From a3da5de5c6e3f1d260afd19259647d2e1a44caed Mon Sep 17 00:00:00 2001 From: Frederic Weidling <fweidli@client61.num.math.uni-goettingen.de> Date: Fri, 23 Dec 2016 09:03:03 +0100 Subject: [PATCH] blatt 9 2.Versuch --- 09_Iterative.ipynb | 280 +++++++++++++++++++++++++++++++ 10_CG_matrixfrei.ipynb | 373 +++++++++++++++++++++++++++++++++++++++++ 2 files changed, 653 insertions(+) create mode 100644 09_Iterative.ipynb create mode 100644 10_CG_matrixfrei.ipynb diff --git a/09_Iterative.ipynb b/09_Iterative.ipynb new file mode 100644 index 0000000..374da5d --- /dev/null +++ b/09_Iterative.ipynb @@ -0,0 +1,280 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Aufgabe 34\n", + "## Teil 1\n", + "Implementation der Jacobi Iteration:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from numpy import array, diag\n", + "from numpy.linalg import norm\n", + "\n", + "def jacobi_iteration(A,b,x0,tol):\n", + " d=diag(A)\n", + " B=-(A-diag(d))\n", + " d=d**(-1)\n", + " k=1\n", + " x=d*(B@x0+b)\n", + " x_old=x0\n", + " q=0\n", + " \n", + " while norm(x-x_old)>tol:\n", + " k=k+1\n", + " x_old=x.copy()\n", + " x=d*(B@x+b)\n", + "\n", + " return x,k" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir testen an einem Beispiel mit starken Zeilensummenkriterium (d.h. wir müssen die $\\infty$-Norm verwenden):" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Startwert: [ 2.69261466 -17.14628008 2.2221343 ],\n", + "Berechnete Lösung: [-0.07144352 0.57141562 -0.64283772],\n", + "Wahre Lösung: [-0.07142857 0.57142857 -0.64285714],\n", + "Differenz: 1.692e-04,\n", + "Iterationen: 24\n" + ] + } + ], + "source": [ + "from numpy.random import randn\n", + "from numpy.linalg import solve\n", + "\n", + "A=array([[3.,1,-1],[3,5,1],[2,1,-4]])\n", + "b=array([1.,2,3])\n", + "xtrue=solve(A,b)\n", + "x0=randn(3)*10\n", + "x,k = jacobi_iteration(A,b,x0,1e-4)\n", + "\n", + "print('Startwert: {0},\\nBerechnete Lösung: {1},\\nWahre Lösung: {2},\\nDifferenz: {3:1.3e},\\nIterationen: {4}'.format(x0,x,xtrue,norm(A@x-b),k))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Teil 2\n", + "Implementation des Gauß-Seidel Verfahren:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from numpy import tril, triu\n", + "\n", + "def gauss_seidel_iteration(A,b,x0,tol):\n", + " k=1\n", + " x=solve(tril(A),-triu(A,1)@x0+b)\n", + " x_old=x0\n", + " q=0\n", + " \n", + " while norm(x-x_old)>tol:\n", + " k=k+1\n", + " x_old=x.copy()\n", + " x=solve(tril(A),-triu(A,1)@x+b)\n", + " \n", + " return x,k" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir testen am selben Beispiel wie oben:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Startwert: [ 2.69261466 -17.14628008 2.2221343 ],\n", + "Berechnete Lösung: [-0.07139824 0.57140518 -0.64284782],\n", + "Wahre Lösung: [-0.07142857 0.57142857 -0.64285714],\n", + "Differenz: 6.062e-05,\n", + "Iterationen: 13\n" + ] + } + ], + "source": [ + "x,k = gauss_seidel_iteration(A,b,x0,1e-4)\n", + "\n", + "print('Startwert: {0},\\nBerechnete Lösung: {1},\\nWahre Lösung: {2},\\nDifferenz: {3:1.3e},\\nIterationen: {4}'.format(x0,x,xtrue,norm(A@x-b),k))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Teil 3\n", + "Anwendung auf die Poissongleichung. Zunächst Import der benötigten Funktionen." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from numpy import eye\n", + "\n", + "def tridiag(a,b,c,n):\n", + " A=zeros([n,n]) \n", + " for iii in range(n):\n", + " if iii==0:\n", + " A[iii,iii]=b \n", + " A[iii,iii+1]=c\n", + " elif iii==n-1:\n", + " A[iii,iii]=b\n", + " A[iii,iii-1]=a\n", + " else:\n", + " A[iii,iii]=b\n", + " A[iii,iii-1]=a\n", + " A[iii,iii+1]=c\n", + " return A\n", + "\n", + "def poisson2d_matrix(n):\n", + " A=zeros([(n-1)**2,(n-1)**2]) # Hier speichern wie die Poissonmatrix rein\n", + " B=tridiag(-1,4,-1,n-1) # Die Matrix entlang der Diagonalen\n", + " C=-eye(n-1) # Die Matrix auf den Matrixnebendiagonalen\n", + " # Jetzt bauen wir Matrix nach dem selben Prinzip zusammen, wie in tridiag:\n", + " for iii in range(n-1): # für \"blockweise\" durchlaufen der Matrix\n", + " ind=iii*(n-1) # Umrechnen von Blockindex zu Matrixindex\n", + " A[ind:ind+(n-1),ind:ind+n-1]=B #Setzen des Diagonalblocks\n", + " # Setzen der Nebendiagonalblöcke\n", + " if iii==0:\n", + " A[ind:ind+(n-1),ind+(n-1):ind+2*(n-1)]=C\n", + " elif iii==n-2:\n", + " A[ind:ind+(n-1),ind-(n-1):ind]=C\n", + " else:\n", + " A[ind:ind+(n-1),ind+(n-1):ind+2*(n-1)]=C\n", + " A[ind:ind+(n-1),ind-(n-1):ind]=C\n", + " return n**2*A\n", + "\n", + "from numpy import array,zeros,ogrid,broadcast_arrays\n", + "\n", + "def rechte_seite(n):\n", + " rechteSeite=zeros([n-1,n-1])\n", + " x,y=ogrid[1/n:1-1/n:(n-1)*1j,1/n:1-1/n:(n-1)*1j]\n", + " x, y = broadcast_arrays(x, y)\n", + " rechteSeite[(1/8<=x) & (x<=1/4) & (1/8<=y) & (y<=5/8)]=2\n", + " rechteSeite[(1/8<=y) & (y<=1/4) & (1/8<=x) & (x<=5/8)]=2\n", + " z=(x-2/3)**2+(y-2/3)**2\n", + " rechteSeite[z<=1/16]=-1\n", + " return rechteSeite.ravel()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "N=[5,10,15,20,25,30,35,40]\n", + "k_jacobi=[]\n", + "k_gauss_seidel=[]\n", + "\n", + "for n in N:\n", + " A=poisson2d_matrix(n)\n", + " b=rechte_seite(n)\n", + " x0=zeros(b.shape)\n", + " tol=0.001/(n**(1/2))\n", + " \n", + " x,k=jacobi_iteration(A,b,x0,tol)\n", + " k_jacobi.append(k)\n", + " \n", + " x,k=gauss_seidel_iteration(A,b,x0,tol)\n", + " k_gauss_seidel.append(k)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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DDX6vCYUGb+mmpTR+pzF7kvYwt9dchYYCKrMdTk2AV4BLgauBYsAXZlbq0AVm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\njuVblzNl1RSmrJrCnHVzOJBygGrlqtG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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7ff59814def0>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "plt.plot(N,k_jacobi,label='Jacobi-Verfahren')\n", + "plt.plot(N,k_gauss_seidel,label='Gauß-Seidel-Verfahren')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/10_CG_matrixfrei.ipynb b/10_CG_matrixfrei.ipynb new file mode 100644 index 0000000..4550fdc --- /dev/null +++ b/10_CG_matrixfrei.ipynb @@ -0,0 +1,373 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Aufgabe 39\n", + "## Matrixfreier CG-Algorithmus\n", + "Es kann direkt das Verfahren wie im Skript verwendet werden, der Unterschied ist, dass nicht eine Matrix $A$ übergeben wird, sondern eine Funktion, die für gegebenes $x$ den Vektor $Ax$ bestimmt. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from numpy import array\n", + "\n", + "def cg_matrixfree(func,b,x0,tol):\n", + " k=0\n", + " tol=tol**2 # So spart man sich sowohl ||r||^2 als auch ||r|| ausrechnen zu müssen\n", + " # Vorbereitung der ersten Iteration\n", + " r=b-func(x0)\n", + " d=r\n", + " residual_norm=r@r # Schnelle Art ||r||^2 zu bestimmen\n", + " # Iteration\n", + " while residual_norm>tol:\n", + " # Update der Näherung\n", + " h=func(d) # Speicherung von Ad\n", + " alpha=residual_norm/(d@h)\n", + " # Update der Parameter\n", + " x0=x0+alpha*d\n", + " r=r-alpha*h\n", + " residual_norm_new=r@r\n", + " beta=residual_norm_new/residual_norm\n", + " d=r+beta*d\n", + " # Vorbereitung der nächsten Iteration\n", + " k+=1\n", + " residual_norm=residual_norm_new.copy()\n", + " # Ausgabe\n", + " return x0,k" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Der Algorithmus wird an einem einfachen Beispiel getestet:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ergebnis: [ 0.67014139 0.98098418 1.07141916 1.05074024 0.99864442 0.9652318\n", + " 0.97100558 1.00687205 1.03414062 0.98452376],\n", + "Norm des Residuum: 0.6352128293259851,\n", + "Iterationen: 4\n" + ] + } + ], + "source": [ + "from numpy import arange,zeros\n", + "from numpy.linalg import norm\n", + "\n", + "def testfunction(x):\n", + " # Funktion, die die Multiplikation mit der Diagonalmatrix simuliert,\n", + " # deren Diagonale die Form 1,2,3,...,n hat.\n", + " d=arange(max(x.shape))+1\n", + " return x*d\n", + "\n", + "\n", + "b=arange(10)+1 # rechte Seite, die Lösung ist entsprechend der Vektor 1,1,...,1\n", + "tol=1\n", + "x0=zeros(10)\n", + "x,k=cg_matrixfree(testfunction,b,x0,tol)\n", + "print('Ergebnis: {0},\\nNorm des Residuum: {1},\\nIterationen: {2}'.format(x,norm(testfunction(x)-b),k))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wird die (oben sehr groß) gewählte Toleranz verringert, lösen wir das Problem quasi exakt, braucen dann aber entsprend mehr Iterationen:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ergebnis: [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.],\n", + "Norm des Residuum: 6.028010073543578e-15,\n", + "Iterationen: 10\n" + ] + } + ], + "source": [ + "tol=1e-2\n", + "x,k=cg_matrixfree(testfunction,b,x0,tol)\n", + "print('Ergebnis: {0},\\nNorm des Residuum: {1},\\nIterationen: {2}'.format(x,norm(testfunction(x)-b),k))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Matrixfreie 2d-Poissongleichung" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from numpy import pad\n", + "\n", + "def poisson2d(x):\n", + " # Vektor in quadratische Matrix umwandeln \n", + " m=max(x.shape)\n", + " n=int(m**(1/2))\n", + " x=x.reshape((n,n))\n", + " # zero padding\n", + " h=pad(x,1,mode='constant')\n", + " # Differenzen bilden\n", + " y=4*x-h[:-2,1:-1]-h[2:,1:-1]-h[1:-1,:-2]-h[1:-1,2:]\n", + " # Ausgabe als Vektor und Skalierung\n", + " return y.ravel()*(n+1)**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Erneut ein einfaches Testbeispiel, um sich von der Richtigkeit zu überzeugen. Ist $x$ ein Vektor, mit $x_i=c \\forall i$, so sollten bei Anwendung der Poissonmatrix alle \"inneren Einträge\" (für $x$ als Matrix) verschwinden und nur am Rand der Wert $c n^2$ bzw. in den Ecken $2 c n^2$ über bleiben." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 200. 100. 100. 100. 100. 100. 100. 100. 200.]\n", + " [ 100. 0. 0. 0. 0. 0. 0. 0. 100.]\n", + " [ 100. 0. 0. 0. 0. 0. 0. 0. 100.]\n", + " [ 100. 0. 0. 0. 0. 0. 0. 0. 100.]\n", + " [ 100. 0. 0. 0. 0. 0. 0. 0. 100.]\n", + " [ 100. 0. 0. 0. 0. 0. 0. 0. 100.]\n", + " [ 100. 0. 0. 0. 0. 0. 0. 0. 100.]\n", + " [ 100. 0. 0. 0. 0. 0. 0. 0. 100.]\n", + " [ 200. 100. 100. 100. 100. 100. 100. 100. 200.]]\n" + ] + } + ], + "source": [ + "from numpy import ones\n", + "\n", + "a=ones((9,9)).ravel() # d.h. n=10\n", + "# Anwendung der Matrix und Umformen in Matrix\n", + "b=poisson2d(a).reshape(9,9)\n", + "print(b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Um zu zeigen, dass sich auch noch größere Probleme als in der Aufgabenstellung in sinnvoller Zeit lösen lassen, hier ein weiteres Beispiel, bei dem die rechte Seite konstant $1$ ist mit einer Zeitmessung und $n=1000$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Es wurden 1851 Iterationen in 285.2502770423889 Sekunden berechnet.\n" + ] + }, + { + "data": { + "image/png": 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PjrYXqr+6UQUQ2a3K7dMd+yulTbuunAFH59ynoQLd5wL4MQCvBvBG59yLSinv\nMup/IIDvBvA6AJ8J4GMBfKtz7h2llO9rdU4A3gTgnQA+BcA7APx7AP6Vcbw/0X77rTe4uvsIjvL2\n6xeMdbrnRqKtRI7l6fgfg+I5wHswqWNZm9oa1W7dwcJseYchAbFZhjHB+dQsxBZX9LlZjwUeCzzy\nCj5hjSxlBCwI63oHN3GNBnTbxV7mtm9Puvdrs991FmCy1Sixyu4CHZP4t+QdsXNGcNP7iXS42e5z\nmyJEl7Ku63IrvijuTG3XenO/QncPGK1HCwh7l6ZbluIIl98p9BTjqu8O84yAOIDrspYlRAR4xBU8\nF6RQjxtCRD4tSEuADx5ZADMFlBiQloycUh10IIXqA7xy3YoUa5FTMjQQsm57w7f9IdExOMo6W4sR\no3uV007YmhycFQKM3f09xhyhdHcAlNKeXFfOW46vBvAtpZTvAADn3OcBeBmAzwbw9Ub9zwfwi6WU\nL23bP+ec+8h2nO9rulcCeF8AH15KkTv7dn0g59x7A/ifAXwOgK84eEWD3ENwFOGou4j4K6Xc0zqp\n2K3KzFAmvJyz8rTFONNbcUltnbKrdSXtVJYpTgvgM3zM1UUaEmJMHQib2zT4Doi+AZ+QWmTdt7L6\n13WBmkluLp3ajwGQCTo9Fjkj6OyTdbbAaG0fIeccJ9/oEXKq2EBaJi3vHvmm7jcn6Rwj4fjp9ox0\no+swAacMukBPu9fpTzqsbto4PPH6hgUsyAgI8MhI634VnMO6npGQvEd44JFyRM4eIYTVzep8QE4B\nOQTkJQM5VUsy+WpNCjiyNcjkmqS2dbjPfjDyEPp2piWva+tVyEE6a6MA/R1h0BuG1MEYs3nmSrPw\nPhTVpQkAKKUU59ybAHzEZLcPR7UKWd4I4Jto+xMBvBnA65xznwzgNwD8bQBfV0rhj/qvA/gHpZT/\nwzl3AcdR+EUUZBOJVEbgyb1MASSLEMO6o+QcXu6le3Ac0ql9TwBcAU65AmNI8KcKiNV1mhqppjSL\nMSG4BZFAqgJhWoFyjC8ua7O3tRo7YPI+43Ibs5Rj1CfCQLmsOmG37hN0eqxyb8CAmW5Pz+Wgc3sc\nktu7tmebHhoNZ6JjQg4TamYEHB48QOKO2rLk35Hj97phWLKfIZN1KMfqXbDY9llWfVjfyLpv8QsW\nH5BCRM4B3mfEuCClgGVp+hSQXalWZPKA80BxFV94pBsBKMYdTb7RcTaHDnzACI4MhhFbYGRLkQk5\nDNLriclSxYkrAAAgAElEQVRzEbcq6EBPYMLjm7pV98P3z29H/jWl/zUAL57s88JJ/ec5555TSnkP\ngD8A4E+jWoUfD+APAvgbqFfwVQDgnPt0AH8MwB8/eCWm3GNw1M2K9ukb0fmZpRhhu1oZ0HTMcQaW\nz8HcBfteE/36V4B4tcYUfUiIpwXOFcS4rC7VGktcEBugies0YBmsQXaXxhUQxc0q9kEn4rDNMMYd\n95isoHrbAQFm8cax7jzWaMUZ9aACss8ePWbMZ3ycbtaerzbPf3QNiLautTHxX8cfdexxjDUutG7F\nHRNROMc44pZ0I3WXZtVwvFGAmIk5oltjjkirMz+uABmaVVnBMyEgICG7hCV4pBCRUoBbCrzPWHxB\nKQsWAcnFAyEAywlt7MEOTuxmDQB+d73UOQHHoTf4DJQSSzyRjtNJ9Dazx5lBux5YlJoT8YTkACHn\nO/91/WP5reuTvR+HeFTA/NxSSgHwU865fxeV9PNVzrn3B/AaAB9bSnmknsY9BkfN/NJvgH5Bsc1z\nYvxkkpkGQouMc/TvEEmntL8FOBEIirUof6E2UacWBWIQjBvdaCV24JuRdGS5QJNw5mA4AuAIhAK6\nWxDcY6xuR9PZJ+l0HTZ6fezbIeOI9PdsO9JNL7cBcgTAZQOI/Xi8LsA1A820fv4OYQXHWjaCYD9u\nWPV+PVZqvcd6LwUI+/4JocGk8J89AhIBpEdExrK+fQWu6a5CQAgRKXn4kBt5pyC5AqBZke1qd0Hm\nvWCTbwT4+k3rwsn9PEABxxsFiNmlK1YrxzxX4UZEZEajvSM5YDl+xu+rfyxv+R3gQ9823eVdqHft\nBUr/AlQyjSXvnNR/d7MaAeBXATxswCjyswBe6JyLAP5DAP8OgLc457gl/4+dc38OwHPUvlO5x+A4\nu35BHPUi8ovM1qJ2oUZ1CO1y1euz2KOOOU7dsKXGFWOCO0k8cVnTMeIpwbmM6KWZkuanA6Pe9uC4\nY6bt6iTzq75Q8zYSb0Z360jCGck5ZVM+izn2AQU62UYPFFCbv17GETtP4CrS6SdjjHG0v46nbFix\nyHOxRRYec1UTcqRsJN7IFff9HqzOaZDdbMUaO2mHyTdxrXu1dkVG8o1YhCPphqPSQr6prlEm3wSE\nZh32t0zcqhUUxaLkdYHORG9thodDrkcKoaYbxQx/lZFCrqzXJVaLMuRqRfoIeGfjpB1GHvVCSWAg\n5OR+HoxAbws4cliGO9zD77Mr6gmPhiOncZP9JlJKuXLO/SSAlwD4LgBoYPUSAK+d7PZmVFcpy8c1\nvcgPAfgMVefFAH61lLI4574fwIeo8tejAuhfOQqMwL0Gx3OuCtVbE8vQIuSwW5UBU4Pm3mg4s7SO\nvVjkKa/WYjhVUPQ+I54SYlyqtdiINmLliVU4gqLUkbhhRpgsPTVXW5KOpl2wziLp2IxWjiGOTfBx\nko6up4FTymvZlqxTlzch5RyTc4DZ8w23pBut1wCoiTjXId/kQRfITt8uNflm1PcItOgs8g2TcuSt\nEWDs5J2Mpe3nEQer0rerT6ipSRkezsWam7u0u+JTdcH6XGPyPtZYJHd2Z6Lji+xK5VgjgyTPBOJI\nJ0uLkCOWpenF0vKE3ayPT74RwOsbSEoqx3NRwQrOua8F8H6llM9q9b8ZwKucc18H4NtQgfRTAXwC\nHfNvtDqvBfBXAbwIwJejulJRSvn/APwMn4Rz7rcB/ItSys9e5+TvOTgCYxdOv3B+rM7VZDd2p1qx\nSF5a7tW9AQBkuQFFkBs1IT5YDBdqJ9v0vnbfdiiIa5Qnbf6EQtFBsaZ4jLFFqVtJKrK+HSTAjjuO\npBx7pB1dpz+K2cABmrTDA66NM3XMyDp1aQ8UwHX67xwPrvBUUfWMbBFQsupsSTf1peyZmGMaB9fX\nCf19PZrlXE/XsZP9O+gJMSe3OkLakbcsNsBbWtloKXrEwWrsYFgtxtJAsrpoa+2MhADnC9ypwPka\ni0xLtSqdK+0tA4AWh2TReDQj32S1FMATa1GWntbZvSp1xY27IZ/O0jbYv3mH4Hgg5jjdb0dKKW9w\nzj0fwFeiukd/GsBLSym/0aq8EMD7U/23OedehspO/UIAvwLglaWUN1GdX3HOvbTVeSuAf97WrdSQ\ndbfrXViVewyOwHh52s+p3gZ2gUTaZeZmZRKsld5xNKdxs12AB6nGFpu1aAIjGBgrcNlAWZujHnPk\nenmj06xW14Cv66svKTRHmY45MrAyCUfHHa2ZO8YBBM4TdbaxyVm8cdTp4elmEs9Ylntiz6zRzwCw\nBhCvZefijuN+54k3pTknuW6f87HHD60kfybWCJHmhKXFGivTJDXrr2DBggBJ4+jxxAWpleUGmqnt\nL3ZobCAob151sUZwvmunI1UgdLGsoMh/KUTkq1wtSIQKknK7mHCzR74B6RgA5btnIGTrkWOMGiAH\negi7m3Qw9I6b5ZuyVQ8AainldahJ/VbZKwzdD6CmgOwd80cB/MlD51jr/+mjdVnuKTjqrpBFS5N6\npLJSObRb9Qj5xrIiGQyZlTpYjR0YXVTAeKqgGMOCiPpXAWq0HpmQE1fSDdcRBmtW+40uVR4gYAaI\nGghHy3KMR3Y363ZsVTm+1Om6o+ua0APaBmzA3Or7q6AHbRPZA8sR0B4Aa1Nuy5yAw/ruGPZUPm6H\nARy3633YOL/WTc3U6XmKDuLEDJC44kJWZbcaS6sr6wJ0QCfaFALAjJ60IW8XVl1u9mEAkJFQ4Jvl\nGJFxhRrBFF7rgoylWZELCpzMP6pucykjTQtw28f9XugsVg2OAoYMjhmdpCM6PRi6uFM1WJqW46xd\nknM+Y5o9LrmFmON9kHt+eXtCL56AH3s3ZizVvSWD4jl36uZPW4wJpwdXNbZ46m7U0xpPXAZgrL3v\nK4yEnN4Xj+j5jQKsfVCArh8JOgKaAqqdjGONqLONPdZ17Url/EiJKW1JOTruKOt5BdceiSuber1c\nE2468FkxRwvOrkPY0cO/WcQbQMccx/hi13cdj34jTmE5Do9qY8UbmYyTIVM4d7co12F/QrXzl7bf\nOOKN6KpFKeseYX2jxgEAJLFIwFBcqhXoPCSGnZCR4OFafSHkAKf1zOsfjdMTMryP60hQiy8AHJLj\n7kwA2oTOYC85E3A4tlhIx9+2pGVY3z9PpqzbEbYuAdwZ8B2RW3KrPtPlWQSOuvumniy7VaV4Bnwc\ne+RtbT3qZcCctLMBxvcgtvUYu5v0hCsCx22s0Yo/snUYW66juE37ctSJ9TfGHbfxStH34eW2ccm+\n7E056wGOMY4cSXkUVtyxwwS7WTkmCQgkiJyLOT5KvFHkSNxxFnPM7T3Ng25M7me7Vscbs9pHLEBA\nJ/hftfpXrU7PQdQDAPQYo0PAmMgvIFf35Xgj5zJWm1TeHE+6gNSAUxI85O3NYLeqR8GCMLhZO0HL\nVc/pJlz3oF2vSIRSbGfXyMZSLEltJWprUQMmsEMKGtNxnijS3KJb9Zks9xQc9YvG5p8gksEIk3c0\nql2458cBdgsEeX8NhtO/Qq7UhNODh5WR2izGEx6u1p4GPbEWGfTCakGKlVddrQx8kud4WgcG6Mdm\nIGRCji6z9L18O4vHFizr/rX83GweNllnBMcRzLrz3NLZo+C4Yb27ea8jegDx2RGs0XP6VFajrpNx\nRnBk0g3PtDECIVZbnuvp0W5G4k0l6EiMkEfEEXJNB8VloxdyjZRVFmq1G68QUbDAt7fUobTr7gPx\n8eiw9bn2eKOIdBeA6tBdkIH4QPFwHnQXa27WI4eh2Y3KblV2jUaM6Rwcc5TvXfIaud1g/SDcoJxQ\nZ1OWnVjuuWn2lMs9BUcW9pdqfROOE7IbhHuCAmRM2olGOVuFMgQc67yuU9M1hHxzenCFeFoaMC6I\nq6Uo8cWepvEAD6FJOFIvrC5P2Vf67Zz6Mf6xpRiaM0wIOZzwzzFKrR9JODr22LPqwrAtLlUm+IwE\nnDHVYz5bhzUDhx4ooNazZ/Cw61xP9mONcpYOZQPQ2wT/EWhHYg4PEZebbSXHiK1V7rFC3wZ4qfW6\n4zus2z2HUYg3aSDnJAiZZhmsRtZ3Qo448sP6DnXQzKvetyOV1XKUerFZlXndFkdvQMZDPBgAVO5H\nwUMgqPlZcaou1tRmxCi+P3aZAouZqSd0oIzogMlzFMedbe5Qa1LfZgorUEWjw34XcrEcTbmH4Kjd\nFWIlnhH9IvO2gCAwWooMfLquHMfKd2SLsaVrdPLNsjJSxSqsccZlcKly7FFblLHV1/FGGd2GwVTn\nOvYYpKRt9yhUUOt23NHKf5R9rGy67SAB9SluZ/LQsccepzw/MHl9xOxe7VbILKY42n/HZaQFjdJd\nqSOAij4qnY49ygABnM6hY43ijMzwOOFq3U9nn44DhnN2ao0h9txF38Ctz7AheYzMPJWEjPp21b2Z\ncMOx7HqcDMuF2pmpcX0OnHhYADzAQ1zRPrUeSXAobZecW3z21J5mPgFNN8QcCzow8vec1DqndvC0\nV5HWuXO9IeTMxGqv7sB6vBByTLnnlzcTQTeMYMcvsRWDZODjWKQVX5zFHpUrFadlzGNso+Cc8BBh\nAowPBouwk3AYJNnCFKDseY89n3ELiJqo03W9ceO4Zdf3dHHWF4xgOR8koN5mBsW0Nn6auLMdAGAs\nG+OM2wECpF6V0V1n1zkuswEAupPQSv4fE/1rnRH06sg1W8INE206vHTbvIIbJ8vYSf78JPsT690g\nJtikZiFWi66PfCO1ZPybjLTqMrrVWH8lwLX9F5QGv7H9clivjt+B+gzdeidnY8s4PARijTnG3DoR\nxWFBaa7VBkLipOAEf/lWWSfbHFtkAOXxwznGyOQcaQcScHNz7RbkQsgx5Sl5Orcl+vJ2LEl+iTl/\nid0mwPhxaHesle+oSTqczygpGipdQ5io3Uq8WoHwBC5nC9ICxg6E3ZLsOZEeDJ59xg1xqfbcxx5H\ntOOOEsPEei46rthJOpabNW/qARxn0oSc/cECZtugfbf6feLNkY7/ORi14olVb8ceZ9uzOCPHF8Wq\nlLp6Bg6284VgM9brcchOzImDXlyy8kbxoOLVvVrfsgqMSwPFuAKlAJ5YjTKw3Rhz3P4BaFZlwQMA\nV+qOlrZ/hkcJ3WIsxaEUh5R9ndUDrhNyxH0qcUUh4HB+I4Mck3CA/o1z7JHbCvMFmrVHd9wsX9yq\nptxjcNzyDg9fribgyKEYDK31SPtZFuXqVq3uVMfAaIx6Ew8AIzNWHzRr02ardmtRwLPGgq4g46nq\n/QR8ZIwTT/X0qDoMmABW61KsU8Ai5dhTXO0B5hYo+7rYWn27qO1+HH7UIo8CkMeAMZl1E5ICQg9U\nG4e2EzQI1vWut4BQrlfqzUCwg54M/1atwpF4I4n6AnCpgVyN+8rbJc+LR7epVqN0eE6QGOMCiS2K\n2zVAj4oTEPAQ/bPUFuPs3kekaiSGGmMUcMzJo6QWXCyuE3KYtSqzcFgM1WCs80DjUyLOTDhuI3KH\nsccLOJpyD8HRqSUwcqtVPbbqNCEHsAk5msGqLUaL1r1aoxJnrKDofV5HvomhAl4FRG09dmA8ra5U\n6bOPrtWZq1UTcDpxpwKgsAu7u3U7mwcPFqCnxOqjnTBJp4+MI2OtjMn+3Zqs2+NsHUy+mY2aw/o+\nqg2X9e2ZrpcpgDw+TnEXNWxZJcVsyTe1rKdasI63xxFwPDCQbZZVH1dizTgaTmotOZNt6nZ/spK0\nzzFEIeR4pLVbVJ2lffopTvaXhA15a+W5Liioc27ItFR1SyzBhDFFQ1uJAHDCVXOp1qDgA3D3od6p\nMd2l71lCtxxT8oinhCuJOS4nILixo8vuU7EoeZutQ4uQIydkEXLk+GbnndHGascucpfy2MHROffl\nAF4O4A8D+B0APwzgy0opP6/qfSWAzwHwvqgjrX9+KeUXqPw5qAPXfhrqODJvBPBfl1J+/eCZ7JQZ\nl61fZO0S4VikBkL5QNja1MzVgZ2a2rRTy5rLWAk4I7t0jDFugVEsyDEGuWWwauC02KodFLvrdSTr\n5AagUoeBrrtkrYECJIoVB50m64z6Tsro5BuOHXYH4rYx3RJymvWYKSW8gR7r1vrZBkQ30QNA8fb7\nlr3DSU1gW3wDLefWN1F0Eh8EetcgGldaAbHzaXtKvMQuPel6Av9IuunlCyRpX0g4ywp4Qr6RYeHy\nCpMVGGvMsUem5fl3lmlub4880w6G9axOU3Csfw/ae9DzWS15gGpR8j2SDkEJ1Wqs8UeHtHjkkoBT\nQPW9YhwFZ5bXqEGOY4tWaGaXkLPX/N6x5XgTK/BiOV5bPgp1tPSfaMf/WgD/yDn3R0opvwMAzrkv\nA/DnAPwZAG8D8JcBvLHVEY/Ja1CnL/nPALwbwF8H8L+24x8QZ6w7dHqaUV2/yPplZzdrMNbZjar3\niQBCAUKGJzdqlOmnCOw4BUNiinEFyJkF2UfMicM+DLZbV6usa6LOOFgAW5hCv+/RKIu9yi7VkSe5\nne1jJFyMAOpXC1KTMrDWl3WUAt9Az5cClwggBQwHXVspgDMIq/5aRuNYORttW1nfrYTs+scnlk0m\ni7MEv25n5wDXR8URO3wk2Ug5E21Gwk1Y621pVEKoKehzrgjhpg4pJ8PCVYpNjR+GZgc6yJwa1eVa\nkOHoDOob6IbnLvHGsALf+B7w/XwIMeG0xQgwuck1u7Ifge9NCQ4lOpTsEGKdezIvGQgeiG4Lgpqs\nxzwEzUmw4otWm7KRk9oBxvoty8WtaspjB8dSCk8vAufcnwXw66iDyf5gU38RgK8qpXx3q/NnUGd3\n/k8BvME59zwAnw3g00sp/1er8woAP+uc+7BSyo+dPxMOFIoYT5MBzHKBsAsVGK3Eo4zVdTsDIcGH\n1FI3GkiqOKOs6xjiCaMFyQAXsQxAunWj9sEC5M+tbtRx/FUdf5TmtRNvCnqaB5cv4DFZpTFksk7X\njXFHiffJoAGajCPNvkBASBR3XHh9HA3HkzfTAUDtn2zeEgBbzyfJIxNy6DXkeskDcHnQ5QiUq0Tb\nNCJOrCQYAEhB7GeBGpuUI0n9Pb7YZ8/QhByx9AQkxc2aSV9BsWBBbvvK7I/sVq1gKCPhVDZqJDiu\nI+MIxPc8Vf7T7lXpHIzSLcZ6Dx7gIUYXa41eFlfBMWePkJYafwypgmMItgtVJ/0zADJLVU7a8iox\nq9UEFFY+gUjXBRxNuYsn8b6or9y/BADn3L+POlXJ90uFUsq7nXM/CuAjALwBwB9v58Z1fs459/ZW\n5wA46k9IUI5E9/IwWZ/1InUcMmL7gchHdKqxRn9KNcm/TVQcvA2McXCfXm3IN2PMkV2rHQT5OLN9\nmblagakYrtfuapWGjcn/kj/ZtyXOWPVi6+jBAkQ3m7kjIK0xv9jAMKS86kIq62MOPQSJqEKKLo3b\nAPr4mhaiWWmPB6xIPUMSgB6DujLqBYqEN13pYUQAwOIBXGXANYLluu4QrxbAOaRmeS4h1B9yY/K/\nABwgSf0SX+xDvEkdiTMmxFXXY4mewLPajn3f/iaxy3TBqXW4qjtWiDdiMYqlWOOQEos8Ne9AT25x\nfJPaGjvauz/oBAcgtRtez2RZreLiHcrJI9deCXIKyMVVsz6R9ShuVeYVyLrVDjDDXT3TYV061cM7\nJo3GE5KLW9WUWwXHNvPzawD8YClFJqB8Iepb/2uq+q+1MqDO/fWwlPLunTrnfh3j28mEHOOyLeYp\n9xI50M7Wo3axMmCu2wXwCfAZPqQ2o3mCc53osjdWqo4ZSgyyA+MVumuVrUg9rdW58VhF36esYnJO\nH0+1W41SV8CM448j2PEgAgoA0Qk2oTSWbM5ALrQsq4ERcuU1udJcn62hcbmvQwHkRr+3LtINmuuJ\nfvVEvFq/UnoPOGY5+hYE8LXtji3BPDsgulKJlr4guAqYwSfAOyTvEX1C8h4BQHIBARI3RAM0hz4m\nTSfUVJ1DT9zvwz+E5j6V6ao4f7FbeTzbhgBhNcnSCnZ8Ywv4RvfQnb7xpY2U2qVvOzpy/fCictQm\n9FGBnKskuJQCfEjI3tfvM4buXrWINrLOViN7lNibxO3INI+Q2yF+Oe6YhHOxHE25bcvxdQA+CMCf\nuuXfUeIwb9XcuKrdpLoqM041YAbjTxNy1h5mgo95GAUn+i1AicXGTFWbXLOQxdiBTxN2xqmt+jH1\n73CKx3guksbBBJ3OVOVRT+zZO3h0HZuM40tGyBk+Z/hc4HKBKwW+WXc+V+ALFhBaYKh1Vh1+PcY8\nin2xys8lQ8/aPe2uny1dq9Z0obnpim8fcDN6gi/IvlriOQDRVUsp+wXZeyTvkV1P2BeyTWzg0Qk4\nNZk/ILd4ohBwZP7FnrmY16P1GTdq90pc4AE9XtyjnFi3afopSDyZWajjd1wBUR6gzM2xkCvZkb6+\neaHB9Ope9QtKdIhpQc7NekwJ8GF0p4oVaX3nGggl79GKL3JHeVO+B4R3DJIXGeTWwNE599cAfAKA\njyql/CoVvRP1qb8Ao/X4AgA/RXUeOOeep6zHF7SyHfl7AH4v6pt6astPBPCprZy6OxILYNE9PwZC\nwO4dMlCC9lvBsgCxWo1RmKqhD802Dv12BSG3aDDkGCTHGLczdrBrdZzaahwooFutbKF6jKDdY5Ns\nReq0Dh1P7IzWMQ5ZY4ghJ/hS4FOqFmDKbYm+RHeJuhoQ66OZiLB7lNf1cKq8TzF0rLf2ua7oXrVu\n54Kh10x+bkiDWpfNpo8B64xMJQDlCsihoLjSxttOyMG3vL+A7BySl0R+QPim0gUa0zf86hKVpyqz\naOTmDhU2qocjt2kn3vSUDbm0Oi/jKNtey7aLyy5U3yCykOVYf0HgXMaYFUty5dGGgBQyYkxIS0KO\nHrgqo+XI3zN/57pt4OdjtR8s0uas7xY/9O8D8A9a4VVb/uvNHXjscrEcTbkVcGzA+MkAPrqU8nYu\nK6X8knPunQBeAuCftPrPA/AfoTJSAeAnUV/RlwD4+63OiwF8AIA37//6p6Aaq78HwPsAeG5bApsW\nSntdZ2wzHW+IVIetRM1cE5dqXOBDBccQKgnHD4Bog5JtMep0jSsFjFbccsZWHWf1EBDszFSJIumB\nAUYLkwk5POjYAIZCykmpAWFBWFqqxtLanQaIWPoSwAhSi1rOyoEtkOpya/9zYu1vfUUzco80KJzd\nEZVOx67EnSdlV0rflgKWro2v7VtZWWq8slzlRvbJSNEjNMBMgYeCk9xFsbdkUIDYQKiXVcCrz1fA\nUAYBkD9xpXoIAUdyFetFcl2s62Ug1GjpkciHq7M1IpEbtfJjuzW5IKzgmNpZLAjRo2QHHxJ8CMhx\nAQrlPco3LPeYn4NuDyzLUXueQPpBRPEJqE62fwPgtwD8NoCfAfDfb+7BY5ULOJry2MHROfc6AJ8B\n4JMA/LZz7gWt6LdKKTLv9msA/AXn3C+gpnJ8FYBfAfC/AytB528B+Ebn3G+idp9eC+CHjjFVZ34u\no7tuuTu4N8h5jrqXryncFinHAZAk/5jgfGnTUHEssK6fwMB1hc4stQg2Y1kkoAzgGTu2blXedwbA\nIzNVA+o4MIAMTQfYM3iElCoYNjJNWMpqIcZm4Tm2Ctny03oYZTDWoerDKGcdHxeT8plcqW3d+LHL\nXo+cogg48KpOwJh0zutJ1ZdjtTLn67YLFShL0y8eCEt1vaaYEZeEFDyiS0ihA59Ykks7oHSXxENQ\nR8xJa31xcNZOUoQ4NHvSP1rHqTSfhkxa3F2t3fZ7iIcN+ERX6APt4FlvvgyAIDcuoY9Ve2q2bAXN\n+qsneOSQkHxAjAklN+txOW1ji/x983fPz7ebxNtmRodvNi/KDGXO+esfk1wIOabchuX4eahNyj9W\n+lcA+A4AKKV8vXPuuQC+BZXN+n8D+HjKcQSAV6N+/n8XdRCA7wXwquOnYTn+jSr6AWuQs9I1oirX\nL/+QD7nAxwznU0vdkNSGDi6uuVBH9ie7XGdzOdrkmxkwjm7YWSxzPD6D5Zacs0ATcGRS41ASIpFq\n/JJr3DCv3KQxblho/ZweqrxQPRh1WDeLL+pY4k3JOCIWKUcTcoAtqUOWsp5IJw22U3XYVSf1/Fbv\nmv7U4pU5VcZv8gXeZ+To4XJB9AmL90guUCxRDypefQqdBtMHhxD3aRoejvU3I9+IdIDUwdoxVaNH\nssVOFUuyD0ogMdVu5QYsCDEi54RlSfAxIIcF8KeRgMPkG/nTaVrcSdagyqK9AqvcERBacrEcTbmN\nPMdDT7mU8pcA/KWd8vcA+IL2d5MzaUuJUOgWCNveX8T2HdW9Qm70NAnHKV0oQExwPiOEBO8LvBcy\nCw/RxtbhCIw9LpgVMGpwk7/twAA6DcRywc4tyJ6q0UGS6/eh49bZOprr1OeMkApcAmJqzNLUrEQG\nN7YOGfC01chWJUgHVQ7MrUVtfULpue6eFEwaOSX6HeN1r/Ta4uByHXPkOlyulzo00JbOV2KPDzVe\nmR2wpBoLT8HBed/WK9w59Cmm0kC26YC4tJsq+ajjyEbjIA56eLh6mSNw1tv8EBxl7HO2AOxGzajp\nJZK3WTMxk6L6LKvLNSEgImPxCd4HhJCQfB29CkvsscdZLFGei24XrA6RthiDrsAPfTJIyUXuXJ5A\nxuldieXbAszujnYrcM9Q9wq1Bck9dB2IjwkuyPipLebolgFcOtuzpzhsY46j+3XMUdTkm9Fi1Nai\nzV61AHfUeQY/8/yr+zSkVGOJpbryQmqf/6JcpxbwtXpTtypom+sw0DEI7hFzOJPgHEP1OjFJ/Xrp\n2OPMfQ+Mg1frTthCZYuqw+5UXrIVo8vbfq6xMkOonZeyAEsoyDGhLAkpVlerD0KoqczUPsJNWcHT\ntwjlgnFuRj/A2HbcVAFFDZUAxxe5pgx4wDHGpelkeq1qt4a2JjQi7pQWOAS31Jhr9PBXGTkklJAA\nH7ff8/pdY2wbZt4lDYimpWUxs6ztW5SL5WjKswgcJ8W6tzcdxWJyaAFG+SBEF0sNqnkgxAXeZ3if\n0UsGmBgAACAASURBVEecGYHOYwQ9TyB2PAdyGda301nNBgawyEB6aqu+zSPreCyIKSEsCT6X+rfU\nDrgDKigysYYJNQyIstRAqMtZzzpNvpkRdoDR3QpV71FcqcA2/gjY7nugvzt8rlyPiTpsLUZVvxFw\nVhegAKCUz8YILaQr9Tm52Ib2TsASAFcyfCoIPiHFgCX0WTn6SDdCztFTTo2f18y4AjQIAlCACLIY\nZYYRhtqIRMDp1kipvMsCmGLTdusxYWnfZogLlqvY2OUFuHL9fotr9TrpiBp09M3YfdfuGBxvKebo\nnHsVgC9BzU9/K4AvKKX8+E79jwHwDQA+GMDbAXx1KeXbqfyzAPyPGH03v1tKea46zvsB+DrUIUif\nC+CfAnhFKeUtxy7uXoNjMNYNl4XVGHEZAx/3GK3eI6B6mqmNn9o+Pr+sDUofpjmv2wxYJ6rTXaya\n4apzGnscshNuxv30jB4acGXfkWzDv9n1PtV0jLAkhKUgpGoputbQgt2nSS2lYT5KxNF6SwfMXa4w\ntrm+1kvZTcCSXaYiDIBWAxtUPSHcSH1NuhGrkAg4K9CGM/oGhmtZRrd+cgPJUAd1yqmmhKRQc09d\nKcguIQcZN2ecUSORX5yHTbf+GCsEGG3yDZfo0W94vFhmo9axUyOqq1U4tTK/ZGxbCQHBL42Yk7HE\nGn8cLEcBRW0Zag7CLOFfd2Y2cjIK79AsuyXL0Tn3aahA97moo5q9GnUM7ReVUt5l1P9AAN+Nmh//\nmQA+FsC3OufeUUr5Pqr6WwBeBH59xuPIZBbfD+ClAN4F4A8B+M3rXN49BkeWSS8sTtY5TrAXg+Rt\nndLhE1ybkgooLX2jE27cCoqcF9iJLyuxZbX49Ewa2wEBeH0cZ3VRwDhapKOrdRxblQcLWJP9S6rW\nYqpEG5+BsFSyjRPrkEFRtjmuyEvWHyHp7BFxrHUNnEdHyTnnbt0TK79tb12AkGOJM4KOjoPrv2SU\nNeCDwwiGnvScitSeZWiGlMtoAzMsyNEjlQKEAud67FGie5LcnyCp99XV2usIO3X8Lh1BpAg7YHuC\nf+0ZsFu1xhz7NFweMl9IPQsh40jktG5XVq1HHTFnuYrwPsOFhOIbQLLVeMQMZlc2P+dZW6PuwBOR\n23OrvhrAt5RSvgMAnHOfB+BlqONmf71R//MB/GIp5Uvb9s855z6yHYfBsZRSfmPnd/88gLeXUj6H\ndL989myVPEvA0ZDZi6sZZtptqmMLmpADYJ19w+c2NVUl44wzW/CoMjy6TFJA1wG1W5lWnNEi2GyB\nMQ5knP192W27ulZzRlwW+CXXeGLjMLgFIwhqy5GtRA2WewQdy3qEUaa5HEdSO7ROW4mP4mK1Qkia\newFDxyEoTfzgGKMsGQj3iDkWSDIjU95juaeynQHngRjra70EIOcMFzJ8zFhigfNir1XmqaRtOMyG\nsOV447YHIhDJ5BsAKyiK81bsT5lBpNqpMixBn+NFBsYLkIxMjzEfN9Rh+GKqnb2QkYIMyeS2HQer\nHWD+AT/bmWdKOjFPg9wCODrnTqiTTXyN6EopxTn3JtTxsS35cABvUro3AvgmpXtv59zbUO/iWwD8\ndzQ8KVBHffle59wbAHw0gH8O4HWllG89c0WD3HNwtPwZTeeVWtZ1/FG/8FB1uKc/BPDzmtMYIifI\nj/Mkslu1J92XtXwEqnGexRm4CWgKK9Wa/Pg0gJ8m8lyhTnzc3bIBeY0thiX3uGJqpA4BuXOgyHFE\nHUNknVUm2xr0WLcXa7QS83dm4tgtOyd7X5ZVJrpZsj+wJd+wq1XqcVmkZUR/Llon8UcFisM2qrs8\nJqA0Ik8uGSgLfAxwAUiqh8GTE8vpay4SUB2wgN03YXDMDRz7eKlCvBmn6arpJ3Vou+pW5XlD+jcn\ncFl1C0KsrNXFx9rr04QcfeKW1SggynUsb+kKjlEVsO4ZLc9HvShrDO0XT/Z54aT+85xzz2kZDD+H\nann+E9TRXf5bAD/snPugUso72j5/ANUK/QYAXw3gwwC81jn3nlLK/3T0Au7FU5iL1UWfVNGEB/2C\nz2KO/Ld++bVnLVNSSfxFA9441FpfbsHOmlVjtDB5bNSRlbqdHPkEOx7Jx5f9HQpiXhCXVFMzloIg\nwChgxy5SsQoX0jE7VccZtQXIIMjuU9Fr65LrWJYlVB1QXWBska1cx5uKBmZ+/RbSOdKxBcikmqT0\nHEMUN6mcr6P6sl2oPsccmZgjQCidGmnk2b2daizS5RqPXAqAkpHa3JkuBsA7yJTJCyKKgsEeb9xC\nYRm2xHqsF1Kdt8t6lAp8mpAjtKA+VFydV7J+VzXBo7tUq0UZ2ndZb4TMs5pCRnG53hT9/c/aAd2x\n1p0aYAuoq1yH6fOY5RYJOY9bSik/AuBHZNs592YAPwvgvwLwF5vaA/ixUspXtO23Ouf+KGoO/gUc\nDwn3Bp3Sid4KsEsZr8sHEGv32vlc4zEObTJjceNw2gYTbjI6SYcZrcugY5CUwQM6eHYrdAQ6Ozap\ngVEGD+ggveAkTNSUEa4aKGbUIcoYELW1aBFyOE2Dmann3Kp7eigdjHXQ9iz/kXWguo+LkMPvi24o\nZ67VRdUNah+VlrGCGrtcmZTDVqI0+HLvZD2retrV2vDNZSCegJiBq1SwnBo5KxZchXrSlTVaI4EP\nN3NqjBDJ9JxxjNROrMGqq+AmMccKh6lZjHWouGW1Cn3bVwYzGIGy6tp3GRLSEuu36zNKTED0QHDb\n+KKFXzokA5xvY54GOeBW/c63AN/5U6Put37XrtvkXahvzQuUfm987HdO6r+7WY0bKaUszrmfAvAH\nSf2rqIDJ8rOoY4selmcBOGpHv7HJrg4mQWh3inadzmIPro44EmQ81QZsDrLeh28Og64DnLg9x8EC\nrhCG7WWz3mOKY6rGlhHLg5UvRv1lcKOKtQhJzZhZiXs6JuJwnXJGZ5F0ilFHE3Q0WcdaskUJ2AB5\nXTnnhl9UPb1MGBtSi3zDQT2LmMP6qPRsFXIcUhFyBuDUulN1syL2uexT6TfLBTk9AcqHqPOAaJdM\nXcpUU92ulPjildI7yFBxMqx5xBW5Vv36/Yi/pluLidYFFBMcZJCDOhG596GOGOTKea6BtBH8vJiM\nw20KtzODzAgQdyQHwPEzPqz+sbzlnwEf+j/Y9UspV865n0QdH/u7AMgUhi9BHQrUkjejpl6wfBx2\nxtN2znkAHwLgH5L6h7B13b4Y1yTlPAvAkcVvVy3PqwZFTtewiBbDcRoZpzFVV7bqCoKVVM4xR7EM\nO1uVh2QTwFwQoBPw9binev5Gm5xj1ZsC41UDxkykGwE8dquypah1hbaPEHIYTBn0dIxxj6ij1y03\nqs0W2bpEr2M96vdDex3YOrQYqrI9I+ZYxBvQtgZKBkEBQg2GGgCZnDPTAT0WKavNzWpd++i97hfa\nH48m2QgztU9JJTHH1IBMwFFGb5WxeoTW1kdzEvZqAMccqzfmtL73V4i9UxtTpV+LmW0FS/mZyH3V\nHARZ5/pa96RNydtzq34jgNc3kJRUjucCeD0AOOe+FsD7lVI+q9X/ZgCvcs59HYBvQwXST0UdkR1t\nn69Adav+AurQo1+KOiEFk22+CcAPOee+HMAbUCe1+BwA/+V1Lu9ZBo4kujcXSa9fcA2gVtxhtRzr\nlFTOFThf4FyBkGzqXx8+rn+kUkdAUiYLYp2AJuchLkM9naIxA03Loty1GMVaFIKIzKbDIMlAybFF\nJthoNivHF62YI9T+MMqPkHE0scYi2hxlDlr77n1FswR/TbbRx2KX6hXpLVKOEHEiHSNRvUj7aUIO\nxyU5JssdErYaLSs7Nzfreo5bgBzBsfcKNBOVLUTZZouQBw+PbVnBEZAsxs6uFgiVvMZC31RGRJ2T\nsoJm/QYX+m59yMiraxV2nFEDn+Vtovswtx6foNwCWxUASilvcM49H8BXorpHfxrASykN44UA3p/q\nv8059zJUcPtC1MkoXllKYQbr7wPwN9u+v4k6g9NHlFL+XzrOTzjnXg7grwD4CgC/BOCLSil/5zqX\n9ywBR8uVA/sF1VRsPoT+GORwQ6+yAK4gCCHHVaYnDyoubtYeT+QJh3VMcbQkexrIGE8U5qqeRYMZ\nrePAADxAefsrVzgtC8JVQmyg6NlNKn8a/BgYtYXI21yHLUMGR8v9Oos9wigTHaguMDTkw/ZezPFR\nANOyGBdVxuQZrhPUOqgeE3Bmif6yLdZhof1YJ8AnsUQm6+hYpP7Tbtf2E6dcDa4l5UrSOeUah6ew\nnRsGFJdT671SPS9jJ9tUXbUO3RrTtHMaqyUZ0ed2rIzxGpdcmvUpuY4S6ghuQQgBIWRcOQmw0ola\nDFVN4LPakCk3ULN47peUUl6HmtRvlb3C0P0AagrI7HhfDOCLD/zu9wD4nuNnupX79zRMmbC/5CWN\naulo3aJm8wcxxCEqGSe08VSd65+7AKH0jcNqIfYh5XgAgA5aWYHbOCCAgKwVh9T6vSmqApYVGAdr\n0XKdWjFHDY6s1zHIGShqd+rR2KOAmJSByi09/4HK9LrITdyqDJi6sRRmKv9JGccFmZ3KFogGSnaj\nChDyceR91YAoACrPgkk5hX7Tul+RlnLdzeXKXJ/14ZzGbzCtN0hYqfWm1J/vQBibXoYwF6CL7c0X\n67EOO1C7kGJhiiUpSR/VeqzTO0vssc8oUgHTAXAezb2aquUYChDdllugwyzceWb2qm5fplbjHbNU\nRW7Jcnymy7MEHIGzlzpjE2rrUTPSrFhEc814z+DD0/ro+CK7WCWtA1Sn78cDAtQ+8hX6jBkLRsLO\naEH6df0KmpUaU1qB8dSAcSDe6HUNlBxvtNiqmpQziztqq5Itx6K2gRFcj8QdZ6Co3YXXBUmrXZPG\nU8cWpUx0Tm3reCOTa5JRzgQd2eY/jhvKOscZGQgFYBn4dAeFrUmWMl5mH6wxoXi/nnedT3GBjJJT\neT16to16UTwbZP2CrprFWC3AhMpGzejRxtC6l0zEEffqdlYZ+fZ6PN/7BOdjYxypZ6efoQYWBkwG\nj7O49wSbYo6PXne/eyzPInCcvJ06B5fvSDDq8eE27NUFvlmOISR4l+ib4thhbaXH+Rz5Qx1HzAnk\netUW4shmTbTvaBWO+ZUFAzmnxRgjWYyHgfEcc9WKQzKhRluQen2PiMN6qDIY6ywWGSdjC5I3Fc1Q\ntTpUukGyUjjYzSp1WCeWotTnbVlablUNmJG2GRhlXUDz4D1hgHRAneminb9AomRDSlxR1nl+xmoF\nAhKxl5hin40joQ803uHQN7uQO5bLCpjj9ydDNcp5e9e/4RQTclyAcLLZqSLn2g2rfTHv2BMQ7Ra+\nzn73WO7h5e11gaK5uluVXazASHe3PhIArvXiOzNVgKy0Q44knf6BCrVcdDJ8nMyGIdak5Ez2sVDH\niYhnM3doZupIvnkkYJwRbvbAUZNyZqQbbXUCIzjq/Xhfrbe2dX1LrH20nHun9KvJRBv5jXOEHCbN\ncFySY5e6HscSeV0TcfQ2MFqL1xT2KubQTfESRJ/WUxxHv+lWZIU6kD3YE/z7SDcRMpC4jPIqiRsC\nitJhrDVKq18vqjPDJf4Y6/dr4ZXuFGvPknalziRON5Tcge/y4lY15R6Co0YzXWaIjglYvUA5rHYl\nrD3vFm+Uv8CjzFQZh4OrERRtPY65jxKHtJml3VLso+PoY21H0elkn5NK1/AzwNsDxoSRvSrbbAVK\n3WKssyuVXaSWTluNrOd11mmX6x4hh/VW2TmZMVN1HHKPkJPRXaQcWyxKZ1mPmpTDVmNROrYmrTJ5\nPieMVilUHetPXboDEDzAaR45VNIMUN2sYYg5+gZqfgXQGlvsVmMn5dTxUqtnuEJfh8buVhWdp8hl\n/Q5j8+SIod2+zxDXb7kyViMQ3BYQpLNseQP22pXNXbIk7pQ9RrmAoyn3EBxFDjw56+ot8hi7rYCR\nkGMx2AA4ilewi5PHBOkfKyAj3Pi1XteJ1eixoKc6C5u1Dx5Qm4ptDmOPNZLFmJdNuoYZM5yBpLhQ\nNTBqEo5FyNExRlmXBrkonUXIsQg7MNaLoWfQBJVb6ywzt6L1DggQWsxFIdnMyDjshvXGupRntfSG\nXjp1rGOXqlwTk2/2CDkFPZg4AcTNvfDt/QIgaR7RXQG+InQfBs63vubS9NVKdPDre17BsL7nHr59\nDwuEcFMgxJsTvft51UnncyEvDn+fVzjVx+KMBy3Py2Kus+t7Qo5f5VCre8+R5xkg9xgcD0aZdY9P\nxwY0MFqEnAAgZLiYEOKyxhtHK7FP59OHepPpfYScIEPLAR5jCkiPPfbh5vrgADJoeQdGzqfkgcvX\nxkKGhFtgJ/jvAaMA3RVGoLRYrdkoZwtSk240UWcGmJY1eYSUo+sBW2uS5brWIzC+L5qMo98dds2f\nI+NwLJHBlfNxdU6jJvrI9cvvZLUtAFrUdRS11NfCouOtLcQQm2WbXUZ0CeVBnRGyYjePk5pRIA5Q\nGQTArduVpFP/JUjqf1rBUmL0UvOKOo51yICyAuZCv9y/p9DjjnHBEiNKyEAINiFHxAJI3a4cMgR1\nI3PLciHkmHKPwRGYulhnblNLtFvVqW35ICxm2ypjmoYQcnruI8/UIQMF1BZ9ZKj2WORIvBkHFRjd\nsz3OuOZHpjaIuIyVKhbgEYtRA6Im4lgknTzR6TijFUPU5BsdX2Sg41ilZTFKGcsslngkxjiTWYI/\nJnoNpmxh6s4al1tJ/+we1WWsE5DURBu2VC1ykraEZ5Y0S6vjPBFdfZ3lpQRgHDi8BxN6SobEFyto\nCtmmOkuFmbqQC7XHIGVg8UTfmUMn5PB3afqE1/XSOxhWOzAjWeljabfr5j27I1eq/skLIWcj9/zy\ngOmLZvV6dEOke4Wg8o01WUf0jzG3eCO7MquVyHQDAbvaF8ZqCfYZOsQd20f46GScTsiRpqS7bUc3\nbh9iroFlzvBLQljKOlbqBoxmMUYBxqJ0bPFZccmidJq0A9hAuQeKWm/V5Xpab21b+zyKCChpYeKN\n3tb7aAIOcP6rZeDbE6uO9pSIWMnsJ2zv4STMIECwenmXguISgnMoPrUvoUKYxA5lUPGAnohRXawL\nhJDT84IBGUBOSDqhWYbybdV+RVm/HbZN2ZpM7btdQv2el5iw+LJ1o+pOtgZAqx3R93MjT4C1eok5\nmvIsAEfAvEzNMgPGWA9/5DPmKtA+igJ4KzcAq84NIFeHruppzdVf2NmqHHvMDQSBzkodZ+7gIeaY\nqdoHOm/1SkJcFsQWZ3TiTmUSzQwY5a9ga2Wym1STdDK2AKrjkAyesxzHc8Qcvv2W6xVGHdA2VB1M\nys+JFXu0yDlMtuHf0KQcAUWLgLO31PFHqHKpw3FHIeCwJSnrq4cENkCyJWXEHFdrGtWCDAvWFzCf\nHILr1mJuLlQ067A+Xr9agWIv1v9z2ycM1mP9PoTYUx23HjLIeP3+LGtyK03nE+AbKYfFshp1LNnq\n1Jjg+ISa44tb1ZRnCTgC5qValqGfbOt4EBNyWj3vM0KzHMc8w562UavXFqcTaTDUGxP+u6t1jD3W\nmOK4zoCqZ+9o7lSeqFgAzIo1akuP3aMWMYfjkFa+o3alCqBpgg7X08QbBkiLmMNgOCPm7JFxNBFn\nRsA5JxoghIADbN2SzEy1iDgcX9QEnExlwdDzgAASV5Q/Aceitjk2Kb8p9wKwXYFC+JHnrmOOomt6\ndwVEBxQHeJcRfQJiJ+ZINzFDSDgyZ0YFxIgabZR8Rk9LZqbKWDmduXpav4ulOXjr7e0pVcOfTFTu\n89gO6G+frcZZ+zHzQg038SJPkzzLnoh6K/VHrNc5/sIvu7YEYobzdQ5Hu0WVT36MEwpBh8kz3doD\nuU/ZRToORC5uWM51ZBLOCq4pIaSMkCjOqGOEFjDKOluL2rrcI+FwnRlbVVuQDI6amAN0cJWGW1uR\nwAiIM3KO1IPxyLQFeQQktcWkY4kzUo4m4ch56Y4Zk3QEyDj/UYMkW4e6E8HvsbUtIKjff03UsUR/\nS/wdtet3SwNID5SUkV2CD+JCrSScbkn2cVO727Wmc8QNAEbUMXWwek88AniQcWZ5szVpfbdAafM7\nJpSYAUcXz7wZbh8sF/Rsfdj5CcnFrWrKswwcDX++5erY6/Vpd6x6QXwYrbawAt/WcmQSDdbYR0/b\nYLaq6DoIci6jRchJYDasL6VajRlwM4CaASYD49VkvzJZ13U4LqnBshj1YCxn8UgrvngTQk4x6t1E\nxD2qRX912q2rCTdcR5ZsrVjH0on+DLxsNULVs64BrfyK6khOpd5HW81SjzsGraPgPOAD6nsZfHu/\nHQJKswxHQg67QuV/manGtTpbtqo4ZscZOVbgQ7ccBUD7t5vhA7882AKJjkOyTm8Dkxb3CcQZWS6E\nHFPu+eVdUywfuhUz8BjvXJuBI8ZUp6pqLcY4zzmTBzJ9qOxiFUBjtupC+/WBAbrzaaFj8WwfBJ4t\n2d/nZjVqYLNcqmwxsouT41PsIrVYrNqqtPbbc6syCDKJB6S34pDazSr1gTHuyAB4Lu5o1ROZtW2z\neCPHD/mY4l71xvosvihkHrYWpTyQjlmpOvaoCZJFlck95/iiQ49P8jOj2OJ6fqB96M+F+j5mD4Ql\noTjXBgcQnqmQZrrLVHRufd+Zmdpn3Ogj5vQBAa4Q0We1aaQbWDHH/v06VxBjHUZuCZTzwnmOFmeB\n5WmPzV1ijqY8O8FRX3U01hkIeVt/AAEY5q8DIINfdfDK60fZLUdA5hqI1GIL6PU4ZJ81QHTd1Vp7\n0wKunZU6xixDY6eGhQg4mhhjAZq1vUfQ2QPGrPQzy1HrC20zOM7ikAyIOu6o44wWKUfHHbl8z7U6\nY2myJcjl7DYV96WON8o6xxu165R/X4+Io92qRen5uvZaAgsgRfYsR46XOtpOWN3DzlWOS3GNvRqq\nPShWo6Rv5AZ1Yj3KdnelChmnrDqJYMpJ9rzGPJxuD19IytRp7bSO15a3XiSr48zbVtti3dcnKRe3\nqinPTnAEtg/WetBWDuQm77EBnRByQh+iyq8fYQe9cQBxGUFyJOTwkHEMlmOMsUBGzOkxx6pD+9A9\nFoSU4HNBSKgTm+/FALUFZ4FZVvvOiDkaIPVvWcxV0H7F+E229mZgyXVm4MggASrnpZaZnmXWk7bI\nOOJyteLbOtbN4Ahs3aTAlqUqv6Hfaw2Os/NnyxQYG3KxmgT45fno69F63oc6DSEAJQE5FISUkIN8\nKX0kHPkeavxRkvk7c9W1WOL4PdQ5O+TbWiCTWnEcf0GlAnUQ7bH/3KefWzs4pQZLNUNVnoHWYaJ7\nmoDl4lY15Z5f3o7onj6vR6U7O2pOadPc9Na2W389HthjjlKnE3DEquQ8R4lLjtNcyXEyHVsIPj1d\nZJ0guYGjTy3WaIGYBZKabaqtySvjODNgZOtRW5fACIgzvY4v6jijtiBZx/WAEUihymfW4ZEY5HUS\nwBkw5Ph7xBz9zlnnaoEmu2yB7oLVdSwglQ6gBZBcR28LqGqrMaC7lMk96xLgHVonLiGFPsh4zW3k\nUXBkEqvujeEYocy4IV6WBRKvl++qz8AhpyvHkW+tnhZ9y236OQS64Xuj4Wi9vk8zL8NFnip59oIj\ncKw3Z7nENkNGZareXZsSA+wE9ZGoI0SAeviy6sRK1AxWAGt+pAwA0F22ff91MIFUx071C+owlhzn\n08DIJBpmj3K6h7Y6s9pPA59eLxjBdm8b2AIlL2d6DY5Q5boOjLpajrq+JP43Ew1mmsVp1eU6e27d\nvd8BRsKNMF5B23uWsXarsjVvNfJyvEXpxFoUYEz92JWYAwRXrbUU/PpuCwFH3u0FPYm/ulltZqpb\n95HUDTtto0+l3Mfn4W+438O8/fb5/gL283yarUbg4ladyLMbHIF5707HEIJarm7V2qo4X0k5Tpkk\n3WhgtirAJJ3+kZYVCENDE78CJFYdxx1lm8EXKAiljp3qipG6YcUZBbzyRMeW4CzGOItRaquQj826\nYvzunk4vgdEqZGuQ1/kRWZYlgKIB5qjlyMnuGji0Faddq8VYt9yps6WcQ5ocSxNy+LwEAC1g5Zgk\nH5PrihUs4CciRCAm8rDV3PSS2pEj6pi/PiE5yW7067vd52Tk6ag6W1WYqDJGarUUu2tVk2/Ecgy0\nzRfuUEe+qmlaqN97DFtvgGamnmtXnia5EHJMeRof1d3L7OXVvUFuyOhl8qElCq/VxolUO3iNM2SM\nrtYRCOtPiHUplPUy6JjwI26lNX0kZ/hcrUYHbEk4Ot5nWXp6XbtItTW5B4xXxn58HmwB6vPTVqrU\n0zFIqPocY9TxxrZd1LZIKSokeSDmSF71es81ODYwdPxezcBRQJFTLmDUAzrbdKH9hKlqWb065ij3\n4IR5J8CppYzZarkLua4GRSbkZFpPgDtV69GHjJgzUhBSTnWY1lk7hMHarUpmtIruCnF1p/axjLsL\ntTNcu6uVv1f5vkS8r2kd62swGw2H75HcJ30Pnza5WI6mPIvAcedJWrEW1s+sRwAIaZ3exjmsSfpu\n06JhoxN3K7tQeeDxXl7WD53HX5XcLxCASqwFuSAkGj/VAkNtESZDf46Mo/efgaiON+pjZfW7heoV\npQMtdcyR44yyr3KjFq4DILV6G2ORgKLAsCZJvBvrB2u8iQwET7/jMOSUr2CoLctZTqP+Ac1i5Tii\ngJJcDDDGEh22ky/PfkeW4hpl8g0DvldLri/vCpNzlnYJqSCFUt2riCvwAZKLKFZkj7sL8Il7tINf\nJeF0V2s2v8PtZZb1u3zYrtm5AgQKDs+sRovIx3pTniDSXAg5ptzzywPqG3rC2OoYMoslWAm93Htu\n696jBu1X90xP6ufk4yHBGJLnCIibtZNxeq9XEvnFZcpWozBTO0En1VhjznCptUkz8o3ouLHUIMU6\njkOeszY1wO2VMwiyRchxxZkb1Yo5squ0rTMgpjQC4dKOZYEfA96sjnMqhBeAvGzrAEChd8uBcmEt\nfwAAIABJREFUOB6uA+gKdFJJu4CHA6t6YtEBPbVDjpupToHdHi/oFuQ5QBYLlN8PthQ59ii/KYQc\nBtWmcwvgYyXohJxRUoIPNatRgDCBBw0XF2plnfrBtSqnUC1Daeo6iUeT3HR4o9907xM8W4VWWpeV\n8D9rUzYiBzrhiZiXF7eqKc8CcDSeunXVmkGmX3btOomAtDy+sVX7rjzyTa0n7FXZFjAUck2gj3p0\n7WhX66gLrVWSjzpggWuj4axWI7AFQ20lcgxwWU9x7ibV1qN2kQqIamDUQGhtc+wTVEeOBWxBkdGp\n6QoB1ELlOTdrkXeZkG6WtG8xanFuXj9G4Ip+Z7AiAUR2y8o6g91MBKT23K/CUmVrMRn7APW5cT6j\ngNh6cuhgbJ0bA6Hsz6ApwBtJ3/BrjT0uGS50NypbitXg7B1CORx/L+IiReO8Sg7jMqRt9DgjcwV4\ngH8R7xN8KO1ySz1JuTY5CG9bzGTrPm3knvsqn0Fyz7F/pxdmvZgW+4zXNUkHaG7V1lN1ZQUp3pVj\nHa65ePpkxxxzZHINwGxUZtbVeOVIyAnrvkBIGS7XGJhjENTkFotUo92fDIQMcmyJFLU/b1vAaBF5\n+PdmcU5tjRr6clVBsSxALhXcrpYKflftb0l1W/6urnoZ//3/7L1/sDdLWR/4eXrm3FtLrBtrl3gp\nShO1EnGtdTVB/FEhanKNlFK7m/gjgpsVUXRxMbrsbiHWajS4CWpKQDawUmWUQmtxkWipVEoErZVE\nJcQLYpUCrguEEL13RREMyr1nZnr/6H6mP/3M0zPz/Z5z3ve83/c8Vd9zZnq6e3pmuvvTz89+9DwB\nacz1bP1iTPkfbdR3fl7fV9vG7RuSRHx+hnhu3stont+mewsZm9b6Fvab2UUQ62c9nbO36LGLI263\nt9gac7+dcj8Gqv5dOMWYVQ8ca1ilKDGPn+ITzDrHsj0VxzeO81gtzHgeU7PaZMpi1UxegBA4xx7e\nrbIlt5h7VJ3job8dOC4izxGR94jIn4nIm0XkSRv5v1BEHhSRj4rI74jIM1byPk1EJhH5KZMeROR7\nROTdIvKnIvK7IvId262t6cQ5x43H8y5XYeHMfyXHQEe6CDb71gg51pm/juvI7h1FF8Kh4NSClQMB\nBEorZfNEMqZZutPJxgKVBUhnclqAoQeMVjTrlbUTr50sW2WsnpLbbUW8+TiSXlG5ROYQp6kY1ejx\nLDiLGdgcLsra4XiM0uySmDO7/vUCnMciXpWcX8V1gbjILpR0ZcIwITmisz4x0H/WS7IhDhvfrE1m\nzDmzsY1ydTDnejzQNc+vUcWnKuIdUfs59pRnKGW6Dhij+j32M5eoBjjqtpHGyRmNk34edyE/MAca\n1zGnY1AXrGyQoxGulAJGiMq/PQMcJW++2JpjXLrF0/IVGeSIyFcB+AEA3wjgLQCeC+D1IvIpMcYP\nOPk/EcDrALwcwFcD+CIAPywivxdjfIOT958CeJNz6+cD+O8BfA2A3wbwWQBeKSJ/HGP8Z3sf78TB\ncQe1RKz8H/BdOToVq04I5OuYwIoj5GgRGwTA6DagVqk61xSLVt61XCito8EckNw3uoGc/nViY9AB\nlkDE4DM6P+YYGNwGk6/FEe4BRivmBer7c1pur4JijAUIR+W+YuH8RgJHIJ2z+JNfk6UtqSZfty6E\nQLY5ibUPuUjOq4AaEiiqWFamBKhzvfr+QwZJq08E6v6qaZxvi7Ye1IoH9ZylEgySI/3XfsbGOyq6\nZT/LMT1fGIFuiJjChNDxbhp1IIwyLrpqnAjOkNYSOg5rW4D6EeoXxBFy5jShIOQdrXI8QPTmD6Xr\nOONenUHOcwG8Isb4KgAQkWcDeCqArwPw/U7+bwLw7hjj8/L5u0TkybmeGRxFJAD4cQD/EMDnA/jz\npp7PA/AzMcafz+fvE5GvBvDZ+x4s0XX8VLee7FvwFOm2w+d0CVMRq0J1gPXg41inJXxcCShe9CPF\nSq5EvaldPMIMhOTTqBzoNCZ94wgETwfIkxSLJy2nxiI05jQNt7bgLtdEd9Hk9ThUOPeybSeQVJ2i\ncoqqz8vMc5XG+fQ2FgjPsU2Dk8bdxwNXoPjOK4WYjYSoDgXvs1yhCHGzffkXJzPvKgfHQGi5Oq/h\nto5xR162ROX+oGW0Dfqd2OhGUIOkpo2o9Y9d6r9hBCRGdNOIIai+sQZItuQuhmrTPIZkNsQp46xs\n6dYhGfKoH+Rk8CxWaSITJEzpFW/MC4tj4NrOtjHUhmKHlGuRiJwBeCKAfzLnjzGKyBuRwMujzwXw\nRpP2egAvNmnfBeDhGOOPisjnO/X8KoBvEJG/EmP8f0TkMwD8dSSQ3U3X9HNdBh34tVsdWZw06hQa\nMk4CZrBKWYoVHSv/W8Sr4iKZYn2Ixk0FlgY5OV+M6Ibk+C8WlCy4MDfGQGm5NytGtaDnASbrpqze\na010a9tmdV8kBo5jFo/GAoCzuDTWolUFGGY++RiUtsY8tb6ggmpLU2RiAwAo9jF6rO0NUp6n79Kz\nhFCDfJDkDygcjk3fOU/S3GBuXERb3DdSHn0hLL7l78z1KmAqwLEIVtMVAK0VK4NnPpcJkAh0w4Sp\nL+oINcApzvxACQLAYtJipKMxWNdJxawKmkWi02GcY6tKiOW1rjn8ry24d9Edb5jzWKSHeNikPwzg\nCY0yj2vkv09E7o0xPpI5yWcC+IyVe38vgPsAvFNEtAf+rzHGnzjkAU4YHA8kNsu2ZN/SPCgyWAlc\na9Vl9XFe2S73eNSqlXMcSOdY79TB7h3z4MWEMCaDnN4CI1ADE7AEKaAGM+Ymrf6wJXrluj2DjzVg\nnMx15mCpXXEgMWksXKL+Z7eMcVqCIIOUB4aTk3YR8qY4xTSP+ghMYxKx6rP0XQL5rksg2XWJ81Tp\nngC+vrHlVrBmAcsBBVgnKI0f38vqDlnH2FE9+p91kurJoFzklPrxCKR+3RWQY7cNjZJTj5NIecrg\nZcmL7u4hzhhMj7O0Vp2DN/QDgHuW80VrNt3wIrvdNHbAuIEEP/Fa4P96bZ32oQ9dXZs8EpGPAfAq\nAN8QY/zgStavQtJZPg1J5/iZAH4w6y5/bO/9Thgcj+iNLQW7l8b6ILJgY+4xVVkMCWQecMUgp97j\nkf0e2c+x1i8yWPa6eo6JYwwOoFTMK+vwRpNmz4EasJQ8EakFUE73uNI9wEicbsz3tNyiumBU3GOs\nQY6bP6F+FE+8Opn/xxB3pbGRrufnzrVpypghPpCOANAXLhJd4rQqcDtkdDMgclq+TwWQeo3Hh75w\n1Ycy6PGxXuM8ng9kBtcwANKn/g0BNJYqj4NazFovTNWCVYMA1OHj2Ee4+B4XUgvZRDzOXTEqGmlH\n+QTcOjSddoDjVz4t/Zje9jbg857cLPIBpC95v0m/H8BDjTIPNfJ/OHONnwrgLwH4OZEqzhRE5FEA\nT4gxvgdJn/nCGONP5jy/lQ14vh3ADTgeTVsxEc2g6GincAZGFomuiVTZIAdmoKbrxRK1iImKJawO\n4G6aUixVZEMcBkNgCXIMRBacLOCxmNVesyDogWKZi9aB0Z4j5VMHftYtKreohjZsYHNeis5vl5cs\nnG6vMbEIdi9ZqdrkXJvoXKWKfE2PRwBnmZOUDF5BI8lkLvKsT9d7AFG5yFYggLVG2wWVpnsGOMr9\njajBUqgOlcRYi1XuTzaIOXOOMfVj0VirUw5IPluoJpeMWg1RRK26IB2qDrg0vqmp6PN5XNYAmUPI\n2UXynRRL1dDYCYbucDAeu/bcFmM8F5EHATwA4GcBIAPaAwBe2qjy1wB8iUn74pwOAO8E8Onm+j8G\n8DEAvgXAv89pj4EvFDpomXIHfLrbQNxPvJVhNWFkEKM0Ng4oRexuALwh8bBY8Rbzc9VhDvMgVWvV\n1Lysc5wS59ixWJQAptIL2nMGL2sMY4F2MHlYHwhK03Ouy4p217jW3C4Wo6oVquUWZ9A0j6vHSixS\ntdzYmjHOli0Lkw4orz67T3BP+fiapnM3O8uLAzbcUVK3jy4HAhCgngYUzPgcWE4fitQaUIC/I39n\nFrtzWf1+ylVqngC/v7FBjsqaFdhznm5MXE2YJqBLY+IcqqJQnaPq9nuoD+PgSGA6Y3zDu+Msx6oZ\nj/MigF6+hyctX+lrTGPXYewPZ2/HznaCBb0IyYXiQRRXjscAeCUAiMgLATw+xviMnP+HADxHRL4P\nwI8gAelXAPhSAIgxPoIkJp1JRP44XYrvoOSfA/AdIvJ+AL8F4K/le//wIc9394GjdWT1qNXBe3O9\nT7NLMD6OsgC5sgFyouWKi8GzuHwU0WthWAeon2OvnGOkPRuBtt7OAz1rkGM5NwY2JctN8jED4GDS\no1PWcqcNYGRuUXWLKkKNphnMMPMaIWL5WKBzYIkX9voatQw9tbswYPaUlw12Oidd/6vhjhrt9F1a\nKHRZJ4k+A2QWRS4aYSdrTWsFKLf5WfSqXKKS1XMy96j9kA1yjAFO1TfJ3UPOkK2vUz8fpUePMYtI\nO5SoN2ykowY5OvZ6h2MsY1DdrpYBPFg8myLkAJjHfZkHGu+sZVNj56BDVl9XQFPXYewOB8epWzdt\njjG+RkQeC+AFSOLR3wDwlBjjH+QsjwPwCZT/vSLyVCTr1G8B8H4AXx9jfOOBTftmAN8D4GUAPg7A\n7wH4P3LabrrLwNFZyvV+cvVmNt4Su3L0FUiy079tSR2Zg4ldPDRvLbKtOUcBIFNMOidr3cm6RQ8p\nePFnxazMIbI+0XIAFtys4U4097sAMLa4Rf3vPSpLClmyzGCpxFLni1JrbmQAtAye3ttK7bg9Kmqt\n6sxi1lWA9Po5c27M+Q0mj2exyn2HRbODKTOhBkR+QHvvHnX/HQDpcv8GUMLHFc5xjmQzj4nismEf\ndSk2ZVpe6zHiUS0vk1OGaGvOkEb6ncJiHkExxpcjOfV7157ppL0JyQVkb/1eHR8B8D/l39F0wuDo\nLZMb5K2q1/IC0ECYrHOsI+QsxaRlu5xpXuWyjlENcpaBAeJcp4a8krn+mIKMR+IcLXABlahqIS51\nwKlCEw9dPB0hzzc8wVlQ9EDXACPrF2dukYDRcotboMhcG6dHLJuueeCk7yHblUZK78w5UD6RilYt\nSEZKs1ykco8Aif7IJ3IBkLoYtBIxtiKdzEMwaAbnmEWqHKCAFz5qkBNNfT3l0WMqK2B/xwlDF2ns\nlF06gAJ8rF9UgxwbIUfH0vlizC3HLo/rrkti3TT+Zb/HhTVgWtDtc91Qr+rDy502nTA42mltA/08\ngPRWgiaPxl2sBpBZfbIzv90MuW5v2cKKuUYV+9Si1rLrB1ik6lmrWu4NdF0nMNCxB5ajqZs5B9Yb\nWq7RilYt28ZpxDECNTCeD0WMqs1gHaN9dK2ypWfca5Rjy3l5rOTd03fq3MiMFkvUPP0jR4rjvBW4\nZjFrzMY5uovIWZ/fo3KQLN7kRrfURp7EjA1y9CVb30b97pZzBOq+xOJXBlfVOSrADmqUA2BK21il\nDY6VcyxBADR8HFCkLzbIeE2xGpfsumHP5yAdYurxDHIszmwCI1d06ymFJLkBR0snCo6ewfwO2ts/\n1CG4qwdTurS0dLMhq0o1vo+VkvpClu2vhhkkZ7DMK2ogWfcB8MGQOUfLNeoEyav22KhrNHXB1GXZ\nOCuJshyklh2WolQPGK0Yddg457S1dO/6XuIv2zLEsTrOLWMcTZ8oTfPx+TmSmBVTsV6dt9liEatW\nbhsCGB8S1P1EQY53/eBvraDIAHeGuh+xqNWK+5lzNNaqeiz5WjdNGGJMfsU0DjQIgHKKiZv0VBll\nzC2v0WKz4jyL6HbO2+UoOa1p5QChVU1HzlsXpMRTHw4FG0LmO55OFBwvQJ4Yyh4rOOZVZNcrl1cP\not6srTgIABvpKKeoYtXiM1z7NAK1HnPmVqeYwsUBS/mi1UOyvNAToVrdIU9u3uRodYe2Lr2/NdaJ\ndd1xXAHGuARGxnSea3nu1//RHPNX8bDC5jmWVBhhDXGYKWNjHI+TZBsWtmBV/8gKIOMKQI4EkAp0\n3kNaMacVjzL3yP1BWV027mFO8gzrfU7r6ExaLpvCIbKUppsXoqVJlpssfo4lqHg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UAAAg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qfo\nre4YYg/3pRch8rD70zpzbL11sfZcqIti/bqWtmqprbyvPAWORXI7jkvyhdv/f50xyM1y7MmZgqOK\nxhgthVIBThMHe8cBrStWY43KrOF45EA6ZtjsqF7/NwnHRfamKe8fQ5I5xkq0dRch1pyiWwOhtSfv\nWPC6k6f3bnjy72Tgfcyxh0Bg6RxLx629Kmu6U2KWx1iTx+wv1S+Kpc/ujyizTl/mnlVpgdGGc3qf\n65TNcuzJ3dBFXIHog6cmFDMCLP3MAiQfJ6gjuBE11sggyZRTDS4ulYG569UAZu+lPjWtwoKLLR+T\ncnGTMcRjn8o7eXrvNNXjTmWNQHOMHNsvHWp3nTFK28YCoa0/ZEH2/s9RxoztD5ggYNk5vXJPz3Wq\n71mRTObRMl+Pyp0+IKfIZjn25EzB0Qq/AMo01YcXqDRS3WeUUReHQ0tBFTpOAZATFke0CYq3Mc/g\nB+bBQ5UOucfu8yHsZtXyIcA7Jlm/dxyw7BI9ZPVdFjCe2nZN1ty7lymLDMgLyCl92Z0A5JIVuXQv\nvXPZfv6YuCX/X+tlPBozLNjYfx7QWnF6Ib2gJPtkl8psDVp3rHW9sqUasPxFb3JTcubgaEHRo32j\nFdS0rW65p9SyneKGtyNtLcPGIwOjDRxaGqoFSzHtVUwvbtmCPeFDegB4CiiuWVyHQOaycxSvAtR4\nsHEn52aD4LINgFNB9hggXWuz9v+WDJxjQLKnuxA+WHNTdQxyXMeBSxuw1HrL4OkFLS1QMigC7fqN\n2pZ1PEErxzSvGyQ3t2pPzhgc9YVQANIHUxc5tqKWIbtV7flsSoiSb9S1anUwut5+r80pdb1yJ7ap\nwjyAU+VudJXeLeSa65KL9J036YK9Yznkq7UBy6Vg41JdWtjXNod0zDTVF4tjkT0ij7ax7legtUKv\nSzZw7MmZgqM+WApyGi/UBEIGyIHq7QhTz8XH6TFAS8Jxph2Dpe6zns+jdVgp25/K1vdQwnV0vXPx\nOVbkOjrHe51kc1Vy1eSdK5clRF8KYFpw6I0KbIduz2XrubzWduzo2QLttV1r1yPuMDDqcTZ4ep2p\nHBd5SO6KB+vK5Jy7kyJMpNF9BTB9WGVlC1TLTV9OXjtKXapAa0UqWN1G9dHxnK5aB1On5dtoxVqj\nNofD6q1YMFVZ85Nai9XKsX7NE/yT44ntZ8du0sqpZuYx7Q/5da21xbJGNOlZLz1Q7OVjjKbcS4ew\nbfgc7D61daPR6/mtvmeFLhF8gDlorn1vVymb5diTMwVHtfY0JqijMrUSeQoaKxxHdHQeoCXrjLTP\nWybeAG1SorbhMjAHqF6bXjt7TbbtUuBs6RiVQ6CobY6RQ/9r7birYMn0rOvrlp5VdNlyUfYPx+EO\nyaHO8VBnv/S/OF54zDFLwUx7jh4ziNtw8iS3t23sddj9HukHmLti+fyjOYb/11XLxlbtyRmCI4/c\nIio4ah3nOWqdzWvgeCXnKDIDFaauV+4BVC/nsTNhwNJsO922fO4lQDkGbI4BRW13iixZrccIT/2z\nybpcRqd6qgVxTKd6jEW0BuZLx1trjvX2fL22bBnaY+NCm17ZgmrPomR9L32kB9L22ja5TjlDcFQJ\naF2oOkpTnbUY2N3CnTnnKNp6m7l/u9OGhdmxLGsxwGNYMG8G8MxO/TGgdGruxEWsuctmzeg1vAHA\nf3WJ571X5OcB/Nmyf5nMxosyJU91Bx7Ttvee8HN+KAB+SoxzyYLtXcOhuOaxscyeRcntr9Mq29yq\nPTljcATaGCPnHwKtRQm0MUYbR7QAyecAalxRhUk4PQuRpcdcPaUeyCDxWQvn78lFQO4y3JyHwP5U\n+dsAnn5Eu5vO+D9Wjk38Pva+j5U1MDlWLuLGPQVUA/Jz/rSVNta6O6V+aSo3a1Wutbfnt1aqPZdN\nYO6B5XXI5lbtyZmCo4Ki7isQ6sPXiztprFAlmnoGRH34rduTwdLW2/1kyr3rstJLwlN370cwf7HX\nZgQ4RS4aNzzmvEC9n971L+l00PLvFupOPde91H7pvo8515Ir8jLklHhlT5gU07t+fc6F2vHn0LnR\naWvP1WvDx/fqbRyzd4yNWeq+Pe/S1D9XKZvl2JMzBUdmpgL1geMOnh9CO80MUH/4HilmraxyEeKH\nJeUcKyOAR+mYywSym35E1r5fve/Hm+h9r2Xm36RcZqfJoHLq770EWse0B47/fo8ppwNte1MGXabL\nfE02y7EnN93zXaEktK5NzmO0D+IS6aUnF01tuKhL0l5L7zwBeUR92XLRGON1yW0A/99NX8QNyN1+\n31eVkhAAfHTh/9l2F5ElMDomdWVJemShJblOQNzkkJwTOD4hbx654n9zN35lvwvg167gvHc7Q/R3\nAfzqTV/EDci9cN9XYVVc1XN+p3KV7sWpP3vC1f2PD+Fi9/CvLvtC7iqRlM5jpCIizwXwN276OjbZ\nZJNNrkC+PKX0Ny/zhCLyiQDeDeD+OzjNRwF8akrpA5dzVXePnBM4/j4Anw/g/QA+drNXs8kmm2xy\nKfIEAJ8E4I0ppUv3pReAfOIdnOKRcwRG4IzAcZNNNtlkk00uS+6F5K9NNtlkk002uVbZwHGTTTbZ\nZJNNjGzguMkmm2yyySZGNnDcZJNNNtlkEyNnA44i8nwReZ+I/HsR+cci8p/f9DVdVETkJSLyNhF5\nVEQ+LCJ/R0Q+pdPue0TkQyLyURF5k4j8YVN/n4i8SkQeEZHfEZGfFpGPv747uTMRkReLSBSRVxj9\n2d23iDxJRF5XrvmjIvJOEfkM0+as7ltEnIh8r4j8RrmnXxeR7+i0O6v73uTekLMARxF5NoAfAvA/\nAPhjAN4J4I0icicU5ZuUzwXwPyHPJv5M5OU1/g8R+T3aQES+DcALAHwN8mzMH0G+51t0nh8B8CwA\nfw7AfwHgSQB+5jpu4E6lDG6+Bvm3ZP3Z3beIfByAtwB4DDkd6VMB/HcAfpvanN19A3gxgK8F8A0A\n/lMALwLwIhF5gTY40/ve5F6QlNI9/wHwjwG8ksoC4IMAXnTT13ZJ9/dE5DnvPod0HwLwQio/AODf\nA/jzVH4MwJdQmyeX8zztpu/pwP3+XgDvAfCnAPyfAF5xzvcN4GUAfulAm3O8758D8D8b3U8D+Ilz\nvu/tc2987nnLUUR2AJ4K4BdVl1JKyIu/Xea6PjcpH4c86eK/AQAR+YMAHkJ7z48C+Ceo9/yZyHPd\ncZv3APgA7v7v5VUAfi6l9A9Yecb3/UUA3i4iry9u9F8Rka/SyjO+718G8AwR+WQAEJGnAPhsAL9Q\nyud635vcA3I3ThR6qjwReRLQDxv9h5FHkPe0iIggu43+75SSTqj5EDJY9u75obL/IIDbpTNZanPX\niYg8B8CnI3d6Vs71vv8QgK9HDg28FNl9+KMi8lhK6XU43/t+GbLl92siEpDDPN+eUvrJUn+u973J\nPSDnAI7nLq8G8GnII+qzFhH5j5EHAs9MKV1kgbl7VRyAt6WUvrOU3ykifxTA1wF43c1d1pXLswE8\nF8BzkGdS/3QArxSRD5VBwSab3Jjc825V5GnrA/IIkuVBAA9f/+VcnojIjwH4QgCfl1L6Lap6GDmu\nunbPDwO4JSIPrLS52+SpAH4/gF8Rkb2I7AH8SQDfLCK3ka2Bc7zv30KeAJrl3QA+seyf6+/9cgAv\nSyn9VErpXSmlvwHghwG8pNSf631vcg/IPQ+OxcJ4B4BnqK64Ip+BHNO4J6UA4xcD+C+Tmdg3pfQ+\n5Bef7/kBZHar3vM7kNeh4TZPRu5w33qlF39xeTOA/wzZgnhK+bwdwP8K4Ckppd/Aed73WzAPATwZ\nwG8CZ/1734/52lYRpV864/ve5F6Qm2YEXcYHwJ9HXjrleciU8B9HXg3299/0tV3wfl6NTOP/XOQR\nsH6eQG1eVO7xi5AB5e8CeC+AW+Y87wPwechW2VsA/KObvr8TvwvLVj27+0aOrz6GbDH9J8iuxt8B\n8Jwzv+//BZk484UA/gCAL0FeJPD7z/m+t8+98bnxC7i0G8m5Uu9Hpnm/FcBn3vQ13cG9ROQRtf08\nz7T7LmSq+0cBvBHAHzb19yHnSz5SOtufAvDxN31/J34X/4DB8VzvuwDEvyj39C4AX9lpc1b3DeA/\nAPCKAmwfKaD33QCGc77v7XNvfLYlqzbZZJNNNtnEyD0fc9xkk0022WSTy5YNHDfZZJNNNtnEyAaO\nm2yyySabbGJkA8dNNtlkk002MbKB4yabbLLJJpsY2cBxk0022WSTTYxs4LjJJptssskmRjZw3GST\nTTbZZBMjGzhusskmm2yyiZENHDfZZJNNNtnEyAaOm2yyySabbGJkA8dNNtlkk002MfL/A/JLctLh\nmIPxAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7f9eec4a5668>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import time\n", + "\n", + "n=1000-1\n", + "b=ones((n,n)).ravel()\n", + "x0=zeros((n,n)).ravel()\n", + "tol=1e-2/(n)\n", + "\n", + "t0=time.time()\n", + "x,k=cg_matrixfree(poisson2d,b,x0,tol)\n", + "t=time.time()-t0\n", + "print('Es wurden {0} Iterationen in {1} Sekunden berechnet.'.format(k,t))\n", + "\n", + "x=x.reshape((n,n))\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.imshow(x)\n", + "plt.colorbar()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Die Lösung $x$ hat in diesem Beispiel im Speicher eine Größe von ca. 10 MB (ein double Wert hat ungefähr die Größe 10 Byte und wir haben etwa $1000^2$ Einträge). Mit unserer (sehr naiven) Implementation von Matrizen bisher hätte die Poissonmatrix einen Speicherbedarf von etwa 10TB (10Byte und eine Größe von $1000^2 \\times 1000^2$), vor ca. 10 Jahren wäre dies selbst für Supercomputer zu groß gewesen. Dies verdeutlicht noch einmal den Gewinn unseres Vorgehens.\n", + "\n", + "Zurück zur eigentlichen Aufgabe:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from numpy import array,zeros,ogrid,broadcast_arrays\n", + "\n", + "def rechte_seite(n):\n", + " rechteSeite=zeros([n-1,n-1])\n", + " x,y=ogrid[1/n:1-1/n:(n-1)*1j,1/n:1-1/n:(n-1)*1j]\n", + " x, y = broadcast_arrays(x, y)\n", + " rechteSeite[(1/8<=x) & (x<=1/4) & (1/8<=y) & (y<=5/8)]=2\n", + " rechteSeite[(1/8<=y) & (y<=1/4) & (1/8<=x) & (x<=5/8)]=2\n", + " z=(x-2/3)**2+(y-2/3)**2\n", + " rechteSeite[z<=1/16]=-1\n", + " return rechteSeite.ravel()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<matplotlib.figure.Figure at 0x7f9ec8f66128>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N=(arange(5)+1)*100\n", + "k_list=[]\n", + "\n", + "for n in N:\n", + " b=rechte_seite(n)\n", + " x0=zeros((n-1,n-1)).ravel()\n", + " tol=1e-2/(n)\n", + " x,k=cg_matrixfree(poisson2d,b,x0,tol)\n", + " k_list.append(k)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.plot(N,k_list)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wir beobachten eine linear mit der Größe des Problems steigende Anzahl an Iterationen.\n", + "\n", + "Zum Abschluss plotten wir die zu letzt berechnete Lösung." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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EOksiHBu7tKIa3mbQtMC6FK9ccqVeogVG62K1TJLLNDEOA6hqZjie2Zl2Hab0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