Skip to content

Instantly share code, notes, and snippets.

@nvictus
Created May 7, 2014 00:03
Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save nvictus/ef013af906173501a6fa to your computer and use it in GitHub Desktop.
Save nvictus/ef013af906173501a6fa to your computer and use it in GitHub Desktop.
zb
Display the source blob
Display the rendered blob
Raw
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from collections import defaultdict\n",
"from pprint import pprint\n",
"import itertools\n",
"import operator\n",
"import math\n",
"\n",
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 34
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def zb_energies(Eh, Ec, En, N):\n",
" \"\"\"\n",
" En: energy of a nucleated H\n",
" Eh: energy of a propagated H\n",
" Ec: energy of a C\n",
" N: system Size\n",
" \n",
" \"\"\"\n",
" E_map = {'H': Eh, 'N': En, 'C': Ec}\n",
" states = [''.join(seq) for seq in itertools.product('HC', repeat=N)]\n",
" \n",
" energies = {}\n",
" for state in states:\n",
" energy = 0\n",
" nucleated = False\n",
" for res in state:\n",
" if res == 'H' and not nucleated:\n",
" nucleated = True\n",
" res = 'N'\n",
" elif res == 'C' and nucleated:\n",
" nucleated = False\n",
" energy += E_map[res]\n",
" energies[state] = energy\n",
" return energies\n",
"\n",
"def zb_partition(energies, kT):\n",
" weights = {state: np.exp(-E/kT) for state, E in energies.items()}\n",
" return weights\n",
"\n",
"def zb_distribution(weights, order_param=None):\n",
" states = weights.keys()\n",
" Z = sum(weights.values())\n",
" if order_param is None:\n",
" return {state: w/Z for state, w in weights.items()}\n",
" else:\n",
" probs = defaultdict(float)\n",
" for state in states:\n",
" probs[order_param(state)] += weights[state]/Z\n",
" return probs\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# define a state property\n",
"def helicity(state):\n",
" return state.count('H')/len(state)\n",
"\n",
"En_range = [-20, -10, -7.5, -5, -2.5, 0, 2.5, 4.9, 5.1, 7.5, 10]\n",
"for En in En_range:\n",
" energies = zb_energies(-2.5, 0, En, N=3)\n",
" kT_range = np.linspace(0.01, 20, 1000)\n",
" expected_helicity = []\n",
" for kT in kT_range:\n",
" weights = zb_partition(energies, kT)\n",
" probs = zb_distribution(weights, order_param=helicity)\n",
" expected_helicity.append( sum(h*p for h,p in probs.items()) )\n",
" plt.plot(kT_range, expected_helicity)\n",
"plt.xlabel('kT')\n",
"plt.ylabel('mean helicity')\n",
"plt.title('system size = %d' % 3)\n",
"plt.legend(En_range, loc='lower right', bbox_to_anchor=(1.25,0), title='Enuc');\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAEVCAYAAABt6tVhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10db6ed50>"
]
}
],
"prompt_number": 36
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# configurational energies\n",
"En = 2.5\n",
"energies = zb_energies(-2.5, 0, En, N=5)\n",
"\n",
"# distribution of helicity\n",
"for kT in [0.1, 2.5, 100]:\n",
" # boltzmann weights at a given temperature\n",
" weights = zb_partition(energies, kT=kT)\n",
" \n",
" probs = zb_distribution(weights, order_param=helicity)\n",
" x, y = zip(*sorted(probs.items(), key=operator.itemgetter(0)))\n",
" plt.figure()\n",
" plt.stem(x,y)\n",
" plt.xlim([-0.1, 1.1])\n",
" plt.xlabel('helicity')\n",
" plt.ylabel('Probability')\n",
" plt.title('kT = %g' % kT)\n",
"\n",
"pprint(energies)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"{'CCCCC': 0,\n",
" 'CCCCH': 2.5,\n",
" 'CCCHC': 2.5,\n",
" 'CCCHH': 0.0,\n",
" 'CCHCC': 2.5,\n",
" 'CCHCH': 5.0,\n",
" 'CCHHC': 0.0,\n",
" 'CCHHH': -2.5,\n",
" 'CHCCC': 2.5,\n",
" 'CHCCH': 5.0,\n",
" 'CHCHC': 5.0,\n",
" 'CHCHH': 2.5,\n",
" 'CHHCC': 0.0,\n",
" 'CHHCH': 2.5,\n",
" 'CHHHC': -2.5,\n",
" 'CHHHH': -5.0,\n",
" 'HCCCC': 2.5,\n",
" 'HCCCH': 5.0,\n",
" 'HCCHC': 5.0,\n",
" 'HCCHH': 2.5,\n",
" 'HCHCC': 5.0,\n",
" 'HCHCH': 7.5,\n",
" 'HCHHC': 2.5,\n",
" 'HCHHH': 0.0,\n",
" 'HHCCC': 0.0,\n",
" 'HHCCH': 2.5,\n",
" 'HHCHC': 2.5,\n",
" 'HHCHH': 0.0,\n",
" 'HHHCC': -2.5,\n",
" 'HHHCH': 0.0,\n",
" 'HHHHC': -5.0,\n",
" 'HHHHH': -7.5}\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEXCAYAAACqIS9uAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10d6c7850>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEXCAYAAABCjVgAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XtQU2f+BvAnkhStoPVCXUyYRgiSVAXRoEsdbNoVYmVL\nxborXbdrLaXUjmDb3Z16+TmCu+1KZ7o7ILNbulVbaxfpSCt2wYi36NYqccWRTrUWWbGRFuuFVtQC\nJp7fH+qpyCUBcpKQPJ8ZZpKT9835vuN4npzznotMEAQBREREAAZ4ugAiIvIeDAUiIhIxFIiISMRQ\nICIiEUOBiIhEDAUiIhIxFMgvqdVq7N6929NlEHkdhgL5JZlMBplM1mF5UFAQgoODERwcjAEDBuDe\ne+8V3xcXF7ts/X/4wx8wduxYDBkyBDqdDu+//36Xbc1mMwYMGCDWERwc3G17or6Qe7oAIm9y5coV\n8fWYMWOwbt06PProoy5fT1BQEP79739j7NixsFgsmDlzJjQaDeLj4zttr1QqYbVaXV4H0d24p0B+\n78SJEwgPD0dJSYnb1pmTk4OxY8cCAKZMmYKEhAQcPHjQbesn6gpDgfxadXU1Zs6cicLCQsybN6/H\n/desWYNhw4Z1+jd8+HCnvuPHH3/E4cOHMX78+C7bfPfdd/jZz36G8PBwvPLKK7h27VqPayVyBkOB\n/Na+ffvwxBNP4P3338esWbN69R1Lly5FU1NTp3+XLl1y6jteeOEFTJw4EUlJSZ1+rtPpcOzYMTQ2\nNmLPnj04cuQIXnnllV7VS+QIQ4H8kiAIKCoqwrRp0zB9+nSP1fHHP/4Rx48fx4cffthlm1GjRkGr\n1QK4edbUG2+8gdLSUneVSH6GoUB+SSaToaioCGfOnOnTr+7XX3+93VlBd/4NGTKk276rVq3Cjh07\nUFlZiaCgoB6t98aNG72umag7DAXyW8HBwTCZTNi/fz+WLVvWq+9Yvnw5mpubO/27fPlyl/3+8pe/\noLi4GDt37sSwYcO6XYfZbMaZM2cgCAKsViteffVVzJ49u1f1EjnCUCC/NnToUOzcuRPbt2/HqlWr\n3LbeFStWwGq1QqPRiHsWa9asET8PDg7GgQMHAABHjx7FtGnTEBQUhGnTpmHixIkoKChwW63kX2R8\nyA4REd0m6Z6CyWSCVqtFZGQk8vLyumx3+PBhyOXydpNnzvYlIiLXkWxPwW63IyoqCrt27YJSqURc\nXByKi4uh0+k6tEtMTMS9996LhQsX4sknn3S6LxERuZZkewoWiwUajQZqtRoKhQJpaWkoKyvr0G7t\n2rWYO3cuQkJCetyXiIhcS7J7HzU0NCAsLEx8r1KpUFVV1aFNWVkZ9uzZg8OHD4s3KHOmb2c3MyMi\nIse6O0Ak2Z6CMxvtl156CWvWrIFMJoMgCGKhzm7wb/dxx9+qVavcuj53/3F8/fvPl8fny2PzxPgc\nkWxP4e67OlqtVqhUqnZtjhw5grS0NADAhQsXsH37digUCqf6EhGR60kWCnq9HrW1taivr8fo0aNR\nUlLS4X70//vf/8TXCxcuxOOPP46UlBTYbDaHfYmIyPUkCwW5XI7CwkIYjUbY7Xakp6dDp9OhqKgI\nAJCZmdnjvp5kMBg8un6pcXz9my+Pz5fHBnjf+PrtxWu35yGIiMh5jradvM0FERGJGApERCRiKBAR\nkYihQEREIoYCERGJGApERCRiKBARkYihQEREIoYCERGJGApERCRiKBARkYihQEREIoYCERGJJLt1\nNhERda28fD8KCirR2ipHYKAN2dlJSE6e7umyGApERO5WXr4fS5bsQF3da+KyuroVAODxYODhIyIi\nNysoqGwXCABQV/ca1q7d6aGKfsJQICJys9bWzg/StLQEuLmSjhgKRERuFhho63T5wIF2N1fSEUOB\niMjNsrOTEBGxot2yiIjlyMpK9FBFP5E0FEwmE7RaLSIjI5GXl9fh87KyMsTExCA2NhaTJ0/Gnj17\nxM/UajWio6MRGxuLKVOmSFkmEZFbJSdPR36+EUbjSgCA0bgS+fkzPT7JDAAyobsnOPeB3W5HVFQU\ndu3aBaVSibi4OBQXF0On04ltrl69isGDBwMAPv/8c6SmpuLUqVMAgDFjxuDIkSMYPnx454U7ePg0\nEVF/IJMB7tyUOdp2SranYLFYoNFooFaroVAokJaWhrKysnZtbgcCAFy5cgUjR45s9zk3+kRE7iXZ\ndQoNDQ0ICwsT36tUKlRVVXVot3XrVixbtgzffvstKisrxeUymQwzZsxAQEAAMjMzkZGR0aFvTk6O\n+NpgMMBgMLh0DERE/Z3ZbIbZbHa6vWShIJPJnGo3e/ZszJ49G//5z3/w9NNP4+TJkwCAAwcOIDQ0\nFOfPn0diYiK0Wi0SEhLa9b0zFIiIqKO7fzDn5uZ2216yw0dKpRJWq1V8b7VaoVKpumyfkJAAm82G\nixcvAgBCQ0MBACEhIUhNTYXFYpGqVCIiukWyUNDr9aitrUV9fT3a2tpQUlKClJSUdm3q6urEeYPq\n6moAwIgRI3Dt2jU0NzcDuDkZXVlZiQkTJkhVKhER3SLZ4SO5XI7CwkIYjUbY7Xakp6dDp9OhqKgI\nAJCZmYnS0lJs3LgRCoUCQUFB2Lx5MwCgsbERc+bMAQDYbDbMnz8fSUlJUpVKRES3SHZKqtR4SioR\n+QK/OSWViIj6H4YCERGJGApERCRiKBARkYihQEREIoYCERGJGApERCRiKBARkUiyK5qJiPqivHw/\nCgoq0doqR2CgDdnZSV7xEBpfx1AgIq9TXr4fS5bsQF3da+Kyurqbj69kMEiLh4+IyOsUFFS2CwQA\nqKt7DWvX7vRQRf6DoUBEXqe1tfODGC0tAW6uxP8wFIjI6wQG2jpdPnCg3c2V+B+GAhF5nezsJERE\nrGi3LCJiObKyEj1Ukf9gKBCR10lOno78fCOMxpUAAKNxJfLzZ3KS2Q34PAUi8mruft6Au/F5CkRE\n5LUYCkREJGIoEBGRSNJQMJlM0Gq1iIyMRF5eXofPy8rKEBMTg9jYWEyePBl79uxxui8REbmeZBPN\ndrsdUVFR2LVrF5RKJeLi4lBcXAydTie2uXr1KgYPHgwA+Pzzz5GamopTp0451ZcTzUT+gRPNrl5f\n99tOye59ZLFYoNFooFarAQBpaWkoKytrt2G/HQgAcOXKFYwcOdLpvgCQk5MjvjYYDDAYDJKMhYio\nvzKbzTCbzU63lywUGhoaEBYWJr5XqVSoqqrq0G7r1q1YtmwZvv32W1RWVvao752hQEREHd39gzk3\nN7fb9pLNKchkMqfazZ49GydOnMAnn3yCp59+moeEiIg8SLJQUCqVsFqt4nur1QqVStVl+4SEBNhs\nNly6dAkqlapHfYmIyDUkCwW9Xo/a2lrU19ejra0NJSUlSElJademrq5O3DOorq4GAIwYMcKpvkRE\n5HqSzSnI5XIUFhbCaDTCbrcjPT0dOp0ORUVFAIDMzEyUlpZi48aNUCgUCAoKwubNm7vtS0RE0uK9\nj4jIq/GUVFevj/c+IiIiJzEUiIhIxFAgIiIRQ4GIiEQMBSIiEjEUiIhIxFAgIiIRQ4GIiEQMBSIi\nEjEUiIhIxFAgIiIRQ4GIiEQMBSIiEjEUiIhIxFAgIiIRQ4GIiEQMBSIiEjEUiIhIJGkomEwmaLVa\nREZGIi8vr8PnH3zwAWJiYhAdHY1p06ahpqZG/EytViM6OhqxsbGYMmWKlGUSEdEtkj2j2W63Iyoq\nCrt27YJSqURcXByKi4uh0+nENgcPHsSDDz6IoUOHwmQyIScnB4cOHQIAjBkzBkeOHMHw4cM7L5zP\naCbyC3xGs6vX56FnNFssFmg0GqjVaigUCqSlpaGsrKxdm/j4eAwdOhQAMHXqVJw9e7bd59zoExG5\nl1yqL25oaEBYWJj4XqVSoaqqqsv269atw6xZs8T3MpkMM2bMQEBAADIzM5GRkdGhT05OjvjaYDDA\nYDC4pHYiIl9hNpthNpudbi9ZKMhkMqfb7t27F+vXr8eBAwfEZQcOHEBoaCjOnz+PxMREaLVaJCQk\ntOt3ZygQEVFHd/9gzs3N7ba9ZIePlEolrFar+N5qtUKlUnVoV1NTg4yMDGzbtg3Dhg0Tl4eGhgIA\nQkJCkJqaCovFIlWpRER0i2ShoNfrUVtbi/r6erS1taGkpAQpKSnt2nz99deYM2cONm3aBI1GIy6/\ndu0ampubAQBXr15FZWUlJkyYIFWpRER0i8PDR9u2bcMvf/lLDBjQs/yQy+UoLCyE0WiE3W5Heno6\ndDodioqKAACZmZlYvXo1mpqasGjRIgCAQqGAxWJBY2Mj5syZAwCw2WyYP38+kpKSejo2IiLqIYen\npM6fPx8HDx7E3Llz8eyzz0Kr1bqrtm7xlFQi/8BTUl29vu63nU5dp/DDDz+guLgY7777LmQyGRYu\nXIinnnoKwcHBLi22JxgKRP6BoeDq9bngOoWhQ4di7ty5mDdvHr755ht8/PHHiI2NRUFBgcsKJSIi\nz3MYCmVlZUhNTYXBYMD169dx+PBhbN++HTU1NfjrX//qjhqJiMhNHE40f/TRR3j55Zcxffr0dsvv\nvfdevPPOO5IVRkRE7udwT2HUqFEdAuHVV18FAMyYMUOaqoiIyCMchsLOnTs7LKuoqJCkGCIi8qwu\nDx/94x//wN///nfU1dW1u3CsubkZ06ZNc0txRETkXl2ekvrDDz+gqakJS5cuRV5enngKU3BwMEaM\nGOHWIjvDU1KJ/ANPSXX1+np5ncLly5cxZMgQXLx4sdOb23X1nAN3YSgQ+QeGgqvX18tQSE5ORnl5\nOdRqdaehcPr0addV2QsMBSL/wFBw9fpccEWzN2IoEPkHhoKr19f9trPLiebq6upuv3jSpEm9r4qI\niLxSl3sKBoOh2wfl7N27V7KinME9BSL/wD0FV6+Ph4+IqB9jKLh6fb08fLRnzx48+uijKC0t7XSP\n4fbzDoiIyHd0GQr79u3Do48+ik8++YShQETkJ3j4iIi8Gg8fuXp9fXyewoULF5CVlYXY2FhMmjQJ\nS5YswcWLF11aJBEReQeHoZCWlob7778fH330EbZs2YKQkBDMmzfPHbUREZGbOQyFxsZGrFy5EmPG\njEF4eDj+7//+D+fOnXPqy00mE7RaLSIjI5GXl9fh8w8++AAxMTGIjo7GtGnTUFNT43RfIiJyPYeh\nkJSUhOLiYty4cQM3btxASUkJkpKSHH6x3W7H4sWLYTKZcPz4cRQXF+PEiRPt2oSHh2P//v2oqanB\nypUr8fzzzzvdl4iIXK/LieagoCDxrKOrV69iwICb+XHjxg0MHjwYzc3N3X7xwYMHkZubC5PJBABY\ns2YNAGDp0qWdtm9qasKECRNw9uxZp/pyopnIP3Ci2dXr6+V1CleuXOnTihsaGhAWFia+V6lUqKqq\n6rL9unXrMGvWrB71zcnJEV8bDAYYDIY+1UxE5GvMZjPMZrPT7R0+oxm4+Su+trYWLS0t4rK7H9F5\nt+5ukXG3vXv3Yv369Thw4ECP+t4ZCkRE1NHdP5hzc3O7be8wFP75z3+ioKAAVqsVsbGxOHToEOLj\n47Fnz55u+ymVSlitVvG91WqFSqXq0K6mpgYZGRkwmUwYNmxYj/oSEZFrOZxozs/Ph8VigVqtxt69\ne3H06FEMHTrU4Rfr9XrU1taivr4ebW1tKCkpQUpKSrs2X3/9NebMmYNNmzZBo9H0qC8REbmewz2F\ngQMHYtCgQQCAlpYWaLVanDx50vEXy+UoLCyE0WiE3W5Heno6dDodioqKAACZmZlYvXo1mpqasGjR\nIgCAQqGAxWLpsi8REUnL4W0uUlNTsX79euTn52P37t0YNmwYbDYbKioq3FVjp3j2ERFQXr4fBQWV\naG2VIzDQhuzsJCQndz/f19/w7CNXr8+Ft842m824fPkyZs6ciXvuucclBfYWQ4H8XXn5fixZsgN1\nda+JyyIiViA/3+hTwcBQcPX6+njvIwA4cuQI8vPzUVNTA5VK5fFAICKgoKCyXSAAQF3da1i7dqeH\nKiJf4DAUVq9ejWeeeQaXLl3ChQsXsHDhQvzpT39yR21E1I3W1s6nBFtaAtxcCfkShxPNmzZtQk1N\nDQYOHAgAWLZsGWJiYrBy5UrJiyOirgUG2jpdPnCg3c2VkC9xuKegVCrx448/iu9bWlp4zQCRF8jO\nTkJExIp2yyIiliMrK9FDFZEv6HJPISsrCwAwdOhQjBs3TrwJ3s6dOzFlyhT3VEdEXbo9mbx27Urs\n2PEnGI0rkZU106cmmcn9ujz76N133xVvNyEIQofXCxYscF+VneDZR0Q/8eUzdHx5bID3nX3k1Cmp\nra2t+OqrrwAAWq0WCoXCdRX2EkOB6Ce+vOH05bEB3hcKDieazWYzFixYgAceeADAzVtTvPfee3j4\n4YddVyUREXkFh3sKkyZNQnFxMaKiogAAX331FdLS0lBdXe2WArvCPQWin/jyr2lfHhvgfXsKDs8+\nstlsYiAAwNixY2GzdX4qHBER9W8ODx9NnjwZzz33HH77299CEAR88MEH0Ov17qiNiIjczOHho9bW\nVhQWFooPwElISMCLL76IwMBAtxTYFR4+IvqJLx9i8eWxAd53+KjbULDZbBg/fjy+/PJLSYrrC4YC\n0U98ecPpy2MDvC8Uup1TkMvliIqKwpkzZ1xeGBEReR+HcwqXLl3CuHHjMGXKFAwePBjAzaTZtm2b\n5MUREZF7OQyFP//5zwDQbnfj9tXNRETkW7oMhR9//BFvvfUWTp06hejoaDz77LNecSUzERFJp8uJ\n5l//+te45557kJCQgIqKCqjVauTn57u7vi5xopnoJ748GevLYwP60UTziRMnsGnTJmRmZqK0tBT7\n9+/v8cpNJhO0Wi0iIyORl5fX4fMvv/wS8fHxGDhwIN588812n6nVakRHRyM2NpZ3ZSUicpMuDx/J\n5fJOXzvLbrdj8eLF2LVrF5RKJeLi4pCSkgKdTie2GTFiBNauXYutW7d26C+TyWA2mzF8+PAer5uI\niHqnyz2FmpoaBAcHi3+ff/65+HrIkCEOv9hisUCj0UCtVkOhUCAtLQ1lZWXt2oSEhECv13c5V8HD\nQ0RE7tXlLoDd3rdH+jU0NCAsLEx8r1KpUFVV5XR/mUyGGTNmICAgAJmZmcjIyOjQJicnR3xtMBhg\nMBj6UjIRkc8xm80wm81Ot+/5cSEn9fW01QMHDiA0NBTnz59HYmIitFotEhIS2rW5MxSIiKiju38w\n5+bmdtve4V1Se0upVMJqtYrvrVZrj57tHBoaCuDmIabU1FRYLBaX10hERO1JFgp6vR61tbWor69H\nW1sbSkpKkJKS0mnbu+cOrl27hubmZgDA1atXUVlZiQkTJkhVKhER3SLZ4SO5XI7CwkIYjUbY7Xak\np6dDp9OhqKgIAJCZmYnGxkbExcXh8uXLGDBgAPLz83H8+HF89913mDNnDoCbN+WbP38+kpKSpCqV\niIhuceoZzd6IF68R/cSXL/Dy5bEB/ejiNSIi8j8MBSIiEjEUiIhIxFAgIiIRQ4GIiEQMBSIiEjEU\niIhIxFAgIiIRQ4GIiEQMBSIiEjEUiIhIxFAgIiIRQ4GIiEQMBSIiEjEUiIhIxFAgIiIRQ4GIiEQM\nBSIiEjEUiIhIJGkomEwmaLVaREZGIi8vr8PnX375JeLj4zFw4EC8+eabPepLRESuJxO6e4JzH9jt\ndkRFRWHXrl1QKpWIi4tDcXExdDqd2Ob8+fM4c+YMtm7dimHDhuH3v/+9030dPXyayJ/48sPtfXls\ngPvH52jbKdmegsVigUajgVqthkKhQFpaGsrKytq1CQkJgV6vh0Kh6HFfIiJyPblUX9zQ0ICwsDDx\nvUqlQlVVlUv75uTkiK8NBgMMBkOv6yUi8kVmsxlms9np9pKFgkwmk7zvnaFAREQd3f2DOTc3t9v2\nkh0+UiqVsFqt4nur1QqVSiV5XyIi6j3JQkGv16O2thb19fVoa2tDSUkJUlJSOm1796RHT/oSEZHr\nSHb4SC6Xo7CwEEajEXa7Henp6dDpdCgqKgIAZGZmorGxEXFxcbh8+TIGDBiA/Px8HD9+HEFBQZ32\nJSIiaUl2SqrUeEoqOaO8fD8KCirR2ipHYKAN2dlJSE6e7umyXM6XT9v05bEB3ndKqmR7CkSeVl6+\nH0uW7EBd3Wvisrq6FQDgk8FA5Aq8zQX5rIKCynaBAAB1da9h7dqdHqqIyPsxFMhntbZ2viPc0hLg\n5kqI+g+GAvmswEBbp8sHDrS7uRKi/oOhQD4rOzsJEREr2i2LiFiOrKxED1VE5P0YCuSzkpOnIz/f\nCKNxJQDAaFyJ/PyZnGQm6gZPSSW/wNMa+y9fHhvgfaekck+BiIhEDAUiIhIxFIiISMRQICIiEUOB\niIhEDAUiIhIxFIiISMRQICIiEUOBiIhEDAUiIhIxFIiISMRQICIikaShYDKZoNVqERkZiby8vE7b\nZGdnIzIyEjExMTh69Ki4XK1WIzo6GrGxsZgyZYqUZRIR0S2SPaPZbrdj8eLF2LVrF5RKJeLi4pCS\nkgKdTie2qaiowKlTp1BbW4uqqiosWrQIhw4dAnDzTn5msxnDhw+XqkQiIrqLZHsKFosFGo0GarUa\nCoUCaWlpKCsra9dm27ZtWLBgAQBg6tSp+P7773Hu3Dnxc94am4jIvSTbU2hoaEBYWJj4XqVSoaqq\nymGbhoYGjBo1CjKZDDNmzEBAQAAyMzORkZHRYR05OTnia4PBAIPB4PJxEBH1Z2azGWaz2en2koWC\nTCZzql1XewOffvopRo8ejfPnzyMxMRFarRYJCQnt2twZCkRE1NHdP5hzc3O7bS/Z4SOlUgmr1Sq+\nt1qtUKlU3bY5e/YslEolAGD06NEAgJCQEKSmpsJisUhVKhER3SJZKOj1etTW1qK+vh5tbW0oKSlB\nSkpKuzYpKSnYuHEjAODQoUO47777MGrUKFy7dg3Nzc0AgKtXr6KyshITJkyQqlQiIrpFssNHcrkc\nhYWFMBqNsNvtSE9Ph06nQ1FREQAgMzMTs2bNQkVFBTQaDQYPHowNGzYAABobGzFnzhwAgM1mw/z5\n85GUlCRVqUREdItM6Ken+Dh6+DTRnfjw9/7Ll8cGuH98jradku0pUP9QXr4fBQWVaG2VIzDQhuzs\nJCQnT/d0WUTkIQwFP1Zevh9LluxAXd1r4rK6uhUAwGAg8lO895EfKyiobBcIAFBX9xrWrt3poYqI\nyNMYCn6stbXzHcWWlgA3V0JE3oKh4McCA22dLh840O7mSojIWzAU/Fh2dhIiIla0WxYRsRxZWYke\nqoiIPI2h4MeSk6cjP98Io3ElAMBoXIn8/JmcZCbyY7xOgQDwXPD+zpfH58tjA7zvOgXuKRARkYjX\nKTjAi7uIyJ8wFLrBi7uIyN/w8FE3eHEXEfkbhkI3eHEXEfkbhkI3eHEXEfkbhkI3eHEXEfkbhkI3\neHEXEfkbXrzm9Pp4AU1/xvH1X748NoAXrxERkRdjKDjN7OkCJGb2dAESM3u6AImZPV2AhMyeLkBi\nZk8X0I6koWAymaDVahEZGYm8vLxO22RnZyMyMhIxMTE4evRoj/q6l9nTBUjM7OkCJGb2dAESM3u6\nAAmZPV2AxMyeLqAdyULBbrdj8eLFMJlMOH78OIqLi3HixIl2bSoqKnDq1CnU1tbi7bffxqJFi5zu\nS0REridZKFgsFmg0GqjVaigUCqSlpaGsrKxdm23btmHBggUAgKlTp+L7779HY2OjU32JiMj1JLv3\nUUNDA8LCwsT3KpUKVVVVDts0NDTgm2++cdgXuDmL7k4yWa5b1+duHF//5svj8+WxAd41PslCwdkN\ndm9PK+2nZ9ISEXk1yUJBqVTCarWK761WK1QqVbdtzp49C5VKhevXrzvsS0RErifZnIJer0dtbS3q\n6+vR1taGkpISpKSktGuTkpKCjRs3AgAOHTqE++67D6NGjXKqLxERuZ5kewpyuRyFhYUwGo2w2+1I\nT0+HTqdDUVERACAzMxOzZs1CRUUFNBoNBg8ejA0bNnTbl4iIJCZQO9u3bxeioqIEjUYjrFmzptM2\nWVlZgkajEaKjo4Xq6mo3V9g3jsa3adMmITo6WpgwYYLw0EMPCceOHfNAlb3nzL+fIAiCxWIRAgIC\nhNLSUjdW13fOjG/v3r3CxIkThXHjxgkPP/ywewvsA0djO3/+vGA0GoWYmBhh3LhxwoYNG9xfZB8s\nXLhQuP/++4Xx48d32cYbti0MhTvYbDYhIiJCOH36tNDW1ibExMQIx48fb9emvLxceOyxxwRBEIRD\nhw4JU6dO9USpveLM+D777DPh+++/FwTh5n9SXxvf7XaPPPKIkJycLGzZssUDlfaOM+NramoSHnzw\nQcFqtQqCcHND2h84M7ZVq1YJS5cuFQTh5riGDx8uXL9+3RPl9sr+/fuF6urqLkPBW7YtvM3FHXp7\nbcW5c+c8UW6POTO++Ph4DB06FMDN8Z09e9YTpfaKs9e3rF27FnPnzkVISIgHquw9Z8b3r3/9C08+\n+aR4YsbIkSM9UWqPOTO20NBQXL58GQBw+fJljBgxAnJ5/3micEJCAoYNG9bl596ybWEo3KGr6yYc\ntekvG05nxnendevWYdasWe4ozSWc/fcrKysTr55397UufeHM+Gpra3Hp0iU88sgj0Ov1eP/9991d\nZq84M7aMjAx88cUXGD16NGJiYpCfn+/uMiXlLduW/hOzbtDbayv6y4alJ3Xu3bsX69evx4EDBySs\nyLWcGd9LL72ENWvWiLcPvvvf0ps5M77r16+juroau3fvxrVr1xAfH4+f//zniIyMdEOFvefM2F5/\n/XVMnDgRZrMZdXV1SExMxLFjxxAcHOyGCt3DG7YtDIU79PbaCqVS6bYa+8KZ8QFATU0NMjIyYDKZ\nut3d9TbOjO/IkSNIS0sDAFy4cAHbt2+HQqHoF6c8OzO+sLAwjBw5EoMGDcKgQYMwffp0HDt2zOtD\nwZmxffbZZ1ix4uaTECMiIjBmzBicPHkSer3erbVKxWu2LR6ZyfBS169fF8LDw4XTp08Lra2tDiea\nDx482K9zIRBzAAADtUlEQVQmYp0Z35kzZ4SIiAjh4MGDHqqy95wZ352eeeaZfnX2kTPjO3HihPCL\nX/xCsNlswtWrV4Xx48cLX3zxhYcqdp4zY3v55ZeFnJwcQRAEobGxUVAqlcLFixc9UW6vnT592qmJ\nZk9uW7incIe+XFvRHzgzvtWrV6OpqUk85q5QKGCxWDxZttOcGV9/5sz4tFotZs6ciejoaAwYMAAZ\nGRl48MEHPVy5Y86Mbfny5Vi4cCFiYmJw48YNvPHGGxg+fLiHK3feU089hX379uHChQsICwtDbm4u\nrl+/DsC7ti399nGcRETkejz7iIiIRAwFIiISMRSIiEjEUCAiIhFDgegO9fX1mDBhgtPtc3Jy8Oab\nbwIAVq1ahd27d3fZ9siRI1iyZAkAYN++fTh48GDfiiWSAE9JJeqDO684zc3t/pGKkydPxuTJkwHc\nvGI8ODgY8fHxktZH1FPcUyC6i91ux/PPP4/x48fDaDSipaUFdXV1eOyxx6DX6zF9+nScPHmyQ79n\nnnkGpaWlAIDDhw9j2rRpmDhxIqZOnYorV67AbDbj8ccfx5kzZ1BUVIS//e1vmDRpEj799FOEh4fD\nZrMBuHmzt/DwcNjtdreOmwjgngJRB7W1tdi8eTPefvttzJs3D6WlpdiwYQPeeustaDQaVFVV4cUX\nX+xwqEgmk0Emk6GtrQ1paWn48MMPMXnyZFy5cgWDBg0S2z3wwAN44YUXEBwcjFdeeQUAYDAYUF5e\njieeeAKbN2/Gk08+iYCAALeOmwhgKBB1MGbMGERHRwO4ecinvr4en332GX71q1+Jbdra2jrtKwgC\nTp48idDQUPFQUVBQUJdtb3vuuefwxhtv4IknnsC7776Ld955x1XDIeoRhgLRXQIDA8XXAQEBOHfu\nHO677z4cPXq00/Z338myN3e2fOihh1BfXw+z2Qy73d4vbk1BvolzCkQODBkyBOHh4diyZQuAm7/w\na2pqxM/v/MUvk8kQFRWFb7/9Fv/9738BAM3NzR3mB4KDg9Hc3Nxu2e9+9zvMnz8fzz77rFRDIXKI\noUB0l85++W/atAnr1q3DxIkTMX78eGzbtq3L9gqFAiUlJcjKysLEiRPFyerbcw4A8Pjjj+Pjjz9G\nbGwsPv30UwDAb37zGzQ1NeGpp56SeIREXeMN8Yi8xJYtW/DJJ5/gvffe83Qp5Mc4p0DkBbKysrBj\nxw5UVFR4uhTyc9xTICIiEecUiIhIxFAgIiIRQ4GIiEQMBSIiEjEUiIhIxFAgIiLR/wM87zTiUzt7\nrwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10d98aed0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEXCAYAAABCjVgAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDAUiIhL+D12qNgyo7pq+AAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10dc1bd50>"
]
}
],
"prompt_number": 37
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment