCP6wIAAHiUiE6dOiWn06m4uNpX9eLi4lRQUNBkRS1YsEB2u939SUxMbLJ9e52zSq7sJdWLxqZVGqWpw7pYWxMAAICP8MnLc3PnzlVxcbH7c+zYMatLunIH1yuoJF+S9KFrsIYnD1C7qDCLiwIAAPANIZ40jo2NVXBwsAoLC2utLywsVHx8fJMVFR4ervDw8Cbbn5XMzkU6/36l152j9RumcwIAAHDz6MpoWFiYhgwZoqysLPc6l8ulrKwspaamNnlxfu+Hb6RD1efqmKu9SjvfpP4JLXQQFwAAQB08ujIqSbNnz1ZmZqaGDh2q4cOH69lnn1VZWZmmT58uqfoW+/Hjx7V06VL3Nrt375YklZaW6uTJk9q9e7fCwsJ0/fXXN9Fh+KjsV2STkSQtd47SvTf0sLggAAAA3+JxGJ0yZYpOnjypefPmqaCgQAMHDtS6devcg5ry8/N19OjRWtsMGjTIvZydna1ly5apa9eu+uabb66uel9WVSFnzlIFS6o0wcqKGKNZ/TpaXRUAAIBPsRljjNVFXI7D4ZDdbldxcbFiYmKsLqdx9r4tvVV9tfg9Z4q+uvl5zR7Ty+KiAAAAmseV5jWfHE0fCJyf1bwE4A1Xhu5JYTonAACAixFGm8Opgwo+8pEk6bCro9r2zVBcTITFRQEAAPgewmhz+HGSe0la5hylzLQky0oBAADwZYTRplZ5VlU5r0mSyk2o9rWfoCFd21pcFAAAgG8ijDa1L9copPy0JGmtK0WTbxggm812mY0AAABaJsJoE6v89O/u5XdDxur2gZ0srAYAAMC3EUabUsFehZ74TJJ0wJWo3sMyFBEabHFRAAAAvosw2oScO2umc1ruHK17eQ89AABAgwijTaW8VK7db0iSzphwnb72p0po28riogAAAHwbYbSp7F2l0KoySdK7zlTddWM/iwsCAADwfYTRJnJ2+9/cy1vttymtxzUWVgMAAOAfCKNN4XiOIk/tkSR94eqm1BszmM4JAACgEQijTaD8k5rpnFbZbtXkwQkWVgMAAOA/CKNX61yxgvatkiQ5TKTCB96pqPAQi4sCAADwD4TRq+T6fIVCXeckSe84b9TUG6+zuCIAAAD/QRi9Gsao7OOagUu5CXeqe/vWFhYEAADgXwijV+PYp4ou/kqStNPVSxnp6dbWAwAA4GcIo1fB8c+X3MvrIsYrvVcHC6sBAADwP4TRK3Xme0UefE+S9INprc5pUxUUxHROAAAAniCMXqFzO19VqKmQJK02t2jy8GstrggAAMD/EEavhDG15hb9vs89srcKtbAgAAAA/0QYvQKur7fIfuaoJOlj5/WaMOomiysCAADwT4TRK/Ddlhfdy59eM0l94mMsrAYAAMB/EUY9VVKotkc/kCSdNDG6buRUiwsCAADwX4RRD53+eLFC5JQkvR+SoYx+iRZXBAAA4L8Io55wOaXsJdWLxibbkPsUEswpBAAAuFIkKQ+U525Qm4p8SdJHJlkTbh5hcUUAAAD+jTDqgZObXnAvH+p6p65pHW5hNQAAAP6PMNpI5vQxdSzaKknKN+00bAwDlwAAAK4WYbSRjn/4koLlkiRtjhqvAV1iLa4IAADA/xFGG8NZpdb7lkuSqkyQ2t44w+KCAAAAAgNhtBG+3/2u2jhPSZI+ChqqkcOTLa4IAAAgMBBGG6H4o5fcy9/3uUfhIcEWVgMAABA4CKOXUX7ysLqd/kSSdNR00I3j7rK4IgAAgMBBGL2MI+sXupdz2k9UnL2VhdUAAAAEFsJoQ6oq1OHwW5KkChOsrqMfsLggAACAwEIYbcA321aojSmWJG0PS9PAPr0srggAACCwEEYbUPXp393LziHTZbPZLKwGAAAg8BBG6/HDkb3qeWa3JClPnZQ6cqLFFQEAAAQewmg9jnzwvHv5cJc7FRkeYmE1AAAAgemKwujChQuVlJSkiIgIpaSkaMeOHQ2237x5swYPHqzw8HD17NlTS5YsuZI/1msqz5Wp+/F3JUnlJlTXjXvQ4ooAAAACk8dhdMWKFZo9e7bmz5+vnJwcJScna+zYsSoqKqqzfV5eniZMmKCRI0dq9+7dmjVrlmbMmKH169dfdfHN5cuNSxWjMklSdnS6OnfqbHFFAAAAgclmjDGebJCSkqJhw4bp+eerb2O7XC4lJibq0Ucf1Zw5cy5p//jjj2vt2rXau3eve93UqVN1+vRprVu3rlF/psPhkN1uV3FxsWJiYjwp94rk/p8R6l25X5L0+a1vKjnt1mb/MwEAAPzZleY1j66MVlRUKDs7WxkZGTU7CApSRkaGtm/fXuc227dvr9VeksaOHVtve0kqLy+Xw+Go9fGWr/d+4g6ih4OSNGBExmW2AAAAwJXyKIyeOnVKTqdTcXFxtdbHxcWpoKCgzm0KCgrqbO9wOHT27Nk6t1mwYIHsdrv7k5iY6EmZV6Vo0wvu5VO9fyZbEGO8AAAAmotPJq25c+equLjY/Tl27JjX/uzuk36nTxLu1zFbJ/UdzxuXAAAAmpNH8xXFxsYqODhYhYWFtdYXFhYqPj6+zm3i4+PrbB8TE6PIyMg6twkPD1d4eLgnpTWZDok91WHGMzKup7kqCgAA0Mw8SlthYWEaMmSIsrKy3OtcLpeysrKUmppa5zapqam12kvShg0b6m3vKwiiAAAAzc/jxDV79mz97W9/0yuvvKL9+/fr4YcfVllZmaZPny6p+hb7tGnT3O0feughff3113rsscd04MAB/fd//7dWrlypX//61013FAAAAPBLHr9WaMqUKTp58qTmzZungoICDRw4UOvWrXMPUsrPz9fRo0fd7bt166a1a9fq17/+tZ577jklJCTo73//u8aOHdt0RwEAAAC/5PE8o1bw9jyjAAAA8IxX5hkFAAAAmhJhFAAAAJYhjAIAAMAyhFEAAABYhjAKAAAAyxBGAQAAYBnCKAAAACxDGAUAAIBlCKMAAACwDGEUAAAAlvH43fRWOP/GUofDYXElAAAAqMv5nObpm+b9IoyWlJRIkhITEy2uBAAAAA0pKSmR3W5vdHub8TS+WsDlcunEiROKjo6WzWazuhyf5HA4lJiYqGPHjikmJsbqcnwW56lxOE+Nw3lqHM5T43CeGo9z1TjePk/GGJWUlKhTp04KCmr8k6B+cWU0KChICQkJVpfhF2JiYviH2Qicp8bhPDUO56lxOE+Nw3lqPM5V43jzPHlyRfQ8BjABAADAMoRRAAAAWCb4iSeeeMLqItA0goODlZ6erpAQv3j6wjKcp8bhPDUO56lxOE+Nw3lqPM5V4/jDefKLAUwAAAAITNymBwAAgGUIowAAALAMYRQAAACWIYwCAADAMoRRH7dgwQINGzZM0dHR6tChgyZNmqTc3NwGt9m8ebNsNtsln4KCAi9VbY0nnnjikmPu06dPg9ts3rxZgwcPVnh4uHr27KklS5Z4p1gLJSUl1dk/Zs6cWWf7ltKftm7dqttuu02dOnWSzWbT6tWra/3eGKN58+apY8eOioyMVEZGhg4ePHjZ/b755pvq06ePIiIi1L9/yP8FUwAACgtJREFUf73//vvNdQhe0dB5qqys1OOPP67+/fsrKipKnTp10rRp03TixIkG97lkyZJL+ldERERzH0qzulx/uu+++y455nHjxl12v4HWn6TLn6u6vn9sNpv++Mc/1rvPQOtTjckC/vwdRRj1cVu2bNHMmTP1ySefaMOGDaqsrNStt96qsrKyy26bm5ur/Px896dDhw5eqNhaffv2rXXM//znP+ttm5eXpwkTJmjkyJHavXu3Zs2apRkzZmj9+vVerNj7Pvvss1rnaMOGDZKkO++8s8HtAr0/lZWVKTk5WQsXLqzz9//1X/+lv/zlL3rxxRf16aefKioqSmPHjtW5c+fq3efHH3+su+++W/fff7927dqlSZMmadKkSdq7d29zHUaza+g8nTlzRjk5Ofrd736nnJwcvf3228rNzdXtt99+2f3GxMTU6l9HjhxpjvK95nL9SZLGjRtX65iXL1/e4D4DsT9Jlz9XF56j/Px8LVq0SDabTXfccUeD+w2kPtWYLODX31EGfqWoqMhIMlu2bKm3zaZNm4wk88MPP3ixMuvNnz/fJCcnN7r9Y489Zvr27Vtr3ZQpU8zYsWObujSf9qtf/cr06NHDuFyuOn/fEvuTJPPOO++4f3a5XCY+Pt788Y9/dK87ffq0CQ8PN8uXL693P3fddZeZMGFCrXUpKSnmwQcfbPqiLXDxearLjh07jCRz5MiRetssXrzY2O32pi7PZ9R1njIzM83EiRM92k+g9ydjGtenJk6caEaNGtVgm0DvUxdnAX//juLKqJ8pLi6WJLVr1+6ybQcOHKiOHTtqzJgx2rZtW3OX5hMOHjyoTp06qXv37rrnnnt09OjRettu375dGRkZtdaNHTtW27dvb+4yfUZFRYVee+01/fznP5fNZmuwbUvsT+fl5eWpoKCgVn+x2+1KSUlpsL/Qx6q/s2w2m9q0adNgu9LSUnXt2lWJiYmaOHGi9u3b56UKrbN582Z16NBBvXv31sMPP6zvvvuuwfb0J6mwsFBr167V/ffff9m2gdynLs4C/v4dRRj1Iy6XS7NmzdINN9ygfv361duuY8eOevHFF7Vq1SqtWrVKiYmJSk9PV05Ojher9b6UlBQtWbJE69at0wsvvKC8vDzddNNNKikpqbN9QUGB4uLiaq2Li4uTw+HQ2bNnvVGy5VavXq3Tp0/rvvvuq7dNS+1PFzr/fGxd/aWhZ2fr62OB9rxtfc6dO6fHH39cd999t2JiYupt17t3by1atEhr1qzRa6+9JpfLpbS0NH377bderNa7xo0bp6VLlyorK0tPPfWUtmzZovHjx8vpdNa7TUvvT5L0yiuvKDo6WpMnT26wXSD3qbqygL9/R/nuu6FwiZkzZ2rv3r0NPgcpVf8j7N27t/vntLQ0HT58WH/+85/16quvNneZlhk/frx7ecCAAUpJSVHXrl21cuXKRv1fdEv08ssva/z48erUqVO9bVpqf8LVqays1F133SVjjF544YUG26ampio1NdX9c1pamq677jq99NJL+v3vf9/cpVpi6tSp7uX+/ftrwIAB6tGjhzZv3qzRo0dbWJlvW7Roke65557LDkYK5D7V2CzgT7gy6iceeeQRvffee9q0aZMSEhI83n748OE6dOhQM1Tmu9q0aaNevXrVe9zx8fEqLCysta6wsFAxMTGKjIz0RomWOnLkiDZu3KgZM2Z4vG1L60/x8fGSVGd/Of+7+rbzdJtAcD6IHjlyRBs2bGjwqmhdQkNDNWjQoBbVx7p3767Y2NgGj7ml9qfzPvroI+Xm5l7Rd1ag9Kn6soC/f0cRRn2cMUaPPPKI3nnnHX344Yfq1q3bFe1n9+7d6tixYxNX59tKS0t16NCheo87NTVVWVlZtdZt2LCh1v9NB7LFixerQ4cOmjBhgsfbtrT+1K1bN8XHx9fqLw6HQ59++mmD/aUl9rHzQfTgwYPauHGjrrnmGo/34XQ6tWfPnhbVx7799lt99913DR5zS+xPF3r55Zc1ZMgQJScne7ytv/epy2UBv/+O8upwKXjs4YcfNna73WzevNnk5+e7P2fOnHG3mTNnjrn33nvdP//5z382q1evNgcPHjR79uwxv/rVr0xQUJDZuHGjFYfgNb/5zW/M5s2bTV5entm2bZvJyMgwsbGxpqioyBhz6Xn6+uuvTatWrcx//Md/mP3795uFCxea4OBgs27dOqsOwWucTqfp0qWLefzxxy/5XUvtTyUlJWbXrl1m165dRpJ55plnzK5du9yjwP/whz+YNm3amDVr1pgvvvjCTJw40XTr1s2cPXvWvY97773XzJkzx/3ztm3bTEhIiHn66afN/v37zfz5801oaKjZs2eP14+vqTR0nioqKsztt99uEhISzO7du2t9Z5WXl7v3cfF5evLJJ8369evN4cOHTXZ2tpk6daqJiIgw+/bts+IQm0RD56mkpMT8+7//u9m+fbvJy8szGzduNIMHDzbXXnutOXfunHsfLaE/GXP5f3vGGFNcXGxatWplXnjhhTr3Eeh9qjFZwJ+/owijPk5SnZ/Fixe722RmZppbbrnF/fNTTz1levToYSIiIky7du1Menq6+fDDD71fvJdNmTLFdOzY0YSFhZnOnTubKVOmmEOHDrl/f/F5MqZ62qKBAweasLAw071791rnNZCtX7/eSDK5ubmX/K6l9qfzU1hd/MnMzDTGVE+d8rvf/c7ExcWZ8PBwM3r06EvO3y233OJuf97KlStNr169TFhYmOnbt69Zu3atl46oeTR0nvLy8ur9ztq0aZN7Hxefp1mzZpkuXbqYsLAwExcXZ/7lX/7F5OTkeP/gmlBD5+nMmTPm1ltvNe3btzehoaGma9eu5oEHHjAFBQW19tES+pMxl/+3Z4wxL730komMjDSnT5+ucx+B3qcakwX8+TvKZowxzXTRFQAAAGgQz4wCAADAMoRRAAAAWIYwCgAAAMsQRgEAAGAZwigAAAAsQxgFAACAZQijAAAAsAxhFAAAAJYhjAKAF6Wnp2vWrFlWlwEAPoMwCgAAAMsQRgEAAGAZwigAWGjt2rWy2+16/fXXrS4FACwRYnUBANBSLVu2TA899JCWLVumn/zkJ1aXAwCW4MooAFhg4cKF+sUvfqF//OMfBFEALRpXRgHAy9566y0VFRVp27ZtGjZsmNXlAICluDIKAF42aNAgtW/fXosWLZIxxupyAMBShFEA8LIePXpo06ZNWrNmjR599FGrywEAS3GbHgAs0KtXL23atEnp6ekKCQnRs88+a3VJAGAJwigAWKR379768MMPlZ6eruDgYP3pT3+yuiQA8Dqb4YElAAAAWIRnRgEAAGAZwigAAAAsQxgFAACAZQijAAAAsAxhFAAAAJYhjAIAAMAyhFEAAABYhjAKAAAAyxBGAQAAYBnCKAAAACxDGAUAAIBl/j/uqJd+hVRf9wAAAABJRU5ErkJggg==", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo5.jl\")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sparse Spikes Deconvolution\n", "---------------------------\n", "We now consider a convolution dictionary $ \\Phi $.\n", "Such a dictionary is used with sparse regulariz\n", "\n", "\n", "Second derivative of Gaussian kernel $g$ with a given variance $\\si^2$." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sigma = 6\n", "g = x -> (1 - x.^2./sigma^2).*exp(-x.^2./(2*sigma^2));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a matrix $\\Phi$ so that $\\Phi x = g \\star x$ with periodic\n", "boundary conditions." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "include(\"NtToolBox/src/ndgrid.jl\")\n", "P = 1024\n", "(Y, X) = meshgrid(0:P-1, 0:P-1)\n", "Phi = normalize(g((X - Y + P/2.)%P-P/2.));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To improve the conditionning of the dictionary, we sub-sample its atoms,\n", "so that $ P = \\eta N > N $." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [], "source": [ "eta = 2\n", "N = P/eta\n", "Phi = Phi[:, 1:eta:end];" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the correlation function associated to the filter.\n", "Can you determine the value of the coherence $\\mu(\\Phi)$?" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c = Phi'*Phi\n", "c = abs(c[:, Int(size(c)[2]/2)])\n", "\n", "\n", "figure(figsize = (8, 5))\n", "plot(c[Base.div(length(c), 2) - 50 : Base.div(length(c), 2) + 50], \".-\")\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a data a sparse $x_0$ with two diracs of opposite signes with spacing $d$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [], "source": [ "twosparse = d -> circshift([1; zeros(d, 1); -1; zeros(Int(N) - d - 2, 1)], round(N/2 - d/2));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display $x_0$ and $\\Phi x_0$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0 = twosparse(50)\n", "\n", "\n", "figure(figsize = (10, 7))\n", "subplot(2, 1, 1)\n", "plot(x0[:], \"r\", linewidth = 2)\n", "subplot(2, 1, 2)\n", "plot((Phi*x0)[:], \"b\", linewidth = 2)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 6__\n", "\n", "Plot the evolution of the criteria F, ERC and Coh as a function of $d$.\n", "Do the same plot for other signs patterns for $x_0$.\n", "Do the same plot for a Dirac comb with a varying spacing $d$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "include(\"NtSolutions/sparsity_6_l1_recovery/exo6.jl\")" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [], "source": [ "## Insert your code here." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Julia 0.5.0", "language": "julia", "name": "julia-0.5" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.5.0" } }, "nbformat": 4, "nbformat_minor": 0 }