{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Performance of ARPACK, Eigen, and Numerical Recipes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Burkhard Ritter, Christopher Polachic, February 2014*\n", "\n", "We compare the performance of the Numerical Recipes (C++ version, 3rd edition), ARPACK and Eigen eigensolvers for different real symmetric matrices with varying sparseness. Both Numerical Recipes and Eigen are dense eigensolvers and always compute the full eigenvalue spectrum, whereas ARPACK uses sparse matrices and is typically used to calculate only a few eigenvalues and not the full spectrum." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def create_data_files():\n", " i_d = 0\n", " for r_ev in [0.01,0.1,1.0]:\n", " for r_zeros in [0.1,0.9,0.98]:\n", " i_d += 1\n", " fn = 'performance_nr.{}.dat'.format(i_d)\n", " !./build/arpaca_performance_plot_nr 100 1000 40 10 $r_ev$r_zeros > $fn" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# Takes a very long time\n", "# create_data_files()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "import re\n", "\n", "def read_data_file(filename):\n", " f = open(filename)\n", " s = f.read()\n", " f.close()\n", " n_req = None\n", " r_ev = None\n", " r_zeros = None\n", " d = None\n", " m = re.search(r'n_rep=(.+)$',s,re.MULTILINE)\n", " if m: \n", " n_rep = int(m.group(1))\n", " m = re.search(r'r_ev=(.+)$',s,re.MULTILINE)\n", " if m: \n", " r_ev = float(m.group(1))\n", " m = re.search(r'r_zeros=(.+)$',s,re.MULTILINE)\n", " if m: \n", " r_zeros = float(m.group(1))\n", " d = np.loadtxt(filename)\n", " return (n_rep,r_ev,r_zeros,d)\n", "\n", "def subplot_data_file(p, filename):\n", " n_rep,r_ev,r_zeros,d = read_data_file(filename)\n", " p.plot(d[:,0],d[:,1],label='ARPACK')\n", " p.plot(d[:,0],d[:,2],label='Eigen')\n", " p.plot(d[:,0],d[:,3],label='NR')\n", " p.set_xlabel('matrix dimension')\n", " p.set_ylabel('time (s)')\n", " p.legend(loc='upper left')\n", " #p.set_xscale('log')\n", " #p.set_yscale('log')\n", " #if r_ev == 1.0:\n", " # p.set_ylim((0,300))\n", " p.text(0.98,0.98,\n", " '$r_{{ev}} = {}$\\n$r_{{zeros}} = {}$'.format(r_ev,r_zeros),\n", " fontsize='12',\n", " verticalalignment='top',\n", " horizontalalignment='right',\n", " transform=p.transAxes)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.gridspec as gridspec\n", "\n", "rows = 3\n", "cols = 3\n", "\n", "fig = plt.figure(figsize=(cols*5,rows*5))\n", "#gs = gridspec.GridSpec(rows,cols)\n", "i_p = 0\n", "\n", "for i in range(1,10):\n", " i_p += 1\n", " p = fig.add_subplot(rows, cols, i_p)\n", " #p = fig.add_subplot(gs[i_p%4,i_p/4])\n", " subplot_data_file(p, 'performance_nr.{}.dat'.format(i))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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EJPs0nk9E7GjfPihWzOvrXImI3JSUFNi715y102Iq+kQk+3SnT0TsaPNmde0U\nEfvZs8dcyzh/fqsjUdEnIjdBRZ+I2NHV5RpEROzkRl07fUxFn4hkz+XLcOCALbooiIiko0lcRMSO\nVPSJiN+JjYXy5c11r0RE7ETLNYiIHanoExG/o66dImJHly+bE7lUrWp1JCIi6WW0MLtFVPSJSPao\n6BMRO9qxAypWhLx5rY5EROQawzDzk+70iYhf0RpYImJHGs8nInZ06BAEBUGhQlZHAqjoE5Hs0hp9\nImJHKvpExI5sNJ4PVPSJSHYkJ9tmcVERkXQ0iYuI2JGKPhHxO7t3Q9mykC+f1ZGIiKSnO30iYkcq\n+kTE72g8n4jY0dmzkJBgTuQiImInKvpExO9oPJ+I2NHWreaXqhz6OiMiNqOiT0T8jpZrEBE72rJF\n4/lExH4SEiAlBcLCrI4kjYo+Ecmaij4RsaPNmzWeT0Ts5+pdPpfL6kjSqOgTkRtLSTEncqla1epI\nRETS0yQuImJH27bZqmsnqOgTkazs3g133gkFClgdiYjINYah5RpExJ5sNp4PVPSJSFbUtVNE7Oj4\ncXC7bTVmRkQEUNEnIn5IRZ+IWGHvXli/PvPnr97ls9GYGRERQEWfiNjQkCHmLFOZUdEnIlYYPBge\nfhiSkjJ+XuP5RMSOkpLM71XlylkdSToq+kQC2YUL8MYb8OGHmb9m61YtzC4ivrdqFRQqBH37Zvy8\nlmsQETvasQOqVIGcOa2OJB0VfSKBbN06qFgRfvgBdu68/vmUFIiNhbvu8n1sIhK4Ll0yi7qff4aR\nI82uUn+l5RpExI5s2LUTVPSJBLZVq6BNG3jrLXjnneuf37fPnCThjjt8H5uIBK5168yLTRUrwnvv\nwcsvm7N1XuV2m13P1QtBROxm+3ZbDovxatHXs2dPSpQoQc0/db/o3bs3pUuXJjIyksjISObMmePN\nEETkRlavhoYN4Z//NCdMWLIk/fMOHc+n3CRic6tWQaNG5s8vvggnTsDkydee378fQkMhJMSS8LxJ\n+UnE5lJT4fPP4eLFjJ8PxDt9PXr0uC4xuVwuXn/9ddavX8/69etp166dN0MQkRtZtcos+vLlg379\n4M03zSvoVzn0Srpyk4jNXc1NALlywZdfmuOPz50zH3PwJC7KTyI2t349vPYadOhgzo3wVzZcmB28\nXPQ1bdqU0NDQ6x43/txFQ0SscfiwOW6mYkXz9yeeMLtPTZp07TVbtzryTp9yk4jN/bnoA2jSBFq1\ngj59zN9CKGcbAAAgAElEQVQdPImL8pOIzS1cCM8/D8WKwUMPpS/8kpPhwAGoXNm6+DJhyZi+L774\ngtq1a/P0009z+vRpK0IQkdWr4Z57rq1xlSMHfPYZ/PvfZjEIju3emRnlJhEbOHLE7DYVHp7+8QED\nYMwY82JUAE7iovwkYhMLF5rzIYwbB3feCQ8+COfPm8/t2mUu1ZAnj7UxZiCXr3f4/PPP06tXLwDe\nf/993njjDUaOHHnd63r37p32c1RUFFFRUT6KUCRA/PVKOsB990GdOvDFF/D66+a0w7fRRSEmJoaY\nmJjbi9NHspubQPlJxKuu5qa/LrpeogR88IE5xi8hAd5++5Z34U+5CfTdScQ2kpNhxQqYONFckmH0\naHjmGWjfHmbNuu3xfN7MTS7Dy/0F9u/fz0MPPcTmzZuz/ZzL5VI3BhFva9YMevUyu0z92c6dZleq\n2bOhUyc4eNBju7RT276V3AT2OgYRR3rrLXOClnffvf65lBRo0AA2bTKvrOfL55Fd2q1d67uTiE0t\nWwavvgpr1157zO2Gf/zDvMvXqJHZc+rjjz2yO0+2a59374yLi0v7edq0aelmpxIRH7lyxZwSvUGD\n65+rWhU6d4YePRw5iUtmlJtEbCKjXghX5coFw4aZV9U9VPD5A+UnEZtYuBBatEj/WI4cMHy4uczM\nJ5/YchIX8HL3zi5durB48WISEhIoU6YMH374ITExMWzYsAGXy0WFChX45ptvvBmCiGRk82azz3mh\nQhk//8EHZl91h84Qp9wkYlPJyebMeBldkLqqYUNz0XaHUn4SsbGFCzNe1zhHDvj6a3MCl9atfR9X\nNni9e+etUBcFES/76iv44w/IZMwaAFOmQNmy5mQvHuKEtu2EYxCxrbVroWdPs/umDzmhXTvhGERs\n7cIFKF4c4uOhYEGf7NKT7drnE7mIiA2sWgVNm974NdHRvolFROSqG3XtFBGx0ooV5mR3Pir4PM2S\nJRtExGL6YiUidqTcJCJ2ldF4Pj9ywzt9x48fZ8qUKSxZsoT9+/fjcrkoV64czZo1Izo6muLFi/sq\nThHxlJMnza4Jfr7+nvKTiAOtXAn/+Y/VUdwW5SYRh1q4EPr3tzqKW5bpmL6nn36aPXv2cP/993P3\n3XdTsmRJDMMgLi6ONWvWMGfOHCpVqsSIESM8H5T6pYt4z6+/wqefmsnLxzzVtpWfRBzo+HGoUgUS\nE81JEXxIuUlEbujMGShdGk6c8OnMwZ5s15kWfZs2baJWrVo3/OPsvOaWglLiEvGeDz4wl2zo18/n\nu/ZU21Z+EnGgmTNh6FCYO9fnu1ZuEpEbmjULPv8c5s/36W59sk5fRgkpMTGRTX+aUcsbSUtEvMwB\nY2aUn0QcSLlJROzKz8fzQTYmcrnvvvs4e/YsiYmJ1KtXj2eeeYbXXnvNF7GJiKe53bBmjUeXYbCS\n8pOIg6xc6fdF31XKTSIOs3AhNG9udRS3Jcui78yZMwQHBzN16lSeeuop1qxZw3wf39oUEQ+JjYXQ\nUChRwupIPEL5ScQhUlPNNfocckFKuUnEQRISYN8+qF/f6khuS5ZFX2pqKnFxcUyePJn27dsDZv9S\nEfFDq1Y55ksVKD+JOMbWrVCqFBQubHUkHqHcJOIgMTHQpAnkzm11JLcly6KvV69etG3blvDwcO6+\n+2727NlD5cqVfRGbiHiaA8bM/Jnyk4hDKDeJiF05YDwf3GD2TitpBioRL6lTB775xrK7fU5o2044\nBhHb6dHDzEvPPWfJ7p3Qrp1wDCK2dNddMHEiREb6fNc+mb2zd+/eHDt2LNM/jIuL44MPPvBIECLi\nA0lJsGuXWfj5OeUnEYdxyJ0+5SYRhzlyxFybr3ZtqyO5bbkye6J+/fo88cQTJCcnU7du3bQFRuPj\n41m3bh158+blzTff9GWsInI7/vgDatWCvHmtjuS2KT+JOMipU3D4MNSoYXUkt025ScRhFi2CqCjI\nkeWIONvLsnvnoUOHWL58OQcPHgSgXLlyNG7cmNKlS3svKHVREPG8AQMgLs5cXNQinm7byk8iDjB3\nLvTvb365sohyk4hkqGdPqFcPXnzRkt17sl1rTJ9IoHjkEejcGZ54wrIQnNC2nXAMIrbSuzdcvgwf\nf2xZCE5o1044BhHbKV8efv0VIiIs2b1PxvSJiIMYhmPGzIiIg6xdC99/D40bWx2JiEh6+/aZF6Tu\nusvqSDwi0zF9IuKHrlyB1ashPt7syhkXZ/585IjZH71cOasjFBEx89J//mNeQe/bFx54wOqIRESu\nWb7cnE34b38Dh6yxqaJPxEk++QRGjzZnmQoLg5IlzSvoYWFQs6ZjEpeI+KnLl81xxZ9+ao6V2bkT\ngoOtjkpExHTyJLzzjnlBatAg6NTJ6og8JsvunTt37qRly5ZUr14dgE2bNtG3b1+vByYit2DhQhgy\nBH76Cb78Et57D55+Gtq3h7JlrY7O45SfRPzIzJlQvTqsWAErV5oXqRxa8Ck3ifgZw4AxY8wcVaAA\nbNsG0dGOulieZdH3j3/8g379+pEnTx4AatasycSJE70emIjcpCtXYM0auPdeqyPxGeUnET9x5Ag8\n9RQMGwYzZkDlylZH5FXKTSJ+ZNcuc1mGL7+E2bNh8GBHXpDKsui7cOEC99xzT9rvLpeL3LlzezUo\nEbkF69ZBeDiEhFgdic8oP4n4iQULoGVLaN3a6kh8QrlJxI+8+io0a2ZOeFevntXReE2WY/qKFSvG\n7t27037/8ccfKVmypFeDEpFbsHQpNG1qdRQ+pfwk4ieuFn0BQrlJxE9cuQLLlsHYsZAzp9XReFWW\nRd/QoUN59tln2bFjB6VKlaJChQpMmDDBF7GJyM1YuhSefNLqKHxK+UnEDxiGWfS9+67VkfiMcpOI\nn/jjD6hQAYoWtToSr8v24uznz5/H7XYTFBTk7Zi0wKjIzXK7oVgx2LwZSpWyOppMeattKz+J2NjO\nndCqFRw8aNtJEZSbRAJUv35w4oQ5U6cNebJdZ3mn79SpU4wbN479+/eTkpKSFsCQIUM8EoCIeMD2\n7eZYPhsXfN6g/CTiB6527bRpwecNyk0ifmLRIvjnP62OwieyLPoeeOABGjVqRK1atciRIweGYeAK\noMQt4hcCcDwfKD+J+IUFC6BjR6uj8CnlJhE/cPmyOXnLjz9aHYlPZFn0Xb58mYEDB/oiFhG5VUuX\nQosWVkfhc8pPIjaXmgoxMfDFF1ZH4lPKTSJ+YPVquOsuKFTI6kh8IsslG/72t7/x7bffEhcXR2Ji\nYtomIjYSoHf6lJ9EbG7DBihePOC6nis3ifiBRYsC6oJ5lnf68uXLx1tvvcX/+3//jxw5zBrR5XKx\nd+9erwcnItlw4IDZRcHhix1nRPlJxOYCbKmGq5SbRPzAwoXw739bHYXPZDl7Z4UKFfj9998p6sOp\nTDUDlchNGD8epk/3iz7pnm7byk8iNte2LTz3HDzyiNWR3JByk0iAuXDB7IUQHw8FC1odTaY82a6z\n7N5ZuXJl8ufP75GdiYgXBGjXTlB+ErG1y5dhxQqIirI6Ep9TbhKxuRUroHZtWxd8npZl984CBQpQ\np04dmjdvTt68eQFNOyxiK8uWwf/9n9VRWEL5ScTGVq0yJ0kIDbU6Ep9TbhKxuUWLoHlzq6PwqSyL\nvo4dO9LxL1Mta9phEZs4eRIOH4ZatayOxBLKTyI2FqDj+UC5ScT2Fi2Cvn2tjsKnshzTZwX1SxfJ\nphkz4KuvYO5cqyPJFie0bSccg4hPNG4MvXtD69ZWR5IlJ7RrJxyDiE+cOwclS8KJE2DzbtiebNeZ\n3umLjo5mypQp1KxZM8MANm3a5JEAROQ2BOh4PuUnEZs7dw42bjQLvwCi3CTiB5YtgwYNbF/weVqm\nRd/gwYMBmDVr1nUVprooiNjE0qXwySdWR+Fzyk8iNrdkifmlqkABqyPxKeUmET+wcGHAjeeDG8ze\nWep/C6l+9dVXlC9fPt321Vdf+SxAEcnE+fOwZQvcfbfVkfic8pOIzQXoeD7lJhE/EGCLsl+V5ZIN\n8+bNu+6xX375xSvBiMhNWLUK6tQJuO4Jf6b8JGJTAVr0XaXcJGJTp05BbGxAXjDPtHvnsGHD+Oqr\nr9izZ0+6vunnzp2jcYD10RexpQAdzwfKTyK2dvw47N9vdu8MMMpNIja3ZAk0bAh58lgdic9lOnvn\nmTNnOHXqFO+88w4DBgxI65seFBREkSJFvBuUZqASyVrLlvD669C+vdWRZJun2rbyk4iNTZoE48fD\nzJlWR5Jtyk0iAeLVVyEsDN55x+pIssWT7dqrSzb07NmT2bNnU7x4cTZv3gxAYmIinTt35sCBA5Qv\nX57JkycTEhKSPiglLpEbu3IFCheGgwf9auFju7TtW81NYJ9jELGtZ5+FatXML1d+wi7tWrlJxMtq\n1YLhw+Gee6yOJFs82a6zHNN3O3r06MGcOXPSPda/f39at25NbGwsLVu2pH///t4MQcSZ1q2DChX8\nquCzE+UmES8K8PF8t0O5ScSLTpwwL5bXq2d1JJbw+uLs+/fv56GHHkq7YnXXXXexePFiSpQoQXx8\nPFFRUezYsSN9ULpaJXJjn30G+/bBl19aHclNsVPbvpXcBPY6BhHLTJ4M8+dDkSLpN8Mw7/TFx4Mf\nLVFgp3at3CTiJVOmwNixMGuW1ZFkm08WZ/eWY8eOUaJECQBKlCjBsWPHfB2CiP/auxfmzDG7JvTp\nY3U0jqLcJJJNhgHvvw9dukDu3HD0KGzeDCdPmts//uFXBZ/dKTeJeMiiRQG5Pt9VPi/6/szlcmmx\nUpEbSUqCmBiz0Js7F86dgzZt4IMPoFMnq6NzLOUmkRvYvh0uXIBevSCHV0eJyF8oN4ncpLNnYf16\nWLsWpk2D2bOtjsgyPi/6rnZPCAsLIy4ujuLFi2f4ut69e6f9HBUVRVRUlG8CFLGLkyehalWoWRPa\ntTO7JdSq5VdfsmJiYoiJibE6jGzJbm4C5ScJcNOmQceOfpWL/kq5ScShkpPh229h9Wqz0Dt40Pzu\nVL8+DB4MkZFWR3hD3sxNPh/T969//YsiRYrw9ttv079/f06fPn3doGT1SxcBRoww7+5NmWJ1JB5j\np7Z9K7kJ7HUMIpaoXx8++QRatLA6Eo+xU7tWbhK5Dd99B//9L7z8spmrqlUzu6H7Kb9ZsqFLly4s\nXryYhIQESpQoQZ8+fejQoQOPP/44Bw8e1JINIjfSujX83/85qhunXdr2reYmsM8xiFji4EGoW9ec\nqCWXpSNEPMou7Vq5SeQ23X8/dO0Kf/ub1ZF4hN8UfbdKiUsC3rFjZtfOo0ehQAGro/EYJ7RtJxyD\nyC0bPBg2bIDRo62OxKOc0K6dcAwit+XECahUCY4cgYIFrY7GI/xmnT4RuUU//QTt2zuq4BMRB5g2\nDR55xOooRESu9+OP8MADjin4PE1Fn4gdTZoEnTtbHYWIyDUnTpiz4LVubXUkIiLXmzjRXEpGMqSi\nT8Rurq551bat1ZGIiFzz88/mkjH581sdiYhIeocOwdat+u50Ayr6ROxmyhR4+GHIm9fqSERErlHX\nThGxq0mTzPyk706ZUtEnYjfq2ikidnPuHCxZYo41FhGxm++/V9fOLKjoE7GTAwcgNhZatbI6EhGR\na379Fe69FwoVsjoSEZH0du6EuDiIirI6EltT0SdiJ5Mnm90T/HghURFxoKlT4dFHrY5CROR6Eyea\nPaRy5rQ6EltT0SdiJ+raKSJ2c/kyzJkDHTpYHYmISHqGoVk7s0lFn4hd7N5tzj6l7gkiYicLFkCN\nGlCihNWRiIikt349pKTA3XdbHYntqegTsYvJk+GxxyBXLqsjERG5Zto0de0UEXuaOBGeeAJcLqsj\nsT2XYRiG1UH8lcvlwoZhiXhX7drwxRfQrJnVkXiNE9q2E45BJNtSU6FkSVi9GipUsDoar3FCu3bC\nMYjcFLcbypUzJ5qqUcPqaLzCk+1ad/pE7GDHDkhIgCZNrI5EROSa5cuhVClHF3wi4qeWLYPQUMcW\nfJ6mok/EDiZNguhoyKEmKSI2oq6dImJXmsDlpmjwkIjVDAN++AFGjbI6EhGRa2JizAWPFyywOhIR\nkfSuXIEff4Q1a6yOxG+o6BOxkmHAzz/DhQvQsKHV0YiIQHw8vPUWLFkC33yjrlMiYj8//wyVKqnr\n+U1Q0SdihZQU+Okn+OwzOHsWvvxSM0+JiLVSU+Hrr6F3b+jZE7ZtgzvusDoqERFTSgrMmgVDh8Lm\nzTBihNUR+RUVfSK+dO6c2Y1z0CAoWxbefx8efFBj+UTEWr//Ds8/bxZ5MTFQvbrVEYmImI4fNwu8\nr7+G0qXhhRfMeRDy5rU6Mr+iok/EV8aPh1dfhRYtzIlb7rnH6ohERMwxMe3bw8CB8Pe/q9eBiNjH\nf/4Dw4aZ6xhPnw5161odkd/SOn0ivpCaCuXLmwuwN2pkdTSWcULbdsIxiKTTsydERJjj+AKUE9q1\nE45BJJ2jR81eB7GxUKyY1dFYQuv0ifib336DsLCALvhExIbOnjWXZXjqKasjERFJ77vvoFOngC34\nPE3dO0V8YdQo82q6iIidTJoEUVFQooTVkYiIXGMY5nenMWOsjsQxdKdPxNsSEmDuXC0gKiL2M3Ik\nPPOM1VGIiKS3YoU5vljLWXmMij4Rb/v+e3OGzpAQqyMREblmyxY4dAjatrU6EhGR9K72kNLEUh6j\n7p0i3mQY5pX0gQOtjkREJL2RI6F7d8ilrwIiYiNJSTB1qrlWqHiMMr2IN61fD2fOQPPmVkciInLN\n5cvmMjKrVlkdiYhIelOmQNOmULKk1ZE4irp3injTqFHQo4cWXxcRe/n5Z6hRA8LDrY5ERCQ9TX7n\nFbrTJ+Itly7BxImwbp3VkYiIpKcJXETEjmJjza19e6sjcRwVfSLeMn061K0L5cpZHYmIyDUHDsDv\nv5vr84mI2Mno0dC1K+TObXUkjqOiT8RbRo2Cp5+2OgoRkfTGjIEnnoD8+a2ORETkmpQUGDcO5s2z\nOhJHUtEn4g0HDpjdOn/+2epIRESucbvNK+lTp1odiYhIevPmQZkyUL261ZE4kmaXEPGGsWPNK+n5\n8lkdiYjINQsWQOHCZtdzERE70QQuXuUyDMOwOoi/crlc2DAskexxu80Z8X76SV+s/sIJbdsJxyAB\nrHNnaNYMXnzR6khsxQnt2gnHIAHsxAmoXNnsKVWokNXR2IYn27Xu9Il4WkyMmbAiI62ORETkmpMn\nYe5c+NvfrI5ERCS9CRPg4YdV8HmRij4RTxs50uye4HJZHYmIiLl8zMyZ0K2bOQ16aKjVEYmIXON2\nq2unD6joE/GUw4fNrlMrV8KTT1odjYgEsvPn4ccfoUsXCAuDzz6DNm1g6FCrIxMRMbndZp6qVQuK\nFTO7novXqOgTuV3JyfDpp1CnDlStClu2QJEiVkclIoHqtdegVCn49luIioKdO2HxYvjnP3WXT0Ss\nZxjmOqGRkTBgAHzyCcyfDzlUlniTlmwQuR0LF8JLL0H58rBqFVSqZHVEIhLIFi6EGTNg715dfBIR\nezEMs6v5Bx+YQ2D69oUHH9RwGB9R0SdyK86dg2efNbtyfv45dOigpCUi1nK74c03oX9/FXwiYj99\n+8LEidCvn743WUBFn8iteO0184rVtm1QoIDV0YiIwPjxkCcPREdbHYmISHrbt8OQIbBunbkAu/ic\nij6RmzV7trnA8aZNKvhExB4uXIB334VJk3T1XETsxe2G//s/s1unCj7LWFb0lS9fnuDgYHLmzEnu\n3LlZs2aNVaGIZN/Jk2a3zu+/h6Agq6MRL1BuEr80aBA0bAj33mt1JOJFyk/il0aONCe9e/55qyMJ\naJYVfS6Xi5iYGAoXLmxVCCI374UXzGUZ7rvP6kjES5SbxO8cOwYDB4IKAMdTfhK/Exdn9kJYsABy\n5rQ6moBmafdOwzCs3L3IzfnhB9i8GcaMsToS8TLlJvErvXubC6+Hh1sdifiA8pP4lVdegX/8A2rW\ntDqSgGfZghgul4tWrVpRv359hg8fblUYItlz9KiZuMaNg/z5rY5GvEi5SfzKtm3w00/w3ntWRyI+\noPwkfmXmTFi/XvnJJiy707d8+XJKlizJiRMnaN26NXfddRdNmza1KhyRzBkGPP202Re9fn2roxEv\nU24Sv/Kvf8G//w3q7hcQlJ/Eb5w7By++aPaO0sVyW7Cs6CtZsiQAxYoV45FHHmHNmjXpElfv3r3T\nfo6KiiIqKsrHEYr8z/DhcOKE2SddbkpMTAwxMTFWh3FTsspNoPwkNrFggTkN+k8/WR2J3/HH3AT6\n7iR+5L33oFUraNHC6kj8ijdzk8uwoHP4hQsXSE1NJSgoiPPnz9OmTRs++OAD2rRpYwblcqnPutjD\n3r1wzz2weDFUq2Z1NH7P7m07q9wE9j8GCRApKdCgAfznP1qXzwP8oV3ru5P4jdWroWNH2LIFihSx\nOhq/5sl2bcmdvmPHjvHII48AkJKSwpNPPpnuS5WILaSkwN//bn6pUsEXEJSbxC8YhjmTcMmS0KmT\n1dGIjyg/iV84fx569DBnFFbBZyuW3OnLiq5WiS306mVOgf7LL5DDsjmPHMUJbdsJxyB+rm9fmDrV\n7IGg9UI9wgnt2gnHIA7wzDPmmnzjxlkdiSP4/Z0+EdtbsgRGjIB161TwiYh9jBljLnS8YoUKPhGx\nlx9+ML8//fGH1ZFIBlT0ifxVYqLZrXPkSAgLszoaERHTvHnw9tsQE2N27RQRsYu9e+Hll2HuXF2Q\nsil17xT5M8Mwx8iULQuDBlkdjeM4oW074RjED23YAG3amN06mzSxOhrHcUK7dsIxiJ9KTjbz0t/+\nBq++anU0jqLunSLeMnw47NkD339vdSQiIqYDB+DBB2HYMBV8ImI/770HJUrAK69YHYncgIo+kau2\nbzfX4luyBPLmtToaERGzu/n998Nbb8Fjj1kdjYhIenPmmBfKN2wAl8vqaOQGVPSJAFy6BF26QL9+\nEBFhdTQiImZe6tAB2rXTFXQRsZ+4OHN5hu+/h6JFrY5GsqAxfSJX17w6cQKmTNGVKi9yQtt2wjGI\nH0hNhc6dIVcu8wuVZhH2Kie0ayccg/iRS5egfXto3Bj69LE6GsfSmD4RT7l8GZ5+Gnbvhl9/VcEn\nItYzDHMyhJMnza5TKvhExE5OnYKOHc1xfL16WR2NZJP+TyKB69Qps9vUxYuwaBGEhlodkYgIfPqp\nufD6tGkaXywi9nLwoDmhVN265rp8uXT/yF+o6JPAtH+/2SUhMhImT4b8+a2OSEQExo+HL780ex6E\nhFgdjYjINRs3mt+dnnnGXNZKvRD8iv5rSeBZu9ZMWs89BwMHQs6cVkckIgK//QZvvAG//AJ33ml1\nNCIi1yxYAK1bw3//C6+9ZnU0cgt0T1YCy8yZ0LOnuR5fx45WRyMiYo7hW7bMXNh46lSoXt3qiERE\nrpkwAV5/3Zzs7r77rI5GbpGKPnG2CxfMdffmzoV58+D0aZg9G+6+2+rIRCRQud2wdas5bm/xYjNH\n5c8P334LTZtaHZ2IBLKEBHPNvfXrr/174QIsXKgLUn5OSzaI85w8CaNGmUXeqlXmuL02baBtW3Pg\nsbpzWsYJbdsJxyAWOXUKXnrJvAgVEmJeMb+6lStndXQBzQnt2gnHIBZJTTVn4Rw3Ds6ehTp1zC0y\n0twiIiBPHqujDEhaskEkM/v2mcVdo0bw8svw008QHGx1VCIS6I4eNXNTixbmZAgasycidpCYCF26\nQEqKOW6vUiVN0OJQ+q8qzrFxo9k16p//hLFj4eGHVfCJiPV27TKnOH/ySfj8cxV8ImIPW7eaw12q\nVTN7IFSpooLPwXSnT5xh8WKIjoahQ+Hxx62ORkTEtH49tG8PffqY05yLiNjB9Onwj3+Ys3E+9ZTV\n0YgPqOgT/zd1qrn8wsSJ0LKl1dGIiJhiYsyLUF9/DY8+anU0IiLmRFJ9+phzH/zyCzRoYHVE4iMq\n+sS/ff21mbzmzDEnaRERsYPp0+HZZ2HSJGje3OpoRETMcXtdukBcHKxZA2FhVkckPqSiT/yTYcCH\nH8J335nTnVeqZHVEIiKm77+HN9/UxSgRsQ/DMOc8OHPGXH5Bs3EGHBV94n8uXzb7oW/fDsuX60qV\niNjHpElmwTd/vjk5gtieljmQgPDf/8KyZeamgi8gqegT/5KYaI6NKVzYnLylQAGrI5JMJCUnseLQ\nChbvX8ziA4v5MOpDq0MS8a4ff4RXX4XfflPBZ3NXUq8wZ/ccxmwcgwuX1eGIeNeUKTB4MKxcqVnN\n/UByajKzYmcxftN4j76vFmcX/7FnDzzwADz0EAwYoEXWbeZyymUW7lvIov2LWHJgCVuObyGyZCT3\nlbuP+8rdR+Oyjbkjzx1+37aVnyRD06ebE0rNnQu1a1sdjWRiY/xGxm4cy4TNE6hSpArdancjulo0\nIflD/L5dKzdJhlasgA4dzItRdepYHY1kwjAM1h5dy9iNY5m0dRLVi1WnW+1u9Kzb02PtWkWf+IcV\nK8w7fB98AM8/b3U08j9XUq+wYN8CJm2dxIwdM6hevDqtKrTivvL3cc+d95A/d/50r3dC23bCMYiH\nzZxpLsfw668aw2czJy+cZO3Rtaw5soapO6Zy8sJJutXuxlO1n6Jykcppr3NCu3bCMYiH7dplrl88\nejTcf7/V0cifuA03R84eYVfiLtYcWcO4jeNITk3mqdpP0bVWVyqEVgA8265V9Ik9uN2wezckJ0Nq\nqvl7aqq5bd4M//43jBunpGUDKe4UlhxYwg9bfmDajmlUKlyJztU7E10tmjuDb7zotBPathOOQTzo\nl1+ge3eYPVtTn1ss1Z3KysMrWXloJWvj1vL7kd9JuJBAvVL1aFCqAW3D29K8QnNyuK5ffNoJ7doJ\nxyAelJAAjRrBW2+ZMwmLZVLcKczdPZelB5eyK3EXu07uYnfibgrlK0TlwpWpVaIWXWp04d4y9+Jy\npYMUiqMAACAASURBVO9urqJPnCM11exr3rcvnD0LBQua3Tb/vBUsCIMGqcuUhc4nn2fennnM2DmD\nWbGzKB9Sns7VO/N49ccpF1Iu2+/jhLbthGOQm7RiBezda04i9eft7FkYMQJ+/hkaNrQ6yoB0JfUK\niw8s5sdtPzJtxzRKBZWiWdlm1C9VnwZ3NqBKkSoZFnl/5YR27YRjkJvkdsPhw+aMnGfPmv9e/Xn0\naHO5mI8/tjrKgLXl+BbGbhjL+M3jKR9SnvaV21OlSBUqF65MpcKVCMoblOV7qOgT/5eSYk5r3q8f\nFCkC778PbduCSwPq7cBtuDl45iAL9i5gxs4ZxOyP4Z7S99ChagcervowZQuVvaX3dULbdsIxSDYZ\nhrkO6IgR0KwZ5M17/dahA9SrZ3WkAcMwDOKT4lkXt46p26cyY+cMwguH0ymiE49Ve4yKoRVv6X2d\n0K6dcAxyE06ehMcfh61boWhRKFTInKSlUCFzq1wZXn8dcmR90UM85/j540zeOpkxG8YQnxTPU7Wf\nolvtblQtWvWW3k9Fn/iv5GRzbb1+/aBsWbPYa95cxZ6F9iTuYeOxjWw7sY3tCdvZfmI7O0/uJCRf\nCI3LNKbjXR15oPIDhOQLue19OaFtO+EYJBsuXoQePWD/fnOSFi0N43Mb4zey7OAy9pzaY26Je9h3\neh935L6DasWq0aFqBx6NePSmehtkxgnt2gnHINm0ZYt5wemxx8w7eZrYzhLHko6xLm6ducWb/568\ncJKHqj5E99rdaVGhBTlz3N5/GxV94p9On4b27SFfPujd2xxcLJbYnbibSVsmMWnrJBIuJFC/VH0i\nikYQUSyCiKIR3FX0LgrlK+Tx/TqhbTvhGCQLcXHmF6pKlWDkSMifP+u/EY84cvYI32/+nu82fceZ\ny2doG96WSoUrER4aTnjhcMJDw7PVJepmOaFdO+EYJBtmzDAnjho0CP7+d6ujCSiJFxP5bc9vzNkz\nh/l753M++Tx1S9ZN2+qVrEd44fBsdSnPLhV94n+OH4c2bSAqCgYOVHcDC+w/vZ/JWyczaeskjpw9\nQqdqnehcvTONyzb2aIK6ESe0bSccg9zA+vVmwffss/Duu+qF4APnLp9j2o5pfLfpO/44+gePRjxK\n11pdaVquqXLTTXDCMcgNGIY5/8E338DUqXD33VZH5Hgp7hTWxa1jzu45zNk9hy3Ht3Bf+ftoF96O\nNuFtqFS40nUTr3iaij7xL4cOQatW8MQT5h0+fYnymlR3KntP7WVHwg52ntyZ7l+AR+96lM41OnNf\nuftuu8vBrXBC23bCMUgmpk83i72vvoJOnayOxpFOnD/BhvgNbIjfwPr49WyI38D+0/tpWbElXWt1\n5aEqD1231IsvOKFdO+EYJBPnz5uzBB86ZBZ8pUpZHZHjuA03sSdjWXt0LWuPruX3o7+zMX4j5UPK\n065SO9pVakfTsk3JmyuvT+NS0Sf+Y9cuaN0a/vlPc0CxeNyhM4eYt2ce8/bOY/7e+QTlCSKiWARV\ni1TlrqJ3pf0bVjDM61eksuKEtu2EY5A/MQxYtgwGDIBNm8wvVPXrWx2VI7gNN9tPbGfxgcUsObCE\n5YeWc+7yOeqE1SEyLJI6YXWoE1aHiGIR5MmZx9JYndCunXAM8hfnzpmzcH7+uTmZ1Ndfm0Nk5Lal\nulNZF7eOBfsWsGDfAlYfXk2xO4pRv1R96pesT/1S9albsq5XhrrcDBV94h82bYJ27czZ7555xupo\nHOHqrJqbjm1i0b5FzN0zl+Pnj9M6vDVtKrahTXibLNfKs5IT2rYTjkEwpzqfOdMs9o4fN9ey6tZN\nX6hukdtwc/TcUXad3MWG+A0sObiEpQeWEpIvhGblmtGsXDOalm1KxdCKll98yogT2rUTjkH+Z/9+\n+OILGDMGWrSA114z19yzYdvxFynuFGJPxhKzP4b5e+cTsz+GkkElaVWhFS0rtqRxmcYUKVDE6jCv\no6JP7G/lSujYEYYMgc6drY7GL529fJY/jv7BpmOb2HJ8C1tObGHr8a0E5w2mZomaNC3blDbhbYgM\ni7Skq+atcELbdsIxBLTLl83lYj79FAoUgLffhkcf1ex3N+Hw2cMsPbCUzcc3E3syll2J5kLDwXmD\nqVy4MtWLVU8r9Ox8EerPnNCunXAMAc0wYPly867eokXQsye89BKUu/3ZaQNJcmoyW49vZduJbexI\n2GHOSp6wnb2n9lIqqBRNyzalVcVWtKjQglJB9u8mq6JP7Ck1FX791RwPs2YNjB1rztYpWTIMg9iT\nsaw8vJKVh1ay8vBK9p7aS+2w2tQuUZuaxWtSo3gNahSvQWj+UKvDvWVOaNtOOIaAtG8ffPstjBoF\ntWubxV6LFrpyngXDMNiRsIOlB5ea24GlnL9yniZlm1A3rC6Vi1SmSpEqVCpcieC8wVaHe8uc0K6d\ncAwBKSkJJkwwvztdvGgOh+nWDYI8P0ut0xiGwcEzB1l1eBWrDq9i9ZHVbDy2kQohFahWrFq6Wcmr\nFKliyXjh26WiT+zlxAlzWvOvv4bixeGFF8y7e5rm/DrnLp9jd+Lu9Nup3Ww5voWgPEE0KtOIRqXN\nrXZYbcvHuXja/2fvvuOjKBP/gX9m03sCaUBCCySQAoSOoAZpoqAooKA/G+XOjmdB/J53RuCLeGcD\n9fx6KBIbKqeAekgTAqgIAgkgXXo6gbRN2/b8/hh2kkBCy87u7OTzfr3mtbszu/M8s5n9ZJ6ZZ2b0\n8NvWwzK0GBYLsGqVnE3btwP33w/8+c9AwrXdJFfPzFYzjpYcxaHiQzh09hAOFR/CwbMHceDMAYT4\nhuD69tfLQ4frkdA6QZNdNJtDD79rPSxDi7J/P/Dee3KDLy0NeOQRYNgwXt28ETWWGhwvOY4/zv2B\noyVHle2n3YW7IYTAwJiBytC3bV8Eege6usoOw0YfuVZtrXxj0KwsYMMG+ejenXfKgcULIACQ9z4d\nLz0uX6EuP0u5Sl1JTQm6tOoiD2FdlOfdwruhTVAbV1dbdXr4bethGXTLZgOOHpWzaccO4IsvgHbt\ngIcfBu66q8XviKoyV8kbTefqbnZ+tOQojpUcQ055DmKCY5AQnoBurbshITxBuQhUVGCUq6uuOj38\nrvWwDLpWUgLs2gXs3CnvjDp8WL7ewfTpQGysq2unCfYjd/Wv8Lu7cDfyK/LRIbQD4sLilPt2dmnV\nBUmRSegQ0kF3O6HqY6OPnMNmA/Ly5Ctw7tsnh9WuXXJQxcUBvXsDAwbIt2Jo1crVtXWqanM1Tpad\nRF5FHvIr8pFvzJefG/ORU56DvYV7EegdiNQ2qUiNPj+0SdV9OF2OHn7belgGXSgtBQ4elPeWZ2fL\nDb3du+Us6tULSE2V77fXq5era+pUQgiU1pTi0NlD2H9mPw6cOYD9xfux/8x+FBgL0Dmss3yj83o3\nO+8c1hkdQzs6/VLkWqKH37UelkEXrFbg1Cng0CE5k3bulIeiIjmP+vSRr8Q5dizg5eXq2jqV1WZF\nYWUhcstzkVuRi7yKPOX5ybKT2F2wG76evkhtk4peUb2UK/x2DuvsNtcucDQ2+shxhADOnpXD6fBh\neThyRH48elTuU961K9C9u9zI690bSEnR5R5zIQQqzZUory1XhoraCuQb83Gs5JiyR/xYyTGcrTqL\n2JBYtA1qKw+BbdEmqI3yOikiCREBEa5eJM3Rw29bD8vgNqxW4ORJOZ8OHZIbefahshLo1k0e7I28\nXr10swNKCIG8ijxkF2QjtyIXBskAD8lDfjR4wEPygMVmQW5FLk6VncLJspPyY+lJCAgktE5QzmlJ\njEhEYkQiOoV1gqfB09WLpkl6+F3rYRncSmlp3XbTwYN1OfXHH0Dr1nI2JSfLjbw+fYD4eN1eMEoI\nAaPJiLLaMpTWlKKspgw55Tk4Xnocx0uOy4+lx3G67DRCfUPRLrgd2gWdH4LboW1QW7QPaY+UyJQW\n0bPgarDRR1fHYgFyc+U9T6dOyZcCtgfVoUNywy8hQQ6k+Hi5kde1K9ClCxDsvifmCyFQbalGRW0F\nKkwVqKitQGlNKXLKc3C6/DROl52WH8tPI6c8B6U1pfDz9EOwTzCCfIIQ7BOMYJ9gRAZEKnvD7UO7\noHYtcq9TTQ1QViYPFRXyYDQ2fG4yyYPZXPdoNss9WHr2dP/fNvPJwaqq5BsOnzwp59Mff9TthDp2\nTD5POD5ezqhu3eQdUN26yTcnduOj5labFZXmSiWfymvLldsdZBfKXZskSEhtk4r2we1hEzZYhRVW\nYZWf26wwSAa0C2qH9iHt0SG0g/wY0gGhvqEtukfBtdDD71oPy6ApQgCFhXI2nTxZt+1kz6fKyrrt\nJns+2belAt3vnDIhBGqttag2V6PaUq081lhqUF5bjryKvIuGfGM+SqpLUF5bDl9PX4T4hiDUNxQh\nPiFoG9QWnUI7oVNYJ+WxQ0gHt7yYiiu5faNv9erVeOqpp2C1WjFt2jQ8//zzDSvF4Lo6ZWV1Dbr6\ng30jqqBA3nBq316+9G/79nUhFR8PRERobuPJarMqe4xKa0pRba5GrbUWtZZa1FhqlOclNSUoqixS\nhjNVZ1BUWYSzVWdhNBnh5eGFIO8gBPkEIcg7CCG+IYgJjkFscKw8hMiPMcExaOXXym0aclar3KCy\nWOTBbK57bjLJp13aB/vr6mqgvFxeXeo/lpfXNc4unF9lZV0jr6xMLjs0VN4XEBRUNwQG1j36+Mg9\nVry8AG/vuscxY4DOnbX/22Y+OZDNJndpqp9Lp083zKfycvl8Fns+de5cl01du8q3VdAoq80Ko8nY\nYKgwVch7vGvKUFhZiAJjQd2jsRBFlUUoqy1DjaUGAV4BCPQOVPKpc1hnpTtTanQqogOj2XhzEnf4\nXTObHMy+Q9zeqKs/nDghZ1VgoJxLHToAHTvWNfLi4zW940kIgQpTBcpqylBeW46y2jKlB5M9m+yn\npuQb81FgLECBsQBWmxX+Xv7w8/KDn6ef8hjkE6T0alJ6OAW1RXRgNFr5tUKwTzC8PFpWV1VncetG\nn9VqRUJCAtavX4927dqhX79+WLp0Kbp3715XKScHV2ZmJtLS0rRXltksN9hycuQhL08ecnPrnufl\nyXuj2re/eIiNRWZ+PtLGj5e3ulVWf9nMVjPOVJ1BobEQhZWFDR7tGzwXDpXmSpRUl6C0phQVpgoE\neQchzC8MIT4h8Pfyh4+nD3w8fODr6YuyQ2WI7RGLMN8wRAZEIiIgApEBkcrQyq8VgryDHBZCTf3d\nbLa6hpW9cVX/6Fb9BpT9yFf999kfa2rkAx5VVcCBA5kID09DVZXc6LI30OxDebn8PnvDytNTHuzP\nvbzkhpePj/xntz/39QVCQuQhOFh+LCzMRN++afDxqZtP/cHfX27k2T/X3PtWa32jRGv55Mxsuqry\nhJC7NuXm1mVTfn7do/15QYG84lyQS4iNRWZxMdLuvFPeIaXy1erqL5cQQsmbSlMljCYjKs3nH02V\nqDJXocpchWpLtfK80lSJc9XnUFxdjOKquqGkugT+Xv4I8glCoHegMtT+UYtOqZ0QFRCF6MBo5TE6\nMBqRAZEI8ZUzzSA1f7k1+//LzcpjNl09za57VmvDbaeCAnkoLKx7bn8dEVHXoDvfuMssK0Pa2LFy\nXgUEqLlYABrPpypzFSrNlUr+NJVXRpMRpTWlOFN1BmeqzqC4qhhnKuVHH08fhPqGKr2Wgn2CUfNH\nDbqkdkFkQCTaBLVBm8A2ymN0YDQCvB23vHrOC3fNJqd37t++fTu6dOmCjh07AgAmTZqElStXNggu\nZ1P9j2ffQMrPR+bixUg7dQo4d65uK98+2A/F2DekzpyRN4hiYuQr0NmHpCR5D1O7dvJjcHCTe5sy\n09ORdokGX/2AsW/oVJurGzTG7Bs/9m5IRpOxrsvk+T1JpTWlOPLNEXjv8kZZjdyoC/cPR1RgFKIC\nopTH6MBodAvvBj8vP/h6+jYY/Dz9EOYXhjDfMAT7BF/yqFt6ejrS70hvMM5+ZKqyUv56cxr5equq\nLu52aB/qHx2rqal7XlUF7N0rN8SMxrrujJWV8v+W+o0rb++6o1v1G2H25/Xfd2GjLCBAbmSdO5eJ\n669Pg7+//Nre4KrfWAsMdMx2cnp6Ju69N635M9IJreWTU/6xmEzyBlBeHjLfew9p+/fLK/eF+VRZ\nKW8k2fPJ07Mum9q2lYeEBGDoUKBNm7qhifN/M9PTkRYdfcmqWWyWBhs89iP8tdbzR/zPP6+olbtH\n2rtx25+X1ZahrKYMB/5zAP57/FFWU4ay2jJ4SB4I9A5EgHeAcrQtwDsA/l7+CPCSH+sPYX5hiGsV\nh3D/cET4RyDcPxzh/uEI8wtr9By59PR0pI9Pd8Rf57L0uqHjivK0TGvZBDjp71NRIW87LVmCtLw8\nec9n/X/o9uclJQ0bea1by/kUEyPnUFSUfF5ddLQ8REXJmdXI9lFmejrSruB7NVvNSsOs/jaTvUeS\nfedS/esEXDiU1ZbhyNdH4Jftp4zzNHgiwCvgokyy71QK8A5AoNf5R+9AdGnVBYNiByHCPwIRARFK\nRjV2Yab09HSk357uiL/MZek5L9w1m5ze6MvNzUVsvUvTxsTEYNu2bc6uRh0h5MM1JpP8aLM1fkjG\nZJKDxb7Vb9/yr//aaJQ3jOq/LiqCyMsDvL0h2kTDWlODGnM1LKHBsPr5wurnA2uoNyzRQbD4esHs\n74uqyFBURITA2CoQNbA02NCptdTCZC1BrbUANUVbUZNbixrL+enKxlDd80NZB7Bm0fq6z1trUWut\nQbW5ClWWKtRYquHt4QM/D3/4ePjB18Mf3gZfeBt84WPwg5fBF16SL3wM/vAzBMHPEAQfQyB8pTbw\nNcQjWApCvCEU/n4hyPT7DHe2+x/4G0LgIwWiqkqSz/XKlb+q8nJgX4X8ldq/9vqPVmvTDTL7n8Y+\nnDkj39qmpqauoWexyA0ne+MpIEDe3rQ3nvz95SNV9bsc2htkXl7ye0ND646K2Rtjfn7AN98Ajz/e\nsBtjQIC83evo3h3p6XJZ5HyazCerVV7prVZ5qH+YuP5wYfY0lkv1H0tKgPx8iNJSICoKtugoWMvK\nUB3oC1uAP6x+PrD4esMSGgqrbyTMvl6oDgtCZWQYKiKCUe3nqeSKyWqC2WqG2WaG2VoIk/U0zPlm\nmHPMDc4Nqb9T6fc9v2NzxmaYrCaYrCZlPtXmaqWrpNlmVhpl9Y/21z/q7+PpgyBv+Rxc+2NUYJTS\nnTvEJwRf7vkSM//fTIT4hCDEN0R397/UG/v/Bfu/Y/tObiEaPr/w/4J9sL/vws9d+HOyP2q4B7FC\nc9lUn/3LbSyXTCa5YdZUNjWWT0aj3HDLz4ew2SDatoHNZEJtZTmsIcGw+XrL204+3rCE+8PqEwJT\nYCdURg+HMSIUFeFBqPUQSj6ZrWY5o2xmmK2nYLYdhSnHhNoTtco5a/XPX9u9dze2frpVzqV6Gacc\ngTu/I0oIoTTM/DzrdmT7eJ7PJg8fBHoHKkfZgryDEBUQha6tuiLIJ0jJo8/2f4bnH3xeeR8vtkRq\ncfqadaXnJ3zZowckCEDg/KOAJABJ2GAQAgab/Ohhs0E6/1oSAgZhg8Emzj+Xp/tZLPCzWOBvscDP\naj3/3ArP8/8RbADM/zsXNgmwQYLFQ0KthwEmgwSThzzUehhQ6yHB6G2A0VuC0Qswekuo8AIqvYEK\nb8DoI1DpJWD0ETCG22Bsa0NRbyvyQsyo9DJDsp2G2GTD/E6bIAlPwOYJyewJmDwglXkCwkMeZ/UB\nrD6AxQfCUvcozOcfLd6wmc5Ps/rAYAsGrD6QrD6QbA0fLQVfoujwn2BQxvtCsvrAU/gjSPgjDH7w\nNHjA01O+qFT9QXgAVg8AHoDNAzB5AEYP+QiT/T0Gg9zokSTg2OF1+K8lRnkdEFB3zldwsLxjLShI\nblBJUt1n6z9e2BDz9oZSt/rve/dd4Mkn5XnZG3o+Pup1r8/KAvr1U2fepB1Xmk9f9ekFSdggoS5r\n7I/2LPI4P85DyaS67PKwyVnlbbXC12yBr8UCX7MVvhYL/MxWeFnl9wKAdc5s2CRJzidJQq2nASYP\nCebzmWTylGAySKj0NqDSW4LRWzr/CFR6ARU+gNFbyJnlI2AMtsEYLlCaYENOkAWFARZAyocBxRAb\nbfhnzDkYhBcM8IRBeEKq8oKhSn5uyPWGh/CBh/CBAfWeC28Y4AVJeMmfPf/aILzgIfzgKULPP/rB\nQ/jBYPOFOP0feG+bAl/b+c8LH0g2b3gKP3jaAuFhC4CH8AWE/DdpqneLkP9NoFQAJY1s5AsB/P77\nFpw51kVpKFyJ+uU11ehorFEhhHzh482br35e9Rsl9Rsm9vfZV097xgJyT9rlyy+uw+WGyy1D/caT\nXUWFfJ/7C99/YYPrwobXheU29p1c+B5Jkp/Pm9dwees/t/9fqD/Y/0dc+F77ePv/r/qPN9548d9f\na640m77o1xsGYQMEzmeIUB496uWQklfigm0pYYOHTR78zBb4WCzwNVvgY7HCz2yBt8UmZ5oArFYb\nbC+/DHunk1oPCSYPA0znM8rkKW9H1XjZt50MqPSWt53q51Oll4DRG6jwFjCGChgjrcjvYUVOkAXl\nPjYYcArIBP6RtLEum+AJCZ4wmM4PFZ7wyPOBB+rl0/nnHvY8glfdc+EFD/iezyZfeMIPnsIXHvCF\nyDPAN+tB+It684CcUV4iAJ4iAF4iQM48SJfMJjuTAM4CKBYXT9uxYz3mGzteNL6peV1pTz8hLn7M\nypJPWWxsemPqr3aN5cal7N4tXwy+sYy5VH0v9byxz9jz5sAB+a5il3v/pR6bKv/CZTh2DNiypekM\nbWreV1q+aoSTbd26VYwaNUp5PW/ePDF//vwG74mLi5MTigMHDroa4uLinB05V4X5xIFDyxyYTRw4\ncNDi4MhscvqFXCwWCxISEvDjjz+ibdu26N+//0UnIxMRuQLziYi0iNlERM3l9O6dnp6eeOeddzBq\n1ChYrVZMnTqVoUVEmsB8IiItYjYRUXNp8ubsRERERERE5Bjq3hypCVOmTEFUVBRSUlKUcefOncOI\nESMQHx+PkSNHorS0VJn2yiuvoGvXrujWrRvWrl17VWWdPn0aQ4cORVJSEpKTk7Fw4ULVyqupqcGA\nAQPQq1cvJCYm4oUXXlB12eysVitSU1MxduxYVcvr2LEjevTogdTUVPTv31/VskpLSzFhwgR0794d\niYmJ2LZtm2plHTp0CKmpqcoQEhKChQsXqlbeK6+8gqSkJKSkpOCee+5BbW2tamUtWLAAKSkpSE5O\nxoIFCwA49m/mqN/yzp07kZKSgq5du2LGjBlXtYyOpNdsAlyTT3rMJsB5+aTnbALUzSe9ZROg33zS\nczYB3HZyx3zS7baTw84OvAqbN28Wu3btEsnJycq45557Trz66qtCCCHmz58vnn/+eSGEEPv27RM9\ne/YUJpNJHD9+XMTFxQmr1XrFZeXn54usrCwhhBAVFRUiPj5e7N+/X7XyKisrhRBCmM1mMWDAALFl\nyxbVyrJ7/fXXxT333CPGjh0rhFDvu+zYsaM4e/Zsg3FqlXX//feLDz/8UAghf5elpaWqf49CCGG1\nWkV0dLQ4deqUKuUdP35cdOrUSdTU1AghhLjrrrvEkiVLVClr7969Ijk5WVRXVwuLxSKGDx8u/vjj\nD4eW1dzfss1mE0II0a9fP7Ft2zYhhBCjR48WP/zwwxUto6PpOZuEcH4+6TGbhHBNPukpm4RQP5/0\nlk1C6Duf9JpNQnDbyd3ySc/bTi5p9Akh/wHrL2xCQoIoKCgQQshhk5CQIIS4+ApVo0aNElu3br3m\ncm+//Xaxbt061currKwUffv2Fb///ruqZZ0+fVoMGzZMbNiwQYwZM0YIod532bFjR1FcXNxgnBpl\nlZaWik6dOl003hnryJo1a8SQIUNUK+/s2bMiPj5enDt3TpjNZjFmzBixdu1aVcpatmyZmDp1qvJ6\nzpw54tVXX3V4Wc39Lefl5Ylu3bop45cuXSr+/Oc/X9EyqkHv2SSEc/JJj9kkhOvySU/ZJIRz8klv\n2SSE/vNJb9kkBLed3C2f9Lzt5JLunY0pLCxEVFQUACAqKgqFhYUAgLy8PMTExCjvi4mJQW5u7jWV\nceLECWRlZWHAgAGqlWez2dCrVy9ERUUpXSPUXLa//OUv+Oc//wmDoe5PqVZ5kiRh+PDh6Nu3LxYt\nWqRaWcePH0dERAQeeugh9O7dG9OnT0dlZaVT1pEvvvgCkydPVm3ZWrVqhWeeeQbt27dH27ZtERoa\nihEjRqhSVnJyMrZs2YJz586hqqoKq1atQk5Ojurf49XO/8Lx7dq1u+a/nxr0kk2Ac/NJj9kEuC6f\n9JRNgGvySW/ZBOgnn/SaTQC3ndwtn/S87aSZRl99kiRd8kakV3qT0vqMRiPGjx+PBQsWICgoSLXy\nDAYDsrOzkZOTg82bN2Pjxo2qlfX9998jMjISqampEE1cj8eR5f3888/IysrCDz/8gHfffRdbtmxR\npSyLxYJdu3bh0Ucfxa5duxAQEID58+erUlZ9JpMJ3333HSZOnNjo/BxR3tGjR/HWW2/hxIkTyMvL\ng9FoxKeffqpKWd26dcPzzz+PkSNHYvTo0ejVqxc8PDxUKetSn2/uPLTEnbMJcF4+6TWbANfkk96y\nCXB9PuktmwD3zie9ZhPAbSd3yydXZ9OVzP9aaabRFxUVhYKCAgBAfn4+IiMjAcgt19OnTyvvy8nJ\nQbt27a5q3mazGePHj8d9992HcePGqV4eAISEhODWW2/Fzp07VSvrl19+wbfffotOnTph8uTJ2LBh\nA+677z7VymvTpg0AICIiAnfccQe2b9+uSlkxMTGIiYlBv379AAATJkzArl27EB0drerf7IcffkCf\nPn0QEREBQJ11ZMeOHbjuuuvQunVreHp64s4778TWrVtVW7YpU6Zgx44d2LRpE8LCwhAfH6/6LoXw\n6AAAIABJREFUun8184+JiUG7du2Qk5PT7HLVordsAtTPJ71mE+CafNJjNgHOzye9ZROgv3zSWzYB\n3HZyx3zS67aTZhp9t912GzIyMgAAGRkZSsDcdttt+OKLL2AymXD8+HEcOXJEufrRlRBCYOrUqUhM\nTMRTTz2lannFxcXK1Xaqq6uxbt06pKamqrZs8+bNw+nTp3H8+HF88cUXuOmmm/DJJ5+oUl5VVRUq\nKioAAJWVlVi7di1SUlJUKSs6OhqxsbE4fPgwAGD9+vVISkrC2LFjVfke7ZYuXap0T7DP19HldevW\nDb/++iuqq6shhMD69euRmJio2rIVFRUBAE6dOoVvvvkG99xzj2rro93Vzj86OhrBwcHYtm0bhBD4\n5JNPlM9ogR6yCXBuPuk1mwDX5JMeswlwfj7pLZsAfeSTXrMJ4LaTu+aTbredLnumoQomTZok2rRp\nI7y8vERMTIxYvHixOHv2rBg2bJjo2rWrGDFihCgpKVHe/7//+78iLi5OJCQkiNWrV19VWVu2bBGS\nJImePXuKXr16iV69eokffvhBlfL27NkjUlNTRc+ePUVKSor4xz/+IYQQqi1bfZmZmcpVqNQo79ix\nY6Jnz56iZ8+eIikpScybN0/VZcvOzhZ9+/YVPXr0EHfccYcoLS1V9Xs0Go2idevWory8XBmnVnmv\nvvqqSExMFMnJyeL+++8XJpNJtbKuv/56kZiYKHr27Ck2bNjg8OVy1G95x44dIjk5WcTFxYknnnji\nqpbRkfSaTUK4Lp/0lk1CODef9JpNQqibT3rLJiH0m096zSYhuO3krvmk120n3pydiIiIiIhIxzTT\nvZOIiIiIiIgcj40+IiIiIiIiHWOjj4iIiIiISMfY6CMiIiIiItIxNvqIiIiIiIh0jI0+IiIiIiIi\nHWOjjy6ye/du/PDDD01O37lzJ2bMmHHN8+/YsSPOnTsHABg8ePA1z6c5pk+fjgMHDrikbCK6dswn\nItIiZhNpHe/TRxdZsmQJdu7cibfffvuiaRaLBZ6ens2af6dOnbBz5060atWqWfMhopaH+UREWsRs\nIq3jkT4dOnHiBLp164aHHnoICQkJuPfee7F27VoMHjwY8fHx+O233wAA27dvx3XXXYfevXtj8ODB\nOHz4MEwmE/7+97/jyy+/RGpqKr766iukp6fjvvvuw5AhQ3D//fdj06ZNGDt2LADgqaeewpw5cwAA\na9aswY033nhRfc6ePYuRI0ciOTkZ06dPR/39DIGBgQCAzMxM3HjjjRg3bhzi4uIwa9YsfPLJJ+jf\nvz969OiBY8eOAQDOnDmDCRMmoH///ujfvz9++eUXAEB6ejqmTJmCoUOHIi4uTgndyspK3HrrrejV\nqxdSUlKwbNkyAEBaWhp27twJAFi6dCl69OiBlJQUzJo1q0HdXnzxRfTq1QuDBg1CUVGR4/5IRC0U\n84n5RKRFzCZmk+4J0p3jx48LT09P8fvvvwubzSb69OkjpkyZIoQQYuXKlWLcuHFCCCHKy8uFxWIR\nQgixbt06MX78eCGEEEuWLBFPPPGEMr+XXnpJ9O3bV9TU1AghhNi4caMYM2aMEEKIqqoqkZSUJDZs\n2CASEhLEsWPHLqrPE088IebMmSOEEOK///2vkCRJnD17VgghRGBgoDLP0NBQUVBQIGpra0Xbtm3F\nSy+9JIQQYsGCBeKpp54SQggxefJk8dNPPwkhhDh58qTo3r27UsfBgwcLk8kkiouLRevWrYXZbBb/\n+c9/xPTp05W6lJWVCSGESEtLEzt37hS5ubmiffv2ori4WFgsFnHTTTeJFStWCCGEkCRJfP/990II\nIWbOnCnmzp17LX8OIqqH+cR8ItIiZhOzSe+ad6yZNKtTp05ISkoCACQlJWH48OEAgOTkZJw4cQIA\nUFpaivvvvx9//PEHJEmCxWIBAAghGuxRkiQJt912G3x8fC4qx8/PD4sWLcL111+PBQsWoFOnThe9\nZ8uWLVi+fDkA4JZbbkFYWFijde7Xrx+ioqIAAF26dMGoUaOUOm/cuBEAsH79+gb9ySsqKlBZWQlJ\nknDrrbfCy8sLrVu3RmRkJIqKitCjRw88++yzmDVrFsaMGYMhQ4YonxVC4LfffkNaWhpat24NALj3\n3nuxefNm3H777fD29satt94KAOjTpw/WrVt3ye+ciK4M84n5RKRFzCZmk56xe6dO1Q8Zg8EAb29v\n5bk9oP72t79h2LBh2Lt3L7777jtUV1c3OT9/f/8mp+3ZswcRERHIzc1t8j3iCk4dvbDO9tf16yyE\nwLZt25CVlYWsrCycPn0aAQEBAKAsIwB4eHjAYrGga9euyMrKQkpKCl588UWlO4WdJEkX1dM+zsvL\nq0F97HUgouZhPjGfiLSI2cRs0jM2+lqw8vJytG3bFgDw0UcfKeODg4NRUVFxRfM4efIk3njjDWRl\nZeGHH37A9u3bL3rPDTfcgM8//xwA8MMPP6CkpOSa6zxy5EgsXLhQeb179+5Lvj8/Px++vr649957\n8eyzzyIrK0uZJkkS+vfvj02bNuHs2bOwWq344osvGu1bT0TOxXxiPhFpEbOJ2eSu2OjTqQv3wtR/\nbX8+c+ZMvPDCC+jduzesVqsyfujQodi/f79yMnJjn7e/njZtGl5//XVER0fjww8/xLRp02AymRqU\n/dJLL2Hz5s1ITk7G8uXL0aFDh0vWq7FlsU9buHAhduzYgZ49eyIpKQnvv//+JT+/d+9eDBgwAKmp\nqZg9ezZefPHFBtOjo6Mxf/58DB06FL169ULfvn2VE62bWmYiah7mk4z5RKQtzCYZs0mfeMsGIiIi\nIiIiHeORPiIiIiIiIh1jo4+IiIiIiEjH2OgjIiIiIiLSMTb6iIiIiIiIdIyNPiIiIiIiIh1jo4+I\niIiIiEjH2OgjIiIiIiLSMTb6iIiIiIiIdIyNPiIiIiIiIh1jo4+IiIiIiEjH2OgjIiIiIiLSMTb6\niIiIiIiIdIyNPiIiIiIiIh1jo4+IiIiIiEjH2OgjIiIiIiLSMTb6iIiIiIiIdIyNPiIiIiIiIh1T\nrdF3+vRpDB06FElJSUhOTsbChQsBAOnp6YiJiUFqaipSU1OxevVqtapARNQo5hMRaRGziYjUIgkh\nhBozLigoQEFBAXr16gWj0Yg+ffpgxYoV+OqrrxAUFISnn35ajWKJiC6L+UREWsRsIiK1eKo14+jo\naERHRwMAAgMD0b17d+Tm5gIAVGpnEhFdEeYTEWkRs4mI1OKUc/pOnDiBrKwsDBw4EADw9ttvo2fP\nnpg6dSpKS0udUQUiokYxn4hIi5hNRORQQmUVFRWiT58+Yvny5UIIIQoLC4XNZhM2m0389a9/FVOm\nTLnoM3FxcQIABw4cdDbExcWpHTlXhfnEgQMHgNnEgQMHbQ6OzCZVG30mk0mMHDlSvPnmm41OP378\nuEhOTr64UlC9LdrASy+9pMuynF2eXstydnl6LUsI5/+2L8Ud8onrufuV5ezy9FqWs8tjNl09va57\nel7P9VqWs8tz12xSrXunEAJTp05FYmIinnrqKWV8fn6+8nz58uVISUlRqwpERI1iPhGRFjGbiEgt\nql3I5eeff8ann36KHj16IDU1FQAwb948LF26FNnZ2ZAkCZ06dcL777+vVhWIiBrFfCIiLWI2EZFa\nVGv0DRkyBDab7aLxo0ePVqvIa5aWlqbLspxdnl7LcnZ5ei1LS9wln7ieu19Zzi5Pr2W5ojwtcJds\nAvS77ul5PddrWc4uz12zSbX79DWHJEm8NDGRDunht62HZSCihvTwu9bDMhBRQ478Xat2pE8NrVq1\nQklJiaur0SKEhYXh3Llzrq4GkdtgPjkHs4no6jCbnIf5RFrmVkf6uBfLefhd04oVK7B//34YDAa0\na9cO9913X5Pvzc7OxqefforXXnvtkvPUw3rFfHItfs8EOD6f9LBeMZtcj981aTmb3OpIHxE5R1lZ\nGebMmYOdO3cCAAYNGoTRo0cjPDz8ove+8cYb+OmnnxASEuLsahJRC8R8IiIt0no2qXbLBiJyX5s3\nb0ZiYqLyumfPnti4cWOj73366adx++23O6tqRNTCMZ+ISIu0nk080kfUghw7dgyLFi1qcvrAgQNx\n++23IycnB6Ghocr40NBQHDlypMnPsTsLETUX84mItEgv2cRGH5Gb2bVrF44cOYL33nsPd9xxBzIy\nMrBy5UrExsZe9rOdO3fGK6+8ctn3lZaWwtfXV3nt7e0No9HY5PslSbqyyhORrjGfiEiLmE3s3qmK\ntLQ0tGrVCiaTSRn34IMPwsfHB0FBQWjVqhWGDRuGffv2KdOXLFkCDw8PBAUFISQkBKmpqfjvf/+r\nTBdCoHPnzkhKSrqoPCEEFi5ciJSUFAQGBiI2NhZ33XUXfv/9d6Xsv/3tb8r79+3bhzZt2uCNN95Q\nY/FJZV5eXujevTs8PT0xY8YMbN269YpC62oEBQU12ANVXV2NVq1aNfl+7kl3D8wmUhvzia4V84nU\nxGzikT6HO3HiBLZv34727dvj22+/xYQJEwDIrfnnn38es2fPRk1NDR555BE89NBD2L59u/LZwYMH\nY/PmzRBC4N1338Vdd92FvLw8hISEYPPmzaitrYXRaMSOHTvQt29f5XMzZszAqlWr8MEHH2Dw4MGw\nWCxYvnw5Vq1aheTkZEiSpOxNyMrKws0334z09HQ88sgjzv1yyCFSUlLw+uuvY+LEiQAAHx+fK/7s\nlXZRiIuLw44dO5TxxcXF6N27d5Of45507WM2kTMwn+haMJ9IbcwmNvoc7uOPP8bw4cMxYMAAZGRk\nKMFVn6+vLyZOnIivvvqqwXh7i1+SJDz00EN48skncfToUfTu3RsZGRkYP348qqurkZGRoQTXkSNH\n8K9//Qu//vqrMs7Lywv33HPPRfPevn07br31Vrz66quYMmWKGotPTrJ+/Xr861//uurPXWkXhRtu\nuAEzZ85UXu/atQuvvvoqAODo0aPo3Llzg7DinnTtYzaRszCf6Goxn8gZWno2sXung3388ce4++67\ncdddd2HNmjU4c+aMMs3+x62srMTSpUsxYMCARudhsVjwwQcfICgoCF27dkVVVRW+/vprZb5ffPEF\nLBYLAODHH39EbGxsg71Xjdm2bRtGjx6Nt956i6Hl5oQQqKqqQqdOnRqMy8jIwKZNm7BmzRrs2bMH\nTz75JGpra/H4449fdRkBAQGYOXMm5s6di9mzZ2PmzJmIjIwEAEycOBHZ2dnKe9955x0sXrwYmZmZ\nePnll1FeXt78hSSHYzaRMzCf6Fown0htzCYAQoOaqpZGq6vYsmWL8PX1FeXl5UIIIXr27CnefPNN\nIYQQDzzwgPD19RWhoaHCYDCIzp07izNnziif/eijj4Snp6cIDQ0V4eHhYtCgQeLHH38UQgjxySef\niJiYGCGEEBaLRYSHh4vly5cLIYSYO3euGDhw4CXr9cADD4jg4GDRuXNnUVxcfEXLovXvmhp65513\nxOLFi8WWLVtEUVGRyMvLE3fffbcQQohVq1a5uHZ19LBeuWM+MZvIldwhn/SwXrljNgnBfCLXaWnZ\npLsjfZLkmOFaZGRkYOTIkQgKCgIgt+ozMjKU6c899xxKSkpw4sQJ+Pj44OOPP27w+YEDB6KkpARn\nzpzBL7/8gptuukmZ75133gkA8PDwwLhx45T5tm7dGvn5+Zf5TiQ89thj6NOnD0aMGIHS0tJrW0DS\nrIMHD2LChAkYMmQIJEmCn5+fcvJwWFiYi2tHALOp8e+E2dQSMJ+0z1XZBDCfyHVaWjbp7pw+V3Xd\nr66uxldffQWbzYY2bdoAAGpra1FWVoY9e/ZAkiSli0JsbCwWLlyIiRMnYvr06UrQNSYnJwcbNmzA\nb7/9pvRjr6qqQk1NDc6ePYthw4bh8ccfx86dO9GnT58m5+Pp6YnPP/8cEyZMwKhRo7B+/fpLlkvu\nZdKkSfj+++/RunVrdO/eHVFRUTAYDPj++++Vf4DkWsymxjGb9I/5pH3Mp8Yxn/StpWWT7o70ucqK\nFSvg6emJAwcOYPfu3di9ezcOHDiAIUOGXLRXCgCGDx+OLl26XPaE0k8++QTdunXD4cOHlfkePnwY\nMTExWLp0Kbp27YpHH30UkydPxqZNm2AymVBTU4MvvvhCOXlUCAEhBDw9PbFs2TKEh4fjlltuQVVV\nlSrfBTnf4MGDMXnyZIwcORKxsbHw9vbGO++8gzFjxsDf39/V1SMXYjaRqzGfqCnMJ3KllpZNbPQ5\nyMcff4wpU6YgJiYGkZGRiIyMRFRUFB5//HF89tlnsFqtF12a9bnnnsPChQthMpkaXBr4wvk++uij\nyjzt83344YeVQFy4cCEef/xxPPbYYwgLC0OXLl2wcuVK3HbbbQDQYN5eXl745ptv4Ovri9tuuw01\nNTUqfzNE5ErMJiLSKuYTkfNIQrjqoH7T6h/Ov5Lx5Hj8rkkNelivmE+uxe+Z1KCH9YrZ5Hr8rsnR\nHLlO8UgfERERERGRjrHRR0REREREpGNs9BEREREREemY7m7ZQESOs2LFCuzfvx8GgwHt2rXDfffd\n1+j7srOz8emnn+K1115zcg2JqCW6kmxavHgx8vLy4OXlhYSEBIwbN84FNSUiPWpOBn333XfIyclB\nTU0NOnTooNxPUm1s9BFRo8rKyjBnzhzs3LkTADBo0CCMHj0a4eHhDd73xhtv4KeffkJISIgrqklE\nLcyVZNPevXvx0UcfYcuWLQCAESNG4Oabb4avr69L6kxE+tGcDDpz5gwOHTqEZ599FgAwbdo0jBw5\nEoGBgarXm907iahRmzdvRmJiovK6Z8+e2Lhx40Xve/rpp3H77bc7s2pE1IJdSTatXr0anTp1Ul5H\nRkbi559/dlodiUi/mpNBxcXFWL9+PUwmEwAgICAA3t7eTqk3j/QRtTDHjh3DokWLmpw+cOBA3H77\n7cjJyUFoaKgyPjQ0FEeOHGn0M7xENRE1lyOzKSgoCGazWXldU1ODAwcOYNiwYY6vOBHpgpoZVF1d\njYMHD+Kxxx6DzWZDv3798Kc//QkjR45ko4+oJdm1axeOHDmC9957D3fccQcyMjKwcuVKxMbGOrys\nzp0745VXXrns+0pLSxt0hfL29obRaGz0vY3dHJeI3J+7ZtOdd96JxYsXQwgBo9GIQ4cOoV+/fg6v\nMxGpSy8ZdPjwYfTv3x8AMGvWLLzyyit49tln8dZbbzl2IS6B3TtV9tlnn2HUqFGurgZpnJeXF7p3\n7w5PT0/MmDEDW7duVSXQrkZQUFCDI3jV1dVo1apVo+/lkT73w2yiK+Gu2RQZGYmPPvoIixYtQmZm\nJlJSUhAZGensqtI1Yj6Rnd4y6PDhw8jMzMS6devw3XffYe7cufjll1+cUm8e6XOQjh07oqioCB4e\nHsq4hx56CAsXLsS9997rwpqRO0hJScHrr7+OiRMnAgB8fHxUK+tKuy/ExcVhx44dyvji4mL07t27\n0c/wSJ92MZuoOdw5mxITE5GUlAQAmD17NubMmeP4SlOzMJ/ocvSUQbNnz8a3336rLMvw4cORkZGB\nn376Cdddd52Dl6YRQoOaqpZGqyuEEKJjx47ixx9/dHU1HEbL37Ve3XzzzeLYsWOurobCaDSK5ORk\n5XWPHj1EYWGhEEKIP/74Q9hsNmXaRx99JB588MHLzlMP65W75ROziZrLHbPp+PHjokePHkIIIfbv\n3y/Gjx9/yXnqYb1yt2wSgvlEV0ZPGfT111+Lzz//XPnsqlWrxKZNm5osy5HrFLt3qmzJkiW4/vrr\nlddr165FQkICQkND8dhjj+HGG2/Ehx9+qExfvHgxEhMT0apVK9x88804deqUMs1gMOD9999HfHw8\nwsLC8Pjjjzt1WUg9QghUVVU1uNITAMyZMwcvv/wy5s+fDyEEMjIysGnTJqxZswaZmZl44IEH8O9/\n/xtvv/02AODDDz/Exo0b8frrrwMAvv76a6xatQo//fTTVdcpICAAM2fOxNy5czF79mzMnDlT6R41\nceJEZGdnAwDeeecdLF68GJmZmXj55ZdRXl7enK+CnITZRFfCXbOpXbt2GDduHP71r3/h3//+9yX3\n3pP2MJ/ITm8ZdOedd6KoqAjz5s3DggULUFRUhBtuuKE5X9GVc1jz0YGaqpZGqyuEkPdWrV+//qLx\nH330kRgyZIgQQogzZ86I4OBgsXz5cmG1WsWCBQuEl5eX+PDDD4UQQqxYsUJ06dJFHDx4UFitVjF3\n7lxx3XXXKfOSJEmMHTtWlJWViVOnTomIiAixevVqVZZHy991S2I2m8Vf//pXUVJSIt555x2xePFi\nsWXLFlFUVCTKy8vFn/70J+W9n332mfjPf/4jhBDi3nvvFUIIMXHiRJGRkeGSujdw/qigHtYrd8sn\nZhOpQTfZVFsrRHW1LtYrd8smIZhPdO10k0GX4ch1ikf6HEQIgXHjxiEsLEwZPvjggwbnOq1atQrJ\nyckYN24cDAYDnnzySURHRyvT/+///g8vvPACEhISYDAY8MILLyA7OxunT59W3jNr1iwEBwcjNjYW\nQ4cOVY62kP4IITB79mw8/vjjMJlMOHjwICZMmIAhQ4ZAkiSYzeYGNwL95ZdfkJaWhtraWnh4eOC9\n997DK6+8gkOHDmHPnj0uXBIAkyYB69a5tg4tFLOJHE1X2bR6NXDHHa6tQwvGfKJroasMupQvv3To\n7HR3IRfpZcdcUEK8dHVXI5QkCStXrsRNN93UYPySJUuU53l5eYiJiWkwvf7rkydPYsaMGXjmmWca\nvCc3N1e5UlH9oPP392/yEvrk/tasWYObbroJL730Eh588EFMmjQJ33//PVq3bo3u3bvj0KFDDda3\nu+++Gxs2bEBpaSleeeUV7NmzB0eOHEF8fHyDm4i6xLZtwNy5rq2DizGbSC90lU27dwM9e8qNvxbM\nEfl0tdkEMJ/o2ugqg5piswHTpjl0lrpr9F1L6DhL27Zt8d133ymvhRDIyclRXrdv3x5/+9vfMHny\nZFdUjzTm5ptvBgCkpaUp4wYPHqw8v/CSxfXPfwDk9U0TSkuBs2eBuDhX18SlmE2kF7rJJkBu9I0f\n7+pauBzzidyJrjKoKUePAq1bAw7cQcHunQ4kLnOvsltuuQV79+7FypUrYbFY8O6776KgoECZ/vDD\nD2PevHnYv38/AKCsrAzLli275vKINGHPHiAlBTAwblyF2UTUBPuRPnIZ5hNRI7KygNRUh86SW2EO\nNHbsWAQFBSnDnXfeCUmSlL7p4eHhWLZsGWbOnInw8HAcOHAAffv2Ve45Mm7cODz//POYNGkSQkJC\nkJKSgjVr1ijzv/BeaPXnTaRZ2dncqHIxZhNRIyoqgNxcID7e1TVp0ZhPRI3IzgZ69XLoLCWhwV0e\nkiQ1uiemqfHuymazITY2Fp9//jluvPFGV1enAb191+RCU6cC/foBDz+si/WqJeQTs4lahF9+AZ58\nEtixQxfrVUvIJoD5RC3ELbcAf/4zpHHjHLZO8Uifk61duxalpaWora3FvHnzAAADBw50ca2IVMTu\nU26B2UQtzu7dDt+TTupgPlGLw+6d7m/r1q3o0qULIiIi8N///hcrVqxQuigQ6Y7FAhw4IJ/TR5rG\nbKIWhzuk3AbziVqUggKgtha44II0zcXundQoftfkEPv2yffAOnwYgD7WK+aTa/F7JocZNAh49VXg\nhht0sV4xm1yP3zU5xJo1cjZt2ODQdYpH+ohIPdyTTkRaZLUCe/cCPXq4uiZERA1lZzu8ayegYqPv\n9OnTGDp0KJKSkpCcnIyFCxcCAM6dO4cRI0YgPj4eI0eORGlpqVpVICJX02ijj/lE1MIdPQqEhwOh\noa6uSQPMJiJCVpYq5xur1ujz8vLCm2++iX379uHXX3/Fu+++iwMHDmD+/PkYMWIEDh8+jGHDhmH+\n/PlqVYGIXE2jjT7mE1ELp9GLuDCbiEiN2zUAKjb6oqOj0et8hQMDA9G9e3fk5ubi22+/xQMPPAAA\neOCBB7BixQq1qkBErqZScDUX84mohdPoDilmE1ELV1kJnDoFdOvm8Fk75Zy+EydOICsrCwMGDEBh\nYSGioqIAAFFRUSgsLHRGFYjI2QoLAZMJiIlxdU0uiflE1AJptNFXH7OJqAXaswdITAS8vBw+a0+H\nz/ECRqMR48ePx4IFCxAUFNRgmiRJkCSp0c+lp6crz9PS0pCWlqZiLYnI4XbvRmb79sh8+WVX16RJ\nzCeililz2zZkduokb2BpELOJqGXK/OorZNpsQL3fssMIFZlMJjFy5Ejx5ptvKuMSEhJEfn6+EEKI\nvLw8kZCQcNHnmqqWytVtlg4dOojIyEhRWVmpjFu0aJFIS0sTQgghSZIICAgQgYGBom3btuKJJ54Q\nZrPZVdW9LC1/1+Qm/vEPIWbMaDBKS+tVS8knZhPRBc6eFSIoSAirVRmlpfWqpWSTEMwnoov86U9C\nvP228tKR65Rq3TuFEJg6dSoSExPx1FNPKeNvu+02ZGRkAAAyMjIwbtw4targdDabDQsWLGgwrv7e\nuD179qCiogKbN2/GN998g3//+9/OriKR82i4+1RLyydmE1E9u3cDKSmAQXt3rWpp2QQwn4gayMpS\n5XYNgIrn9P3888/49NNPsXHjRqSmpiI1NRWrV6/GrFmzsG7dOsTHx2PDhg2YNWuWWlVwKkmS8Oyz\nz+K1115DWVnZJd8bFxeHwYMHY//+/U6qHZELaPQiLkDLyidmE9EFNHrlTqBlZRPAfCJqwGIB9u1T\n7f6hqp3TN2TIENhstkanrV+/Xq1iXapv375IS0vDa6+9hjlz5lw0XT5KCxw8eBBbtmzhJZdJv2pq\n5PtgJSa6uiaNamn5xGwiqmf3bmDQIFfXolEtLZsA5hOR4vBhoG1b4ILzeB1Fe30b3JgkSZg9ezbe\nfvttFBcXA6gLKwDo3bs3AgMDkZiYiAkTJuD+++93VVWJ1LV/P9ClC+Dj4+qaEJhNRA1YdJQ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M03gVdfdXWNHOayjb7p06dj3rx58Pb2BgCkpKRg6dKlqleMiK5BYSHwzDNAbCzw4otAv37A4cPy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\nERHQvDn07QsNG5obj1988eLzGzak/v66Xz6CiIiIGw7TH9Kbm0D5ScTn9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T/LbzN2ZtncWcbXM4feE0NYvW5M4id5qvRe+kRJ4SXr/3xQ3nthuOQa5hxw6zjKB2bfjii8Bq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\ne8R/RyKiYDBIOTk51Nb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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The time the eigensolvers take to diagonalize a random matrix of a given size. Here, $r_{ev}$ is the \"ratio\" of eigenvalues. Hence $r_{ev} = 0.1$ means calculating 10% of the eigenvalues, for ARPACK only. Eigen and Numerical Recipes always calculate all eigenvalues. $r_{zeros}$ is the \"ratio\" of zeros. Hence $r_{zeros} = 0.25$ means 25% sparse. Both Eigen and Numerical Recipes are not affected by $r_{ev}$ and $r_{zeros}$ and thus the corresponding curves should be the same for all plots above.\n", "\n", "This test was run on OS X 10.9.1, the compiler was GNU G++ 4.8.2 (installed from MacPorts). Arpack is 3.1.4 (it's Arpack-ng), installed from MacPorts. Arpaca was used as the Arpack wrapper." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def subplot_chris(p,xlim=None,ylim=None):\n", " # columns are: N NRg++4.1.2 Arpack4.1.2 Eigen4.1.2 NR4.8.2 Eigen4.8.2\n", " filename = 'performance_chris.dat'\n", " d = np.loadtxt(filename)\n", " p.plot(d[:,0],d[:,2],label='ARPACK G++ 4.1')\n", " p.plot(d[:,0],d[:,3],label='Eigen G++ 4.1')\n", " p.plot(d[:,0],d[:,5],label='Eigen G++ 4.8')\n", " p.plot(d[:,0],d[:,1],label='NR G++ 4.1')\n", " p.plot(d[:,0],d[:,4],label='NR G++ 4.8')\n", " p.set_xlabel('matrix dimension')\n", " p.set_ylabel('time (s)')\n", " p.legend(loc='upper left')\n", " if xlim: p.set_xlim(xlim)\n", " if ylim: p.set_ylim(ylim)\n", "\n", "rows = 1\n", "cols = 2\n", "\n", "fig = plt.figure(figsize=(cols*5,rows*5))\n", "i_p = 0\n", "\n", "i_p += 1\n", "p = fig.add_subplot(rows, cols, i_p)\n", "subplot_chris(p,(0,1000),(0,25))\n", "\n", "i_p += 1\n", "p = fig.add_subplot(rows, cols, i_p)\n", "subplot_chris(p)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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++AImT7ZNvTSqJLdINqbRaMzeRRWWXtHp9Xr8/f3ZsGEDPXr0KOvqVHqV9XtU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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A very similar test, this time run on WestGrid's Jasper (Linux). Uses latest Arpack from Rice university and Arpack++ as the wrapper. The matrix is the Hamiltonian from a real physical problem, it's about 1% to 2% sparse. Numerical Recipes and Eigen are compiled with two different versions of the GNU G++ compiler, as indicated. The full spectrum of eigenvalues is computed. This scenario corresponds to the $r_{ev} = 1.0$ and $r_{zeros} = 0.98$ (the bottom right-most) plot in the last graph.\n", "\n", "While the general trends agree, there are some notable differences: Arpack is much slower here than above. Reversely, Numerical Recipes is faster in this test, compared to the last.\n", "\n", "It should be noted that ARPACK was used in a black box like fashion (via the wrappers) and there might be considerable room for improving its performance, for example by compromising on precision (we use machine precision) or just using it in a cleverer way. To compute the full spectrum we actually run ARPACK twice, once to get all but one eigenvalue, starting from the smallest, and once the compute the missing largest eigenvalue. (ARPACK does not seem to allow to compute the whole eigenvalue spectrum directly, at least not in the simple direct manner we are using via the wrappers.)\n", "\n", "We summarize the results of these tests: \n", "\n", "1. Never ever use Numerical Recipes, it's extremely slow. \n", "2. Use new compilers. They are significantly faster than the old ones, especially for sophisticated C++ libraries like Eigen.\n", "3. To calculate only a couple of eigenvalues, use Arpack; and it's increasingly faster for increasingly sparse matrices. No surprises here.\n", "4. To calculate all eigenvalues, use Eigen." ] } ], "metadata": {} } ] }