{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Este es el c\u00f3digo completo, incluyendo las figuras, del art\u00edculo http://pybonacci.wordpress.com/2013/08/15/ajuste-e-interpolacion-unidimensionales-basicos-en-python-con-scipy/." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Interpolaci\u00f3n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy import interpolate" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "from scipy.interpolate import barycentric_interpolate\n", "\n", "def runge(x):\n", " \"\"\"Funci\u00f3n de Runge.\"\"\"\n", " return 1 / (1 + x ** 2)\n", "\n", "N = 11 # Nodos de interpolaci\u00f3n\n", "\n", "xp = np.arange(11) - 5 # -5, -4, -3, ..., 3, 4, 5\n", "fp = runge(xp)\n", "\n", "x = np.linspace(-5, 5, num=1000)\n", "\n", "y = barycentric_interpolate(xp, fp, x)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "l, = plt.plot(x, y)\n", "plt.plot(x, runge(x), '--', c=l.get_color())\n", "plt.plot(xp, fp, 'o', c=l.get_color())\n", "leg = plt.legend(['Interpolaci\u00f3n', 'Real'])\n", "leg.get_frame().set_facecolor('#fafafa')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAECCAYAAAD9z2x7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8glaE3WDAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy.polynomial import chebyshev\n", "\n", "coeffs_cheb = [0] * 11 + [1]\n", "T11 = chebyshev.Chebyshev(coeffs_cheb, [-5, 5])\n", "\n", "xp_ch = T11.roots()\n", "fp_ch = runge(xp_ch)\n", "\n", "y_ch = barycentric_interpolate(xp_ch, fp_ch, x)\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n", "\n", "l1, = ax1.plot(x, y)\n", "ax1.plot(x, runge(x), '--', c=l1.get_color())\n", "ax1.plot(xp, fp, 'o', c=l1.get_color())\n", "ax1.set_title(\"Nodos equiespaciados\")\n", "\n", "leg1 = ax1.legend(['Interpolaci\u00f3n', 'Real'])\n", "leg1.get_frame().set_facecolor('#fafafa')\n", "\n", "l2, = ax2.plot(x, y_ch)\n", "ax2.plot(x, runge(x), '--', c=l2.get_color())\n", "ax2.plot(xp_ch, fp_ch, 'o', c=l2.get_color())\n", "ax2.set_ylim(ax1.get_ylim())\n", "ax2.set_title(\"Nodos de Chebyshev\")\n", "\n", "leg2 = ax2.legend(['Interpolaci\u00f3n', 'Real'])\n", "leg2.get_frame().set_facecolor('#fafafa')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlsAAAEMCAYAAADzpnOjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXd4VNXWxt+ZSZ8kk0x6g5CEEor0UAPBEKQXpQhXBMXr\nFRXhWq6CDcUCIuXyXcVCExVFkA4CoRM6JEgLCQFJIJAEMull6v7+CBkZ0qafOTPr9zw8D2fOOfu8\ns8+ZlXX2WnttAWOMgSAIgiAIgrAIQq4FEARBEARB2DPkbBEEQRAEQVgQcrYIgiAIgiAsCDlbBEEQ\nBEEQFoScLYIgCIIgCAtCzhZBEARBEIQFIWfLzpg7dy4mT57MtQy98fLyws2bN7mWUYejR4+iTZs2\nRp178+ZNCIVCaDQaM6siCMfDGjZtzZo1iI+Pt7m2LaHr0KFDiIiIMGubRNOQs8UxkZGRCAoKQmVl\npfazFStWYMCAAUa1JxAIzCXNKpSVlSEyMpJrGXWIj4/H1atXuZZBELzDEW3anj170K9fP3h7eyMw\nMBAJCQnYvn0717IIG4KcLRtAo9Hgv//9L9cyCIIgzIIj2bSNGzdi/PjxmDp1KnJzc1FQUICPP/6Y\nnC1CB3K2OEYgEODNN9/El19+iZKSknqPOX78OLp37w4fHx/ExcXhxIkT2n1//fUX+vfvD29vbwwa\nNAj379/XOXfbtm1o164dfH19MWDAAJ3RmgULFiA8PBze3t5o06YNDhw4UO/15XI53nzzTTRv3hzB\nwcGYPn06qqurtfsXLlyI0NBQhIeHY9WqVRAKhbhx4wYAICEhAStXrtQe++iw+MPHNnad+/fvY/jw\n4fD19YWfnx/69eunbSMyMhLz589Hu3btIJVK8fzzz0MulwMAiouLMXz4cAQGBkIqlWLEiBHIzc3V\nniuTyfDcc88hLCwMUqkUY8aMAVB3qH3+/PmIiYmBt7c32rVrhy1btmj3aTQavPnmmwgICEB0dDR2\n7typ03937tzByJEj4efnh5YtW2LFihXafadPn0a3bt0gkUgQHByMN954o957QBB8gQ82rbCwECNH\njoREIkGPHj1w/fp1nf1Xr15FUlIS/Pz80KZNG2zYsKHedhhjeP311/HBBx/g+eefh5eXFwCgX79+\n+O6773SOfeuttyCVShEVFYXdu3drPy8pKcG0adO0NvT999/XSUFgjGHGjBnw8fFBbGys9jtt2LAB\n3bp107nG4sWLMXr0aADArl270K5dO3h7eyM8PByLFi2qc2xQUBBCQ0OxZs0a7eeN2eHY2Fgd+6ZS\nqRAQEIDz58/X2z/EQzCCUyIjI9m+ffvYk08+yd577z3GGGPff/89S0hIYIwxVlhYyHx8fNhPP/3E\n1Go1++WXX5ivry+TyWSMMcZ69uzJ3njjDaZQKNiRI0eYl5cXmzx5MmOMsYyMDCYWi9m+ffuYSqVi\nX3zxBYuJiWEKhYJdvXqVRUREsLt37zLGGMvOzmbXr1+vV+OsWbPYqFGjWFFRESsrK2MjRoxgs2fP\nZowx9scff7CgoCB2+fJlVlFRwSZOnMgEAoG2rYSEBLZy5UptW6tXr2Z9+/bVbj98bGPXeeedd9hL\nL73EVCoVU6lULCUlRdtG8+bNWYcOHdjt27eZTCZjffr00fZlYWEh27RpE6uqqmJlZWVs3LhxbPTo\n0dpzhw4dyp5++mlWXFzMlEolO3LkCGOMsYMHD7Lw8HDtcRs2bND21fr165lYLGZ5eXmMMcaWL1/O\n2rRpo71+QkICEwqFTK1WM8YYi4+PZ6+88gqTy+Xs/PnzLCAggB04cEB7/3766SfGGGMVFRXs5MmT\njT0uBGHz8MGmTZgwgU2YMIFVVlayS5cusbCwMBYfH88YY6y8vJyFh4ezNWvWMLVazdLS0pi/vz+7\ncuVKnXbS09OZQCBgN2/ebLA/Vq9ezZydndmKFSuYRqNhy5cvZ6Ghodr9o0ePZi+99BKrrKxkBQUF\nLC4ujn377bfac52cnNjSpUuZSqVi69evZxKJhBUVFbHq6momlUpZenq6tq1OnTqxTZs2McYYCw4O\n1trJ4uJilpqayhirsW1OTk7sww8/ZCqViu3atYt5eHiw4uJixljjdvjjjz9m//jHP7TX27FjB2vb\ntm2D3534G3K2OCYyMpLt37+fXbp0iUkkEnbv3j0dw7R27VrWo0cPnXN69erF1qxZw7Kzs5mTkxOr\nrKzU7ps0aZLWMH388cdswoQJ2n0ajYaFhYWxw4cPs2vXrrHAwEC2b98+plAoGtSn0WiYWCzWMVrH\njx9nLVq0YIwx9txzz2l/iIwxlpmZaZSz1dR1PvjgAzZq1CiWlZVVbx/WGifGGNu1axeLjo6u9/uk\npaUxX19fxhhjd+7cYUKhUGtkHuZRZ+tROnXqxLZt28YYY2zAgAE619+7dy8TCARMrVaznJwcJhKJ\nWHl5uXb/7Nmz2dSpUxljjPXr1499+OGH7N69ew1eiyD4hK3bNJVKxZydnVlGRob2szlz5mjt0q+/\n/qp1vGp58cUX2UcffVSnrZSUFCYQCJhcLm/weqtXr2YxMTHa7YqKCiYQCFh+fj7Ly8tjrq6urKqq\nSrt/3bp1bMCAAdpzH3bMGGMsLi6O/fjjj4wxxl566SX27rvvMsYYu3TpEvP19dV+92bNmrFvv/2W\nlZSU6Jx/8OBB5u7urn0ZZIyxwMBAdurUqSbt8LVr15iXl5dW76RJk9i8efMa/O7E31AY0UZo164d\nhg8fjvnz5+skhN65cwfNmjXTObZ58+bIzc3F3bt34evrC3d3d519DZ0rEAgQERGB3NxcxMTEYOnS\npZg7dy6CgoIwceJE3L17t46ue/fuobKyEl27doWvry98fX0xZMgQ7dD+3bt3dcJtj2rVl6au89Zb\nbyEmJgaDBg1CdHQ0FixYoHP+oxru3LkDAKisrMS//vUvREZGQiKRoH///igpKQFjDLdu3YJUKoVE\nImlS39q1a9G5c2ettkuXLunVB3fu3IFUKoVYLNbZXxvKXLlyJTIzMxEbG4u4uLg6IUiC4Cu2bNNU\nKlWDv9ns7GycOnVK+1v39fXFunXrkJ+fX6ctPz8/AKj3Og8THBys/b+HhwcAoLy8HNnZ2VAqlQgJ\nCdFe66WXXsK9e/e0x4eFhdXpq9rrTZkyBevWrQMA/Pjjj5gwYQKcnZ0BAL///jt27dqFyMhIJCQk\n4OTJkzq6hcK///x7eHigvLy8STscExOD2NhYbNu2DZWVldi+fTsmTZrU6HcnaiBny4b46KOP8P33\n3+vkFIWFhSE7O1vnuOzsbISHhyMkJARFRUU6s34ePvbRc2sdjNof78SJE3H06FFkZ2dDIBDg7bff\nrqPJ398f7u7uuHLlCoqKilBUVITi4mKUlpYCAEJCQpCTk6M9/uH/A4BYLEZFRYV2Oy8vr97v3tR1\nPD098eWXX+L69evYtm0bFi9ejIMHD9Z73ZycHO13XLRoETIzM3H69GmUlJTg8OHDYDUjuoiIiIBM\nJmswr+ThPn3xxRfx1VdfQSaToaioCO3btwdjrMk+CA0NhUwmQ3l5uc7+8PBwADXGa926dbh37x7e\nfvttjB07FlVVVY3qIQi+YIs2LSAgAE5OTg3+Zps1a4b+/ftr7VBRURHKysrw1Vdf1WmrdevWiIiI\nwMaNGw3pFi0RERFwdXVFYWGh9lolJSW4ePGi9piH+w6o6Y/Q0FAAQM+ePeHi4oIjR47gl19+0SmR\n0a1bN2zZsgX37t3D6NGjMX78+Cb1NGWHgZo+/uWXX7B161a0a9cOUVFRRn13R4OcLRsiOjoaEyZM\n0JnFM2TIEGRmZuKXX36BSqXC+vXrcfXqVQwfPhzNmjVDt27d8OGHH0KpVCIlJQU7duzQnjtu3Djs\n3LkTBw4cgFKpxKJFi+Dm5obevXsjMzMTBw4cgFwuh6urK9zc3CASiepoEgqF+Oc//4lZs2Zp37Zy\nc3Oxd+9eAMD48eOxZs0apKeno7KyEh999JHO+Z06dcKmTZtQVVWFrKwsnWR5Q66zc+dOZGVlgTEG\nb29viEQi7ZsZYwxff/01cnNzIZPJ8Omnn2LChAkAat4e3d3dIZFIIJPJdPSFhIRgyJAhePnll1Fc\nXAylUokjR47U0VZRUQGBQAB/f39oNBqsXr0aly5d0u4fP348li1bhtzcXBQVFWH+/PnafREREejd\nuzdmz54NuVyOCxcuYNWqVXjmmWcAAD/99JP2+0okEggEAp03ToLgM7Zo00QiEZ588knMnTsXVVVV\nuHLlCn744Qft6NuwYcOQmZmJn376CUqlEkqlEmfOnKm3FIxAIMDixYsxb948rFmzBqWlpdBoNEhJ\nScG//vWvJvsnJCQEgwYNwuuvv46ysjJoNBpcv35dxw4VFBRg2bJlUCqV2LBhAzIyMjB06FDt/smT\nJ+PVV1+Fi4sLevfuDQBQKpX4+eefUVJSApFIBC8vr3r74lGassMA8PTTT2PPnj345ptvaFTLELiL\nYBKM/Z3fUMutW7eYm5ubNmbPWE1eQNeuXZlEImHdunVjx44d0+67ceMGi4+PZ56eniwpKYnNmDFD\nm9/AGGObN29mbdu2ZRKJhCUkJGiTPC9cuMDi4uKYl5cXk0qlbMSIEdrE0keprq5mc+bMYVFRUczb\n25vFxsay//u//9Punz9/PgsODmZhYWFs1apVOjlb9+/fZ4MGDWJeXl6sb9++bO7cuTr5EEKhUHts\nY9dZsmQJi4yMZGKxmIWHh7NPPvlEpw/nz5/P2rZty3x8fNjUqVO1OQV37txhCQkJzNPTk7Vu3Zp9\n++23OsnrMpmMTZkyhQUFBTFfX1/21FNPMcZq8hoiIiK013j33XeZVCpl/v7+7PXXX9fJRVOpVOzf\n//438/PzY1FRUeyrr77Sucbt27fZ8OHDmVQqZdHR0Tr5Xc888wwLDAxknp6erH379mzr1q313gOC\n4At8sGn37t1jw4cPZ97e3qxHjx7s/fff17FLGRkZbNiwYSwgIID5+fmxxMRE9ueffzb4nXfv3q3V\nHBAQwAYMGMB27drFGGNszZo1dXLAHrZ7JSUlbPr06Sw8PJxJJBLWuXNntn79eu25ffv2Za+++iqT\nSCSsdevWLDk5Waet7OxsJhQK2dy5c7WfKRQKNnjwYObr68u8vb1ZXFycto8ftW2M6d6zpuw9Y4wl\nJiYyZ2dnlp+f32CfELoIGHsQCzGC+/fv46uvvkJJSQkEAgESExN1PO5aVq1ahfPnz8PV1RUvv/wy\nWrRoYZKDSNg2QqEQWVlZVhtebtGiBVauXInHH3/cKtcj7AOyX4Q9UFVVhaCgIKSlpSE6OpprOUQD\nOJl0spMTpkyZgsjISFRXV+Ptt9/GY489ps1HAYDU1FTk5+dj2bJluHbtGlasWIFPP/3UZOEEQRCm\nQPaLsAeWL1+OuLg4crRsHJOcLR8fH/j4+AAA3NzcEBYWhqKiIh1jdfbsWfTv3x8A0LJlS1RUVKC4\nuFh7HmF/8GF5DYIg+0XwncjISAgEAp0iy4RtYpKz9TAFBQW4efMmWrZsqfO5TCbTTo8FaqacymQy\nMlZ2jFqttur1/vrrL6tej7A/yH4RfOTmzZtcSyD0xCzTnqqrq7F48WJMnToVbm5udfabkBZGEARh\nUch+EQRhaUwe2VKpVFi0aBHi4+MRFxdXZ79UKkVhYaF2u7CwEFKptMH29u7dq9cUVYIg7AMfHx90\n7dqVk2uT/SIIwlT0sWEmOVuMMXzzzTcICwvDsGHD6j2mW7du2LNnD/r06YPMzEyIxeJGh+BFIhG6\ndOliiiyCIHhEamoqJ9cl+0UQhDnQx4aZFEbMyMjA0aNHcfnyZfznP//Bf/7zH6SlpSE5ORnJyckA\ngC5duiAwMBAzZszA999/j2nTpplySbNRVilHUZnxlbpTUlLMqMZykE7zwxetxurMLyyHQmndvDsu\n4LP9MhV7f4a5gC9aSSc3mDSy1aZNG6xfv77J42zRQM38cjdu5BZh39fPwklEFbsJAgDuFVVgyMyf\nMT6pHd6Z0pdrORaFz/aLIAh+4ZBeRoGsAjfvFCPYzxPn0u8Y1Ubfvvz4Q0Q6zQ9ftBqjc++p6+gW\nG4r9p29Ao6HEcHvFnp9hruCLVtLJDQ7pbF2+UYD20YHo0zECqVcbX62dIByJC5n5GNm/NZydRLhd\nUNr0CQRBEESTmK3OFp/IyC5Eq+Z+aB8diE0H0o1qIyUlhReeN590enl5Wb1GF6HLhL5+AMrxyZRY\n3L9zHfeNG/itF5FIhI4dO5qvQcJo+GQX+KATIBvmCJhiwxzS2bp7vwydW4egRagP/rpTxLUc4gFq\ntRr9+vXjWgZhIY4cOcK1BIKwKGTD7BtTbJhDhhHzCssR7OeJsEBv3C+uRLVCZXAbfHnbIp0EQTwK\nX35vfNEJ8EsrYX0c0tm6e78cIf6ecBIJER7kjey7xVxLIgiCIAjCTnE4Z0ujYSgoqkCQnycAICJI\ngtv5hicC86UGCOkkCOJR+PJ744tOgF9aCevjcM6WrLQKHm7OcHOpSVcL9vNEnqycY1UEYR4GDhyI\n1atXm9TGunXr6q2ofu3aNXTr1g23bt0yqX2CIIj6sGf75ZDOlr/EQ7sdJBUj777hzhZf4vOk0zy0\nbNkSBw4caPI4cxgLUxAIBBAIBCa1MWnSJOzcuVPns9LSUrzyyitYv349IiIiTGqf4B5b/73Vwhed\ngG1rJfvFvf1yuNmIxWXVkHi6areD/T1x+cY9DhURfEBfI2CqodBoNBAKbe8dyNvbG3v37uVaBkEQ\nRkD2i3v7ZXu9YmFKyqsh8XLTbgdLPZFXaPjIFl/i86TTfDDGsHbtWiQkJOCdd95BUFAQWrdujT17\n9gAA3n//faSkpGDmzJmQSqX497//DQC4evUqhgwZguDgYLRv3x4bN27Utjlt2jS8+uqrGDlyJHx9\nfXHo0CFMmzYNr7zyCoYOHQo/Pz8MHDgQOTk52nNOnDiBXr16ISAgAL1798bJkyfr1Xv9+nUMGjQI\nISEhCA0NxZQpU1BSUqLdf+vWLYwbNw5hYWEICQnBrFmzAABr167FgAED9LrewIEDMXfuXCQkJMDP\nzw/Dhg1DYWGhGXqbsCR8+L0B/NEJ2L5Wsl/c2i8HdLbkuiNbfsY5W4TjUfvWd+bMGbRu3Rp5eXl4\n44038K9//QsAMG/ePPTt2xfLli2DTCbDkiVLUFFRgaFDh2LixIm4c+cOfvrpJ7z22mtIT/+7mO76\n9esxZ84cFBUVoU+fPgCAX3/9Fe+++y7u3r2Ljh07YsqUKQAAmUyGUaNGYcaMGcjPz8fMmTMxatQo\nFBXVXy/unXfeQU5ODi5cuIDbt29j3rx5AGrqAY0ePRotWrRAVlYWbt68iQkTJtQ5X5/r/fbbb1ix\nYgVyc3OhUCiwePFiM/Q2QRDmhOwXt/bL8cKI5dXw8fx7ZMvf1wPFZdVQqtRwdhLp3Y4tx+cfhk86\nU1NTmzyu1ehFZrle5pY3jD63efPmeO655wAAzzzzDGbMmIGCggIEBgYCqHmDrGXnzp2IjIzEs88+\nCwDo1KkTRo8ejd9//x3vvfceAGDkyJHo2bMnAMDVteZFYOjQoVrD9fHHH8Pf3x+3b9/GoUOH0KpV\nK0yaNAkAMGHCBHz11VfYvn279hq1REdHIzo6GgDg7++P1157DZ9++imAGoObl5eH+fPna4f9e/Xq\nVee77tq1q9HrCQQCPPvss4iJiQEAjB07Fjt27DC6bwnrwCe7wBf0sWFkvxzXfjmes1VWjSCpWLst\nEgrh7+OBe0WVCA3w4lAZoQ+mGBlzERQUpP2/h0fNZIvy8nKtsXo47yEnJwenT5/W7gMAlUqFZ555\nRntsWFiYTvuPfiYWiyGVSnH37l3k5eXVSfBs1qwZ7t6tu8Znfn4+Xn/9dRw/fhxlZWXQaDSQSqUA\naobgmzVr1mR+xd27d5u8XnBwsPb/7u7uKC+nkWKCqA+yX45rvxwwjFgNyUMjWwAg9XaHrLTKoHZs\nPT5fC+m0Lo8mmEZERKBfv34oKCjQ/pPJZFi2bFmDbTDGcPv2be12eXk5ZDIZQkNDERISopP/ANQY\nxNDQ0DrtvP/++xCJREhLS8P9+/exevVqaDQara5bt241uY5baGio3tcj+ANffm980QnwS2tDkP2y\nHI7nbJXp5mwBgFTijsKSSo4UEXzh4eH1hggMDMT169e128OGDcO1a9fw888/Q6lUQqlU4uzZs7h6\n9Wqjbe7evRvHjx+HQqHA3Llz0bNnT4SFhWHw4MG4du0afv31V6hUKvz222/IyMiot65MeXk5xGIx\nvL29kZubq5OL0L17dwQHB+Pdd99FZWUlqqurceLEiTpt6HM9ffqFIAhuIfvFrf1yOGertFIOb7Gu\ns+UncYesxLCRLb7kEpBO81H71vfo29/D2zNmzMCmTZsQFBSEN954A56enti5cyc2bNiAyMhINGvW\nDO+99x4UCoX23Prae/rpp/HJJ58gODgY58+fx5o1awAAfn5+2LJlC5YuXYqQkBAsWbIEW7Zs0Q6v\nP8x7772HtLQ0+Pv7Y8yYMRgzZoz2WiKRCJs3b0ZWVhaio6MRFRWlM8uo9jh9rtdYfxC2CR9+bwB/\ndAK2r5XsF7f2S8Bs7LV0//796NKli8XaH/fOb/jslUS0jPDTfvZ/60/B3c0ZL4yy3HWJpklNTUW/\nfv24lsE5L7zwAsLCwvDRRx9xLcWsHDlypN7fdmpqKhITEzlQZH4sbb8I24ZsmP3aL8A0G+ZwI1sV\nVUqI3Vx0PvOTeBg8ssWX+Dzp5B829v5D2CF8+b3xRSfAL62WhOxX/Tigs6WA2N1Z5zOpN+VsEbaD\nOZasIAiC4AKyX/XjUKUfGGOorFbCw+0RZ4tytjhH3zpbjsCKFSu4lkDYOXyyC3yBbFgNZL/qx6FG\ntqoVKjiJhHWKl/pJ3FFoYOkHgiAIgiAIfXAoZ6uiSgmxu0udz40Z2eJLfJ50EgTxKHz5vfFFJ8Av\nrYT1cShnq74QIgBIxG6orFZCqWq8QBpBEARBEIShOJSzVV6lgGc9I1tCoQA+Xm4oKq3Wuy2+5BKQ\nToIgHoUvvze+6AT4pZWwPg7lbNU3E7EWY5bsIQiCIAiCaAqHcrYqq5TwaMDZkni6oqRc/5EtvsTn\nSaftcvjwYURFRXEtg3BA+PJ744tOgF9azQHZL8NwKGeroTAiAPh4uqHYAGeLcCxatmwJiUQCqVSK\niIgITJ06FaWlpVzLIgiCaBKyX9zjUM5WlVwFN9f6S4tJvNxQXEY5W1xh6zoFAgG2bNkCmUyGs2fP\n4tKlS/jss8+4lkUQRmHrv7da+KITsG2tZL+4x6GcrWqFCu6ujYUR5VZWRPCRoKAgDBw4EOnp6QCA\nU6dOoV+/fggMDES3bt1w5MgR7bE//PADHnvsMfj5+aFNmzZU8I8gCE4h+8UNDudsubk0MLLl6YYS\nA0a2+BKfJ53mo3bNr9u3b2Pv3r3o3r07cnNzMXr0aLz77rsoKCjAggULMGHCBBQWFgIAAgMDsXXr\nVhQWFuL777/Hm2++ibS0NC6/BkHw4vcG8EcnYPtayX5xi0Mt11PdSBjRx9MN6X/ds7IiwlCW/XIc\n/1t/os7nr07ohdcm9tbr+IaObQzGGMaOHQuBQIDy8nKMGDECs2fPxuLFizF48GA88cQTAIDExER0\n7doVu3btwuTJkzFkyBBtG/Hx8Rg4cCCOHTuGzp07G3R9giD4D9kvx8WxnC2FCj6ebvXu8/FyMyiM\naMvx+Yfhk0591hV7bWJvgwyNocc3hEAgwO+//44BAwbg6NGjGDNmDFJTU5GTk4Pff/8dO3fu1B6r\nUqmQkJAAANi9ezc++eQTZGVlQaPRoLKyEh06dDBZD0GYAp/sAl/Qx4aR/XJcHMvZaixB3sDSD4Tj\nEh8fj5dffhlz5sxBUlIS/vGPf2D58uV1jpPL5ZgwYQLWrFmDkSNHQiQSYezYsdrhfIIgCGtD9osb\nKGfrARJPw2Yj2np8vhbSaRlee+01nDlzBn369MHOnTuRnJwMtVqN6upqHD58GLm5uVAoFFAoFPD3\n94dQKMTu3buxb98+rqUTBG9+b3zRCfBLK9kv6+NQzpZc0UjOloFhRMKx8ff3x+TJk7F06VJs2rQJ\nCxYsQFhYGKKjo7FkyRIwxuDl5YUlS5Zg0qRJCAoKwvr16zFixAiddgQCAUffgCAIR4Xsl/URMBPH\nBL/++mukpaXB29sbixYtqrP/8uXL+OKLLxAUFAQA6NGjB5566qkG29u/fz+6dOliiqQGmbFwFyYk\ntUffTs3q7NNoGHpM/R7HV02Ds5PIItcnGic1NRX9+vXjWgZhIY4cOVLvbzs1NRWJiYkcKOKX/SJs\nH7Jh9o0pNszknK0BAwZgyJAh+N///tfgMW3btsXbb79t6qVMplqugqtL/Y6UUCiAl9gVpRVy+Ek8\nrKyMIAgu4JP9IgiCv5gcRoyNjYVYLG70GFtJqGssZwuoKf+gbyiRL/F50kkQDcMn+2VO+PJ744tO\ngF9aCetj8dmIAoEAmZmZeOuttyCVSjF58mSEh4db+rL1Ut1IzhZQk7dVVFYFwNd6ogiCsFlsyX4R\nBMFfLJ4g36JFCyxfvhwLFy7E4MGDsXDhwibPefgNISUlxWzbcoUaly782eB+iacrTp45r1d7tfVf\nzKnPEtu1n9mKnqb6k7Bv6rv/towt2S9zbpP9Mv822TDHoKnntSFMTpAHoC3zX1+C6aO88sorWLBg\nATw9Pevdb8kE00Gv/IifP3kSAb71hw3mfncIHVsGYcyAWItcn2gcSi61b2wxQR7gj/0ibB+yYfaN\nKTbM4iNbxcXF2pyHrKwsAGjQUFmapsKIhixGbetv5LWQToIwHluyX+aEL783vugE+KWVsD4m52wt\nXboU6enpKC0txfTp0zFu3Dio1WoAQFJSEk6ePInk5GQIhUK4urpi5syZJos2Fn0S5IupijxniEQi\nnRXnCftCJLK9kip8sl+E7UM2zL4xxYaZJYxoTiw1DK9UqdH7+ZU4/cM/GyzEtulgOi5cy8fcFxPM\nfn2CsEWdPJNHAAAgAElEQVSe/3grXhnfHV3bhNa7P/tuMV778g9sXTTRYhq4DiOaEwojEoTjYRNh\nRFuhdlSrsYq3Es+aOlsE4SiUVsjhLXZtcL+LswgKpdqKigiCIOwPh3G25Ap1o/laAOAt1t/Z4kt8\nnnSaH75o1UdnaYUcErFbg/tdnZ2gUJGzZW/Y0zNsK/BFK+nkBodxtprK1wIMc7YIgu8wxmpGtjyb\nGNlSkLNFEARhCo7jbMlVcNXD2SrT09niS00V0ml++KK1KZ3VChUANPoS4uIsgpzCiHaHvTzDtgRf\ntJJObnAcZ0vPka0SGtkiHISyCkWj+VoA4OwkhFqjgUZjU/NoCIIgeIXDOFtyRcOLUNfi4eYMlUoD\npR45KnyJJ5NO88MXrU3pLKmohqSRECJQs1yNi5OI8rbsDHt5hm0JvmglndzgMM6WQqWGi3PjzpZA\nIICX2IXytgiHoLRcDi+Pxp0tAHCmGYkEQRAm4TjOllINZ6emC5J5e+hXRZ4v8WTSaX74orUpnaUV\n8iZHtgDA1VkE+YP8LsI+sJdn2Jbgi1bSyQ0O5Wy5NjGyBQBeBiTJEwSfKWmixlYtLs4iKFUaKygi\nCIKwTxzK2WoqjAjoX9iUL/Fk0ml++KK1KZ2l5XJIPBuusVWLq7MT5Eoa2bIn7OUZtiX4opV0coPD\nOFtKlUa/MCLNSCQchKaqx9fi7CyknC2CIAgTcBhnS9+RLX3DiHyJJ5NO88MXrfrkbOnjbNWMbJGz\nZU/YyzNsS/BFK+nkBsdxtlRqODs1/XUlVEWecBBKypsu/QA8yNkiZ4sgCMJoHMbZUhowskU5W9aH\nLzoB/mhtSmdZhQJe+iTIO1EVeXvDXp5hW4IvWkknNziMsyXX09mi9REJR6GkohoSPWcjUs4WQRCE\n8TiMs6VUqeGiZ4K8Ps4WX+LJpNP88EVrkzlb5Y0vQl2LKzlbdoe9PMO2BF+0kk5ucBhnS98E+ZrF\nqBVWUEQQ3KJvgryLCzlbBEEQpuA4zpZKzwryYleUlFc3eRxf4smk0/zwRWtjOtUaDSqrlfD0cGmy\nnZqcLaqzZU/YwzNsa/BFK+nkBodxtpRKDY1sEcQDyisVELu7QCRs2gRQzhZBEIRpOIyzJVeq9MvZ\n8nRFaaUcjLFGj+NLPJl0mh++aG1MZ0m5fiFEgJwte8QenmFbgy9aSSc3OIyzpVTpN7Ll5uIEAKim\nhXcJO0bffC2gpqgpOVsEQRDG4zDOlr4J8gDg7dF0KJEv8WTSaX74orUxnaUV+s1EBGpGtqjOln1h\nD8+wrcEXraSTGxzH2dKzgjzwIJRItbYIO6bUwDCiUkXOFkEQhLE4jLOlbwV5QL9aW3yJJ5NO88MX\nrY3mbOlZ0BSgkS17xB6eYVuDL1pJJzc4jLOl0LOoKQB4iV1oZIuwa8oqFAaFERUKcrYIgiCMxXGc\nLQNGtiRityadLb7Ek0mn+eGL1sZ0lpRXGxRGpDpb9oU9PMO2Bl+0kk5uIGerHmhki7B3DJuNKIJS\npbGwIoIgCPvFYZwtpUqjVwV54EHOVjnlbFkTvugE+KO1MZ2lFXJIPN30aocqyNsf9vAM2xp80Uo6\nucFhnC2DwoiebiitpJEtwn4pKZfDS9z0Uj0A4OQkhIpGtgiCIIzGcZwtQxLkPVxQRjlbVoUvOgH+\naG2qzpZErN/IlpNICKWanC17wh6eYVuDL1pJJzc4jLOlVKrh7KxnnS2xK0qaCCMSBJ+pCSPql7Pl\n7CSikS2CIAgTcBhnS65Uw9XZSa9j9Slqypd4Muk0P3zR2pBOxhhKK+Tw0jNB3tlJCBWNbNkVfH+G\nbRG+aCWd3OAQzpZGw6BSa/SvIC92bTKMSBB8pVqhggB/rwPaFM5OVEGeIAjCFBzC2VI+WKpHIBDo\ndby32LXJBHm+xJNJp/nhi9aGdBpS0BSoGdmi0g/2Bd+fYVuEL1pJJzc4hLNlSHI8UDuypQBjzIKq\nCIIbSir0L2gKPEiQp5EtgiAIo9EvjtAAX3/9NdLS0uDt7Y1FixbVe8yqVatw/vx5uLq64uWXX0aL\nFi1MuaRRKJUaOOtZ9gGoCZs4OwlRWa2E2L3+6fF8iSeTTvPDF60N6TSkoClQG0a0z5Etvtgwc8P3\nZ9gW4YtW0skNJo1sDRgwAHPmzGlwf2pqKvLz87Fs2TK8+OKLWLFihSmXMxpD8rVq0WcxaoLgI6Xl\nhjpb9psgzxcbRhAEvzHJ2YqNjYVYLG5w/9mzZ9G/f38AQMuWLVFRUYHi4mJTLmkUSpUaTiIDna0m\nZiTyJZ5s6zqT9x/CpGkzkTR6CiZNm4nk/Ye4ltQktt6ntTSks8TAkS17LmrKFxtmbvj+DNsSfLNh\nfOhTgD869cWkMGJTyGQy+Pn5abf9/Pwgk8ng4+NjycvWoWZkS/8wIgB4e9DIlqVJ3n8I85b8gHKf\nnoAnUCgH5i35AQCQlJjArTg7pszQMKLIcWcj2ooNI2wTsmGEvlg8Qd4WksyVKo3hI1tNhBH5Ek+2\nZZ2r122uMVIPUe7TE2vWbeFIkX7Ycp8+TEM6S8r1XxcRqBnZcuQK8rZgw8wN359hW2H56g28s2G2\n3qe18EWnvlh0ZEsqlaKwsFC7XVhYCKlU2uR5KSkp2o6uHUo0ZfvW/Sptzpa+53t71ixGbY7r03bd\n7bgevXD1pgwIQR0yswvAGINAILAZvfa0nZl1B327t9P7eI2GaUe2LKHHw8MDtooxNszc9ou2bW+7\nQ6du+PLH4zifWQCfVqhDnqzCpvTStmW39bFhAmbia1tBQQEWLFhQ70ye1NRU7NmzB7Nnz0ZmZiZ+\n+OEHfPrpp422t3//fnTp0sUUSXW4mJWPL9Yew48fP6n3OUvWnYDU2x1Thneqd//DBtWWsUWd1QoV\npn++A4d3/gifVoPq7FfkHMQz017F28/20bs2mjWxxT6tj4Z0vvO/fUjoEonBvWP0bqvb5O9w6ocX\nIBKafzA8NTUViYmJZm9XX8xpwyxhvywB359hLrl5pxgzFu6CWsNw78ofUAfF1zmm6uYB/HP6LMya\n2BNCoW3ZMFvs0/rgi05APxtm0sjW0qVLkZ6ejtLSUkyfPh3jxo2DWl3zBpyUlIQuXbogLS0NM2bM\ngJubG6ZPn27K5YxGpTY8jOhFsxEtAmMMc787hKzbMkx+ehQOHjioMwwvLjqBj955AetS8rByaype\nGN2VQ7X2SWm53KCipsDfhU1FLvZVmo8vNoywDW7ll+DFz7ajXVQAKquVeG34NHz237V1bNgH70zD\n1nP5+HzNUcx5Lt4mXxoJ62KSszVr1qwmj5k2bZoplzALSpVxCfIFD4aC64MvHret6VyffBnnM/LQ\nqVUw5v57CPp2bIY167ZArtLA1UmIqa9PRVJiAo5c24sfd11A19hQdG5dT6yRQ2ytTxuiIZ2G1tkC\n/l6yR98lfvgCX2yYueH7M8wFRWVVeGXBLjw9qD1+2nUB6z59CsF+nhAJBXVsmDggGpKMS7h8/R5W\nbUvDtFG2M9ppS33aGHzRqS/2ZTkbwJiRLYmnK0rKqy2kyDG5c78M3206h+WzhyHARwyBQICkxIR6\nZ+2MTWyL85l5eG/5AWycPx7ubs7WF2ynGONsOYnst/wDQTQFYwwffXcYCV0j8fzIzhjcKwbBfp4A\nUK8NkytU+Gz1Ucx8ugcW/ngcHVsGo1vbUA6UE7aCfcUEGkCl1sDJwKKmXg+W7GmI2sQ4W8dWdDLG\nMH91CiYN6YDWzf0hlbjr7H9UZ4/24WgbFQBvsStWbU+zptQmsZU+bYqGdBrlbNH6iHYF359ha7M+\n+TIKSyoxY0IcACA0wKvOMQ9rdXVxwmsTemD19vOY+2J/vP/NARSX2cbLu630aVPwRae+OISzpVSp\n4Wzm0g+EYZy6lIuc/BJMGdZR73OmP9Ud94srsXHfFeQWlFpQneOg1mhQUaWAl7j+Zagawp6ryBNE\nY+QVluO7TefwyfTHDUpHSeoRBZVKA8aAAd1aYNmvpyyokrB1HMLZMmZki+psmQ/GGP7322m8PLZ7\ng8aqPp1tIv3RqpkfHmsZhBVbUy0tU29soU/1oT6d5ZUKeLg5GzyrsDZni7AP+PwMW5uFPx7D+KR2\naB7SeCHbR7UKBAJMHdEJa7afx8tju+P4hVtIy7hrSal6YQt9qg980akvDuFsWaKoKaE/B8/ehEbD\nMDAuyuBz//VUNwzsEYXD57JxK7/EAuocC2NCiMDfsxEJwpE49mcOruXI8NyI+ksANcWgntHo0iYE\nri4ivP6PXljwwzFoNPZXJJdoGodwtowr/eCCiipFgz8MvsSTudbJGMPq7WnoGhuC1KsNv9U1pPOx\nmCCMiG+N8UntsGqbbeRucd2n+lKfTmPKPgCOvWSPPcLnZ9haaDQ1I/IzJ/ZASbkc320+1+jx9Wl1\nEgkx/cGIflKPKLg4i7D7RJalJOsF3XtucAxny4jSDyKhEO5uziirpNEtU0jLyENphRwHz92Eq4th\n9+Bhnh7UHgfO/IXCkkozqnM8SiuNG9ly9CV7CMdj3+kbEAmFeLxbC2zcfwWy0iqT2hMIBJj5dA98\nvfEMFEp6cXE0HMPZMiJnCwB8PN1QUl6/s8WXeDLXOn/64wJ6tA+D1NsdHWKCGjyuKZ0+Xm5I6hGN\njfuvmFuiwXDdp/pSn87SciOdLSr9YFfw+Rm2Biq1Bss3nsGr4+OgVGmw6WA6JiS1a/QcfbR2jQ1F\ni1AfbD6Ubi6pBkP3nhscw9lSaQyejQhQ3pap5OSV4M9recgrrMCTj8ea3N6kwR2wcf8Veis0gRIj\nna2anC3qd8Ix2H0iC34+HujRPgxH0rIRFeaLFqG+Zmn7n2O6Yu3OP+n35GA4hLOlVKmNGtlqrLAp\nX+LJXOrccugqErtH4XxmHpKaSI7XR2dEkDdiwqXYe+q6uSQaBZ/vvbFhRGcnEZV+sCP4/AxbGsYY\n1u74E8+P7AyBQIDtRzMwsl/rJs/TR6tcocJjMUEIC/TGnhPc2DG699zgEM6WSq2Bs8jwfCFJI2FE\nonGUKjW2H82An7c7ErpEQuxuWF2n+pi1aDfaxwRiy6GrZlDomJSWyyHxdDP4PJqNSDgKxy/cgkAI\n9OoQjtIKOS5cy0di9xYmt7vr2DV89P1hAMDzIzpj9fY0mpnoQDiEs6VUGZez1djIFl/iyVzpPJKa\njeYhPvjnmK5469neTR6vj87+XSKRfbcEN+8UI/tusTlkGgWf731JebXROVsU9rAf+PwMW5ofdvyJ\nZ4d2hEAggLfYFVsXTdRrubCmtPZ6LBwpf+agrFKOHu3D4O7qjCNp2eaSrTd077nBIZytmpEtI3K2\nPF1pZMtINh1Mx5iENhAKBfDyMPyPe3080SsaJy/dRlKPKGw9nGGWNh2NskoFhREJogGu3LiH2wWl\nGNQzWvuZMb+X+vD1ckf3tqHYd+oGBAIBJg3ugF/3XjJL24Tt4xDOlrE5WzWzESlny1Du3C9D+l/3\nkWhAEVN9dEo83dCjXRh8vNyw42gmZ3/8+XzvjR3ZojCifcHnZ9iS/LL3IiYktTO4VBCgn9YR8a2x\n/WgmAGBgXBSu35bhRm6RwdcyBbr33OAQzpYxRU0Bmo1oLHuOZ2Fgjyi4uTiZve0R/VrjxMXbCAv0\nwrE/c8zevr1TVqEwqqipE81GJOycorIqHE7Nxqj+bSx2jT4dI5CdV4ycvBK4OIvw5IBYrE+m0S1H\nwCGcLaURRU2BmtpODa3Uzpd4Mhc6k0/dwKAe0U0f+BD66uzVIRxBUjGe6BmD3ce5qcTM53tfUmHs\nyJaIRrbsCD4/w5Zi2+EMJHSJhI+X4RNIAP20OjuJMHloRxTIKgAAYxPbYs+J61Ytnk33nhscwtmi\nkS3rkZNXgvvFlSgqq7KIAXF2EmHBjCQ80Tsaxy7cQmW10uzXsGdKy+WQUFFTgtBBo2H4/UA6xg1s\nCwC48tc9ZGYXWuRaU4d3Qre2oQCAAF8xenYIx/YjmRa5FmE7OI6zZdRsxIZLP/AlnmxtnXtPXUef\nThGYt/IIBBDofZ6hOn293NGpVTAOnbtpoELT4eu9r1aooGEMbq6Gh3epqKl9wddn2FKcuHgLnh4u\naB8dCAD4btM5XM2+b1AbxmodN7AtNh1MB2PWKQNB954bHMLZUqrURs1G9PFqOEGeqJ+9J6/D3dUZ\n/To3h6eH6bW1GmNIb+5CiXykrKKmoKlAoL8TXIuziGYjEvbLxv1XMC6xLQQCAQpLKpGacRcDDZjg\nYwpdWodApdbgQla+Va5HcINDOFvGjmx5urugslpZ7x8ZvsSTranzRm4RSsvlSL16FyPiWxl0rjE6\n+3eJxPlreSgycYFYQ+HrvS+tMK56PECzEe0Nvj7DluBeUQVSr97F4F4xAIA/jmUhoUskPPSorfUw\nxmoVCAQY3b8Nth6yTjkbuvfc4BDOllJlXM5WbY0oayYv8pnkU9fRtW0ISivk6N42zOLX83BzRt+O\nzZB86obFr2UPGLsuIvCgqKmawoiE/bEz5RoGxkVpC5duT8nAiH6GvSyayvD4Vth/5gYqqhRWvS5h\nPRzC2VKpjZuNCDwobFpW19niSzzZmjqTT92ARs0wtE9LCIWGhaqM0bk++RICfD2w+4R1Q4l8vfel\nFXKjyj4ANaUf1GpaWsRe4OszbG4YY9h2NAMjHqx9mJF9H+WVCnRtE2pwW4Zqzb5bjA+/PQgA8Pfx\nQNfYUKu8ONK95wbHcLaMHNkCHizZU0F5W02RdUuGymolpg7vhPED21nlmkFST1zMKsCN3CLtVGqi\nYYrLquFjxLqIACASCilni7A7Ll4vgEbD0LFlEAAg2M8Tn7860OCXRWMIDfDC0fM5yC0oBQCMTmiD\nLYdp3Vd7xTGcLSNLPwCARFz/jES+xJOtpXPvyetI6hGF1pH+CJSKDT7fGJ19OkYgJ68E3WJDsP+M\n9UKJfL33xeXVRtcQchIJoSZny27g6zNsbrYfycCI+FbaSSMSTzc8FhNkVFuGanV2EmFwrxjsSKkp\n+9D7sQjcvV+G67dlRl1fX+jec4NDOFtKlRrORiTIA4DEyxUlDRQ2JWpgjCH51HWDC5mairOTCIN7\nx8DJSYR9pylvqylMGtkSCWhki7ArqhUq7Dt9A8P7Wjc/62FGxLfCjqOZ0GgYnERCDO/bSrucD2Ff\nOISzZcrIlrfYFSX1FDblSzzZGjozcwqhUmvQNirA6DaM1TkivhUuXMvHtZxC3CuyTiiRr/e+xMSR\nLXK27Ae+PsPm5NDZm4htEYAgP0+ztGeM1jaR/nB3dUZa5l0AwLC+rfDH8WtQayz3W6N7zw0O42wZ\nmyDf2GLURA01IcRoo+o3mUrr5v7w9/FA59YhOHD2L6tfn08Ul1VDYvTIFjlbhH2x7WgGRsa35lSD\nQCDAiH6tcPpyLgAgKswXAT5inLl8h1NdhPlxCGfL2NIPQM1sxFLK2WqQmhDiDXRqZVyeQy2m6Fz9\n4Sg8OSAW+6xUAoKv976kXG70yJYzOVt2BV+fYXORV1iO9L/uIaFbpHbb1OfbWK2TBnfA9Ke6a7eH\n9W2pzeOyBI5+77nCIZytmpEt476qj6cbimlkq0HSb96HUqXGZ6tToNFwUxpAJBSiZ4dwZOYUorCk\nkhMNfKC4zMQEeY7uL0GYm50pmRgYFwU3FycwxjBr0W6cS+dmNEkk1P3b9ETPGBxJy6Z1X+0Mh3C2\nlCq1aSNblLPVIHtPXofU2x2jElqbNF3aVJ2uLk7o26kZDpyxfCiRr/e+uNyUBHlaiNqe4OszbA4Y\nY9hxNFNbW+vS9QJUVitNLsRsLq1SiTs6tw62mC1z5HvPJQ7hbJmSsyXxdKu3qClRY7T2nMxCTn4J\nxiTEci0HA+OiaFZiA2g0rGZtRGOLmoqEFk3aJQhrcel6ARiADg8Wnf79QDqeHBBrldpa+jK8byuL\nhhIJ6+MYzpZKA5HIuB+SRFx/UVO+xJMtqfPS9QKoVBp0aR2CYBNn9JhDZ6/HIpB+8z5kJZZdK5GP\n976sUg4PN2ejR3ip9IN9wcdn2FzsPHYNw/q0hEAgQFmFHAfO/oWR/UxPlDen1n6dm+PqzfvILyw3\nW5u1OPK95xKHcLbUD2qYGIPEs/6ipkTN8jxCoQBPJbblWgoAoEBWgYhAbxw8R7MSH8WUmYhAbVFT\nytki+I1Spcbek9cxtE9LADWOV68O4ZBK3DlWVhMp+N9vp1ElV8LVxQmJcS3wx3HrLkVGWA6HcLZU\nag1ERjpbYndnKJRqKFW6i/DyJZ5sKZ0aDcPek1lIiotCn44RJrdnDp0ebs64ebfY4msl8vHem1I9\nHqDleuwNPj7D5uDYn7cQGeKDsEBvAEBYgBeeHdrRLG2bqlUgECAzpxB7T14H8HcokTHzvuQ46r3n\nGodwttQmFDUVCAQ1hU1pdEuHi1n58BK74s3JferMpuEKfx8P9H4sAhezClBUZtlQIt8wpXo8ULMQ\nNTlbBN/ZmZKJ4fF/V4yP79wc7R7kbtkC4xLbYuP+KwCATq2CIVeocPXmfY5VEebANv5KWhDGGNQa\nBpEJyY8ST9c6hU35Ek+2lM7aQqbmwlw6n36iPZxFQhy04KxEPt57U2psAYATjWzZFXx8hk2ltEKO\nU5dykRQXZbY2H8YcWnt3jEBRWTUuXy+AQCDAUAvU3HLEe28LOJnawPnz57FmzRpoNBo8/vjjGD16\ntM7+y5cv44svvkBQUE3Ryx49euCpp54y9bJ6o1JrIBIKTKpu7uvtjqJSqrVVi0bDkHz6Br6dM5xr\nKXXo0joEXmJXbNyfjicft41cMlvAlBpbgP0u12Pr9oswH3tPXkfPDuHwEhs3I9caiIRCjEtsi3V7\nLuLTlxMxrE8rPP/xVsya2NPoGfWEbWDSyJZGo8HKlSsxZ84cLF68GMeOHcPt27frHNe2bVt88cUX\n+OKLL6xuqNQaZnS+Vi2+Xm51wlJ8iSdbQmda5l34eruhRaiv2do0l06BQIAXRnfGtduFFpuVyMd7\nX1JeDYmRZR+AmtmIajtztvhgvywFH59hU9n1YBaipTCX1icfj8WJi7dRXFaNZsESRAR54/iFW2Zp\nG3DMe28LmDSylZWVheDgYAQG1sS8+/Tpg7NnzyI8PFznOHMn+BmCKflatfh6u0NWSjlAyfsPYfW6\nzcjMKYKHqwjJ+wOQlJjAtaw6jIhvjQ1b9mDslFchlYjh4iTAc5PG2KRWa1FcVo3QAC+jz7fHkS0+\n2C/CPNwuKEV2XjF6d4xAlVwJMMDdzZlrWfXi5eGKrV8+rR2BGx7fCjuOZqJ/l0huhREmYZIXIpPJ\n4Ofnp92WSqWQyWQ6xwgEAmRmZuKtt97C559/Xu+boyUxNV8LeDCyVerYOVvJ+w9h3pIfcFXeFpqg\nPij36Yl5S35A8v5DZmnfnP156PBRZF05h2LPONxQt8NVeVub1WpJHtZpSvV4wD6X6+GD/bIUfHyG\nTWHXsWsY1CMazk4i/L4/HQvWHjNLuw9jzj59ONQ5qEc0Tl3OrZM3bCyOdu9tBYsnyLdo0QLLly/H\nwoULMXjwYCxcuNDSl9ShpqCp6SNbjj67bfW6zSj36anzWblPT6xZt4UjRQ2zet1mqIPidT6zVa3W\nwtScLUddrodr+0WYTu3yPMP6toJcocKPf/yJCUntuJalN15iV/R+LAJ7TlznWgphAiaFEaVSKQoL\nC7XbhYWFkEqlOse4u/9dLK5z585YsWIFysvL4enZcMXxlJQUrVdbG7c1dvvEyZPQqFU6bRvaXsGd\nEhSXuujsrz3GVH2W3l6+fDk6dOhgcnsKVf2jGgWFRWa5X7WfmeP73yssBup5vOQqjVnav3jxIqZP\nn27S97XGtm7OlhwSTzej22vTvgvUGvP036PbHh4e4AI+2C9Lbdd+Zit6LGm//sqrhJNIiHZRAfj8\n220I9BYitkWA2fU+2rfmbH9EfCt8u+kcQt2LTG6Pj/bLFvQ0tq2PDRMwExIS1Go1Zs2ahffffx9S\nqRSzZ8/GzJkzdXIeiouLIZFIIBAIkJWVhSVLluCrr75qsM39+/ejS5cuxkqqw937ZZg2bxt2/fcf\nRrdx+nIuvt98Dt+/N1L72cMG1ZYxl85J02biqrzu7L5Y13T8vHKpye2bsz/5pNWSPKxz4Mtr8etn\nY+HvY5xjU1RWhSffWo+D30w1o8IaUlNTkZiYaPZ2m4IP9stS8PEZNpbPVx9FgFSMZ4d2xKg3fsHC\nmYPQ3gK1tSzZpyq1BkNf+xnfvTsCkaE+JrXlSPfeWuhjw0wa2RKJRHj++efx6aefaqdOh4eHIzk5\nGQCQlJSEkydPIjk5GUKhEK6urpg5c6YplzSY2tIPpuDr7YaiMsfO2Zo6aQxeefd/8IpJ0n4mLjqB\nqa9PNUv75uzP5yaNwbwlP+iEPW1VqyWp1anRMJRWyE2ajWiPy/XwwX5ZCr49w8aiUKqRfOoGfpr3\nJLYdyUBUmK9FHC3AMn2q1mjw+eoU/HtSTwzpE4PtRzMwY0IPk9p0lHtva5jkbAE1Q+udO3fW+Swp\n6e8/yIMHD8bgwYNNvYzRqNWml36QUs4WBg7oj+jY41AWnYGvxAOuTkJMfX2qTc7wq9W0Zt0WZObI\nICutxFv/mWaTWq1BaUXNItSm1Omx16Kmtm6/CNM4mpaN6HBfhAZ4oWUzKTrE2E61eH0QCYWorFbi\n172XMDy+FV5b+AdeHtfdZlbtIPTH7u+YWmN66QeJpxvKKhRQa/7+Y/NwPNmWMZfOaoUKlc4h2Pjj\n/2HjD8vw88qlZnVezN2fSYkJ+HnlUnyzbD4iu45A+j3jk8MfhW/3XlZaBam3aQvt0nI99gXfnmFj\n2Xo4A6P6twEAdGwZjNbN/c0hq14s1acvjumKn3dfRLDUE75e7jh75Y5J7TnKvbc17N/ZUjOIRKaF\nEZ1EQojdnVHqwOsj7jt9A11ah8DXy7Q/2tamc+sQuDiJkHI+B1f+use1HE6QlVRBKjHtvtUuRE01\npwCctvsAACAASURBVAi+UCCrwIWsfCR2b8G1FJOIDPXBgG6R+G7zOQyPb4XtR827fA9hHeze2arJ\n2TL9a/p6uevkbfElnmwunduOZGBkv9Zmaas+LNWfQqEAo/q3QUyEFF/+eNwszgLf7r05RraEQgGE\nAoHd1dpyVPj2DBvD9qMZGBgXZbXipZbs01fGxmFnyjW0jw7AkbRsVFQpjG7LEe69LWL/zpYZwogA\n4OPlhiIHrSJ/K78Ef90pQnznZlxLMYoR8a1wLacQEk9X3Cuq5FqO1ZGVVsHX2/QwqpOT0O6W7CHs\nE42GPQghWu4F0ZpIJe7455guyMkvRdc2IUg+fYNrSYSB2L2zZY7leoCah/3hkS2+xJNN0fnXnSLs\nOZGF7UcyMaR3S4suhGrJ/gwL9EbL5n4Y2qclAqVik9vj272XlZg+sgUAIqGA8rbsBL49w4aSlnEX\nLs5CpF69W7M8jxWwdJ9OfKIDhvdthdH922DzwXSj27H3e2+r2L2zZY7SD0Dtkj2OM7LFGMPna1JQ\nUFSBHSmZGBnP7zfEkf1aY+vhDK5lcIKstAp+EtMLh9rjkj2EfbLl8FXEhPsh+dQNuDhb7iWRC/p0\naoYCWQUycwqbPpiwGeze2VKrGZyczJOz9fBi1HyJJxurc/vRTJRVyNE8RAIfLze0au7X9EkmYOn+\nTOzeAhez8pFfWG5yW3y790VmCiM66pI99gjfnmFDKKuU4+C5mzh9JRdzno+3WpkEa/Wpk0iIUf3b\n4PcDV4w6357vvS1jcp0tW0etMVOCvLcbsvNKzKDI9rl7vwxLfzmJb94Zjv/9dhrjebSOWEO4uzpj\nSJ+W2HjgCl4ZF8e1HKtSaIYEeaB2ZIucLcI2Sd5/CKvXbcbtgnIUFJZiyKAktH2wLI+9MSahDYa9\nMB/nD22AmgEuTgI8N2mMw9YS5AN2P7KlUmtMLv0APChs+tDIFl/iyYbq1GgY5n53CJOHPAY3Vydc\n/qsAg3vFWEjd31ijPycktcOmg+mQK1RQqtQ4fO6mUe3w7d7LSswXRlRSzpZdwLdnuCmS9x/CvCU/\n4Kq8LcolcfCMGojUM8eRvP+QZQU+hDX79ML5syjLz8A1VTvcULfDVXlbzFvyg17f197uPV9wCGfL\nyQwjWz5edZfssUeKyqoQ4u+FZ4d3xIZ9lzGqXxu4udjHAGiLUF+0ae6PPSevo7JaiQVrj+FIWjbX\nsiyOucKINUv2kLNF2B6r123WWZ4LACp8e2HNui0cKbIsq9dthjhqoM5n5T497fb72gN272yp1cws\nsxF9HxnZ4ks82VCdfhIPzH0xAXKFGjtTrmHswLoLOlsCa/XnxCc64Nc9l+AtdsWnLz+OeSsOG5zH\nxad7X61QQanWwNPdxeT2aDai/cCnZ1gfFKr6J27IrZhjaM0+NeX72tu95wv272xpNCavjQgA/hIP\nFBY7zmzEDfsuI659GEL9vbiWYlZ6PxaBaoUKpy/nonPrEEx8ogP+83/JkCtUXEuzCLUFTQUC00Pp\ntGQPYau4ONX/fLuaYXKULeJo39cesPs7o1KZJ2fLx8sN5VUKKFVqAPyJJxujs0quxM9/XMS0UZ2b\nPthMWKs/hUIBnh/VGd9uOgfGGKYO74RgqSc+XnFY7+ryfLr3RSXmCSECNUv2qNVU+sEe4NMzrA/P\nTRoD1e1DOp+Ji05g6qTRFlBVP9bs0+cmjYFn8Umdz9wKj+n1fe3t3vMFu3e21BrzhBGFQgGk3u64\nX2xfFcg1GlbHydh88Co6xASiZYRlyz1wxeBeMSgsqcSZK3cgFArw0UsDECgVQ6FUcy3N7JhrJiJQ\nk7NFI1uEraHWaNC7d2+4SGPQQnARUaLLiHVNxwevT7Xb2XlJiQl4/99TEOuaDuf7J6C5cwQvTH7K\nbr+vPWAfmc+NYK61EQHA38cD94srEeLvxZt4cmM6GWNY+OMxRARJMGlwBwBARZUCa3acx3/fGGwt\niQCsG593Egnxz9Fd8c3vZ9G9bSjcXJww8+meTZ/4AD7d+y2Hr5rP2aLleuwGPj3DjXHu6h189dsZ\nJHRtjoGP98f8Vwc2erwlsXafJiUmICkxAbkFpZj8wWY8/eRQvc6zl3vPNxxgZMs8YUTgb2fLHmCM\nYdn6U0jLyMOIfq20n6/aloZeHcIRa6f1aWoZ0icGldVK7D11nWspFkVWUgWpxDzOFiXIE7bEn5l5\neOu/yZg2qjPW7b6EKcM6ci2JE8ICvdGtbSi2HLrKtRSiEeze2TJX6QdA19niMp6sb24RUL9Oxhj+\n++spnLx4G9/MHg4vD1cAwO2CUmw+eBWvjrd+0U9r96dIKMRbz/bGf385hapqw9ZO00crY3XDs9Ym\nJSUF94oqEOBj+nqQAIUR7Qm+5MM0pPN8Zh5eX7oHn0x/HIUlVWgR5sP5CyKXfTp1RCes3fmnXhN9\n+H7v+YrdhxHNtVwPwO3IVrVChfV7L2H3iSz8dacYQoEA0eG+6NupGZ4cEIsAX/3+oKrUGixcewwX\nswrwzezhkHjWJE9rNAwffXcIz43spHdbfKdrm1B0bh2MZetP4e0pukPW1QoVDp+7iScMKOh6I7cI\nmw6m4+TF27iVXwInkRCxLQIwun8bDO3TEkIzrNFpKPeKK9GlTYhZ2hKRs0XYAMf+zMEH3x7EJ9Mf\nR7fYUIx9+ze8+3w/rmVxStsWAYht4Y9NB9Mx8YmalJD9Z26gR7tweHqYXvaFMB27H9lSWyBnC7Bu\nPDkzpxDj39mAS9cL8NbkPjj4zRQkfzUZsyb2hKykCuPe2YCFa4+huJ6iq4/qrJIrwQB8++7fjhYA\n/PTHBag1TJu7ZW24is+/PaUvDqdm49ifOTqfl1XI8e3mc/jvryeheWTx5Ue15haU4j/LkvHSZzsg\ndnPGxy8NwOHvnsPu/3sGk4c+ht8PXMELn2yzuqPet2/fmpEtMznPtBC1/cCXfJj6dF69eR+LZz2B\nXh0isONoJoL9PBHXLowDdbpw3af/erIb1uw4j+oHo1tnr9zBPz/dhntFFTrHca1TX/iiU1/s3tky\n13I9ABDg44F7Vv6DmZF9H9Pn78D0sd2wcOYgdGkTAndXZ4jdXdA1NhSzn4vH5oUToNJo8NTb6/Hr\n3ktQqTVI3n8Ik6bNxNgpr2HStJnaZRy8PFwx57l4begQAE5cvIWfdl3AJy8/brVFW20Fb7Er5r00\nAB9+ewg37xRrPw/wFWPl+yNx4Vo+Zi3ejbIKeZ0+3bF7P77acBrPfLAJrZr5YduSiZg+tjvatgiA\nm4sTvDxc0b9LJFa+Pwrd24Xi+Y+3Wt3huldUiQAf05fqAR6EEWkhaoJjpo3qgo6tgiFXqPD9llS8\nwkHagy3SJtIf7aMCsXF/zQLV/3m2DwbGRWHyB5txPjOPY3WE3f9lVWk0Zin9AFg/Z6tAVoHXvvwD\ns6fGY0jvlg0e5+vtjtlT4/HdnBE4ePYvPDH1M7y7YCWuyts2uW7WufQ7eG/5AXw+I5HTAqZcxue7\nxobi1fFxeHXhLtzK/3uxcV8vd3wzezgiAr0x7IUFeH/hKp0+nTV3OY4fP471n43DC6O7NLiskVAo\nwPSnumNEfCvMXPSH1UpMHDl6FPeLK+FvTmeLwoh2AV/yYRrTuWH/FbRsJsVjMUFWVNQwttCnL43t\nhjXbz6OkvBoCgQDTRnXBe9P64Y2le/Dr3ktgjNmETn3gi059sXtnS61mZqkgD1g3Z6t2Qeixj7fF\nwLgovc6JDpfim9nD4VSVA1Wg7hDso+tmMcbw+4EreGtZMj5/ZSC6tgk1q36+MTqhDaYM64hpH2/T\nCSk6O4nw1rN94Cq/BYV/H51zvGOSgNKbCJTqF6Z7YXQXBEs98b/fTptVe0NUVKshdneGq5nWthQJ\nBVBryNkirEdZVf0J34UllVi1Lc2gki2OQMsIPyTGtcA3v5/Vfta3UzOs/mA0jqRlo7jc/tf3tVXs\nPkHenLMRpRJ3FJdVQ63RWDyevOlgOsqrFHhupGFV3AUCAbzEbrhXz+BJYWk10jLuIiO7ENsOZ0Ao\nFGDFeyMRFeZrJtXGYwvx+XED26FZsASfrjqK8KCLGNwrBs1DJFCpNJAr63cyDFl7TSAQ4P0X+v9/\ne3ceEFW9/3/8OYuyyTbsi6CymBsKobjgkkKL3lLLskxLrW4/W75Z/Syta1lm1m29ZWbl1uq3tKS6\nt27uC2kqorkvKOKCiOyL7MP3DwJFZhCGGWYOvh//4ZwZXh4Ob97nfD7ncxj/wkriYrpY/Iw8JLwX\nXm4XzfZ5Wq0MI7YVtvD71pic/BLe+DyRokvl3Bbf8PUPv93J7YPDbaJ21bKVfTrtrr7c9fy33DW8\nO6EddQAE+bqy8PlRgO3kvBal5Gyq6+DKlvnmbLXTanB2ak9ugWXPDgqLy1j0fRL/mDqk2UOgF7KL\nSDufa/C19IsFvL/iDw6nXmTauGi+fHWsTRUrWxDTM5CVb9zNyEFhbNt3hne+2s5HK3dRVl5ucPvm\nPovMzdmeJ8fH8NYXvzeYeG9uF/OK8XQ3zxAi/PW4HpkgLyyoorKK/11zgLtnfUeAtzPvPnNLg22S\nj5xn+/4zPDLmRisktH1uzvb8feyNzFu6Ra5E25C232yZ6XE9tWqHEi05nrz4x2SGRgUTHtz0x+VU\nV1fz2erd3PviKgYOHIxj7vZ6rzvlbued2X/n8zljeeXRmxgcGWyWhxObiy2Nz9u11/K32HDeeCKO\nL14Zy9KXRvPacw81eBaZU+524uNHsGr9obpnZjbFyIE1y0D8d3uKuaPXs23nn2abHA+g0ciipm2F\nLf2+1dp9JJ3xL6xic/IpPpl1O0/d25+knfV/54pLynn5k428MHmwzS1pYEv79O4RPdBq1Hz1y74G\nr12ZU6+v+buRmVPcYDtrs6X9aQ5tfhjRnEs/AHi6WnbeVm5BCT9uPsp38+9u1vtUKhUdHNvz9dy7\n8PdyZu36cJZ/k0Bmdi7eHu5MbsPPCWsNtfvu6n3aOTyCd7/ezuf/3svDY6IYOSiMdlpNo59VO2H+\nrS9/59YBoRZbfyv/UgW+fuZbM02rVlv8apy4fun11Uy/rz+D+wQZPRF856vt9O0ewNAbO7VuOIVR\nq1XM+fswJr28mgG9Oho9cS+vrKK4tILxL6xk5KAwptwe2aIbamoXcralE3lb0eabLXMu/QDgo+vA\nhZwi7hpumfHkFb8dIK5flyZPur5S7WJ2cPm5WUqhhPF5Y/t04cxRJB85z6Ifklj0fRLj43sybkT3\nRs+8Y3oG4OTQng1JqU2+AaK5HF288DLnMKJGLcMSbYQpv2+VVXq27kljc3IaB05kkn6xkIrKKhzt\n2xHg7UJEmA8DegbSv1dg3U0Za9dvYtk3qymvrKa9VsWUCWON1qW+3RuulXVlzh82HmbvsQy+fHVs\ns7O3BlurYQHeLjw3aRDPvv8bX7w6Fnfnmsd2XZnTvr2W6ff1Z+JtESz7eQ93Pfctw27sxKSRvevm\ne4Hxn2N6ViEbdqaSfPQ8R9OyyMkvobJKj0sHO0ICdfTt5s8tA0IJ8nVtdn5b258tdV00W+YcRvT1\n7EBGdpHZPu9KRZfKWbX+EJ+/Msbg65VVenYcOEvquTwmjoywSAZhmqgb/Pj0hds5nHqRb9cevOZw\nm0ql4uExUSxalcSIvp0tciZ4MbeYmJ7mW+xRo1ZRVSVXtq43VXo9P2w4zPJ/78Xb3YlbBoQy4ZZe\nBPq40L6dhsJLZZy5UMCeI+f5+rf9vPLZZm4ZEEKAQz6ffrGKIre/7hisgpfeWsqPW44w/7kpODvZ\nNf6Nr7Dz4DkWrtzFktl34ORgW8OHtuzWgaEcO53N8x+s48MZtxm9M9nTzZEZkwbxyJgbWb3xMCfO\n5dQ1W2vXb2Lue5/X+znOmr+Y91f8QYnWj5v6duLWAaFMv68/Xm6OaLVq8gpLOXY6m9//PMPUV38k\nsqsvj94ZXa+Bu960+WarSm++pR8AfD06sOvQORITE83WedeeNZy7WETRpTKOHAimo88woOay7IET\nmfx3WwprdpzA16MD98T1aPJnmzOnJSklJzSetVtnL+b8fZjB16qrq+s1VbG9g/jHPz/njvvWYWfX\n7ppn/s2VknYBPzNOItZo1FTKla02oam/b8fSsnn50410cGjPm0/G0zPEu8E27s4OuDs7EBHqw4N/\n60P6xUISNh3hlXeX4xwSV2/bMs9B7Nm1nSr95CbntNd1YeaCdfzzyXiC/dya9D5rsNUa9vg9fXlx\n4Qaeee833n36Fnbt/MNoTjdn+wZ3wC/7ZvXlRusvet/BVOXt5rf/nWFw2oSXuxNe7k4M6h3Ek+P7\nsWr9IR6d/zNjh3XjkTFRTVqOxlb3p6nafLNlzqUfoKbZysgqAszTodc7a3ABXGDue58DEDd8KPe+\nuIqy8ipuGxjK4n/cYdPFRjQuce9pPvh2B0OjOnHTjZ04l3qIwowjFAUMhSqg6vLP3hwNV25RBX6e\nHVr8ObVqrmxJs3U9qFmH7zALV+3i6fv687fB4U2++urv5cxjd/dl3U++nDJwIdTPywU3Z/uGLxiw\n40gu/9m9ljefjCO6+/W9FqCpNGo1r00bzkuLNvL313/m7v7N+xtSUmb45h9HB7trzk8FcLBrx6SR\nvbltYBjzl21l6twfefupm/Gz4iLa1tD270Y085wtX4+aYURzddyGzhpqFyBVqVS8/8ytrH5rPI/e\nGW1So6WUMwOl5ATTsw7qHcTsh4ei11cz+5ONPDH7I1QBQ+ttc/Xis6YqLilHX61q8h+1ppBnI7Yd\njR3DlVV6Xluyhe/WHWTp7NHcPqTrNRutsvKGi4/atzf85yW/sIRLpRWNfl5GdhEzF6wj8Ugxi/9x\nh8H5XLbGlmuYVlPTcA2JDOZfP5/hh42Hrzn/8viZbN768ncOpFww+Pq+4+d55LWfWP7vvU3K4Onm\nyNvTb+bWAaE8+HICSYfSG93elvenKdr8lS1zL/3go3MiM7eYKr3pdzkWFJdxOPUih1OzOJSajdrA\nCVvtYpnXW/fflqnVKiJCfYgI9eF/7o3hjglbOGtgu9qf/dXDjs2RkV2Er0cHs84F02jUcmXLyqqr\nq8nKu4S7i4PZ6tqVk581aqhyCsa74w0se2m0wflRFZVVnDyXy+HULP48nsHuw+cJC9LxzvT6a2JN\nmTC2/lwfQHNhK65hkdz65Ff06xlAZFdfQgN1uDjZcamsgjMZBST+eZqkQ+ncE9eDlx8ZioNdO7P8\nP693anXN43sGRnTkna+3szghmVsHhBIR5oOXmyPV1KzTeOBkJtv3nSWvsJRRsWHMmzmVBYu/q/dz\ndMrdzqsvT8PdP4z0i4UGv5+h+qVSqZg0sjfhQR7MXLCO5x8cBEVnmnwTRXMUFpfV3aVvC9p8s1Vz\nN6L5mq0tWxPJPbqG+NFb8fV2b/aB8ckPSXzxnz/pGuxJt06e+Lg7YGiN7+YulmmMUsa9lZITzJe1\ng4MWyhr+e+3PfuaCdZy5UEDXYA9CAnWEddQREqjDw9Wh0SZq7fpNvLtoBacz8pjw0DazFS+NWkVZ\nuTRb1nIqPY8ZH6whK+8SGrWah8dEcU9cD5OWDqk9hg1Nfi77cwMP3RFpsNE6eS6XibN/wM+zA906\ne9EzxJsJt/YiJKDhtIorl0spq9Rjp1UzeebDxI8YRn5RKVuS09h/IpONSacoulSOo307/Dw7ENs7\niJcfGYqzo911WRcsLfvcURb/4w6OpWWzbudJvt9wiJyCEqqray4m3NDJkxkPDKRPuG/dBQV3Z4f6\nP8cmLCW0ISmVd77aTvcuXoQEuhMaqCO0o46OPq7E9Axk4fOjeOD/f0B59nHw/+sK/xVTKRzstCbt\nz/NZhfzzi9/Z9deVs3EjuvPUvTFWX47i+mi2zLSOUW1h6hASRx6QVwavvrec4pJywrtHkp5VyKnz\neaSeyyUizIfx8T0bfMbE2yJ4eExU3UHcJ6CCWa9/ht5vSN02TrnbmfzMZLNkFrbL0Jn/lT/7Vx69\niaNpWRw/ncOJszls3n2KlLM5vP/srfQO823weeUVVWzesrXuM+2C4UiZ+eaBaWQY0WpKSiv4n7d/\n5YFRvblreDdOnsvl1cWb2X04nZtu0PDVdz+ZdGXA0DQGu+DhzP7nMm67eXiD7YN8XVn70aQm3xFo\nbLkU1w723D6kK7cP6dqkzxHmFx7s0eSFs01ZSmh4dGfCOnpw+NRFTpzJ5ddtKaScyWFg747MfDCW\n8GAP/O2yOOVveCrFtCnjmvR9rrwyW1ZewYVyLx59YAzzn4ijtKySJ9/6ha9/3W/1O/jbdLO1dv0m\nfv/v15zY5YyHq71JZ/jFJeVk5V1CpVIZLEzFbgOY8dpnRI8Yj7+nM0F+NV27sefeXV2k4kcMY3FC\nMjnnknB1dmjyWUNTKeFMC5STE8yX9coz/5PpeahV8NKzl3/29u219A7zrddY1S4aaMjEl35g76bv\n6HDVHWC1xaslx9Ta9ZtY/ukXlJbr2bluhVnvmhTG1f4hScsopKysHNdRfqhU3QkJ1PHZi3cwecYH\nPPPtdhy7jKh5w1U3WVRUVpGdX0J23iW6d/GqO7uvPYaNPfNT5+ZocBhIq1GjbcWlF67HumBprZVT\npVIR5Otas8bWFX82r6xhao2m5uagqxxMzWLzMT1HspIZ0CuQHgbuggUDy1JoQFOwlaAOBdi312Lf\nXsvI3va89OpcVn3jg6Odxmq1q802W7U/BE3AUC4CF/+6ClVWXklUdAzV1dUEeLs0eN+fxzL44Nsd\nZOVdIivvEtXUrBofH9OF8krDf+h6d/VjxbymdeFXK7pUzvlSd/7z5YJmrTsj2obaM8aT53L5f/P/\nzU3DhjS6fWOXwr99fRxjJm7ijIHXDD0we8a/1qDRqHF3tsfdxQGdiwPuzvYMjgymfbvLdxldXdDM\nebVMGFdvv//1CNNX311OflEpfaL60TnAjeqCU5cbrb8UufVn+pxF+KxKo+hSOe4u9ni6ObJ09ugG\nt9yXl1ca/CvgdY2haiFMdeVx1V6rMths+Xk4ER7kwYWcYvKLDcy1AFauO8j8+Z+BX/2aWeUzuO7k\ncu36TXy8bCXOoXGcBrBi7Wpxs7V3716WL1+OXq9n+PDhjBnTcEHOpUuXsnfvXuzs7Hjsscfo3Llz\nS7/tNRm7CjX9lUWEx1xgcJ8gZk0Z3OB9HX1cmXZXXzzdHPF0c8TJoV3dwbF9zTcGD4yWzK/alHyK\nqBv8LNZoKWUegVJygmWydglwx8vdkaRD6fTvFWjSZ6hUKpzsG58HdqV74nuQnVdCbmEJOQUlHDmV\nRW5BCQN7dwQuN1uN3TGr9GbLVusXGKlh7gN44Y2lRAwpYOlLo6kwsshsJ393vnjjbtyc7Q3eyJOY\nmEg+3pyv8ESTvZUqn8u10JamMVzvdcESbCmnoakUxSfW8fALD+Njn8vd9xjP2a9HADpXJ3IMvFZ7\ncmlLtatFzZZer2fJkiXMnj0bnU7HrFmziI6OJjDw8h+L5ORkLly4wAcffMDx48dZvHgx8+bNa3Hw\nazF2FapPV39W/et+o+/TuTqgc3Uw+Nq15tiYYu2OE9wcE2Ly+0XbcXNMCGt3njC52YLmHaNNvZ3e\n2O+SoatlSmLL9QuM7/eIcF9WvXkPYPzKgFsHOzxcDT+qqaSsglWJ5zmZeYYV70/n1LH9zZ78LIQ5\nXH0TRXutGp/bbubTNZmMj/WisZawo48r5eUVYOAwrz25tKXa1aJmKyUlBV9fX7y9a8ZTBw0aRFJS\nUr1ilZSUxNChNRPgwsLCKC4uJi8vDzc3yy7OaawIteQqVO2BsXDZSg6fyubGrr4tKkwFxWXsOZLB\nvGkjrr2xiWzlDOZalJITLJc1rl8XJr28mlmTB5t8W3/8iGFUVul5YvZC+nT1x75dy/94WuJ3yRbY\ncv2Cpu13Q811/rE1BN45ipLSChzsLy+bUKXXs35nKgu+20mPLl58+UQsrh3sCetou89RlbpgfraW\n09Dk+x0HzvLSJxs5lbuRR++8scGUn5QzObz91TY6+HSlMn0bpR4D61678uTSlmpXi5qtnJwcPDwu\n382g0+lISUlpdBsPDw9ycnIsXqwscRUKag6MoUMGM/iRpSz/ZGqTVtA1ZmNSKn17+NvMOiDCugK8\nXfD3dGb34XRiepp+datrj0giBo/j+7fvNUsuS/0uWZst1y+o2e8vv73M6B8SMLy8wqjnHiL5nJZR\n078hurs/Xu6O5BWWsutgOv7ezsycHMvAiI4Wzy+EqWJ6BvLDP8ez7Oe9THppNcF+roQH1fweHj6V\nRfrFQh4aHcm4GbexafNWo1dmbal2tcoE+cbuoDLkyjHlxMREgGZ/Xbuz31u4jIoq8PZwZ/Izk3Gw\n05rl853tNZzPKuJ0yn6T3h8bG8vaHScJ8642Sx5jX3/88cf06tXLYp9vrq9r/81W8jT29f79+5k2\nbZpFPj/UW82XP24jpuc9Jn/evtQCgvxcG+xbUz/PwU7L7KcfZPk3CWRm59JOA08/M4X4EcPM8v93\ndDQ83GUrrFG/YmNjiR8xjO//u4M/dm0gNNgHO62afrf2w8FOW+97Odhp+XrJ+/XeP2FcLBnZRaz4\ncROFBcXE9OrGo3dGczplP/qCNBIT0xTx+6aU+nXlvrSVPMa+tmT9MufXe3bvpI8/9Li3M46eXUhN\nz+PEiRMM7ebAA7PvoJ1WY/T4r+Vgp+WuW/qyc+9hikorOHjiApMm3FTXH5grb1NqmKq6uZXkCseO\nHWPlypW8+OKLAKxevRqVSlVvkumnn35Kjx49GDRoEADTp09nzpw5Rs8M169fT1RUlKmRWs19z3/F\nExOGMKh3kEnvzyss5Y5nVvDfDyfiaG+5FZJtaTJkY5SSEyyb9VxmAZNeXs2aBZNMHkr8/N97ycq7\nREwnvSL2aXJyMiNGWG4o3Rgl1K/S8kqKLpXj6WbehlQpv29KyQnKyXo950y/WIifp3mfrAFN50B9\nRwAADjhJREFUq2EtGrgMCQkhIyODzMxMKisr2bZtG9HR0fW2iY6OZsuWLUBNcXNycmqVS/CWFnFD\nMGcuFJj8/g1JqQzoFWjRRgtsb3zeGKXkBMtmvXIo0VSnM/IJ9nNT1D61BiXUL/v2WrM3WqCc3zel\n5ATlZL2ec/p7OVttSZMWDSNqNBqmTp3KvHnz6m6dDgwMZO3atQDEx8cTFRXFnj17ePLJJ7G3t6+7\nfKl0HX1cOZ2Rb/L71+44wV3Du5sxkWgr4mK6sHbHSZPnbZ3OyOfm/nKH67Vcz/VLCNG6WjxnKzIy\nksjIyHr/Fh8fX+/rhx56qKXfxuYU5pzjdIZpI7A5+SUcPHmRd5+2/CTV6/mSsaVYOmt8vy48MGc1\nMyfHmjSUmJaRT5Cvq6L2qbVcr/VLKceGUnKCcrJKTutQ9r3bVuTt1t7kK1vrd50ktneQPM1eGNSS\nocTiknKKLpXjo+tggWRCCCFMIc2WiUbfdhNZeZe4VFrR7Peu3XGS+JguFkjVkFLODJSSE1ona3xM\nCGt2nGj2+1LO5tAlwB21WqWofSpal1KODaXkBOVklZzWIc2WibQaNZ383Thx1tDDAoy7mFvM0bQs\nWedGNCoupgsbk05RUWlgRb5GHD+dQ1iQzkKphBBCmEKaLRMlJiYS1lHH8TPNa7bW70plSFRwgwfC\nWsrV647YKqXkhNbJ6u/pTKC3C7sONW8o8fiZbMI61iz+p6R9KlqXUo4NpeQE5WSVnNYhzVYLhAV5\ncPx0drPe89v2FHkWomiSm2NCWNvMoUS5siWEELZHmi0TxcbGNvvKVvrFQtIy8lv0oOHmUsq4t1Jy\nQutljYvpwqbdTR9KrK6uJuVMDqEda5otJe1T0bqUcmwoJScoJ6vktA5ptlogPNiDY6ez0eubtgTE\nb9tTiOvXpUXPUxTXD1+PDnTyc2PnwXNN2v7cxUIc7LW4OztYOJkQQojmkGbLRImJibg7O+DubM+J\nc027uvXr9hRuGdC6Q4hKGfdWSk5o3azxMSGs+aNpQ4n7jl8gItSn7msl7VPRupRybCglJygnq+S0\nDmm2WqhPuC9/Hrtwze1SzuRQWFxGZLhfK6QSbUVcvy5sTk6jpOzaS4zsS7lARJjPNbcTQgjRuqTZ\nMlHteHLvcF/2Hsu45va//H6cWwaEola37nOZlDLurZSc0LpZvXVO9AzxZv2u1Gtuu+9Y/WZLSftU\ntC6lHBtKyQnKySo5rUOarRaqubLVeLNVUVnFz1uPMmboDa2USrQlY4bdwI+bjjS6TUFxGWcu5NOt\nk1crpRJCCNFU0myZqHY8uZOfG2XlVY0+umdzchqd/Nzo5O/WWvHqKGXcWyk5ofWzDo0K5mR6bqPH\n2B/7zxLZ1Y/27S7ffKGkfSpal1KODaXkBOVklZzWIc1WC6nVKgZHBrElOc3oNivXHeTO4d1aMZVo\nS9ppNdwxpCvfrjlgdJvf/zzNwN7yVAIhhLBF0myZ6Mrx5CFRwWzcbXhOzYETmZy5UEBcv9Z5FuLV\nlDLurZScYJ2sE27pxX9+P05eYWmD18orqti69zRDIoPr/buS9qloXUo5NpSSE5STVXJahzRbZjCg\nV0fSzueTdj6vwWtLfkzmgVG9ZW0t0SJe7k6M6NuZFb/tb/Dalj1phAbq8PdytkIyIYQQ1yLNlomu\nHE9u307D6KFd+W7twXrb7DhwluNnchgzzHoT45Uy7q2UnGC9rA+NjmLlukOczSyo+7fq6mr+d80B\nRg/t2mB7Je1T0bqUcmwoJScoJ6vktA5ptszk3pt78uv2FE6eywUgt6CEVxdv5rkHBmHfSg+dFm2b\nv5czk0ZG8MqnmyivqHmEz4akVHLyS7hlQKiV0wkhhDBGVV1d3bRnzbSS9evXExUVZe0YJvl5y1E+\n/j6Je+J78POWo8T168K0cX2tHUu0IVV6Pc9/uI6CojL69Qjgm9/28/6zt9ZbOV5pkpOTGTFihLVj\nmIWS65cQwjRNqWFyycWMbh/SFZ2rA1v3nubxu/sxvG9na0cSbYxGreaNJ+JI2HSE1PRcFj4/ihs6\neVo7lhBCiEbIMKKJjI0nD+odxMwHY22m0VLKuLdScoL1s2o1asaN6M6MSYMabbSsnVPYLqUcG0rJ\nCcrJKjmtQ5otIYQQQggLkjlbQgirkjlbQggla0oNkytbQgghhBAWJM2WiZQyniw5zU8pWZWSU7Q+\npRwbSskJyskqOa1Dmi0hhBBCCAuSOVtCCKuSOVtCCCWTOVtCCCGEEFYmzZaJlDKeLDnNTylZlZJT\ntD6lHBtKyQnKySo5rUOaLSGEEEIIC5I5W0IIq5I5W0IIJZM5W0IIIYQQVibNlomUMp4sOc1PKVmV\nklO0PqUcG0rJCcrJKjmtQ5otIYQQQggLkjlbQgirkjlbQgglkzlbQgghhBBWpjX1jUVFRbz33ntk\nZWXh5eXF008/jZOTU4PtHn/8cRwcHFCr1Wg0GubPn9+iwLYiMTGR2NhYa8e4JslpfkrJqpSc1nI9\n1zClHBtKyQnKySo5rcPkZishIYGIiAhGjx5NQkICCQkJ3H///Qa3nTNnDh06dDA5pBBCmJvUMCFE\nazF5GDEpKYmhQ4cCMGzYMHbt2mV0WxubFmYWSum4Jaf5KSWrUnJay/Vcw5RybCglJygnq+S0DpOv\nbOXn5+Pm5gaAq6sr+fn5BrdTqVTMnTsXtVpNXFwccXFxpn5LIYQwG6lhQojW0mizNXfuXPLy8hr8\n+3333Vfva5VK1ehnuLu7U1BQwNy5cwkICKBbt24mxrUdShlPlpzmp5SsSslpSVLDDFPKsaGUnKCc\nrJLTOhpttmbPnm30NVdXV/Ly8nBzcyM3NxdXV1eD27m7uwPg4uJCv379SElJabRQubm5kZyc3JTs\nVuXo6Cg5zUgpOUE5WZWSs/bqkiW0dg2T+mVeSskJyskqOc2vKTXM5GHE6OhoNm3axJgxY9i8eTN9\n+/ZtsE1ZWRl6vR4HBwdKS0vZt28f48aNa/Rzb7zxRlMjCSFEk1mihkn9EkIYYvKipsZum87JyeGT\nTz5h1qxZXLhwgbfffhsAvV5PbGwsY8eONet/QAghTCE1TAjRWmxuBXkhhBBCiLZEVpAXQgghhLAg\nabaEEEIIISzI5AnylvTrr7+yZs0a1Go1kZGRTJw40dqRjPr555/56quvWLJkic2uMP3ll1+SnJyM\nVqvFx8eHxx57DEdHR2vHqrN3716WL1+OXq9n+PDhjBkzxtqRGsjKyuKjjz4iPz8flUrFiBEjGDly\npLVjGaXX65k5cyY6nY6ZM2daO45RxcXFLFq0iLNnzwIwbdo0wsPDrZyqZZRUv8D2a5jUL/OQGmZ+\nzalfNtdsHThwgKSkJN566y20Wi0FBQXWjmRUVlYW+/btw9PT09pRGtW7d2/uv/9+1Go1X3/9NatX\nrzb6WJLWptfrWbJkCbNnz0an0zFr1iyio6MJDAy0drR6tFotDz74IJ06daK0tJTnn3+eiIgIm8tZ\n65dffiEwMJCSkhJrR2nUsmXLiIyM5Nlnn6WqqoqysjJrR2oRJdUvUEYNk/plHlLDzK859cvmhhHX\nrFnD2LFj0Wpr+kAXFxcrJzLuiy++sPmzVoCIiAjU6pofdVhYGNnZ2VZOdFlKSgq+vr54e3uj1WoZ\nNGgQSUlJ1o7VgJubG506dQLA3t6egIAAcnNzrRvKiOzsbPbs2cPw4cNt+jEzly5d4siRIwwfPhwA\njUZjU1csTKGk+gXKqGFSv8xDaph5Nbd+2dyVrYyMDA4dOsSKFSto164dkyZNIiQkxNqxGti1axc6\nnY7g4GBrR2mWDRs22NSqvDk5OXh4eNR9rdPpSElJsWKia8vMzOTUqVOEhYVZO4pBn3/+ORMnTrTp\nM0Ko2Y8uLi4sXLiQtLQ0OnfuzJQpU7Czs7N2NJMppX6BMmuY1C/zkBrWcs2tX1Zpthp7hEZVVRXF\nxcXMmzePlJQU3nvvPRYsWGCFlI3nTEhI4MUXX6z7N2t3341ljY6OBuCHH35Aq9XaVLFSmtLSUt59\n910mT56Mvb29teM0sHv3blxcXOjcuTMHDx60dpxGVVVVkZqaytSpUwkNDWX58uUkJCQwfvx4a0dr\nlFLqFyinhkn9aj1Sw8yjufXLKs1WY4/QWLNmDTExMQCEhoaiUqkoLCzE2dm5teLVMZbz9OnTZGZm\nMmPGDKDm7GbmzJm8/vrrRh/5YWmN7VOATZs2sWfPnmtu19p0Ol29YYHs7Gx0Op0VExlXWVnJO++8\nw+DBg+nXr5+14xh09OhRdu/ezZ49e6ioqKCkpIQFCxbwxBNPWDtaAx4eHuh0OkJDQwHo378/CQkJ\nVk51bUqpX6CcGib1q3VIDTOf5tYvmxtG7Nu3LwcOHKB79+6kp6dTWVlptUJlTFBQEJ999lnd148/\n/jhvvvmmTd7JAzV3y/z000/MmTOH9u3bWztOPSEhIWRkZJCZmYlOp2Pbtm089dRT1o7VQHV1NYsW\nLSIgIIBRo0ZZO45REyZMYMKECQAcOnSIn376yeaKVC03Nzc8PT1JT0/H39+fffv22exk3aZSQv0C\nZdUwqV/mITXMvJpbv2yu2brpppv4+OOPefbZZ9FqtTa5k6+mUqmsHaFRS5cupbKyktdeew2A8PBw\nHn74YSunqqHRaJg6dSrz5s2ru3XaFv/gHj16lK1btxIUFMRzzz0H1BSFPn36WDlZ42z92JwyZQof\nfvghlZWVdbf1K5kS6xfY9nEi9cs8pIaZX3PqlzyuRwghhBDCgmxu6QchhBBCiLZEmi0hhBBCCAuS\nZksIIYQQwoKk2RJCCCGEsCBptoQQQgghLEiaLSGEEEIIC5JmSwghhBDCgqTZEkIIIYSwoP8DlLpU\nQoRGDCYAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.interpolate import InterpolatedUnivariateSpline\n", "\n", "puntos = [(0.9, 1.3), (1.3, 1.5), (1.9, 1.8), (2.1,2.1), (2.6, 2.6), (3.0, 2.7),\n", " (3.9, 2.3), (4.4, 2.1), (4.8, 2.0), (5.0, 2.1), (6, 2.2), (7, 2.3),\n", " (8, 2.2), (9.1, 1.9), (10.5, 1.4), (11.2, 0.9), (11.6, 0.8), (12, 0.6),\n", " (12.6, 0.5), (13, 0.4), (13.2, 0.2)]\n", "xi, yi = zip(*puntos)\n", "\n", "print(\"N\u00famero de puntos: {}\".format(len(xi)))\n", "\n", "x = np.linspace(min(xi), max(xi), num=1001)\n", "\n", "y1d = InterpolatedUnivariateSpline(xi, yi, k=1)(x)\n", "ysp = InterpolatedUnivariateSpline(xi, yi, k=3)(x)\n", "\n", "plt.plot(xi, yi, 'x', mew=2)\n", "plt.plot(x, y1d)\n", "plt.plot(x, ysp)\n", "leg = plt.legend(['Puntos', 'Lineal', 'C\u00fabico'])\n", "leg.get_frame().set_facecolor('#fafafa')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "N\u00famero de puntos: 21\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAECCAYAAAAFL5eMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nH++4TQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ajuste de curvas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$y = A e^{-B x^2} + C$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def func(x, A, B, C):\n", " \"\"\"Modelo para nuestros datos.\"\"\"\n", " return A * np.exp(-B * x ** 2) + C" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.optimize import curve_fit\n", "\n", "Adat, Bdat, Cdat = 2.5, 1.3, 0.5\n", "\n", "xdat = np.linspace(-2, 4, 12)\n", "ydat = func(xdat, Adat, Bdat, Cdat) + 0.2 * np.random.normal(size=len(xdat))\n", "\n", "(A, B, C), _ = curve_fit(func, xdat, ydat)\n", "print(A, B, C)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.42771659756 0.98757131605 0.467096144552\n" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "curve_fit(func, xdat, ydat)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "(array([ 2.4277166 , 0.98757132, 0.46709614]),\n", " array([[ 0.01622572, 0.0041953 , -0.00302369],\n", " [ 0.0041953 , 0.01786279, 0.00479835],\n", " [-0.00302369, 0.00479835, 0.00422546]]))" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.linspace(-2, 4, 1001)\n", "\n", "l, = plt.plot(x, func(x, Adat, Bdat, Cdat), '--', label=\"Sin ruido\")\n", "plt.plot(xdat, ydat, 'o', mew=2, mfc=\"none\", mec=l.get_color(), label=\"Datos\")\n", "plt.plot(x, func(x, A, B, C), label=\"Ajuste\")\n", "plt.ylim(0, 3.5)\n", "leg = plt.legend()\n", "leg.get_frame().set_facecolor('#fafafa')\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAECCAYAAADuGCyPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIBP/Dw7cIl0C7EG+AAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 } ], "metadata": {} } ] }