test.ipynb

{
 "metadata": {
  "name": "test"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# import packages\n",
      "from scipy import *\n",
      "from numpy import *\n",
      "from matplotlib.pyplot import *\n",
      "from math import e, sqrt\n",
      "\n",
      "eps = 0.1\n",
      "\n",
      "t = arange(0., 1., 0.001)\n",
      "\n",
      "while eps > 10**-4:\n",
      "    a = -1 + sqrt(1 - eps)\n",
      "    b = -1 - sqrt(1 - eps)\n",
      "\n",
      "    c1 = (1 + sqrt(1 - eps))/(2*sqrt(1 - eps))\n",
      "    c2 = (-1 + sqrt(1 - eps))/(2*sqrt(1 - eps))\n",
      "    \n",
      "    u = c1*e**(a*t) + c2*e**(b*t)\n",
      "    \n",
      "    plot(t, u, label='$\\epsilon = $' + str(eps))\n",
      "    \n",
      "    eps = eps/10\n",
      "    \n",
      "plot(t, ones(len(t)), label='$\\epsilon = 0$')\n",
      "legend(loc = 3)\n",
      "figsize(10, 6)\n",
      "show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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uekfUdshlIiGEwwgNha+/Vv0QoqLgP//ROyJRF9IyEPUi9S/q41//UqOgTp6s\nei67u+sdkXOTloGTKSkpYezYsXh7exMSEkJaWto1yy5dupSYmBg8PDyYMmVKC0YpxPWNGKEmz8nJ\nUTeaf/pJ74jEtUgycEC///3v8fDw4OTJk6xdu5annnqK3NzcWssGBgYyd+5cpk6d2sJRClE3/v7w\nySfwm9+o2dTs/G0jdCSXiRzMuXPn6Ny5M/v37yc0NBSASZMmcdNNN7Fw4cJrfm7u3LkcPXqUVatW\nNWt8zl7/onnt3q1uLt9xh3riyNtb74icS2N+P+2OWiqaxk8//WSdIKg2AwcO5Ne//jUAP/zwA25u\nbtZEAGo2uevNZiRf0KI1GDAAvvsOnnlGvU9Lg1tv1TsqAU6YDAyGpjlOQ79bc3JySElJwWg0cued\nd9K3b1969uxp96/6y/3yyy907NjRZpuPjw9nz561+zlDU524EM3M21s9cvr++zBqFMyZA889By5y\n0VpXTpcM9PwD+ejRo4wdO5bvvvuOLl26NOgY3t7enDlzxmZbeXk5Pj4+dj8nLQPR2iQkqHsIEybA\nZ5/B6tUy4J2enC4Z6Gn9+vXceOONfPjhh3To0IHHH38cqN9loj59+mA2mzl48KD1UtHevXuJiIiw\n+7OlZSBaox494MsvYd48ddnovffgnnv0jqptkhvITejdd9/l+PHjzJkzp1HHGT9+PAaDgRUrVrB7\n927uv/9+duzYQd++fa8qa7FYqK6uZv78+RQVFZGcnIybmxuurq6NiuFaHLn+Rev2r3+pmdRmzIC5\nc9VczKJ+pJ+Bg7jYEkhPT2fTpk2Ul5c36DjLli2jsrISf39/HnvsMf7xj39YE8Ho0aNJSkqyln3t\ntdfo0KEDixYtYs2aNXh6evL66683/mSEaGEjRqinjb78Uo1v9PPPekfUtkjLQNSL1L9obhYLvP66\nmknt3Xdh5Ei9I2o9ZD4D0WKk/kVL2bYNHntMzZXw2mvgJnc4r0suEwkhnE5cnLpslJOj3hcW6h2R\nc5NkIIRwWP7+sGWLmlIzJgY++kjviJyXXCYS9SL1L/Ty9deqT8LDD8PChdCund4ROZ5mvUyUmZlJ\neHg4vXv3ZtGiRVftLy0tZezYsRiNRmJjY9m/f79138KFC+nXrx+RkZFMmDCBqqoqQI3KOXz4cPr0\n6cOIESMoKytrUPBCiLbjzjvVZaP8fDUC6qFDekfkXOwmA4vFwsyZM8nMzCQ3N5e0tDTy8vJsyixY\nsIABAwbFkExeAAATLklEQVSwd+9eUlNTmTVrFgAFBQUkJyeze/du9u3bh8Vi4f333wcgKSmJ4cOH\n88MPPzB06FCbRyWFEOJaunSBjIxLvZc3btQ7IudhNxlkZ2cTGhpKSEgI7u7uJCQkkJGRYVMmLy+P\nIUOGABAWFkZBQQHFxcV07NgRd3d3KioqMJvNVFRUEBgYCMDmzZuZNGkSoEbk3LRpU3OcmxDCCRkM\naiyjjz+GF1+Ep5+G8+f1jqr1s/uwVlFREcHBwdb1oKAgsrKybMoYjUY2btzIoEGDyM7O5vDhwxw9\nepTo6GheeOEFbr75Zjw9PRkxYgTDhg0D4MSJEwRcGIQkICCAEydO1PrzExMTre/j4uKIi4tryDkK\nIZzQbbepy0bTp6tLSB98AD176h1Vy9q2bdt1RzSuK7vJoC7j3cyZM4dZs2YRHR1NZGQk0dHRuLq6\n8uOPP/LXv/6VgoICfH19eeSRR1i7di2PPvroVT/jWj/n8mQghBBX8vNTSWDpUhg4EN55B8aM0Tuq\nlnPlH8nz589v8LHsXiYKDAyk8LKHewsLCwkKCrIp4+PjQ0pKCjk5OaSmplJcXEzPnj3ZtWsXd9xx\nB126dMHNzY0HH3yQb775BlCtgePHjwNw7Ngx/P39G3wCQoi2zWBQl4o++giefRZeeAGqq/WOqvWx\nmwxiYmLIz8+noKAAk8nEunXriI+PtylTXl6OyWQCIDk5mcGDB+Pt7U1YWBg7d+6ksrISTdP4/PPP\nueWWWwCIj49n9erVAKxevZoxbSmV10F95kC+XlmZI1m0FbGxauKcAwdg8GDppFZfdi8Tubm5sXTp\nUkaOHInFYmHatGn07duX5cuXAzBjxgxyc3OZPHkyBoOBiIgIVq5cCUBUVBQTJ04kJiYGFxcXBgwY\nwJNPPgmoS0vjxo1j5cqVhISEsH79+mY+zdbl8jmQc3JyuO+++zAajdZkWp+yF+dI/vTTT6msrGzp\nUxGiRXXpoloIf/4z/OpXao4EGduobqTTmYOpzxzI9SnbVHMkO3v9C+exfbvqpDZtmpovoS0MiS1z\nIDu45poDuT5l5QtctDWDB6unjSZMUK2DtWtlJjV7nC4ZGOY3zYxf2ryGfXm25BzI9SkrM6GJtigg\nQE2ak5gIt94K//wn3H233lE5JqdLBg39Em8KLT0Hcn3KSstAtFWurmoI7DvvhHHjVIe1P/wBXGSY\nThtOlwz01NJzINenrLQMRFs3ahR8+y385jfw//6furncubPeUTkOuYHchPSYA/l6ZZt6jmRHrn8h\n6sJkgjlzID0d1q1TPZmdRaN+PzUHda3QHDhkzWw2awsXLtQ2btyopaena2VlZQ06TklJiTZmzBjN\ny8tL6969u5aWlmbdd++992oLFy6sU1lN07R58+ZpBoPBZpk/f37DTlBz7PoXoj42btS0bt00bckS\nTaup0TuaptGY309pGYh6kfoXzuTHH+GRR6B3b1ixAmq53daqyLSXQgjRAL16wTffgK+vulyUm6t3\nRPqRZCCEaNM8PNQAd3/8o+qbsG6d3hHpQy4TiXqR+hfOLCcHHnoI4uPhjTfA3V3viOpHLhMJIUQT\niI5Wg90dPAhDhsDPP+sdUcuRZCCEEJfp1Ak2b1b9EmJi1BhHbYFcJhL1IvUv2pJ//QsmTlTTa77w\ngpo7wZE15vdTkoGoF6l/0dYcPgwPPwzdu0NKClwxHJhDkXsGQgjRTLp3V8NXdO2q5kjYv1/viJqH\nJAMhhLiO9u3hH/+Al1+GuDiwM/lgqyWXiUS9SP2Ltm7PHvX46X33wZtvQrt2ekd0iVwmcjJNOQey\nvf0yP7IQ9RcVBbt2waFDqpVQVKR3RE1DhrB2QE05B7K9/TI/shAN06kTZGRAUpK6j7B2reqX0JrJ\nZSIH05RzINf1WPWZH9nZ61+I+vr8c3jsMXj+eTVpjp6Pn8ocyA5OrzmQ63os+XIXouGGDYPsbDX6\n6c6datKc1jj6qfMlg6ZKyw38gnSkOZDreiyZBU2Ixrn5ZvjyS3j6aTX66aZNEBamd1T143zJQMe/\nch1tDuS6HktaBkI0Xvv2avTT5GQYNEjNj3Chwd8qXDcZZGZm8uyzz2KxWJg+fTqzZ8+22V9aWsrU\nqVP56aef8PDwICUlhX79+vH999+TkJBgLffTTz/x2muv8cwzz5CYmMiKFSvo1q0bAAsXLmTUqFFN\nfGotz9HmQK7rsaRlIETTeeIJ6N9f9VretQsSE6GBs8y2LHvToJnNZq1Xr17aoUOHNJPJpBmNRi03\nN9emzIsvvqi9+uqrmqZp2oEDB7ShQ4dedRyLxaLdcMMN2pEjRzRN07TExERt8eLFdqdgu1Zo1wlZ\nV6tWrbKZkrKhEhIStPHjx2vnzp3TvvrqK83X1/eqeq9rWXv7zWazVllZqc2ZM0d7/PHHtfPnz2tm\ns9lubI5c/0I4kuPHNe3uuzXt3ns1raSkZX5mY34/7fYzyM7OJjQ0lJCQENzd3UlISCAjI8OmTF5e\nHkMuPFMVFhZGQUEBxcXFNmU+//xzevXqRXBw8OVJqClymUO52BJIT09n06ZNlJeXN+g4y5Yto7Ky\nEn9/fx577DH+8Y9/WCe4Hz16NElJSXUqe739r732Gh06dGDRokWsWbMGT09PXn/99YaevhDiMgEB\n6kmjPn3U46f79ukdkX12Hy398MMP+fTTT62XONasWUNWVhZLliyxlvnTn/5EZWUl//d//0d2djZ3\n3nkn2dnZREdHW8tMnTqVmJgYfve73wEwf/58Vq1aha+vLzExMSxevBg/Pz/bwAwG5s2bZ12Pi4sj\nLi5OHm3UmdS/EPW3Zg089xwsWQKXXT1vtG3bttk8HTh//vzmGbV0w4YNZGZm2k0GZ8+eZdasWeTk\n5BAZGcmBAwdYsWIF/fv3B8BkMhEYGEhubq71HsHJkyet7+fOncuxY8dYuXKlbWBttJ+Bo5P6F6Jh\n9uyBBx9US1ISuDXD4zvN1s8gMDCQwsJC63phYSFBQUE2ZXx8fEhJSbGu9+jRg549e1rXt27dyq23\n3mr98gfw9/e3vp8+fToPPPBAg4IXQojWIioKvv0WJkyAESPUXMuXfS3qzu49g5iYGPLz8ykoKMBk\nMrFu3Tri4+NtypSXl2MymQBITk5m8ODBeHt7W/enpaUxfvx4m88cO3bM+j49PZ3IyMhGn4gQQji6\nLl1gyxaIjVWzqO3apXdEl1x3OIqtW7daHy2dNm0aL730EsuXLwdgxowZ7Nixg8mTJ2MwGIiIiGDl\nypX4+voCariE7t27c+jQIZtn2ydOnMiePXswGAz06NGD5cuXExAQYBuYXCZySFL/QjSNDRvgt7+F\nP/8ZmmqcSJnpTLQYqX8hmk5uLowdC0OHwl//2vjhsGUIayGEaIVuuUWNa1RUpEY9/fln/WKRZCCE\nEDry9YX0dBg1SvVH+PprfeKQZCCEEDpzcYG5c9W4RmPHwrJlLT/MmtwzEPUi9S9E8zp4UCWE2Fh4\n+201AF5dyT0DIYRwEqGhsGMHlJaqaTVb6j6CtAwc0KZNm8jNzcXFxYXAwEDrmEeOoC3UvxCOQNNg\nwQL4+9/hgw/g9tuv/xl5tNSJlJeXc8899/Ddd98BcPvtt/PRRx/RtWtXnSNTnL3+hXA0H38MU6eq\nxDB9uv2ycpnIiXz55Zc2E98bjUa++OILHSMSQujp/vvhq6/gzTfh97+HCwM+NDnnm+nMAdVncpuj\nR4/ajODq5+dHfn5+s8cohHBcYWGQlQWPP67mXP7gAzVEdlNyumRgqGXi+IbQ4uIa9LnGzoFcVlaG\nh4eHdb1du3b88ssvDYpFCOE8fH3V3Mrz56v+CBs3qvGNmorTJYOGfok3haaYA9nHx4fTp09b1ysr\nK68at0kI0Ta5uKhkEBUF994LixfDxIlNc2ynSwZ6aoo5kHv16sWuy4YyPHXqFAMGDGjewIUQrcrY\nsWoGtTFjICcH3nij8fMjyNNETejdd9/l+PHjzJkzp8HHOHfuHAMHDmTfhTnyjEYjn332mc0cEHpy\n5PoXoq0pLVXzI5hMF+dHkEdLHYLFYuGNN94gLCwMg8HAkCFDrMN518d7773H4cOHqampoVevXjz6\n6KPNEG3DOHL9C9EWWSzwpz+pZFBQIMlAtBCpfyEc07p1kJAgyUC0EKl/IRyXdDoTQgjRKJIMhBBC\nSDIQQgghyUAIIQStsNNZp06dMBgMeofRZnXq1EnvEIQQzaDVPU0khBCidvI0kZPb1kSD77V2Ug+X\nSF1cInXRNK6bDDIzMwkPD6d3794sWrToqv2lpaWMHTsWo9FIbGws+/fvB+D7778nOjrauvj6+vK3\nv/0NgJKSEoYPH06fPn0YMWIEZWVlTXxazkX+sytSD5dIXVwiddE07CYDi8XCzJkzyczMJDc3l7S0\nNPLy8mzKLFiwgAEDBrB3715SU1OZNWsWAGFhYeTk5JCTk8N3331Hhw4dGDt2LABJSUkMHz6cH374\ngaFDh5KUlNRMpyeEEKIu7CaD7OxsQkNDCQkJwd3dnYSEBDIyMmzK5OXlMWTIEEAlgIKCAoqLi23K\nfP755/Tq1Yvg4GAANm/ezKRJkwCYNGkSmzZtarITEkII0QCaHR988IE2ffp06/p7772nzZw506bM\nyy+/rD333HOapmlaVlaW5ubmpu3evdumzJQpU7S3337buu7n52d9X1NTY7N+ESCLLLLIIks9l4ay\n+2hpXR7hnDNnDrNmzSI6OprIyEiio6NxdXW17jeZTHz00Ue13m+4+DNq+zmaPEkkhBAtxm4yCAwM\npLCw0LpeWFhIUFCQTRkfHx9SUlKs6z169KBnz57W9a1bt3LrrbfSrVs367aAgACOHz/ODTfcwLFj\nxxxmrH4hhGir7N4ziImJIT8/n4KCAkwmE+vWrSM+Pt6mTHl5OSaTCYDk5GQGDx6Mt7e3dX9aWhrj\nx4+3+Ux8fDyrV68GYPXq1YwZM6ZJTkYIIUTDXLfT2datW3n22WexWCxMmzaNl156ieXLlwMwY8YM\nduzYweTJkzEYDERERLBy5UrrhC7nzp2je/fuHDp0CB8fH+sxS0pKGDduHEeOHCEkJIT169fj5+fX\njKcphBDCrgbfbWgiW7du1cLCwrTQ0FAtKSmp1jJPP/20FhoaqvXv3/+qm9PO5Hp1sWbNGq1///5a\nZGSkdscdd2h79+7VIcqWUZf/F5qmadnZ2Zqrq6u2YcOGFoyuZdWlLr744gstKipK69evnzZ48OCW\nDbAFXa8uiouLtZEjR2pGo1Hr16+ftmrVqpYPsgVMmTJF8/f31yIiIq5Zpr7fm7omA7PZrPXq1Us7\ndOiQZjKZNKPRqOXm5tqU+eSTT7R7771X0zRN27lzpxYbG6tHqM2uLnXxzTffaGVlZZqmqV+KtlwX\nF8sNGTJEu++++7QPP/xQh0ibX13qorS0VLvlllu0wsJCTdPUF6IzqktdzJs3T5szZ46maaoeOnfu\nrFVXV+sRbrP68ssvtd27d18zGTTke1PX4Sjq0o/h8j4JsbGxlJWVceLECT3CbVZ1qYvbb7/degku\nNjaWo0eP6hFqs6tLXQAsWbKEhx9+2ObhBGdTl7r45z//yUMPPWR9uKNr1656hNrs6lIXN954I2fO\nnAHgzJkzdOnSBTe3Vjce53XddddddgeNbMj3pq7JoKioyNoRDSAoKIiioqLrlnHGL8G61MXlVq5c\nyejRo1sitBZX1/8XGRkZPPXUU0DdHoNujepSF/n5+ZSUlDBkyBBiYmJ47733WjrMFlGXunjiiSfY\nv38/N910E0ajkbfeequlw3QIDfne1DVl1vUXWLviHrcz/uLX55y++OILUlJS+Prrr5sxIv3UpS6e\nffZZkpKSrKM0Xvl/xFnUpS6qq6vZvXs3//73v6moqOD2229n4MCB9O7duwUibDl1qYsFCxYQFRXF\ntm3b+PHHHxk+fDh79+61eYClrajv96auyaAu/RiuLHP06FECAwNbLMaWUpe6APjvf//LE088QWZm\nptPOLVCXuvjuu+9ISEgA4NSpU2zduhV3d/erHn1u7epSF8HBwXTt2hVPT088PT25++672bt3r9Ml\ng7rUxTfffMOf/vQnAHr16kWPHj34/vvviYmJadFY9dag780mu6PRANXV1VrPnj21Q4cOaVVVVde9\ngbxjxw6nvWlal7o4fPiw1qtXL23Hjh06Rdky6lIXl5s8ebLTPk1Ul7rIy8vThg4dqpnNZu3cuXNa\nRESEtn//fp0ibj51qYvnnntOS0xM1DRN044fP64FBgZqp0+f1iPcZnfo0KE63UCu6/emri0DNzc3\nli5dysiRI639GPr27WvTj2H06NFs2bKF0NBQvLy8WLVqlZ4hN5u61MWrr75KaWmp9Tq5u7s72dnZ\neobdLOpSF21FXeoiPDycUaNG0b9/f1xcXHjiiSe45ZZbdI686dWlLl5++WWmTJmC0WikpqaGP//5\nz3Tu3FnnyJve+PHj2b59O6dOnSI4OJj58+dTXV0NNPx702FnOhNCCNFyZKYzIYQQkgyEEEJIMhBC\nCIEkAyGEEEgyEEIIgSQDIYQQwP8HQm9ZkcRXdB4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import e, sqrt\n",
      "\n",
      "eps = 0.1\n",
      "\n",
      "t = arange(0., 1., 0.001)\n",
      "\n",
      "plot(t[1:], zeros(len(t)-1), 'k-', label='$\\epsilon = 0$')\n",
      "\n",
      "while eps > 10**-4:\n",
      "    a = -1/eps\n",
      "    b = -3/eps\n",
      "\n",
      "    c1 = 3./2\n",
      "    c2 = -1./2\n",
      "    \n",
      "    u = c1*e**(a*t) + c2*e**(b*t)\n",
      "    \n",
      "    plot(t, u, label='$\\epsilon = $' + str(eps))\n",
      "\n",
      "    eps = eps/10\n",
      "\n",
      "legend()\n",
      "figsize(10, 6)\n",
      "axis([-0.1, 1.1, -0.1, 1.1])\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ITwCA2BcfH6877rijy8dJT0/Xc8891+5zK1ascDzW7vlZs2Zp1qxZna7TKb8pZ+fOncrJ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\nRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import e, sqrt\n",
      "\n",
      "eps = 0.1\n",
      "\n",
      "t = arange(0., 1., 0.001)\n",
      "\n",
      "while eps > 10**-4:\n",
      "    a = -1/eps\n",
      "    b = 0\n",
      "\n",
      "    c1 = 1. + eps\n",
      "    c2 = t - eps\n",
      "    \n",
      "    u = c1*e**(a*t) + c2*e**(b*t)\n",
      "    \n",
      "    plot(t, u, label='$\\epsilon = $' + str(eps))\n",
      "\n",
      "    eps = eps/10\n",
      "\n",
      "legend()\n",
      "figsize(10, 6)\n",
      "axis([-0.1, 1.1, -0.1, 1.1])\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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A66+HceNMA/X221A39JJEkaDzGNtFRUUxYcIEOnbsSH5+Pv379yc5OZlJkyYB\nMHDgQJKSkujUqRNNmzYlIiKCAQMGhF/zRGB22xW49VaztfeWWwLy7UXETg6M6A4fNqeCv/sujB4N\n994LkZF2VyUSOlxut9sd8BdxuQjCywRGejo89RTD8z6lVuVaPHrto35/iR9+MC+TlQUROrZUJDzs\n2QPDh5sHuo0fz4lbO/HMkrFMXjWZEe1HMOTqISE3aTpzBv75T7OmqWtXGDsWwnEDtYgVq75Fb9VW\nArjbrkCTJlCzJhTZyCgiTuTQiO677+Caa2DSJDMJnzRJjZNISfRsOyuFdttl5wVuVXevXvDBB9C2\nbcBeQkQCrUhE931tF0Nn92TP8T0hG9EdOGAO6p07F559Fvr21QRcxIr+FfHG2QXjp/JOBewlCpon\np6abIuVaCbvo2k1px80JN4fkLrr8fHjtNXPQZeXKsGUL9OunxknEG/rXxErh2C4Au+0KpKaa03m/\n+y5gLyEi/ubQiO6bb6BlS3jvPbPT9+9/hxo17K5KxDkU21k5G9tViqoUsDVPBS9z++3mwMxWrQL2\nMiLiLw6M6PbuhUcfNQ3TSy/BHXec+0+ciPhAkydvBPCcp8IU3Yk4gAMjutxcGD/eTLjr1jXP1Ozd\nW42TSGmpebIShN12BdLSzHqDNWsC+jIiUhoOjegWLjT/bVmwwMR1zz8P1arZXZWIsym2sxLgZ9sV\nfamC6VOLFgF9KRHxhQMjusxMePhhWLkSXn4ZunXTpEnEXzR58kaQJk/w67onRXciIcCBEd2pU+bI\ngebN4corYfNmuO02NU4i/qTmyUqhZ9sF8qiCAi1amHRg/fqAv5SIlMSBEZ3bbc5quvJKM21auRKe\nesocQyAi/qXYzsrZH9cqR1cOSvPkcpmFnO++a9YpiEiQOTCi27oVHngAfvoJXn8dbrzR7opEwpsm\nT95wu6kcFZzmCUxC8M475jlTIhIkDozojh6Fv/wF2reHjh1h3To1TiLBoObJytnYrlJUJbJzA/d4\nlsKuvNI8U2rRoqC8nEj55sCIruABvklJcOgQbNwIDz4I0aFTokhYU2xnpVBsF8hn2xVVMH26/vqg\nvaRI+ePAiG7lShg61Px+9my4+mp76xEpjzR58kaQYzuAPn1g1iyzc0ZE/MyBEd2+fdC/vzlyYNAg\n+PZbNU4idlHzZMWG2A4gLs5sNf7kk6C9pEj4c2BEl5trzmlKTYXYWLM4vG9fPcBXxE6K7azYFNsB\n/PGPMH1E5ntcAAAgAElEQVQ69OwZ1JcVCU8OjOg+/xzuvx8uuwy+/tqscRIR++lnF2+43URHRHPG\nfYa8M3lBe9mePeHLL+HgwaC9pEj4cWBEt2MHdO8O991nHqfy6adqnERCiZonK2djO5fLRaWoSkFd\n93TRRWb78fvvB+0lRcKHAyO6Eydg5EizlqlVK9i0Cbp21engIqFGsZ2VQv/VqhxVmezcbKpVCN5T\nNfv2hTFjYODAoL2kiPM5LKJzu80PSX/5C1x7LaxdC/HxdlclIiXR5MkbZx80F6xTxgvr2BGysmDD\nhqC+rIgzOTCiW7/eHEny7LPmeJJ331XjJBLq1DxZORvbwdnJU5AXjUdFQb9+8OabQX1ZEWdxYER3\n8CAMGWJOBO/dG1atMieFi0joU2xnpVBsF+zjCgrcc49ZAzFuHFSsGPSXFwltDovo8vNh8mTz0N7b\nb4ctW8wRBCLiHJo8ecPG2A6gYUPzkODZs4P+0iKhy4ER3ddfQ8uWMGMGfPYZTJigxknEidQ8WbE5\ntivw5z/DG2/Y8tIiocWBEV1WFvzhD+bstsceg4wM8wORiDiTYjsrhZonu2I7gNtuM8+z2rnTTKJE\nyiWHRXTZ2TB+vDkhfNAgE9dVrWp3VSJSVpo8WSl8VIFNsR1ApUrmp9YpU2x5eRF7OSyic7vhgw8g\nJQVWr4YVK8yRI2qcRMKDmidvhEBsBzBggNl1l5NjWwkiweXAiG7tWnP0wJgx5oedDz+ERo3srkpE\n/EmxnZUQie0ArrwSrrgCZs0yW5tFwprDIrqff4YnnjAbO55+2qxTjIy0uyoRCQRNnqyESGxXYOhQ\nePVVW0sQCSyHRXQ5OWZdU0oKVKkCW7eaJwKocRIJX2qevBEisR2Y51xlZZl1FCJhxYER3bx5ptwv\nvjDHELz8MtSsaXdVIhJoiu2sFD6qILqyrbEdmBPHBw0y06epU20tRcR/HBbRbdkCDz1kdr++/DJ0\n7mx3RSISTJo8WSl8wnhkJU7l2xvbgVlLMXu2WWMh4mgOi+gOHYIHHoAOHeCmm8xz6dQ4iZQ/ap68\nEUKTJ4DataF7dx2aKQ7msIguPx9efx2SkuDUKdi8GR58ECpUsLsyEbGDYjsrIXLCeFFDhpiDM//y\nF4gOjfcXEe84LKL76iszbapZExYsgGbN7K5IROymyZOVIg8Gtnu3XYEWLczZMTNn2l2JiJccFtHt\n2AE9e5oHcz/5pGmi1DiJCKh58k6IxXYFHn0UXnjhXHkioclhEd2xY/D443D11eaHlM2bTRNV6Oco\nESnnFNtZKRTbVYmuwsnckzYX9KtOncxDRufPh5tvtrsakWI4KKI7cwamTTON0w03wLp1EBdnd1Ui\nEoo0ebJS6MfNqtFVOZF7wsZizudywfDhMG6c3ZWIFOGwiG7xYjNpeu01c4L/22+rcRKRkql58kaI\nTp4Afv972LULli+3uxIRHBfRbd9uIrm77oKHH4alS6F1a7urEpFQp9jOSqHYrmqFqpzICZ3JE5id\ndg89ZNY+ffih3dVIueagiO7wYRg71hw0+9BDMH06VK5sd1Ui4hSaPFkpFNtVia4SUrFdgf79zaMh\ntm61uxIplzxEdJ0TO4dURJeXBxMnmvOaDh+GjRvNGic1TiLiCzVP3iiYPEVXDbnYDqBqVbj/fnjm\nGbsrkXLFi4jugTYPhExE9+mn0LSpWdO0YAFMnmyGZCIivlJsZyXEY7sCw4ZBQoLZVp2SYnc1EvYc\nFNFt3GgOk921C156Cbp00bEDIlI2mjxZKRLbncw9iTsED1aKiTELXkePtrsSCWsOiuj274f77oPf\n/tY0TBs2wC23qHESkbJT8+SNs81SVEQUkRGR5OTn2FxQ8QYPhkWLzJuEiF85KKI7dcoc35GSAlWq\nmLWAQ4fqMUYi4j+K7awUiu3g17OeKkZVtLGo4lWtas59GjVKO+/EjxwS0bnd8P775uT9tDRz7EBi\not1ViUg4spw8zZ8/n6SkJBITExnn4TTGlStXEhUVxaxZs/xaoO2KzPhD8aynwu67z7xprFljdyXi\neA6K6FasgPbt4bnnYMoUmD1bjZOIBI7H5ik/P58hQ4Ywf/58Nm/ezIwZM9iyZUux1z366KN06tQp\nJNcDlVnhyVMILxoHE1P89a/ml0ipOCii27EDeveG7t3NkR3ffQfXX293VSIS7jw2TytWrCAhIYEG\nDRoQHR1N7969mTNnzgXXvfrqq/Tq1YuLL744YIXapoTYLpQNHGhOTv7sM7srEcdZvBiaN4dPPjER\n3cN303F2T0YvGs207tOY3mM6dWPq2l0lv/wCDz4IrVrBlVfCDz9Av34QGWl3ZSJSHnhc87R7927q\n169/7s/x8fEsL/IckN27dzNnzhy+/PJLVq5ciauErSyjRo069/v09HTS09NLX3UwOSy2A6hQwSyY\nfeQR84BTvaGIpT17zIK5RYtg/HhO3NqJZ5aMZfLcyTzR4QkGtxocEpOmU6fg1VfNifq3326O5qhT\nx+6qRMTpMjIyyMjI8Pp6j81TSY1QYQ888ADPP/88LpcLt9tdYmxXuHlyHAfFdgW6d4fx481T4u++\n2+5qJGTl5cGECeaE1QEDcG/axIeZC3hoYgodLu/AhkEbQmLSdOYMvPsujBgBLVrAkiVwxRV2VyUi\n4aLoUGe0xbk/HpunuLg4MjMzz/05MzOT+Pj4865ZtWoVvXv3BuDAgQN8+umnREdH07VrV19rD01F\nYjsnTJ7AlP3SS9Crl3l4cJUqdlckIcchu+i+/NJMUaOjzTPo2re3uyIRKe88rnlq2bIl27ZtY9eu\nXeTk5PDee+9d0BTt2LGDnTt3snPnTnr16sVrr70WPo0TXBDbOWHNU4E2beDaa+H55+2uREKKQ3bR\nbdwInTvDgAHm+IGlS9U4iUho8Ng8RUVFMWHCBDp27EhKSgp33HEHycnJTJo0iUmTJgWrRvs5MLYr\n8NJL5kGoP/5odyViO4fsotu9G/78Z7Ner2NH2LLFTE91MriIhArLQzJvvvlmbr755vM+NnDgwGKv\nnTp1qn+qCiUOje0KxMebdcDDhpkNVHoDKqccENEdO2YWgk+caJqn77+HGjXsrkpE5EJ6PIsVB8d2\nBR54AHbuhLlz7a5Egs4BEd3p0/DKK+ZQy//8xxzwOm6cGicRCV1qnrzhsHOeiqpQwWyouv9+OOGs\n0qW0HBDR5efD22+bXXOff27OJXv7bbjsMttKEhHxip5tZ6WY2G7vib02FlQ6N9xgFo+PHGmOMJAw\nFuIRndsNH38Mjz9upkvTpmkhuIg4iyZPVorGdhWqcjznuE3FlM3f/w4zZsCyZXZXIgHhgIju669N\nEz9ihNkF+vXXapxExHnUPFlxucwJfWfFVIjh2OljNhZUerVrmwbqnnvMOhMJEw6I6Natgy5d4E9/\ngkGDYO1auOUWbWAQEWdSbGclIuK82C6mYgzHcpzZPIHZ8v2vf8GYMeZQaXG4EI/otm+HJ5+EhQvN\ntGnWLKhY0daSRETKTJMnKxERYTN5AvOT/sSJMHkyFHlMoThJiEd0e/eanq51a0hKgm3bYOhQNU4i\nEh7UPFkp2jw5fPIEULeuaaD++Edzto44SIhHdD//bB6lkpJiGqWtW80mhZgYW8oREQkIxXZWwmjN\nU2E9e8K8eeb4gilT7K5GvBLCEd2hQ+Y0+9dfhzvugPXrzQGtIiLhSJMnK2G25qmwV14xu53ef9/u\nSsSjEI7ojh6Fp582B1zu2werVpmpphonEQlnap6sFIntqlesHhaTJ4Bq1eDdd80wY9s2u6uRC4Rw\nRHfihDlqICHBPDdx2TJ44w1o0CDopYiIBJ1iOytFmqeKkRXJd+eTm59r+wNU/aFVKxg9Gnr0MG+A\nVavaXZEAIRvRZWfDa6+ZZ9Clp8OiRZCcbEspIiK20eTJSpHmyeVymXVPYRLdAdx3H7RoAffee15C\nKXYI0Yju1CnziJ+EBBP1fvaZOfJCjZOIlEdqnqwUaZ7g7LqnMInuwKyJf+012LQJ/u//7K6mnArR\niO7kSXj5ZWjc2DRMc+fCRx9B06ZBLUNEJKQotrNSZLcdEHaTJ4AqVeDDD+Gaa8y5PL/7nd0VlSMh\nGNEdO2YWfr/8MrRrB//+NzRvHvQyRERCkiZPVorstoPwmzwVaNzY7Lz7wx9g40a7qykHQjCiO3zY\nnD7fqJF5hMoXX5imWo2TiMiv1DxZKS62C8PJU4EOHUx6dMst5r1dAiAEI7qDB81jVBISzM7Lr782\nD5FOTQ1aCSIijqHYzkpEhHmzKySmYgxHTx+1qaDA+8MfYMcO00AtWmSONBA/CbGIbt8+E81Nngzd\nu5tH9jRuHNQSREQcR5MnKyVNnsIwtitsxAj4zW/g1lvNomEpoxCL6LZtg4EDzfq2o0fN4ZZvvKHG\nSUTEG2qerJS02y5MY7sCBTvw4uPNROLUKbsrcqgQi+i++w5uv91sDLjkEvj+e7MwXIdbioh4T7Gd\nlZJ224X55AkgMhKmTjUx3u9/Dx98ABUq2F2Vg4RIROd2w+efw7hx8MMP8NBD5p+r4lgRkdLR5MlK\nMbvtqlesHvaTpwJRUfDOO6aH7NnTnDAtFkIkosvNNYu+f/Mb0zD17Qvbt8ODD6pxEhEpCzVPVoqJ\n7WpUqsHhU4dtKij4oqPNEQYxMdCpExw5YndFISpEIrpffoHnnjPHDbz+unlw7/r18Kc/aXIoIuIP\niu2sqHkCzJvu9OkwdChcfz3Mn2/WzMhZIRDRbd4Mr7wCM2fCbbfBxx9Ds2YBf1kRkXJHkycrap7O\niYgwzze75Raz4HjzZrsrCgE2R3RnzsC8eXDTTXDDDVCvHmzdatY0qXESEQkMNU9W1Dydx+UyMdDI\nkZCebh7bUS7ZHNEdOmSmTMnJ8MQTpnfbtQueegrq1AnIS4qIyFmK7ayoeSpW375wxRVmEfnQofDo\no6axKhdsiujcblixwqxjmj0bOnc2ZzNde205uvciIiFAkycrxRxVoObJaNPGnEg9e7aJ8vbvt7ui\nALMpojt2DCZNghYtzLERycnmyIF33oH27dU4iYgEm5onK8UcVaDm6Vfx8eY5aGlp5uGxn39ud0UB\nYENE53bD0qXmFPDLLoMFC8w5Tdu2wfDhcPHFfnspERHxkWI7K8XEdpWiKgFwKu/Uud+XZ9HR8Oyz\nZsFy377QrZvZKl+9ut2V+UGQI7qsLJg2Dd56yzRQd98NGzdCXJxfX0ZERMpAkycrxTRPoOlTcW64\nATZsgJwcuPJKmDPH7orKIIgRXXa2OcyyY0do2tQs/H7rLfPolMcfV+MkIhJq1DxZUfPkk5o1YfJk\nMz0ZPhy6doUtW+yuygdBiuhOnzbN5R//CHXrmmapXz/Yvdusb2rbVmuZRERClWI7K2qeSiU93Zxq\n/X//Bx06QK9eMGpUiG+jD3BEl5MDX3wB771nDrBs2tQ8M3D8+BC/LyIich5NnqwUs9sO1Dx5o2JF\n80y177+HSpXMLrEHHoDMTLsrKyKAEd2RI6ZZuvNOM2EaO9Y8a27jRsjIgP/5HzVOIiJOo+bJSjG7\n7UDNky9iY+Hll03DEB1tdubdcw+sWmVzYQGK6LZvN9/2hhugfn14+21zFtO6dfDNNzBsmDkJXERE\nnEmxnRXFdn5Trx68+CL89a/moMdevaBWLbMd//bboUaNIBbjx4hu/3748ktYuND874kT5tyrYcPg\nd7+DqlUD+PcQEZGg0+TJSgnNU83KNTmYfdCGgpwvNtbsIvvxR3jmGfOQ4csvh1tvNVOaQ4cC+OJl\njOjcbrMb7l//gvvvN+uWmjSBd9+F1FSzCHzPHnPyd7duapxERMKRJk9WSmiealWuxZ7je2woKHxE\nRkKnTubX0aNmEfXMmTBkCCQlmanN734HV18N1aqV8cXy8sxTjZ95BgYMwL1pEx9mLuChiSl0uLwD\nGwZtoG5M3fO+xO0267M2bDCL31esgGXLzOfatoXWreEf/4CWLSFK/yaJiJQb+k++lRKap9pVarNh\n/wYbCgpP1aubbft//KPZxr90qdmZ9vjjpnFp2NAstG7RAhITISEBGjQwi9IteYjo3r5tGk0vuo6d\nP8A3O2HnTrNmaeNG86tyZbMk6qqroHdvs5bpsst0jICISHmm5slKCbvtalepzYGTB2woKPxVrGiO\nOkhPN4OinBzYtMksMF+71sR827fDTz9B7drmUSUFv6pVM19fsSLUyt3DzV8O5/L/LGJWu/Esqd+J\nFa+NZVvMZOp8/wSulYPp8pdooqNNc9awoWnIUlPhjjtMw1S7ts03Q0REQo6aJysl7LarXaU2v5z8\nxYaCyp8KFcxz85o3P//jeXlmfdHPP//668QJyDmZx5VfTaDNwmdY/ZsBTL19ExurLGBOdgrJVTow\nNWEDV9xWl9q1TXNU5khQRETKFTVPVjzEdpo82SsqyhwFUL9+oQ8WjuhWLeHi2i7mf2oiuo96+f9Z\ndCIiUv5ot50VDwvG1TyFkCA+i05ERMo3NU9WSmieLqp0ESdyT5Cbn2tDUXJOkJ5FJyIiUkCxnZUS\nmqcIVwSxlWP5JfsXLq12qQ2FSaCfRSciIlIcTZ6slLDbDrRo3DaK6ERExEZqnqyUMHkCrXsKOkV0\nIiISAiybp/nz55OUlERiYiLjxo274PPvvPMOaWlpNG3alHbt2rF+/fqAFGqbEo4qAO24C6rFi81Z\nBZ98YiK6h++m4+yejF40mmndpzG9x/QLTggXEREJBI/NU35+PkOGDGH+/Pls3ryZGTNmsGXLlvOu\nadSoEYsXL2b9+vWMHDmSe++9N6AFB52HydPFVS9m/4n9QS6onFFEJyIiIcZj87RixQoSEhJo0KAB\n0dHR9O7dmzlz5px3Tdu2bbnooosAaN26NVlZWYGr1g4emqdLq13KvhP7glxQOaGITkREQpTH3Xa7\nd++mfqETCOPj41m+fHmJ17/55pt07ty52M+NGjXq3O/T09NJT0/3rVK7eGqeql7K2n1rg1xQOaBd\ndCIiEkQZGRlkZGR4fb3H5snlw9NPv/rqK6ZMmcI333xT7OcLN0+O4qF5qhtTl/nb5we5oDC2Zw8M\nHw6LFsH48Zy4tRPPLBnL5LmTeaLDEwxuNViTJhER8buiQ53Ro0d7vN5jbBcXF0dmZua5P2dmZhIf\nH3/BdevXr2fAgAHMnTuXmjVr+lhyiPNwVMGl1S5lz7E9QS4oDCmiExERB/E4eWrZsiXbtm1j165d\n1KtXj/fee48ZM2acd81PP/1Ejx49mD59OgkJCQEt1hYedtvVrVaXvcf3BrmgMKOITkREHMZj8xQV\nFcWECRPo2LEj+fn59O/fn+TkZCZNmgTAwIEDefrppzl06BCDBg0CIDo6mhUrVgS+8mDxENvVqVaH\nfSf24Xa7fYo4BUV0IiLiWC63u4Sxij9fxOUiCC8TGMuWwQMPmP8tRuy4WLYN3UatKrWCXJhD5eXB\nhAnwzDMwYADuxx/nw8wFPLTgITpc3oEXb3xR5zWJiIitrPoWPdvOiofJE5h1T3uP71Xz5A1FdCIi\nEgb0eBYrFs1T3Zi67DmuReMe6aBLEREJI2qerHjYbQdQL6Yeu4/uDmJBDqJddCIiEoYU21nxsNsO\n4LKLLuOnIz8FsSCHUEQnIiJhSpMnKxax3eUXXc5PR9U8neMhors54WZFdCIi4nhqnqxYNE+aPJ3l\nIaLLOprFhkEbeLDtg4roRETE8RTbWfGiefrP4f8EsaAQVCSi21obhs7uwd7je5neYzodLu9gd4Ui\nIiJ+o8mTFYvmqX71+vx05CfnnmNVFkUiuuP/nsVjWW/Rfmp7uiR2YfW9q9U4iYhI2FHzZMVit11M\nxRgqRVXil+xfgliUzYqJ6N5PdpMy8Up2H9vN+vvWaxediIiELcV2Vix228Gv0V3tKrWDVJSNSojo\n9h3fp4hORETKBU2erFjEdgCNajZix6EdQSrIJh4iulsSb2H1QEV0IiJSPqh5suJF85RYK5FtB7cF\nqaAgKyGiS56Ywn+P/ZcNgzZwf5v7iYrQEFNERMoHveNZiYiA/HyPlzSJbcLXP30dpIKCqJiIbshH\n3dl/Yj/v9niX9pe3t7tCERGRoNPkyUpkpGXzFHaTp2IiukezptJ+antubXIrqweuVuMkIiLllpon\nK9HRkJvr8ZImtZqw7ZcwaJ6KiehmJp8heWIKe47tUUQnIiKCYjtr0dGQk+PxkjpV65Cdl83hU4ep\nUalGkArzsyIR3ZZaboYqohMREbmAJk9WvJg8uVwurqh1BVsPbA1SUX5UQkTX4a0OdL2iqyI6ERGR\nItQ8WalQwbJ5Amhapynr9q4LQkF+4iGi23t8LxsGbWBY62GK6ERERIrQO6MVLyZPAGl10li/f30Q\nCvKDYiK6IR/dxoGTB5jRcwbXXnat3RWKiIiELE2erERGmv+12HHniMlTkYju2McfMjxzCh3e6sBt\nV9zGqntXqXESERGxoObJG15Mn9IuTWP9vvWccXs+UNMWxUR07yXlk/Lalew/sZ+NgzYytPVQRXQi\nIiJe0LulNwqap0qVSrwktnIsNSrVYPvB7STWSgxicRaKRHSba51h6Ee38cvJX/hXz3/R7rJ2dlco\nIiLiKJo8ecPLdU9t67dladbSIBTkhWIiukcy3+S6t67jtitu47t7v1PjJCIiUgpqnrzhZfN0Tfw1\nfJv5bRAK8qCYiO5fSXkkT0zh5xM/K6ITEREpI72DesPb5qn+Nby55s0gFFSCYiK6IbO6cTD7IO/1\nek+TJhERET/Q5MkbXjZPzS5txq7DuziYfTAIRRXiIaLrkdxDEZ2IiIgfqXnyhpfNU3RkNNc1uI7P\ntn8WhKIoNqKbcUUuyRNTOHDyABsHbWTI1UMU0YmIiPiR3lW94WXzBNA5oTPzts2jd2rvwNZUJKJb\nW+MUQz/ozImcE8y8fSbX1L8msK8vIiJSTmny5A1fmqfEzsz/cT55Z/ICU0uRiO6X2TP4n+3/S8fp\nHbmr6V2sHLBSjZOIiEgAqXnyhg/N0+U1LqdBjQYs3LHQvzUUiejyN27gtct/JuW1K4mMiGTL4C3c\n+5t7iYyI9O/rioiIyHkU23nDh+YJ4K6md/H2+rfpmNDRP69fJKJbXHk/w969jhqVavD5XZ/TtE5T\n/7yOiIiIWFLz5A0fm6c+V/XhyYwn2X9iP5dUvaT0r7tnDwwfDosWwfjxZP7uah5d+Bhf//Q1L934\nEr+/8ve4XK7Sf38RERHxmWI7b/jYPNWuUps+qX343+X/W7rXKxLRHVm9lL/WXEWzfzSnUc1GbB28\nlTtS71DjJCIiYgM1T97wsXkCeOSaR3j9u9fZfXS3b6+1eDE0bw6ffELuoq/4v+7xXPHWb9h7fC/r\n7lvHM799hqoVqvr2PUVERMRvFNt5oxTNU8OaDRnUahBDPh3CrN/Psp4SFYro8l96kXeanOKZL3vS\noEYDFty5gLRL08rwFxARERF/0eTJG6VongBGtB/B7qO7eXrR0yVfVCiiy6t3Kf9891Gu2DuCKWun\n8votr/PZXZ+pcRIREQkhmjx5o2JFOH3a5y+rFFWJ2b1nc+O0G9lzfA8v3PgC1StW//WCxYtxDx7M\n8dhqvD6uGy8e/CfNdzVnSrcpdLi8gx//AiIiIuIvap68ERMDx46V6kvrxdRjSb8lPPL5IzT4ewNu\naHQDLahHp38spP7anTxxSxUWpFXl9sva8233b0mITfBz8SIiIuJPLrfb7Q74i7hcBOFlAucvf4E6\ndeCRR8r0bXYf/A97xz1B8qRZrLnlN2QO+RNpjduRVDtJO+dERERChFXfosmTN6pXh6NHy/Y9Fi8m\nbvBg4i69FJatol1Skn9qExERkaBS8+SN6tVh587SfW2Rgy7p2RM0ZRIREXEs7bbzRmkmT0UOumTz\nZujVS42TiIiIw2ny5I2LLvKteSryLDoU0YmIiIQNNU/e8HbypIhOREQk7Cm280b16nDkSMmfV0Qn\nIiJSbmjy5I169SAzs/jPKaITEREpV3TOkzfcbjN9ysyEGjXMx/77XxPRLV6siE5ERCSMWPUtlrHd\n/PnzSUpKIjExkXHjxhV7zbBhw0hMTCQtLY01a9aUvtpQ5XLBFVfApk2QkwMvvABNm8JllymiExER\nKWc8xnb5+fkMGTKEL774gri4OFq1akXXrl1JTk4+d828efP48ccf2bZtG8uXL2fQoEEsW7Ys4IUH\n3W23waBBcPw4pKTAsmWQoEepiIiIlDcem6cVK1aQkJBAgwYNAOjduzdz5sw5r3maO3cuffv2BaB1\n69YcPnyYffv2UadOncBVbYdHHjHrmpo2hauvtrsaERERsYnH5mn37t3Ur1//3J/j4+NZvny55TVZ\nWVkXNE+jRo069/v09HTS09PLULYNKlaEP//Z7ipERETEzzIyMsjIyPD6eo/Nk7cPqy26qKq4ryvc\nPImIiIiEiqJDndGjR3u83uOC8bi4ODILbdHPzMwkPj7e4zVZWVnExcX5UrOIiIiIY3hsnlq2bMm2\nbdvYtWsXOTk5vPfee3Tt2vW8a7p27crbb78NwLJly6hRo0b4rXcSEREROctjbBcVFcWECRPo2LEj\n+fn59O/fn+TkZCZNmgTAwIED6dy5M/PmzSMhIYGqVasyderUoBQuIiIiYgcdkikiIiJSSJkPyRQR\nERGRX6l5EhEREfGBmicRERERH6h5EhEREfGBmicRERERH6h5EhEREfGBmicRERERH6h5EhEREfGB\nmicRERERH6h5EhEREfGBmicRERERH6h5EhEREfGBmicRERERH6h5EhEREfGBmicRERERH6h5EhER\nEfGBmicRERERH6h5EhEREfGBmicPMjIy7C6h3NE9Dz7d8+DTPQ8+3fPgC+d7rubJg3D+Bx+qdM+D\nT/c8+HTPg0/3PPjC+Z6reRIRERHxgZonERERER+43G63O+Av4nIF+iVERERE/MZTexRldwEiIiIi\nTtShlg4AAATESURBVKLYTkRERMQHap5EREREfKDm6az58+eTlJREYmIi48aNK/aaYcOGkZiYSFpa\nGmvWrAlyheHH6p6/8847pKWl0bRpU9q1a8f69ettqDK8ePP/c4CVK1cSFRXFrFmzglhdePLmnmdk\nZNC8eXNSU1NJT08PboFhyOqeHzhwgE6dOtGsWTNSU1N56623gl9kGLnnnnuoU6cOV111VYnXhN37\np1vceXl57saNG7t37tzpzsnJcaelpbk3b9583jWffPKJ++abb3a73W73smXL3K1bt7aj1LDhzT3/\n9ttv3YcPH3a73W73p59+qnteRt7c84Lrrr/+eneXLl3cH3zwgQ2Vhg9v7vmhQ4fcKSkp7szMTLfb\n7Xb//PPPdpQaNry550899ZT7sccec7vd5n7Hxsa6c3Nz7Sg3LCxevNi9evVqd2pqarGfD8f3T02e\ngBUrVpCQkECDBg2Ijo6md+/ezJkz57xr5s6dS9++fQFo3bo1hw8fZt++fXaUGxa8uedt27bloosu\nAsw9z8rKsqPUsOHNPQd49dVX6dWrFxdffLENVYYXb+75u+++S8+ePYmPjwegdu3adpQaNry553Xr\n1uXo0aMAHD16lFq1ahEVFZT9U2Gpffv21KxZs8TPh+P7p5onYPfu3dSvX//cn+Pj49m9e7flNXoz\nLz1v7nlhb775Jp07dw5GaWHL2/+fz5kzh0GDBgE6ZqSsvLnn27Zt4+DBg1x//fW0bNmSadOmBbvM\nsOLNPR8wYACbNm2iXr16pKWl8corrwS7zHIlHN8/1Wrj/RuEu8iRC3pjKT1f7t1XX33FlClT+Oab\nbwJYUfjz5p4/8MADPP/887hcLtxut44ZKSNv7nlubi6rV69m4cKFnDx5krZt29KmTRsSExODUGH4\n8eaeP/vsszRr1oyMjAy2b9/OjTfeyLp164iJiQlCheVTuL1/qnkC4uLiyMzMPPfnzMzMcyP0kq7J\nysoiLi4uaDWGG2/uOcD69esZMGAA8+fP9zgWFmve3PNVq1bRu3dvwCyq/fTTT4mOjqZr165BrTVc\neHPP69evT+3atalcuTKVK1emQ4cOrFu3Ts1TKXlzz7/99ltGjBgBQOPGjWnYsCHff/89LVu2DGqt\n5UVYvn/au+QqNOTm5robNWrk3rlzp/v06dOWC8aXLl0aFgve7OTNPf/Pf/7jbty4sXvp0qU2VRle\nvLnnhd19993uDz/8MIgVhh9v7vmWLVvcN9xwgzsvL8994sQJd2pqqnvTpk02Vex83tzzBx980D1q\n1Ci32+1279271x0XF+f+5Zdf7Cg3bOzcudOrBePh8v6pyRMQFRXFhAkT6NixI/n5+fTv35/k5GQm\nTZoEwMCBA+ncuTPz5s0jISGBqlWrMnXqVJurdjZv7vnTTz/NoUOHzq2/iY6OZsWKFXaW7Wje3HPx\nL2/ueVJSEp06daJp06ZEREQwYMAAUlJSbK7cuby5548//jj9+vUjLS2NM2fO8MILLxAbG2tz5c7V\np08fFi1axIEDB6hfvz6jR48mNzcXCN/3z6A8205EREQkXGi3nYiIiIgP1DyJiIiI+EDNk4iIiIgP\n1DyJiIiI+EDNk4iIiIgP1DyJiIiI+EDNk4iIiIgP/h/T3Mm1uJqddAAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import e, sqrt\n",
      "\n",
      "eps = 0.1\n",
      "\n",
      "d = -1.\n",
      "\n",
      "t = arange(0., 0.1, 0.001)\n",
      "\n",
      "while eps > 0.01:\n",
      "    a = 0\n",
      "    b = -d/eps\n",
      "\n",
      "    c1 = 1. - eps/d\n",
      "    c2 = eps/d\n",
      "    \n",
      "    u = c1*e**(a*t) + c2*e**(b*t)\n",
      "    \n",
      "    plot(t, u, label='$\\epsilon = $' + str(eps))\n",
      "\n",
      "    eps = eps/2\n",
      "\n",
      "legend(loc = 3)\n",
      "figsize(10, 6)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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amXFx+q+zztL/4T2OYUHwAgAAPbotP187W1u1rq7O7lJiHsELAAD0KN7h0MMl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\nAABECMELAAAgQv4fxGigixqxDjwAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
      "print a\n",
      "print a[:-1]\n",
      "print a[-1:]\n",
      "temp = a[-1:]\n",
      "a.insert(111, 'w')\n",
      "print a\n",
      "print a[-len(a)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
        "[0, 1, 2, 3, 4, 5, 6, 7, 8]\n",
        "[9]\n",
        "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 'w']\n",
        "0\n"
       ]
      }
     ],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = []\n",
      "b = []\n",
      "for i in range(4):\n",
      "    b.append(i)\n",
      "    b.append(0)\n",
      "    for j in range(4):\n",
      "        if j <= i:\n",
      "            a.append(0)\n",
      "        else:\n",
      "            a.append((i+1)*2*(j+1))\n",
      "a = array(a)\n",
      "a = reshape(a, [4, -1])\n",
      "print b\n",
      "for i in range(4):\n",
      "    b[2*i+1] = sum(a[:, i]) - sum(a[i, :])\n",
      "print b\n",
      "print a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0, 0, 1, 0, 2, 0, 3, 0]\n",
        "[0, -18, 1, -24, 2, -6, 3, 48]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "[[ 0  4  6  8]\n",
        " [ 0  0 12 16]\n",
        " [ 0  0  0 24]\n",
        " [ 0  0  0  0]]\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = range(1, 5)\n",
      "b = range(6, 10)\n",
      "c = range(11, 15)\n",
      "\n",
      "\n",
      "d = a + b + \\\n",
      "    c\n",
      "d"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14]"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# import packages\n",
      "from scipy import *\n",
      "from numpy import *\n",
      "from matplotlib.pyplot import *\n",
      "from math import e, sqrt\n",
      "from numpy.linalg import norm\n",
      "from scipy.integrate import ode"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Body:\n",
      "    def __init__(self, rgPosInit, rgVelInit, dMassInit):\n",
      "        self.rgPos = rgPosInit\n",
      "        self.rgVel = rgVelInit\n",
      "        self.dMass = dMassInit\n",
      "    def getState(self):\n",
      "        return [self.rgPos, self.rgVel]\n",
      "    def setState(self, rgPosSet, rgVelSet):\n",
      "        self.rgPos = rgPosSet\n",
      "        self.rgVel = rgVelSet"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class System:\n",
      "    def __init__(self, rgBodiesInit = None):\n",
      "        if rgBodiesInit is None:\n",
      "            rgBodiesInit = []\n",
      "        self.rgBodies = rgBodiesInit\n",
      "    def getSize(self):\n",
      "        return len(self.rgBodies)\n",
      "    def getBody(self, iBody):\n",
      "        if iBody >= len(self.rgBodies) or -iBody > len(self.rgBodies):\n",
      "            print 'ERROR: index out of range'\n",
      "            return\n",
      "        return self.rgBodies[iBody]\n",
      "    def setBody(self, iBody, BodySet):\n",
      "        if iBody >= len(self.rgBodies) or -iBody > len(self.rgBodies):\n",
      "            print 'ERROR: index out of range'\n",
      "            return\n",
      "        self.rgBodies[iBody] = BodySet\n",
      "    def addBody(self, BodyAdd, iBody = -1):\n",
      "        self.rgBodies.insert(iBody, BodyAdd)\n",
      "    def rmBody(self, iBody = -1):\n",
      "        return self.rgBodies.pop(iBody)\n",
      "    def getSysState(self):\n",
      "        rgSysState = []\n",
      "        for iBody in self.rgBodies:\n",
      "            rgSysState.append(iBody.getState())\n",
      "        return rgSysState\n",
      "    def setSysState(self, rgSysState):\n",
      "        for iState in len(rgSysState):\n",
      "            self.rgBodies.setState(iState[0], iState[1])\n",
      "    def __str__(self):\n",
      "        strSys = 'System: \\n'\n",
      "        for iBody in range(len(self.rgBodies)):\n",
      "            strSys = strSys + 'Body ' + str(iBody) + ':\\n'\n",
      "            strSys = strSys + '\\tLoc: ' + str(self.rgBodies[iBody].rgPos) + '\\n'\n",
      "            strSys = strSys + '\\tVel: ' + str(self.rgBodies[iBody].rgVel) + '\\n'\n",
      "            strSys = strSys + '\\tMass: ' + str(self.rgBodies[iBody].dMass) + '\\n'\n",
      "        return strSys"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Force:\n",
      "    def __init__(self, SystemInit, rgtInit):\n",
      "        self.System = SystemInit\n",
      "        self.rgt = rgtInit\n",
      "    def __call__(self, System, rgt):\n",
      "        rgSysState = self.System.getSysState()\n",
      "        self.rgDeriv = []\n",
      "        self.rgAcc = zeros((len(rgSysState), len(rgSysState)))\n",
      "        for iState in range(len(rgSysState)):\n",
      "            self.rgDeriv.append([rgSysState[iState][1], 0])\n",
      "            for jState in range(len(rgSysState)):\n",
      "                if jState >= iState:\n",
      "                    self.rgAcc[iState, jState, :] = zeros([len(System.rgBodies[iState]), 1)\n",
      "                else:\n",
      "                    self.rgAcc[iState, jState, :] = self.fnAcc(System.rgBodies[iState], \\\n",
      "                                                    System.rgBodies[jState])\n",
      "        \n",
      "        for iState in len(rgSysState):\n",
      "            self.rgDeriv[iState][1] = self.System.rgBodies[iState].dMass * \\\n",
      "                (sum(self.rgAcc[:, iState, :]) - sum(self.rgAcc[iState, :, :]))\n",
      "        \n",
      "        return self.rgDeriv\n",
      "             \n",
      "    # calculates the force of Body1 on Body 2\n",
      "    def fnAcc(Body1, Body2):\n",
      "        return Body1.dMass * Body2.dMass * (Body2.rgPos - Body1.rgPos) \\\n",
      "                / norm(Body2.rgPos - Body1.rgPos)**3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Body1 = Body(array([0., 0.]), array([0., 0.]), 1.)\n",
      "Body2 = Body(array([1., 0.]), array([0., 0.8]), 1.)\n",
      "Body3 = Body(array([-1., 0.]), array([0., -0.8]), 1.)\n",
      "\n",
      "Sys = System([Body1, Body2, Body3])\n",
      "\n",
      "f = Force(Sys, [])\n",
      "\n",
      "print f.System\n",
      "rgSysState = f.System.getSysState()\n",
      "print rgSysState\n",
      "print rgSysState[1][1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "System: \n",
        "Body 0:\n",
        "\tLoc: [ 0.  0.]\n",
        "\tVel: [ 0.  0.]\n",
        "\tMass: 1.0\n",
        "Body 1:\n",
        "\tLoc: [ 1.  0.]\n",
        "\tVel: [ 0.   0.8]\n",
        "\tMass: 1.0\n",
        "Body 2:\n",
        "\tLoc: [-1.  0.]\n",
        "\tVel: [ 0.  -0.8]\n",
        "\tMass: 1.0\n",
        "\n",
        "[[array([ 0.,  0.]), array([ 0.,  0.])], [array([ 1.,  0.]), array([ 0. ,  0.8])], [array([-1.,  0.]), array([ 0. , -0.8])]]\n",
        "[ 0.   0.8]\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i = ode(f(Sys, []))\n",
      "\n",
      "i.set_integrator('vode', method='adams')\n",
      "\n",
      "dt = 0.01\n",
      "yf = [Sys.getSysState()]\n",
      "\n",
      "times = arange(0., 10., dt)\n",
      "\n",
      "for t in times[1:]:\n",
      "    i.integrate(i.t+dt)\n",
      "    yf.append(i.y)\n",
      "    Sys.setSysState(i.y)\n",
      "    \n",
      "yf = array(yf)\n",
      "\n",
      "plot(yf[:, 0], yf[:, 1])\n",
      "plot(yf[:, 4], yf[:, 5])\n",
      "plot(yf[:, 8], yf[:, 9])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "TypeError",
       "evalue": "fnAcc() takes exactly 2 arguments (3 given)",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-34-71262d317237>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mi\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mode\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mSys\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mset_integrator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'vode'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'adams'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mdt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.01\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m<ipython-input-31-c3774f33aada>\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, System, rgt)\u001b[0m\n\u001b[0;32m     14\u001b[0m                 \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     15\u001b[0m                     self.rgAcc[iState, jState] = self.fnAcc(System.rgBodies[iState], \\\n\u001b[1;32m---> 16\u001b[1;33m                                                     System.rgBodies[jState])\n\u001b[0m\u001b[0;32m     17\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     18\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0miState\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrgSysState\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mTypeError\u001b[0m: fnAcc() takes exactly 2 arguments (3 given)"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}