analysis_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal components analysis for order parameter construction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from analysis_tools.read_gsd import ReadGSD\n",
    "from analysis_tools.feature_creation import FrameToFeatures, TrajectoryToFeatures\n",
    "from analysis_tools.feature_creation import FrameToFeaturesComposition, TrajectoryToFeaturesComposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import array, arange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hard disks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_nn = 5000 #number of nearest nighbors for pca analysis\n",
    "split = 1 #chunks the data up so it can be processed by the pca tool if really large\n",
    "particle_inc = 500 #skip this many particles in generating features\n",
    "nn_inc = 10 #reduces the number of nearest neighbors to include as features\n",
    "method = ['distance']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#specify what data to read in and process\n",
    "file_data = [(arange(0.550, 0.690001, 0.005), '../hoomd_disks/trajectories_4000p'), \n",
    "             (arange(0.695, 0.820001, 0.005),'../hoomd_disks/trajectories_4000p_longer')]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Widom-Rowlinson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_nn = 5000 #number of nearest nighbors for pca analysis\n",
    "split = 2 #chunks the data up so it can be processed by the pca tool if really large\n",
    "particle_inc = 100 #skip this many particles in generating features\n",
    "nn_inc = 10 #reduces the number of nearest neighbors to include as features\n",
    "method = ['distance']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#specify what data to read in and process\n",
    "file_data = [(arange(0.100, 2.06001, 0.04), '../hoomd_disks/trajectories_ww_4000p')]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Density range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "etas = []\n",
    "[etas.extend(etas_) for etas_, _ in file_data]\n",
    "etas = array(etas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perfom PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import array_split\n",
    "from sklearn.decomposition import IncrementalPCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train on ideal gas structure first to identify trivial variance contributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_components_ig = 50  #for this the more the better, however, 50 is probably enough"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.55\n",
      "1\n",
      "eta=0.555\n",
      "1\n",
      "eta=0.56\n",
      "1\n",
      "eta=0.565\n",
      "1\n",
      "eta=0.57\n",
      "1\n",
      "eta=0.575\n",
      "1\n",
      "eta=0.58\n",
      "1\n",
      "eta=0.585\n",
      "1\n",
      "eta=0.59\n",
      "1\n",
      "eta=0.595\n",
      "1\n",
      "eta=0.6\n",
      "1\n",
      "eta=0.605\n",
      "1\n",
      "eta=0.61\n",
      "1\n",
      "eta=0.615\n",
      "1\n",
      "eta=0.62\n",
      "1\n",
      "eta=0.625\n",
      "1\n",
      "eta=0.63\n",
      "1\n",
      "eta=0.635\n",
      "1\n",
      "eta=0.64\n",
      "1\n",
      "eta=0.645\n",
      "1\n",
      "eta=0.65\n",
      "1\n",
      "eta=0.655\n",
      "1\n",
      "eta=0.66\n",
      "1\n",
      "eta=0.665\n",
      "1\n",
      "eta=0.67\n",
      "1\n",
      "eta=0.675\n",
      "1\n",
      "eta=0.68\n",
      "1\n",
      "eta=0.685\n",
      "1\n",
      "eta=0.69\n",
      "1\n",
      "eta=0.695\n",
      "1\n",
      "eta=0.7\n",
      "1\n",
      "eta=0.705\n",
      "1\n",
      "eta=0.71\n",
      "1\n",
      "eta=0.715\n",
      "1\n",
      "eta=0.72\n",
      "1\n",
      "eta=0.725\n",
      "1\n",
      "eta=0.73\n",
      "1\n",
      "eta=0.735\n",
      "1\n",
      "eta=0.74\n",
      "1\n",
      "eta=0.745\n",
      "1\n",
      "eta=0.75\n",
      "1\n",
      "eta=0.755\n",
      "1\n",
      "eta=0.76\n",
      "1\n",
      "eta=0.765\n",
      "1\n",
      "eta=0.77\n",
      "1\n",
      "eta=0.775\n",
      "1\n",
      "eta=0.78\n",
      "1\n",
      "eta=0.785\n",
      "1\n",
      "eta=0.79\n",
      "1\n",
      "eta=0.795\n",
      "1\n",
      "eta=0.8\n",
      "1\n",
      "eta=0.805\n",
      "1\n",
      "eta=0.81\n",
      "1\n",
      "eta=0.815\n",
      "1\n",
      "eta=0.82\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "randomize = True\n",
    "incpca_ig = IncrementalPCA(n_components=n_components_ig, whiten=False)\n",
    "\n",
    "frames = None\n",
    "features = None\n",
    "split_features = None\n",
    "\n",
    "for etas_, file_base in file_data:\n",
    "    for eta in etas_:\n",
    "        print 'eta={}'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True, randomize=randomize)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeatures(frames_partial, \n",
    "                                                    N_nn=N_nn, \n",
    "                                                    method=method, \n",
    "                                                    particle_inc=particle_inc, \n",
    "                                                    nn_inc=nn_inc)\n",
    "            incpca_ig.partial_fit(features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "        frames_split = None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train on actual data with trivial data variance removed by the ideal gas model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_components = 20 #this number will not affect the quality of the result just the computation time and amount of info returned"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.55\n",
      "1\n",
      "eta=0.555\n",
      "1\n",
      "eta=0.56\n",
      "1\n",
      "eta=0.565\n",
      "1\n",
      "eta=0.57\n",
      "1\n",
      "eta=0.575\n",
      "1\n",
      "eta=0.58\n",
      "1\n",
      "eta=0.585\n",
      "1\n",
      "eta=0.59\n",
      "1\n",
      "eta=0.595\n",
      "1\n",
      "eta=0.6\n",
      "1\n",
      "eta=0.605\n",
      "1\n",
      "eta=0.61\n",
      "1\n",
      "eta=0.615\n",
      "1\n",
      "eta=0.62\n",
      "1\n",
      "eta=0.625\n",
      "1\n",
      "eta=0.63\n",
      "1\n",
      "eta=0.635\n",
      "1\n",
      "eta=0.64\n",
      "1\n",
      "eta=0.645\n",
      "1\n",
      "eta=0.65\n",
      "1\n",
      "eta=0.655\n",
      "1\n",
      "eta=0.66\n",
      "1\n",
      "eta=0.665\n",
      "1\n",
      "eta=0.67\n",
      "1\n",
      "eta=0.675\n",
      "1\n",
      "eta=0.68\n",
      "1\n",
      "eta=0.685\n",
      "1\n",
      "eta=0.69\n",
      "1\n",
      "eta=0.695\n",
      "1\n",
      "eta=0.7\n",
      "1\n",
      "eta=0.705\n",
      "1\n",
      "eta=0.71\n",
      "1\n",
      "eta=0.715\n",
      "1\n",
      "eta=0.72\n",
      "1\n",
      "eta=0.725\n",
      "1\n",
      "eta=0.73\n",
      "1\n",
      "eta=0.735\n",
      "1\n",
      "eta=0.74\n",
      "1\n",
      "eta=0.745\n",
      "1\n",
      "eta=0.75\n",
      "1\n",
      "eta=0.755\n",
      "1\n",
      "eta=0.76\n",
      "1\n",
      "eta=0.765\n",
      "1\n",
      "eta=0.77\n",
      "1\n",
      "eta=0.775\n",
      "1\n",
      "eta=0.78\n",
      "1\n",
      "eta=0.785\n",
      "1\n",
      "eta=0.79\n",
      "1\n",
      "eta=0.795\n",
      "1\n",
      "eta=0.8\n",
      "1\n",
      "eta=0.805\n",
      "1\n",
      "eta=0.81\n",
      "1\n",
      "eta=0.815\n",
      "1\n",
      "eta=0.82\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "randomize = False\n",
    "incpca = IncrementalPCA(n_components=n_components , whiten=False)\n",
    "\n",
    "frames = None\n",
    "features = None\n",
    "split_features = None\n",
    "\n",
    "for etas_, file_base in file_data:\n",
    "    for eta in etas_:\n",
    "        print 'eta={}'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True, randomize=randomize)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeatures(frames_partial, \n",
    "                                                    N_nn=N_nn, \n",
    "                                                    method=method, \n",
    "                                                    particle_inc=particle_inc, \n",
    "                                                    nn_inc=nn_inc)\n",
    "            features_partial_ig_projection = incpca_ig.inverse_transform(incpca_ig.transform(features_partial))\n",
    "            incpca.partial_fit(features_partial - features_partial_ig_projection)\n",
    "            count = count + 1\n",
    "            print count\n",
    "        frames_split = None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the order parameters based on two nested models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.55\n",
      "1\n",
      "eta=0.555\n",
      "1\n",
      "eta=0.56\n",
      "1\n",
      "eta=0.565\n",
      "1\n",
      "eta=0.57\n",
      "1\n",
      "eta=0.575\n",
      "1\n",
      "eta=0.58\n",
      "1\n",
      "eta=0.585\n",
      "1\n",
      "eta=0.59\n",
      "1\n",
      "eta=0.595\n",
      "1\n",
      "eta=0.6\n",
      "1\n",
      "eta=0.605\n",
      "1\n",
      "eta=0.61\n",
      "1\n",
      "eta=0.615\n",
      "1\n",
      "eta=0.62\n",
      "1\n",
      "eta=0.625\n",
      "1\n",
      "eta=0.63\n",
      "1\n",
      "eta=0.635\n",
      "1\n",
      "eta=0.64\n",
      "1\n",
      "eta=0.645\n",
      "1\n",
      "eta=0.65\n",
      "1\n",
      "eta=0.655\n",
      "1\n",
      "eta=0.66\n",
      "1\n",
      "eta=0.665\n",
      "1\n",
      "eta=0.67\n",
      "1\n",
      "eta=0.675\n",
      "1\n",
      "eta=0.68\n",
      "1\n",
      "eta=0.685\n",
      "1\n",
      "eta=0.69\n",
      "1\n",
      "eta=0.695\n",
      "1\n",
      "eta=0.7\n",
      "1\n",
      "eta=0.705\n",
      "1\n",
      "eta=0.71\n",
      "1\n",
      "eta=0.715\n",
      "1\n",
      "eta=0.72\n",
      "1\n",
      "eta=0.725\n",
      "1\n",
      "eta=0.73\n",
      "1\n",
      "eta=0.735\n",
      "1\n",
      "eta=0.74\n",
      "1\n",
      "eta=0.745\n",
      "1\n",
      "eta=0.75\n",
      "1\n",
      "eta=0.755\n",
      "1\n",
      "eta=0.76\n",
      "1\n",
      "eta=0.765\n",
      "1\n",
      "eta=0.77\n",
      "1\n",
      "eta=0.775\n",
      "1\n",
      "eta=0.78\n",
      "1\n",
      "eta=0.785\n",
      "1\n",
      "eta=0.79\n",
      "1\n",
      "eta=0.795\n",
      "1\n",
      "eta=0.8\n",
      "1\n",
      "eta=0.805\n",
      "1\n",
      "eta=0.81\n",
      "1\n",
      "eta=0.815\n",
      "1\n",
      "eta=0.82\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "frames = None\n",
    "features = None\n",
    "raw_OPs = []\n",
    "\n",
    "for etas_, file_base in file_data:\n",
    "    for eta in etas_:\n",
    "        print 'eta={}'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True, randomize=randomize)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        means = []\n",
    "        raw_OPs_single = []\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeatures(frames_partial, \n",
    "                                                    N_nn=N_nn, \n",
    "                                                    method=method, \n",
    "                                                    particle_inc=particle_inc, \n",
    "                                                    nn_inc=nn_inc)\n",
    "            features_partial_ig_projection = incpca_ig.inverse_transform(incpca_ig.transform(features_partial))\n",
    "            transformed_features_partial = incpca.transform(features_partial - features_partial_ig_projection)\n",
    "            raw_OPs_single.append(transformed_features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "            \n",
    "        raw_OPs.append(raw_OPs_single)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute order parameter stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import array, mean, std, abs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "OPs = []\n",
    "OPs_std = []\n",
    "OPs_abs = []\n",
    "\n",
    "for single_eta in raw_OPs:\n",
    "    merged_data = []\n",
    "    for split in single_eta:\n",
    "        merged_data.extend(split)\n",
    "    \n",
    "    OPs.append(mean((split), axis=0))\n",
    "    OPs_std.append(std(split, axis=0))\n",
    "    OPs_abs.append(mean(abs(split), axis=0))\n",
    "\n",
    "OPs = array(OPs)\n",
    "OPs_std = array(OPs_std)\n",
    "OPs_abs = array(OPs_abs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Check out the results of PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explained variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:9: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n",
      "  if __name__ == '__main__':\n"
     ]
    },
    {
     "data": {
      "image/png": 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2XSX5pqbgLiIiVajVmnubMbMjgcmEwXZHufu65DbuflZi0T+BY8xsKnAU8H3C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\neOKJUtrkyfDUU+GZie7bDh8Og8omDq1Fz0XWtzU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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0c018ae0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "\n",
    "plt.plot(incpca.explained_variance_ratio_, marker='o', linewidth=1.0, markersize=12, color = 'red', markerfacecolor='None')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#plt.yscale('log')\n",
    "\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'Explained variance', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('Explained variance for pricipal components', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Principal component weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:16: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n",
      "  app.launch_new_instance()\n"
     ]
    },
    {
     "data": {
      "image/png": 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j9b2vpy0vLSjlvpn3cffzdzOwdCBfef9XAq3CqsFVWccCOzpOqCiK4iUfUwhO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ZH7JfUzMSmd9DrF4318+mPsbdxrakYrtjUSz5+hSvZ9OB62taIRHbBf9aMj0uHqpMX7b3122XPy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\n5AwGg8GQtxghZzAYDIa85f8HHeBN7calpiAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0c0189e950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "#plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "#plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "#plt.axvspan(0.781, 0.781001, alpha=1, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "for i in range(0,1):\n",
    "    p_data = incpca.components_[i]\n",
    "    plt.plot(range(len(incpca.components_[0])), p_data, marker='o', linewidth = 1.0, markersize=5, color = colors[i])  \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "#plt.xlim(0.1,3000)\n",
    "#plt.ylim(-1,0)\n",
    "#plt.ylim(0,0.5)\n",
    "#plt.ylim(-2,1.5)\n",
    "#plt.ylim(5, 13)\n",
    "#plt.ylim(1, 0.001)\n",
    "#plt.ylim(-2000.0, 2000)\n",
    "\n",
    "#plt.xscale('log')\n",
    "plt.xlabel(r'$n$th nerest neighbor', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'$P_{i}$ weight', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA feature weights', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Order parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:16: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n",
      "  app.launch_new_instance()\n"
     ]
    },
    {
     "data": {
      "image/png": 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IsW/bDm7DGMPSrUvJKcwhpzCHrLwsdhzewdYDW7lzxZ328/34+48IwvSPp9O+VXv7til7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\noIAlIiJh4f8BniMK6HeQSTQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0c064a0510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "#plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "#plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "for i in range(0,1): #12,13\n",
    "    p_data = OPs[:,i]\n",
    "    plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i], markerfacecolor='None')\n",
    "    p_data = OPs_std[:,i]\n",
    "    #plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i])\n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "#plt.xlim(0.60, 0.84)\n",
    "#plt.ylim(-0.1,0.1)\n",
    "\n",
    "#plt.ylim(-0.1,0.1)\n",
    "#plt.yscale('log')\n",
    "\n",
    "#plt.yscale('log')\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'$\\langle P_{i} \\rangle$ and $\\langle |P_{i}| \\rangle$', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# END"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.55\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.555\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.56\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.565\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.57\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.575\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.58\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.585\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.59\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.595\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.6\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.605\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.61\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.615\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.62\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.625\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.63\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.635\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.64\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.645\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.65\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.655\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.66\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.665\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.67\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.675\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.68\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.685\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.69\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.695\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.7\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.705\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.71\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.715\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.72\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.725\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.73\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.735\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.74\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.745\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.75\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.755\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.76\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.765\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.77\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.775\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.78\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.785\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.79\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.795\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.8\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.805\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.81\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.815\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.82\n",
      "\n",
      "1\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "randomize = False\n",
    "incpca = IncrementalPCA(n_components=16, whiten=False)\n",
    "\n",
    "frames = None\n",
    "features = None\n",
    "split_features = None\n",
    "\n",
    "for etas, file_base in file_data:\n",
    "    for eta in etas:\n",
    "        print 'eta={}\\n'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True, randomize=randomize)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeatures(frames_partial, N_nn=N_nn, method=method, particle_inc=particle_inc, nn_inc=nn_inc)\n",
    "            incpca.partial_fit(features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "        frames_split = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.1\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.14\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.18\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.22\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.26\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.3\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.34\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.38\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.42\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.46\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.5\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.54\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.58\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.62\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.66\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.7\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.74\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.78\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.82\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.86\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.9\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.94\n",
      "\n",
      "1\n",
      "2\n",
      "eta=0.98\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.02\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.06\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.1\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.14\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.18\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.22\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.26\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.3\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.34\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.38\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.42\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.46\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.5\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.54\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.58\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.62\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.66\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.7\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.74\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.78\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.82\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.86\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.9\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.94\n",
      "\n",
      "1\n",
      "2\n",
      "eta=1.98\n",
      "\n",
      "1\n",
      "2\n",
      "eta=2.02\n",
      "\n",
      "1\n",
      "2\n",
      "eta=2.06\n",
      "\n",
      "1\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "OPs = []\n",
    "frames = None\n",
    "features = None\n",
    "raw_OPs = []\n",
    "\n",
    "for etas, file_base in file_data:\n",
    "    for eta in etas:\n",
    "        print 'eta={}\\n'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True, randomize=randomize)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        means = []\n",
    "        raw_OPs_single = []\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeatures(frames_partial, N_nn=N_nn, method=method, particle_inc=particle_inc, nn_inc=nn_inc)\n",
    "            transformed_features_partial = incpca.transform(features_partial)\n",
    "            means.append(mean(transformed_features_partial, axis=0))\n",
    "            raw_OPs_single.append(transformed_features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "            \n",
    "        means = array(means)\n",
    "        op = mean(means, axis=0)\n",
    "        OPs.append(op)\n",
    "        raw_OPs.append(raw_OPs_single)\n",
    "    \n",
    "OPs = array(OPs)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['distance']"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import std, abs, power\n",
    "from scipy.stats import moment\n",
    "\n",
    "OPs = []\n",
    "OPs_std = []\n",
    "OPs_abs = []\n",
    "OPs_third = []\n",
    "for single_eta in raw_OPs:\n",
    "    merged_data = []\n",
    "    for split in single_eta:\n",
    "        merged_data.extend(split)\n",
    "    \n",
    "    OPs.append(mean((split), axis=0))\n",
    "    OPs_std.append(std(split, axis=0))\n",
    "    OPs_abs.append(mean(abs(split), axis=0))\n",
    "    OPs_third.append(moment(split, 4, axis=0))\n",
    "\n",
    "OPs = array(OPs)\n",
    "OPs_std = array(OPs_std)\n",
    "OPs_abs = array(OPs_abs)\n",
    "OPs_third = array(OPs_third)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "etas = arange(0.550, 0.820001, 0.005)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:23: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n"
     ]
    },
    {
     "data": {
      "image/png": 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2yFo/fjpVm9XGe1iLbV+HiEiQm2HtfYBTwM+enExExgAzgDSgv7asVG3g7gkB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\nAxwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe999959050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "plt.axvspan(0.76, 0.76001, alpha=1, color='black')\n",
    "\n",
    "#plt.axvspan(0.72, 0.72001, alpha=10, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "for i in range(0,1): #12,13\n",
    "    p_data = OPs[:,i]\n",
    "    plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i], markerfacecolor='None')\n",
    "    p_data = OPs_std[:,i]\n",
    "    #plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i])\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "#plt.xlim(0.60, 0.84)\n",
    "#plt.ylim(-0.1,0.1)\n",
    "\n",
    "#plt.ylim(-0.1,0.1)\n",
    "#plt.yscale('log')\n",
    "\n",
    "#plt.yscale('log')\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'$\\langle P_{i} \\rangle$ and $\\langle |P_{i}| \\rangle$', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Load in the saved model data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#load the pickled model\n",
    "with open('./processed_data/incpca.pkl', 'rb') as handle:\n",
    "    incpca = pickle.load(handle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.55\n",
      "0.555\n",
      "0.56\n",
      "0.565\n",
      "0.57\n",
      "0.575\n",
      "0.58\n",
      "0.585\n",
      "0.59\n",
      "0.595\n",
      "0.6\n",
      "0.605\n",
      "0.61\n",
      "0.615\n",
      "0.62\n",
      "0.625\n",
      "0.63\n",
      "0.635\n",
      "0.64\n",
      "0.645\n",
      "0.65\n",
      "0.655\n",
      "0.66\n",
      "0.665\n",
      "0.67\n",
      "0.675\n",
      "0.68\n",
      "0.685\n",
      "0.69\n",
      "0.695\n",
      "0.7\n",
      "0.705\n",
      "0.71\n",
      "0.715\n",
      "0.72\n",
      "0.725\n",
      "0.73\n",
      "0.735\n",
      "0.74\n",
      "0.745\n",
      "0.75\n",
      "0.755\n",
      "0.76\n",
      "0.765\n",
      "0.77\n",
      "0.775\n",
      "0.78\n",
      "0.785\n",
      "0.79\n",
      "0.795\n",
      "0.8\n",
      "0.805\n",
      "0.81\n"
     ]
    },
    {
     "ename": "IOError",
     "evalue": "[Errno 2] No such file or directory: './processed_data/raw_OPs_0.8100.pkl'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mIOError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-29-ac25164f1fca>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0meta\u001b[0m \u001b[0;32min\u001b[0m \u001b[0metas\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mprint\u001b[0m \u001b[0meta\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m     \u001b[0;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'./processed_data/raw_OPs_{:.4f}.pkl'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'rb'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mhandle\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m         \u001b[0mraw_OPs_split\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpickle\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhandle\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m         \u001b[0mraw_OPs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIOError\u001b[0m: [Errno 2] No such file or directory: './processed_data/raw_OPs_0.8100.pkl'"
     ]
    }
   ],
   "source": [
    "from numpy import mean, var, abs, arange, array\n",
    "import pickle\n",
    "\n",
    "#load the pickled model\n",
    "raw_OPs_mean = []\n",
    "raw_OPs_abs = []\n",
    "raw_OPs_var = []\n",
    "etas = arange(0.550, 0.820001, 0.005)\n",
    "for eta in etas:\n",
    "    print eta\n",
    "    with open('./processed_data/raw_OPs_{:.4f}.pkl'.format(eta), 'rb') as handle:\n",
    "        raw_OPs_split = pickle.load(handle)\n",
    "        raw_OPs = []\n",
    "        for split in raw_OPs_split:\n",
    "            raw_OPs.extend(split)\n",
    "        raw_OPs_mean.append(mean(raw_OPs, axis=0))\n",
    "        raw_OPs_abs.append(mean(abs(raw_OPs), axis=0))\n",
    "        raw_OPs_var.append(var(raw_OPs, axis=0))\n",
    "raw_OPs_mean = array(raw_OPs_mean)   \n",
    "raw_OPs_abs = array(raw_OPs_abs) \n",
    "raw_OPs_var = array(raw_OPs_var) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The amount of variance explained by the components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:12: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
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DxImhnGsqNxEpT1knF3cf7+5d3P296P37wPbAtcBk4Hpge3efWpBIK8H06fDg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe999856b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "\n",
    "plt.plot(incpca_ig.explained_variance_ratio_, marker='o', linewidth = 1.0, markersize=12, color = 'red', markerfacecolor='None')\n",
    "plt.plot([sum(incpca_ig.explained_variance_ratio_[:i]) for i in range(1,len(incpca_ig.explained_variance_ratio_))], marker='o', linewidth = 1.0, markersize=12, color = 'red')\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "plt.ylim(0.0,1.0)\n",
    "#plt.yscale('log')\n",
    "\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'Explained variance', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:12: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
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dJUBdvd4kHQb8BHiMFEb3NFiuUttb3ppVXdzLzsysv44HUkTcB1wFTCfduFruFFIN5fyI\nWFyaKWmGpBmV+5J0BPBD4CFgj8Ga6STtIGlMtfmkm3Ehjf7Qcr4Pycysv264hgRwHGnooDMl7Qvc\nCexKukdpLvCpivXvzKarnvctaW9SL7pRpFrXkVrzceDPRkT5RZ8PA2+RdAPwMLAMmEHqlTcaOIdU\n22o5N9mZmfXXFYEUEfdJ2gn4LCkM3gg8DpwBnBIRz9Sxm81ZXeN7b411HiT1uiu5FJgC7ADsA4wH\n5gO/Ac6JiMtzfpW6uYZkZtZfVwQSQEQ8DBxZ57prVH0i4jyqD5A60H4uJYXSkIspU3wNycysTMev\nIRWVm+zMzPpzIHWIm+zMzPpzIHXIykmTUpNdRKeLYmbWFRxInTJmDIwbB4sXD76umVkBOJA6aepU\nN9uZmWUcSJ00dap72pmZZRxIneQakpnZKg6kTvJD+szMVnEgdZKb7MzMVnEgdZKb7MzMVnEgdZKb\n7MzMVnEgdZKb7MzMVnEgdZKb7MzMVnEgdZKb7MzMVnEgdZKb7MzMVnEgdZKb7MzMVnEgdZKb7MzM\nVnEgdZKb7MzMVnEgdZKb7MzMVnEgdZKb7MzMVnEgddLEibB8ObzwQqdLYmbWcQ6kTpJ8HcnMLONA\n6jQ325mZAQ6kznPHBjMzwIHUeW6yMzMDHEid5xqSmRngQOo8X0MyMwNgrUY2kjQD2A6YFBHnt7ZI\nBeMmOzMzIGcNSdIrJN0G/AO4CDivbNmekpZIektrizjCucnOzAzIEUiStgGuA7YFzgB+U7HK9cDT\nwMGtKlwhuMnOzAzIV0P6DDAW2DUiPgz8sXxhRATwB2Dn1hWvANxkZ2YG5AukfYGLI+KfA6zzMLBJ\nc0UqGDfZmZkB+QJpHeCRQdYRqRZl9XKTnZkZkC+QngC2GmSdl5NqSVYvN9mZmQH5Auka4C2Stq22\nUNLOpGa9K1tRsMJwk52ZGZAvkE4FXgSul3Qs2bUiSS/PPv8SWAh8teWlHMncZGdmBuS4MTYi7pZ0\nEPAT4KxstoC/ZdNngbdFxEMtL+VI5iY7MzMg50gNEXGFpJcBRwC9wHrAAuBm4PsR8XTrizjCTZkC\nCxfCypUwyiM5mVlx5R46KCKeJd0Ye0bri1NAo0fDhAmwaFEKJzOzgvKf5N3AHRvMzHINHXSMpPsk\nVb3xVdKm2fKjWle8gvB1JDOzXDWkdwGPR8Rj1RZGxKOkG2ff3YqCFYprSGZmuQJpW+Cvg6zzN2BG\n48UpKHf9NjPLFUhTSV27B/IcaYih3CRtJulcSY9JWiapT9IcSXXtT1KPpMMk/VjSXZIWS1oo6TZJ\nH5FUc0gjSf8m6WeSnpS0VNLdkk6RNKGR75Kbm+zMzHL1snsc2GGQdXYAnspbCElbAjcB04DLgLuA\nXYATgP0k7RYR8wfZze7Aj0iPwLgWuJQUjvuTbtZ9m6R9I2JpxbF3JY1CMYb0jKeHgX2ATwP7Ztss\ny/udcnGTnZlZrhrStaRw+I9qCyXtDrwBuLqBcpxNCqPjI+KtEfFfEbEP8HVSU+EX6tjHPNL1q40j\n4uBsH0cD2wB/Bl4LfKCizKOB7wMTgYMj4l0R8XFgV+AXwG7AiQ18n3zcZGdmliuQvgy8APyfpNMl\nzcyGDZop6evAb4Fl2Xp1y2pHM4E+4JsViz8DLAYOl9Qz0H4i4vaIuCAiXqiYvxD4WvZxr4rN9iQ9\niv36iLi8bJuVwMeyj8dIUt1fqBFusjMzqz+QIuJu4O2k0JlNemLs37LpCcBS4JCIuDNnGfbOpldl\nQVB+zIXAjaQaTG/O/ZZbnk1frJi/Tza9onKDiLgfmAtsDmzRxLEH5yY7M7PcQwf9r6QtgFmkZq21\nSR0dbgZ+UMd1nmpKo4fPrbH8HlINahsaaw4EeG82rQyeeo69Tfa6r8FjD85NdmZmDQ0dNJ/VTWCt\nMDWb1vqNXJq/diM7l/RBYD/gduDcVh979uzZq9739vbS21tfRW7evHmr3k9ctoyeefN4qq+vrm2t\n//mz/Hz+muPz1x65A2k4kfQ2YA6pw8NBEbF8kE1ymzNnTsPbTp8+Pb3ZemtYvpye0mery3Sfr6b4\n/DXH56/1cgeSpGnATqQu1aOrrRMRP8yxy1ItZGqN5aX5g90D1Y+ktwIXAk8Ce2fXhIbk2Lm5yc7M\nrP5AkjQG+DbwHmp3hhAQQJ5AujubblNj+dbZtNZ1njULIR0C/JhUM9onIu4ZqmM3xL3szMxy1ZA+\nBxxJurh/AekG0spea424NpvOlDSqvKedpMmke4GWkDpODErSYcAPgEepXTMquQb4FOka06kV+9mC\nFFQPAgPto3nuZWdmliuQ3kWqKbwyIp5vVQEi4j5JV5F60n0A+EbZ4lOAHuA7EbG4NFPSjGzbu8r3\nJekIUseFB0lh9OAgh/8dcCewh6T9S/ciSRrF6vupvh0R0ej3q4ub7MzMcgXSNODsVoZRmeNIQwed\nKWlfUkjsSrpHaS6pFlOudK/TqhtWJe1NCqNRpFrXkVXuZ302Ilb1QoiIFZKOJNWULpJ0EfAQsC/p\nOtmNpNEi2mv8eIiAZctg3Li2H87MrBvlCaSHgLY80jSrJe0EfJbUfPZG0th5ZwCnRMQzdexmc1Zf\n23pvjXUeJPW6Kz/2LZJ2JtXGZgKTs/U+C3yp7ePYAUirm+2mTWv74czMulGeQDoP+ICkqRHR8val\niHiYdI2qnnXXqPpExHmkMjZy7H8ChzSybcuUmu0cSGZWUHnGsvsS8HvSWHZ7S2pLbamw3NPOzAou\nTw2pdFOpgP8DqDHmaETEiL7hti3c087MCi5PcNxAusfI2sGBZGYFV3cgRcRebSyHueu3mRVcnmtI\n1k6+hmRmBedA6hZusjOzgmtkcNWNSTeObgpUu4szIuJzzRascKZMgSef7HQpzMw6JlcgSToF+K+K\n7UoDqpa/dyDlNXUq3Htvp0thZtYxdTfZZYOW/g+pt93BpPD5AWmMu3OAlaTHPexTax82ADfZmVnB\n5akhHQs8AuwXES9m9yD1RcSFwIWSLgH+F/hJ64tZAO5lZ2YFl6dTw78Dv46I8kdOrHpAX0RcCVwJ\nnNSishWLe9mZWcHlCaQxwPyyz8+z5pNW7wB2bLZQheQmOzMruDyB9Diwcdnnh4AdKtbZhNY8tK94\n3GRnZgWXJ5D+Amxf9vkaYHdJh0vqkfQmUmeHv7SygIXhJjszK7g8gfQrYHtJL8s+fwlYQHrkw3PA\n5aSed//dygIWxuTJsHgxrFjR6ZKYmXVE3YEUEedFxMSIeCD7/DCwM/At4Crgu8DOEXFzW0o60o0a\nBT09sHBhp0tiZtYRTT0mIgunD7aoLFZqtlt77U6XxMxsyHksu27innZmVmA1a0iSXpq9fTQiVpR9\nHlREPNR0yYrIgWRmBTZQk10faVy67YC5ZZ8HE4Ps12qZMsU97cyssAYKjh+SwmVBxWdrF9eQzKzA\nagZSRMwa6LO1gQPJzAosz2jf75H0+nYWpvA8WoOZFVieXnbnAvu1qyCGR2sws0LLE0jzcq5vebnJ\nzswKLE/AXAHsLcmh1C5usjOzAssTLp8CJgPfk7R+m8pTbG6yM7MCy3O/0E9IXcDfAxwqqY/UjFfZ\nFTwiYt/WFK9g3GRnZgWWJ5D2Kns/Dtg2e1XyvUqNcpOdmRVY3YEUEb521G5usjOzAnPIdBM32ZlZ\ngTmQukmpyS7c6mlmxdPQIKiSNgM2JV1LWkNEXN9MoQpr3DgYPRqWLoUJEzpdGjOzIZUrkCTNBL4O\nzBhk1dENl6joSs12DiQzK5g8Y9n1Ar8C1gbOAgRcD5wD3JV9/iXw2dYXs0Dc087MCirPNaRPAEuB\nnSPihGzetRFxDLA98Hng/wEXtbaIBeOedmZWUHkC6TXA5RHxWOX2kXwauBM4pYXlKx73tDOzgsoT\nSFOB8keTvwD0VKxzI7BHs4UqNAeSmRVUnkB6Elin4vOWFeuMAXw1vhl+jLmZFVSeQJpL/wC6GXid\npG0AJG0EHATc07riFZBrSGZWUHkfP7GnpHWzz2eQakN/kfRHUk+7DYA5rS1iwTiQzKyg8gTSd0jX\nh5YDRMSNwCHAA6Redo8Dx0bED1tdyEJxk52ZFVTdgRQRz0XELRGxsGzeJRGxfURMiIjtIuK7jRZE\n0maSzpX0mKRlkvokzZG0zuBbr9rH6yR9TdLVkuZLCkm/H2SbGOB1c6Pfp2GuIZlZQdU9UoOkURGx\nsh2FkLQlcBMwDbiM1Py3C3ACsJ+k3SJifh27+gBwAOl+qXuBdQdefZUHgfOqzH+kzu1bx4FkZgWV\nZ+ighyX9CPhhRPyjxeU4mxRGx0fEN0ozJZ0OnAh8ATimjv18mfRk27uAl5CaE+vRFxEn5ylw23ik\nBjMrqDzXkCYCJwF/k/RHSR8o6+DQsKx2NBPoA75ZsfgzwGLgcEmV9zytISL+EBH/iIgVzZarYzxS\ng5kVVJ5A2hA4lNTb7hXAmcBjkn4haX9JjQ6ounc2vaqySTC7XnUjKQx7G9x/PdaW9F5Jn8yCtp3H\nGpib7MysoPJ0anghIn4WEW8CNgM+Rro36UDgElI4fV3SK3OWofQY9Lk1lpfua9om537z2BH4Hqlp\n8CzgD5Jul/TvbTxmdW6yM7OCauh5SBHxBPA14GtZAB1Bqj2dAHwo536nZtNav4VL89duoKj1OB34\nBSkQl5IerfFx4GDgGkmviIhHa208e/bsVe97e3vp7a2vcjVv3ryq87VoES9ZsICH+vrqLH4x1Tp/\nVh+fv+b4/LVHQ4FULiL+ImkRsAyY3Yp9DqWI+EjFrNuAQyRdRBp54qOkjhVVzZnT+H3A06dPr1Yg\nWLqU6ZttBmsNq1M55KqeP6ubz19zfP5ar+FHmEuaKuloSTeRerV9FHgeODfnrko1oKk1lpfmP5u/\nlE35djYd2sFiJZg82R0bzKxw8j4xdhSwH6mJ7i2kR5gHcDXpPp5LIuL5nGW4O5vWuka0dTatdY2p\nXZ7KpoP27mu5Uk+7dZvuxGhmNmzkuTH2a8C7SPcLiRQQPwDOj4hmbiC9NpvOrLz5VtJkYDdgCWkw\n16FUuhh0/xAf1z3tzKyQ8jTZnQiMJz2yfLeImBERpzYZRkTEfcBVwHTSSAvlTiHVUM6PiMWlmZJm\nSJrRzHGz/ewgaUy1+aQedwA/avY4uTmQzKyA8jTZvRO4NCKWtaEcx5GGDjpT0r6kJ8/uSrpHaS5p\n9IVyd2ZTlc+U9B/A+7KPk7Lp1pLOK60TEbPKNvkw8BZJNwAPkzpmzCA1S44mhe9PmvhejfEAq2ZW\nQHUHUkT8tF2FiIj7JO0EfJYUBm8kjR5+BnBKRDxT5662Il3fKjetYt6ssveXAlOAHYB9SDXA+cBv\ngHMi4vJ836RFXEMyswLqmn7FEfEwcGSd66rG/POoPkhqrf1cSgql7uJAMrMCarjbt7WRm+zMrIAc\nSN3INSQzKyAHUjdyIJlZATmQupGb7MysgBxI3cg1JDMrIAdSN3IgmVkB1ez2LSnvIKklERFHNbit\ngZ+JZGaFNNB9SLNqzA8qRkiomB+AA6kZfoy5mRXQQIH0sorPo4CvA7uTHl9+HTAP2Ig0xM+HgOtJ\nw/FYM9xkZ2YFVDOQIuLB8s+STiSF0asqlt0N/E7SD4A/AQcAjT+1zlb3sotIz0cyMyuAPJ0a3g/8\nrDKoSiLiAeDn2XrWjDFjYOxYWLKk0yUxMxsyeQJpOoM/tfWZbD1rlpvtzKxg8gTSv4DX11ooSdny\n+c0WynBPOzMrnDyB9HPgFZJ+Jqlfh4fs809Jj3Fo22MqCsU97cysYPI8fuLTwH8ABwMHSnoUeALY\nENiU9EC7PwInt7iMxeQmOzMrmLprSBGxiBRI/w30AS8Fds6mD5Ce6rp7tp41y4FkZgWT6wF9EfEC\n8EXgi5ImAVOBBQ6hNvAAq2ZWMA0/MTYLIQdRu7iGZGYFkzuQJG0AHARsB/RExPvK5r8M+HtEPN/S\nUhaRA8nMCibXaN+SjiJdP/omaaigI8sWbwj8AXhXqwpXaG6yM7OCqTuQJL0O+C4wFzgQ+Fb58oi4\nA/gH8NZWFrCwXEMys4LJ02T3ceBxYM+IeE7SK6us8zfgNS0pWdE5kMysYPI02e0E/CoiBmpHeoQ0\n+rc1y012ZlYweQJpLLB4kHXWBlY0XhxbxTUkMyuYPIHUB7x6kHV2JT2OwprlQDKzgskTSJcBu0s6\npNpCSUeSxrL7RSsKVnhusjO2cvObAAAgAElEQVSzgsnTqeE04FDgJ5IOJo3SgKQPkh7c9zbgHuAb\nrS5kIbmGZGYFU3cgRcQzkvYEfgiU15LOzKY3AO+KiMGuM1k9Jk6EF16A5cvTA/vMzEa4vGPZPQTs\nJWkHUvfu9YAFwM0R8ac2lK+4pNXPRFp//U6Xxsys7Roayy4i/ka658jaqfRMJAeSmRVArqGDbIj5\nOpKZFUiuGpKkMcABwC7AOqSH8lWKiDiqBWUzB5KZFUjdgSRpE+C3wAxAA6wagAOpFdz128wKJE8N\n6WukR078BDgHeBh4sR2FsoxrSGZWIHkCaSZwfUQc1q7CWAUHkpkVSJ5ODeOBW9pVEKvCTXZmViB5\nAukOYPN2FcSqcA3JzAokTyB9Bdhf0r+1qzBWwYFkZgWS5xrSk8AvgZsknQH8CXi22ooRcX0LymZu\nsjOzAskTSNeRunQL+J/sfS3V7k+yvFxDMrMCyRNIn2XgELJWcyCZWYHkGe375DaWw6pxk52ZFUjX\njGUnaTNJ50p6TNIySX2S5khaJ8c+Xifpa5KuljRfUkj6fR3b/Zukn0l6UtJSSXdLOkXShOa+VZNc\nQzKzAmlotO9Wk7QlcBMwjfRk2rtI4+WdAOwnabeImF/Hrj5AGmtvKXAvsG4dx94VuAYYA1xEGoFi\nH+DTwL6S9o2IZbm/VCs4kMysQGoGkqRrSNeMjoiIR7LP9YiI2DdnOc4mhdHxEbHqibOSTgdOBL4A\nHFPHfr4MfIoUaC8BHhhoZUmjge8DE4EDIuLybP4o4GfAQdnxv5Tz+7TG5MmwcCFEpOcjmZmNYAPV\nkPYiBdLEss/1yNXxIasdzQT6gG9WLP4M8H7gcEkfGexptBHxh7L91nP4PUnj811fCqNsPyslfYwU\nSMdI+nJEDH2HjrXWggkTYNGiFE5mZiNYzWtIETEqIkZHxNyyz/W88nb53jubXhURKyvKsBC4kRSK\nvTn3W499sukVlQsi4n5gLml0ii3acOz6uNnOzAqiGzo1bJtN59ZYfk823WaEHbs+pceYm5mNcN3Q\nqWFqNq31W7c0f+1uPPbs2bNXve/t7aW3t76K3Lx58+pab+Px43n67rtZ1tNT1/pFUe/5s+p8/prj\n89ceDQWSpM2ATYFx1ZYXaeigOXPmNLzt9OnTB19p2jQ2njgR6lm3YOo6f1aTz19zfP5aL+8jzGcC\nXyc9NXYgea4jlWohU2ssL82vOm5ekzp57Pr4GpKZFUTd15Ak9QK/IjVfnUUa0+560tNj78o+/5I0\nxFAed2fTWtdpts6mta7zNKOTx66PR2sws4LI06nhE6QbTneOiBOyeddGxDHA9sDngf9Hurk0j2uz\n6czs/p9VJE0GdgOWADfn3G89SvdW7Ve5QNIWpKB6ELi/Dceuj2tIZlYQeQLpNcDlEfFY5faRfBq4\nEzglTwEi4j7gKmA6aaSFcqcAPcD55fcgSZohabBmw3r8jlTmPSTtX7b/UaSbbAG+3ZF7kEocSGZW\nEHmuIU0FHir7/AIpLMrdCLyrgXIcRxo66ExJ+5JCYlfSPUpzSaMvlLszm/a7+1XSfwDvyz5OyqZb\nSzqvtE5EzCp7v0LSkaSa0kWSLiJ9x32BnbLv8/UGvk/rTJkCDww44ISZ2YiQ9wF961R83rJinTFA\n7gFJI+I+STuRrj/tB7wReBw4AzglIp6pc1dbAUdUzJtWMW9WxbFvkbQzqTY2E5hMaqb7LPCljo1j\nV+IakpkVRJ5Amkv/ALoZeIOkbSJirqSNSEPt3FN160FExMPAkXWuW3VcoIg4DzivgWP/Ezgk73ZD\nwoFkZgWR5xrSFcCekkojaJ9Bqg39RdIfST3tNgAavzHH1uRedmZWEHkC6TvAHsBygIi4kVSreIDU\ny+5x4NiI+GGrC1loriGZWUHkeWLsc8AtFfMuAS5pdaGsjAPJzAqiGwZXtYG4yc7MCsKB1O1cQzKz\nghjoibGNjk4QEVHZHdwaNX48rFwJy5bBuKpj2ZqZjQgD1ZBGkW48zftyrauVJDfbmVkh1KwhRcT0\nISyHDaTUbLfBBp0uiZlZ27g2Mxz4OpKZFUDDT4yVNIU0vt2CrEu4tYub7MysAHLVkCSNlfQpSfcB\nzwB9wDOS7svmj21HIQvPNSQzK4C6a0jZs4muBl4NBGlU7HnARsDmpMFI95e0b0QsakNZi8uBZGYF\nkKeGdArpkQyXAFtHxMsi4jUR8TLSk1UvBUqjZlsrOZDMrADyBNIhwO0RcXBE9HtAT/b5YOCvwNtb\nWD4DX0Mys0LIE0jrA1fWWpg9VfVKYL1mC2UVXEMyswLIE0h9wNqDrDM1W89ayYFkZgWQJ5DOAd4u\nabNqCyW9FHhHtp61kpvszKwA8tyHdDHpeUh/ljQHuB54AtgQ2BM4AfgdcEkWTqtExEOtKW5BuYZk\nZgWQJ5DuJ3X3FvC5KssF7J+9ykXO41glB5KZFUCeoPghKVxsqLnJzswKIM8TY2e1sRw2ENeQzKwA\nPLjqcOBAMrMCqDuQJO1R53onNF4cq2rSJFi8OD2oz8xshMpTQ7pa0n/XWihpbUmXAac3XyzrZ/Ro\n6OmBhQs7XRIzs7bJE0j3AqdI+q2kDcsXSHotcDvwFtKYdtZqbrYzsxEuTyC9GvgRsC9wu6TXAUj6\nBHAd6X6kD0bEQa0upOGedmY24uXpZbcEOELSNcBZwG8k/RN4OTAXeEdE/K09xTTXkMxspMt9w2pE\n/EDSJOAbwPbAU8AeEfFUqwtnZRxIZjbC5X1i7ChJXwDOABYBNwEbANdJ+vc2lM9Kpk51k52ZjWh5\nun2/hDRW3SeAvwM7RcR/AJ8iPaDvFknHtaWUlq4huYZkZiNYnhrS7cBuwLeA3oiYCxARpwJ7kZru\nviHp4lYX0nCTnZmNeHmuIY0CDo6INQInIm6StCPwfeCAVhXOyjiQzGyEyxNIr4yIvloLI+JZ4EBJ\nH2y6VLamKVPgiSc6XQozs7apu8luoDCqWO+shktjtbmGZGYj3ICBJGmPyoftDbL+jpLe03yxbA0O\nJDMb4QarIV0LzCqfIenjkubXWP+tpOtI1moeqcHMRrjBAklV5o0H1m5DWWwgriGZ2Qjn5yENFw4k\nMxvhHEjDhZvszGyEcyANF6UaUkSnS2Jm1hYOpOFi3DgYNQqWLu10SczM2qKeQPKf5N3CzXZmNoLV\nE0gnS1pRegGfBiifV7msEZI2k3SupMckLZPUJ2mOpHVy7mfdbLu+bD+PZfvdrMb6fZKixmteo9+n\nLdyxwcxGsHqGDqrW9XsguWtUkrYkPcpiGnAZcBewC3ACsJ+k3SKi1r1P5ftZL9vPNsA1wIXADOBI\n4E2SXhMR91fZdAEwp8r8RXm/S1s5kMxsBBswkCJiqK4xnU0Ko+Mj4hulmZJOB04EvgAcU8d+vkgK\no9Mj4iNl+zme9Ayns4H9qmz3bESc3HDph4qb7MxsBOt4p4asdjQT6AO+WbH4M8Bi4HBJPYPsZxJw\neLb+yRWLzwIeBF4vaYvmS90hriGZ2QjW8UAC9s6mV0XEyvIFEbEQuBGYCPQOsp9eYAJwY7Zd+X5W\nAldWHK/cOEnvlvRJSSdI2lvS6LxfpO0cSGY2guV5/ES7bJtN59ZYfg+pBrUNcHWT+yHbT6WNgPMr\n5j0g6ciI+N0Axxxafoy5mY1g3RBIU7NprT/9S/MHGz+v0f18H7gB+AewENgC+CDwfuA3WUeIv9Y6\n6OzZs1e97+3tpbd3sIpcMm9e/g58a69cSTz4IAv6+nJvO9I0cv5sNZ+/5vj8tUc3BFJHRcQpFbPu\nAI6RtAj4COl61IG1tp8zp1rnvPpMnz493wabbw6PP846ebcboXKfP+vH5685Pn+t1w3XkEo1l6k1\nlpfmPztE+yn5djbdo871289NdmY2gnVDIN2dTatd2wHYOpvWujbU6v2UPJVNB+zdN6SmTHGnBjMb\nsbohkK7NpjMl9SuPpMnAbsAS4OZB9nMz8DywW7Zd+X5GkTpGlB9vMKWLQdVupO0M97IzsxGs44EU\nEfcBVwHTgQ9ULD6FVEM5PyIWl2ZKmiFpRsV+FpF6yvWw5n1IH8z2f2X5SA2Stqt2f5Ok6aR7lwB+\nlPMrtY8DycxGsG7p1HAcacifMyXtC9wJ7Eq6Z2gu8KmK9e/MppXDGn0S2Av4sKRXALcC2wEHAE+y\nZuC9A/iIpOtJN84uBLYE3kR6Mu6vga82+d1axyM1mNkI1hWBFBH3SdoJ+CxpaJ83Ao+Thvs5JSKe\nqXM/8yW9hjTCw1uB3YH5pK7dn46IRyo2uZZ0/9IrSU2DPaROD78n1bbOj+iiBxC5hmRmI1hXBBJA\nRDxMGgS1nnVrDvgaEU+TBmU9oY79/A7onhtfB+NAMrMRrOPXkCyHnh54/nlYsaLTJTEzazkH0nAy\nahRMnuzrSGY2IjmQhhs325nZCOVAGm7c087MRigH0nDjGpKZjVAOpOHGgWRmI5QDabjxAKtmNkI5\nkIYbD7BqZiOUA2m4cZOdmY1QDqThxk12ZjZCOZCGGzfZmdkI5UAabtxkZ2YjlANpuHGTnZmNUA6k\n4cZNdmY2QjmQhhs32ZnZCOVAGm4cSGY2QjmQhhsPrmpmI5QDabiIgFtugRNPhKefhtGjYd11YdYs\nuPXWtNzMbBhzIA0Hy5fDUUfBoYfCDjvA+PEplO64A17+cnjHO9Ly5cs7XVIzs4Y5kLpdBBx9NDz2\nWAqgk05K15GWLIFNNkmf77gDHn00rVerplSqYR1xRKpZuYZlZl3GgdTtbr0Vrr0WfvEL6OlJ8yo7\nNvT0wMUXp/X++Mc191Few9p++xRgy5a5hmVmXcWB1O2+9S047rjVYQTVe9r19MCxx6b1y1WrYW2y\nCay1Vr4alplZm63V6QLYIC6/HL74xf7zpkyBm29OTW4bbwyTJqX5hx2WrjGVK9Ww7rijf6iVK9Ww\ntt8+1bB22aX138PMbBAOpG63YAFMm9Z/3oEHwk9+AmeeCY8/nq4HbbwxbLghPPNM6om38cbpdf75\n8La3pSa6iRNBqn6c8hpWtUCKSOF29tnwy1+mck2dCvvvn2pwO+9ce99mZnVwk123mzoVnnyy/7wP\nfAB+/3u47z5YvBgeeSTVpD70oRQsm22WtrniilQ7uuwy2GILmDABpk+H17wmhchFF8G//rV6v4cd\nlvZTqRXXoNypwswG4UDqdvvvDxdcUHu5lEJrxgzo64ODD4aPfAS++tW03cqVcNdd8Oyzqav4NdfA\nV74CW20F550HW24JO+4Is2enwKi8NtWKa1BtCLTNt9zSgWY20kSEXw2+0ulrzAMPPFDfijffHDF9\nesSiRQOvt3BhxOabR9xyS//566wT8eijtbdbvjwd44tfjNh99wiI2GmniJNOivjNbyKuuaa+4y9a\nlNarPP7KlRFHHhnx+tfX3seiRREzZ6b1Vq5cc/kLL6Rl06dHnHZaxKOPxgP33JO+12mnpflHHpnW\nq2XlyvQ93/OedE5GjUrTI45IZa523BGs7p8/q8rnr3HZ782qv1NdQ+p2u+wCe++drgMtXlx9nUWL\n4KCDYJ990rWccoPVsNZaC3bdFT7xCXjzm+Hww+H001PT36mnwsyZqfZx6qmpdvX889X3U6uXX7Vu\n69W2rdVtvUtraG5yNGuDWknlV5fUkCL61xC+/OWIRx5J8x55JH3efPPaNYRW1LB+8pOIT34yorc3\noqcnYq+9Io4+Os372tcifvCDiF/9KuKyyyLWXjvi6acjVqxI2x9xRKrF1OPLX46YNauu8q9x/oa4\nhhbLlw/rGpr/wm+Oz1/jGKCGpPBfdg2TFI2ev76+PqZPn17/BhGp9jBQL7da2x11VKpBXHxx9VpK\nqYa16abwve/17y03enSqTayVdchcuDB1qHjgAZg/P73+9a80feop+NOfUrkWLYJ11knXrV71qlSb\nWW+9/q911+3/WroUenvTvkpmzUq1mJNOGvz8nXYa3HknfP/7q+fdckuqGQ3U7R1S7XP77eGnP+3f\ny7B0/h57rHYtb/HiVIOtdv4g1byOPjrVAI87LnUemTYtdTy54IL0b7r33vCd78CYMdXLF032cqzY\nPhYsQE1sX/Relrn//9oqkoiIqj8sDqQmDGkgNaP8F+Kxx1b/hbjPPtV/Ia67bvplvskmgx/n0UfT\nfVDz56djPv102u7//i/9AisPsKefTq9nnln9fv781CS40UarQ+qWW1I398026xde85YvZ6Ptt4cN\nNoD114dx4/ofv6RGoFU1UgOtyvZ9S5YwfeLEhrfPHagjjAOpcQMFUsebvYbzi6FqsmuFlStT09AR\nR0Ssu27E6NFpOmtWxK231t6u2Sa3wTpVlHvkkVSmxx6LuOOOiOuvT01b55wT8dWvpibCY46JOOSQ\nWPLa10bssEPExhtHjBkTMWlSajqDiDe+MTWNffjDERMmRHzlKxGXXBLx+99H3HVXxL/+lZrcah2/\nld+/3ibTdjU51ti+389fA9vXffzy/TTTZOkmzxGDAZrsOv5LfTi/hlUgNarZa1BtCrR+52/lyohn\nn02BM2VKxC9/GfH976fjSmmfb3lLxGteE7HVVhFTp6ZfaGPHpv1vumnENttEvOIV6b/EzJkRBx4Y\ncdhhEePGRfznf0Z86lOpJ+IZZ6SAvPDC1AvxpptSeD78cAq7bgu0Zq/BNXv8iOavwXXhNbxh8/+3\nCw0USG6ya8KwabJrRjR5DareJq9Fi1KT189+1r/Jq9lrSLWaHCPStbHFi9NryZJ0XezQQ1OzW2n+\nrFnwpS+l61tLlqyev3BhelDiggXp9dxz6V6vJUvStZWpU9MQT3fdBXvskZq4yudPnpxGzih/LV4M\nRx6ZhoUqzZs9OzVDfuxjA/0r1f7+zZ6/Zps8o8kmy2a3h7Zcwxvya3DNbt9F3GTnGlJzmunlV2ry\nmTmz9l/ZCxfWbvKp9y/8Ia6hVVVq8nv66YgHHoi4/fb0l/ill0b86EcRZ58dceqpEf/1XxEf+lDE\nUUdFvPOdEQccEPG616UaHERsu23ES14Ssd566TOkpsf11kvzt9024pWvTPeNveENEYcckso9a1bE\n+PERn/98xNe/nmpyPT0R552X7ie79daIf/4z4qGH4sFbb4144omIJ5+MeOqp1Iz597+n7/vMM6nG\nuWBB6jU5d246/4sXRyxZEvH889VrFNWaPNtUw6t7+264D24k1BBbWMPETXYOpKY1eg0qoi2B1u/8\nNRBoa+imQCs3alTEsmUpDJ56KuLBB1Oo3HZbxHXXpe72P/1pxPe+F3H66Wn9T34y4vjjI9773tRk\n+YY3ROy5Z8SrXx0xY0bEppvGi+utF7H++ink1l03lXPq1PQrYcqUiMmT03W5UhhOmJDCbty4dM1u\n7NiIzTZLN1G/+c0R73tfxCc+kY7/859H3HBDxD33RLzrXc2dv043eXb6Glw33LbQikAsM1Agucmu\nCYVosmuVaLDbOlTtJbhGL7FavQSjO5scq8rT5FhNtV6GNbav+vOXY3uWLYMnnoB581a/5s6Fs86C\nN71p9bz7709jKG6ySeo9ueGGaTp1arqVoPy1eHEa8uorX1k97/jj4ctfTj0py9edMCE1fZY3g86f\nP2S9LNc4f7V6WTbbS7PTvTyb3b4Kd/tuEwfSEKoItKpt+LU00+19uAdap68hjR6duvn/61+rQ+rx\nx9M1uBUr4MUXV7+WLYNvfAOOOWb1vPPOg7e/PY3JWJq3YkW6Vle6dle6jgfp33rLLVcH1e9/Dwcc\nkEa+Lw+wnp50q8C4cTB2bJo+9xy85z1w442r55100urvP3Zs+j5Def46fdtCs9tX4UBqEwdS5wzZ\njcUwvAOt3r/wc25f9/HbVMNbQ0Sqje28c+oUUgqqmTPhu99N5SsPsMWLUwAuWwYvvJCmzz+ffka2\n2271vEcfTd97+fL0efRoGDeOFePGMXrSpLSspyd1QBk9Gm66KZ2viRPT/G9+Mw12vNFGq9ft6YHx\n4/vX+MaMSd/7kENS54XS/B13hN/9Lt2HN2ZM/20qayLtuA+v2e2rcCC1iQOpc4b8/A3XQKuxfb/z\n18D2dR+/078Qmw3E8pFKIlbV5B66+25euv76q3tdLl6cwu7AA9M5KPXI/PjH0/PJli7tv+7SpWvW\nEJcvh7//HbbeevW8hx9OzZWV6774Ymq2LO+lOWEC/OUv8PrXr5530UXw7nenn7fydcePTzW+sWPT\nz9zYseln+uij4corV8/bfXf4zW/gJS9ZPa9Ue1xrrcHPXxXuZedODSPOsDt/neoUUmP7B+bObWr7\nIRtLsUs7pVT9+avWKaXZTi21tl+xIp2TJ5+M6OtLHV1+/evUIeWKKyIuvjji/PNTp5avfjXiC19I\n99KdeGIah/I970k9PA86KN2jt99+aYxKiNh119SLc/vt0+fNN0/36m2wQer4MnFiukev0gsvpJ/r\nQeBedg6kkaZw56+ZQKuy/comt6/7+M12+2/TbQNV95Ej0Kr+/LWjl2Cne3k2u30VwyKQgM2Ac4HH\ngGVAHzAHWCfnftbNtuvL9vNYtt/NWn1sB1Ln+Pw1Z0jPXxtqeMPmPrjhXkNsdvsquj6QgC2BJ4AA\nLgW+BFyTfb4LWK/O/awH3J1td3W2n0uzz08AW7Ty2A6kzvH5a86wGUuxFdt38j644V5DbHb7KoZD\nIF2ZBcCHKuafns3/dp37+U62/tcq5h+fzb+ilcd2IHWOz19zCnf+WhxoQ3YNrtntOx2IVXR1IGU1\nlAAeAEZVLJsMLAIWAz2D7GcSsCRbf3LFslFZM1yU15KaPbYDqXN8/prj85dTp67BtWL7TgZiFd0e\nSO/LQuE7NZaXajD7DrKf/5etd2WN5aXa01GtOrYDqXN8/prj89ecYXf+OhmIFQYKpIqO5B2xbTad\nW2P5PcBMYBvSdaFm9kO2n1Yf28yse0nphuVBRlFo2/Z16oZAmppNF9RYXpq/dhv20/SxZ8+evep9\nb28vvb29A5cyM2/evLrWs+p8/prj89ccn7/26IZAGtbmzJnT8LYeqaE5Pn/N8flrjs9f643qdAFY\nXQuZWmN5af6zbdhPq45tZmZN6oZAujubblNj+dbZtNZ1nmb206pj53bzzTe3epeF4vPXHJ+/5vj8\ntUc3BNK12XSmpH7lkTQZ2I3UnXuwn4CbgeeB3bLtyvczitQ5ofx4rTx2bv6Bbo7PX3N8/prj89ce\nHQ+kiLgPuAqYDnygYvEpQA9wfkQsLs2UNEPSjIr9LALOz9Y/uWI/H8z2f2VE3N/Msc3MrD26pVPD\nccBNwJmS9gXuBHYF9iY1l32qYv07s2nlEOafBPYCPizpFcCtwHbAAcCTrBk6jRzbzMzaodYNSkP9\nAl4CfB94HHgBeJAaA5ySblatenMVaXDVM7LtX8j2N9jgqnUfu1o5/PLLL7/8qv9V63eqH9BnZmZd\noePXkMzMzMCBZGZmXcKBZGZmXcGBNIQkbSbpXEmPSVomqU/SHEnrdLps3S47V1Hj5YHFAEkHS/qG\npBskPZedmx8Nss1rJf1a0tOSnpf0N0mzJY0eqnJ3kzznUNL0AX4mQ9KFQ13+4a5bun2PeJK2JHUv\nnwZcRnoa7S7ACcB+knaLiPkdLOJwsIDU+7HSoqEuSJf6b2BH0vl4BJgx0MqSDgB+ASwFfgo8DbwF\n+DrppvBD2lnYLpXrHGb+SnradKU7WliuQnAgDZ2zSWF0fER8ozRT0unAicAXgGM6VLbh4tmIOLnT\nhehiJ5J+id4L7En/UUn6kTQFOAdYAewVEbdl8/8HuAY4WNKhEVG0v/LrPodlbvfPZWu4yW4IZLWj\nmaSn1n6zYvFnSE+lPVxSzxAXzUaQiLg2Iu6J+u7lOBjYALiwFEbZPpaSagkAx7ahmF0t5zm0FnMN\naWjsnU2vioiV5QsiYqGkG0mB1YsfBDiQcZLeDbyUFOJ/A66PiBWdLdawtE82vaLKsutJYzi+VtK4\niFg2dMUaljaRdDSwHjAf+ENE/K3DZRqWHEhDw0+mbY2NSOMVlntA0pER8btOFGgYq/kzGREvSnoA\neDmwBauH6rLqXpe9VpF0HXBERDzUkRINU26yGxqteipukX0f2JcUSj3AvwPfIQ2M+xtJO3auaMOS\nfyabtwT4HPBqYJ3sVbrutBdwtZvh83Eg2bAQEadExDUR8URELImIOyLiGOB0YAJrjvBu1lYR8WRE\nfDoi/hwRz2av60mtHbcAWwHv62wphxcH0tDwk2nb59vZdI+OlmL48c9km0TEi8D/l330z2UODqSh\n0bEn0xbAU9nUTSP51PyZlLQW8DLgReD+yuVWF/9cNsCBNDRK9zIM+ZNpC6A3m/oXZz7XZNP9qizb\nA5gI3OQedg3zz2UDHEhDwE+mbY6k7apdHJY0HTgr+zjgEDm2houAfwGHStqpNFPSeODz2cdvdaJg\nw4WkV1X+gZnN35d0gy345zIXPw9piFQZOqjyybSv9dBB1Uk6GfgI6f6YB4GFwJbAm4DxwK+BAyPi\nhU6VsRtIeivw1uzjRsDrSX+h35DN+1dEfLRi/YtIQwddSBo6aH9Sl/CLgLcX7QbRPOcw69q9Nen/\n9SPZ8h1YfY/X/0REKdytDg6kISTpJcBnSc0k65GeUHsJcEpEPNPJsnUzSXuShlV6Jau7fT8L3E66\nL+n8ov3irCYL7s8MsMqDETG9YpvdgE8BryGF+72kJyyfWcQbjvOcQ0lHAQcC2wPrA2OAJ4A/AGdF\nxA21dmLVOZDMzKwr+BqSmZl1BQeSmZl1BQeSmZl1BQeSmZl1BQeSmZl1BQeSmZl1BQeSmZl1BQeS\nmZl1BQeSmZl1BQeS2Qgh6R+SlkiaKOkTkv4paamkxyV9RdLoTpfRbCAeOshsBJA0gTTo7IOkUbzH\nkwYEHQu8izT+3+yIOKNjhTQbhGtIZiPDjsBoYAvgYuAVEfHBiHg/8P5snX1qbWzWDdbqdAHMrCVe\nmU0viYgvVyz7czb1H/SdCkMAAAETSURBVKDW1fwDajYyvCqbfrfKsmnZ1E8vta7mQDIbGV4JrAB+\nV2XZjtn0L0NXHLP8HEhmw5ykMaSHxN0ZEc9XWeXV2fRPQ1cqs/wcSGbD378B46gdOK8Gngf+OWQl\nMmuAA8ls+CtdP/pz5QJJE4HtgL8W8ZHkNrw4kMyGv1IPu2o1pFJ3cDfXWddzIJkNf68EVgK3V1lW\nqj05kKzr+T4ks2EuInYfYLE7NNiw4RqS2cj2amAp7tBgw4ADyWyEkjSe1APvrxHxYqfLYzYYB5LZ\nyLUjqVnezXU2LHi0bzMz6wquIZmZWVdwIJmZWVdwIJmZWVdwIJmZWVdwIJmZWVdwIJmZWVdwIJmZ\nWVdwIJmZWVf4/wHO1aWkzjw5HgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe99d6484d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "\n",
    "plt.plot(incpca.explained_variance_ratio_, marker='o', linewidth = 1.0, markersize=12, color = 'red', markerfacecolor='None')\n",
    "#plt.plot([sum(incpca.explained_variance_ratio_[:i]) for i in range(1,len(incpca_ig.explained_variance_ratio_))], marker='o', linewidth = 1.0, markersize=12, color = 'red')\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#plt.ylim(0.0,1.0)\n",
    "#plt.yscale('log')\n",
    "\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'Explained variance', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check out the components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:12: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
      "image/png": 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yDmaZFStWpFy2Nmxx5ZXs1rcvyw87jF9btMh0c5Kqa9cv2/j1S49fv5oRpid2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\nERFJLQUxERFJLQUxERFJrf8Hpa7MYiqZRjcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe99d9dd210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "\n",
    "plt.plot(incpca.explained_variance_ratio_, marker='o', linewidth = 1.0, markersize=12, color = 'red', markerfacecolor='None')\n",
    "#plt.plot([sum(incpca.explained_variance_ratio_[:i]) for i in range(1,len(incpca_ig.explained_variance_ratio_))], marker='o', linewidth = 1.0, markersize=12, color = 'red')\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#plt.ylim(0.0,1.0)\n",
    "#plt.yscale('log')\n",
    "\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'Explained variance', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "raw_OPs_abs = array(raw_OPs_abs)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#load the pickled model\n",
    "with open('./processed_data/incpca.pkl', 'rb') as handle:\n",
    "    incpca = pickle.load(handle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.55\n",
      "0.555\n",
      "0.56\n",
      "0.565\n",
      "0.57\n",
      "0.575\n",
      "0.58\n",
      "0.585\n",
      "0.59\n",
      "0.595\n",
      "0.6\n",
      "0.605\n",
      "0.61\n",
      "0.615\n",
      "0.62\n",
      "0.625\n",
      "0.63\n",
      "0.635\n",
      "0.64\n",
      "0.645\n",
      "0.65\n",
      "0.655\n",
      "0.66\n",
      "0.665\n",
      "0.67\n",
      "0.675\n",
      "0.68\n",
      "0.685\n",
      "0.69\n",
      "0.695\n",
      "0.7\n",
      "0.705\n",
      "0.71\n",
      "0.715\n",
      "0.72\n",
      "0.725\n",
      "0.73\n",
      "0.735\n",
      "0.74\n",
      "0.745\n",
      "0.75\n",
      "0.755\n",
      "0.76\n",
      "0.765\n",
      "0.77\n",
      "0.775\n",
      "0.78\n",
      "0.785\n",
      "0.79\n",
      "0.795\n",
      "0.8\n",
      "0.805\n",
      "0.81\n"
     ]
    },
    {
     "ename": "IOError",
     "evalue": "[Errno 2] No such file or directory: './processed_data/raw_OPs_0.8100.pkl'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mIOError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-24-ac25164f1fca>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0meta\u001b[0m \u001b[0;32min\u001b[0m \u001b[0metas\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mprint\u001b[0m \u001b[0meta\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m     \u001b[0;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'./processed_data/raw_OPs_{:.4f}.pkl'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'rb'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mhandle\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m         \u001b[0mraw_OPs_split\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpickle\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhandle\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m         \u001b[0mraw_OPs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIOError\u001b[0m: [Errno 2] No such file or directory: './processed_data/raw_OPs_0.8100.pkl'"
     ]
    }
   ],
   "source": [
    "from numpy import mean, var, abs, arange, array\n",
    "import pickle\n",
    "\n",
    "#load the pickled model\n",
    "raw_OPs_mean = []\n",
    "raw_OPs_abs = []\n",
    "raw_OPs_var = []\n",
    "etas = arange(0.550, 0.820001, 0.005)\n",
    "for eta in etas:\n",
    "    print eta\n",
    "    with open('./processed_data/raw_OPs_{:.4f}.pkl'.format(eta), 'rb') as handle:\n",
    "        raw_OPs_split = pickle.load(handle)\n",
    "        raw_OPs = []\n",
    "        for split in raw_OPs_split:\n",
    "            raw_OPs.extend(split)\n",
    "        raw_OPs_mean.append(mean(raw_OPs, axis=0))\n",
    "        raw_OPs_abs.append(mean(abs(raw_OPs), axis=0))\n",
    "        raw_OPs_var.append(var(raw_OPs, axis=0))\n",
    "raw_OPs_mean = array(raw_OPs_mean)   \n",
    "raw_OPs_abs = array(raw_OPs_abs) \n",
    "raw_OPs_var = array(raw_OPs_var) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'raw_OPs_mean' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mNameError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-41-d6c90233220e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mraw_OPs_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mraw_OPs_mean\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mraw_OPs_abs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mraw_OPs_abs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mraw_OPs_var\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mraw_OPs_var\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'raw_OPs_mean' is not defined"
     ]
    }
   ],
   "source": [
    "raw_OPs_mean = array(raw_OPs_mean)   \n",
    "raw_OPs_abs = array(raw_OPs_abs) \n",
    "raw_OPs_var = array(raw_OPs_var) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "etas = arange(0.550, 0.805001, 0.005)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'raw_OPs_mean' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mNameError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-40-91c3c7ffdb36>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0mcolors\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m200\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'green'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'purple'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'orange'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'teal'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'black'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'red'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m#12,13\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m     \u001b[0mp_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mraw_OPs_mean\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0metas\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmarker\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'o'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmarkersize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcolors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmarkerfacecolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'None'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m     \u001b[0mp_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mraw_OPs_var\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'raw_OPs_mean' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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iC3DKr6Wqnpjk7UleMcb4v6XM7Ph931rGGLeNMZ6V5GlJXl5VT1ja7OY3u47fSnJ4jHFk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\nKQEHaErAAZr6f89e5ubNhb1XAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe99afd5d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "plt.axvspan(0.76, 0.76001, alpha=1, color='black')\n",
    "\n",
    "#plt.axvspan(0.72, 0.72001, alpha=10, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "for i in range(1,2): #12,13\n",
    "    p_data = raw_OPs_mean[:,i]\n",
    "    plt.plot(etas, -(p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i], markerfacecolor='None')\n",
    "    p_data = raw_OPs_var[:,i]\n",
    "    plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i])\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "plt.xlim(0.60, 0.81)\n",
    "#plt.ylim(-0.1,0.1)\n",
    "\n",
    "#plt.ylim(-0.1,0.1)\n",
    "#plt.yscale('log')\n",
    "\n",
    "#plt.yscale('log')\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'$\\langle P_{i} \\rangle$ and $\\langle |P_{i}| \\rangle$', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "etas = arange(0.550, 0.82001, 0.005)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:20: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n"
     ]
    },
    {
     "data": {
      "image/png": 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zzjlXul67/zV2q92tSwU28ODmnHMuAzPj2V8+y/Dvd70VSrxb0jnnXNo12yp7VFJRXcFO\n/XbCzDp9OH97eHBzzrlurqWphennT2fxnxfTvKV564jIlsYWWj5qYepnpjL49NIbEZmNd0s651w3\nZmZbA1vT5qYds5EY262oHdLolj4Pbs45143lumZbc0Mzi2csZsW8FZ3Usvbx4Oacc91YnDXbmhua\nefaXz3ZwiwrDg5tzznVjcdZsK8aK2vny4Oacc91Y3DXbOntF7Xx5cHPOuW6suld1rPKdvaJ2vrpG\nK51zzrVburlsceauFWNF7Xx5cHPOuW4g01y2OEP7i7Gidr48uDnnXJlLncuWj2KtqJ0vD27OOVfm\ncp3Llk6xV9TOlwc355wrc3HmsgGoUmCU/Jpt2Xhwc865MhdnLhuEZ2uXb7y8A1vU8XwqgHPOlbly\nncuWjQc355wrc+U6ly0bD27OOVfmBo0ahCpyGwjSleayZePBzTnnytyICSNyvhvrSnPZsun6957O\nOee2SpeFpKpnFb326EXTpuzP3rraXLZsPLg551yZyJSFpLmhmQ/rPwSFbkeM7UZPdtW5bNnkHNwk\nVZtZflPbnXPOdaicspAYVFRV0GfvPjS810DzluYuPZctmzh3bvWS7gBuM7M3OqpBzjnn4ss1C0lL\nYwsN6xoY9+Q4BhxdPsEsVZwBJRXAD4DFkh6XdKakyg5ql3POuRjKdUXtfMUJbv2BrwJzgJOB+4Dl\nkq6VVNueRkj6haQnJC2T1CBpnaT5kq6UtGeGOiMlPRKVbZC0QNL4bAFX0mmSZklaL2mjpOckjWuj\nbeMkPR+VXx/VPy1L+UpJl0btSXwvj0gamfsn4pxz8ZTritr5yjm4mdlHZvYHMzsBGAJMJnRr/gh4\nI/oP/AxJ+UwvuBToAzwO/Ar4PdAMXAUskLR/cmFJZwCzgeOAB4FbgB7AjcA96S4g6bvADOATwN3A\nbYSAPUXSpAx1JgFTgH2j8ncDhwMzovOllld0/Rui9twSte84YHbUbuecK7jumIUkm7xGS5rZ68AE\nST8CxgIXA6cAnwfelfRb4H/MbEWOp9zFzLak7pR0LXA5IYD+v2jfLoRA0wKcYGYvRPt/AswExko6\nx8zuSTpPLTAJWAccZWZ10f5rgHnR9zLNzJ5NqjMSmAC8CQwzs/ej/dcDLwKTJD2cOFfknOjzmAuc\nnPieJN0KPA3cJmmmmX2Y4+finHM5qe5VHSvrfzlkIcmmXZO4zewj4C+Eu5MVgAh3Qz8F3pI0WVJN\nDufZIbBF7ou2g5L2jQX2Au5JBLakc1wRvf12ynkuAmqAW5KDURSwrovefiulTuL9tYnAFtWpA34d\nne/ClDqJ616R/D2Z2Tzg3qjdY9N8n8451y7dMQtJNnkHN0nDo9GTKwjdgX2Am4ChhGCyGLiE0H2Z\nr9Oj7YKkfSdF28fSlJ8NbAZGpgTVbHUeTSmTVx1JPYGR0fXnxLiOc861W3fMQpJNrPtSSTsD5wHf\nJDy7EjAf+C/gD2bWEBVdIOkuQmAYy453UpnOfxmwE7ArcBTwaUJg+3lSscHRdoenoWbWLOkt4DBg\nILAwhzrvStoE7Cept5ltltQHGABsNLN30zR1SbRN/tPnIKASWGpm6Tqz09VxzrmCGHD0AAafPpiF\n0xfSsqUlY7lyykKSTZxJ3LcDXwZ6A43AXcB/mdnz6cqbWYukWcS7U7kM6Jf0/jHgAjNbk7Rv12i7\nPsM5Evt3i1mnT1RucwdeI7XOdsaPH7/19fDhwxk+fHimot3GypUri92EkrNu3Tpqatrs7c9LbW0t\na9fWFeRcGzZAXWFOlZN8f1Zqa2up68yGdqAjrzmSN2e+SWNLI60trdCadLACKmsq2e8z+3HkNUfy\n9ttvF62dnSHOnduFhMEVtwJ3mNm6HOrMAq7J9QJmtg+ApH6ELr6fA/MlnWZmL8Voa5c0eXJ7enDL\nV21tbbGbUFLq6+vp379j/uquq6ujb9/agpzLDDr7ny6fn5W6urqy+Rmrm1VHj949OHva2Tx/0/Mh\nt+TmJqp7V5dlFpJs4gS3U8zs/+Kc3MyeAZ6J1yQws1XAg5JeInQlTiV0g8K2O6Bd09VN2v9B0r71\nQN/o2HtZ6qxP2ca9Rtw6zjkXW7rkyNW9qqmsqWT4pcM54JgD+NinPwaUV/COI86Akn0kHZGtgKRP\nSDq/nW3ayszeBl4DDpPUN9q9ONru8OxKUhVwIGGO3NKkQ9nq7EvoklxuZpuj624C6oGdouOpEqM3\nk5/hvUmYnjAwakcudZxzLpaWphYe+MoDTD1pKgsfWBiG/xs0bW5iy/tbeObnz/DAVx6gpSnzc7fu\nIE5wmwKMbqPMGcAdebcmvUT/S+Jfama0PSVN2eMIzwTnmllj0v5sdU5NKZNXnWjo/9zo+sfGuI5z\nzuUkNTlyuowkTZubWPTQIqafPx2z3DKWlKNCL1ZaCcT6NCUdImmHrjxJFdEk7r0JwSox1+x+YC1w\njqSjksr3BCZGb3+Tcro7CINgvpucKkzS7oRJ4hCeJSZLvP9xVC5Rpxb4TnS+1ECeuO7EqD2JOsOA\ns4E1wLTU79U553KRa3Lk5oZmFs9YzIp5uebRKD+FnqJ+CPB+m6W29wXgZ5KeBt4iPBPrBxxPGM6/\nkpABBQAz2yDpYkKQmyXpHkLmkS8ShvzfT5gwTVKdtyT9gDAP7wVJ9wIfEaYp7Af8Mjk7SVRnrqQb\ngO8TpjbcT0ipdTawB3BJSnYSCKm3xkTnnS9pBrBnVKcSuNjMNsT8fJxzDsgvOfJRvziq7cJlKGtw\nk/S7lF2jMyRJrgQOIHTH/SVmG/4KHEyY03YkYaj8JsKzqbuAm1JHZprZdEnHAz8GzgR6Am8QAtFN\nluZe3MxullRHmG5wPuGu9TVCNpE70zXMzCZI+jvhTu0bhIG1LwHXm9nDacqbpHMJ3ZMXESaxbyFM\nLp9oZnNjfC7OObedfJIje3BL74Kk10bIPjI0Q1kDniMkQc6Zmf0D2CEJcQ71niHc9cWpM4OQPDlO\nnSmE5425lm8mZGy5Mc51nHOuLZ4cOXdtBbcDo60Iow8nE7L2p2oB3o9GGTrnnOsAnhw5d1m/82go\nPgCSrgaeTN7nnHOu8wwaNYiF0xbm1DXZHZIjZxNnPberzWx2RzbGOedcZp4cOXcZPyVJB0Qv66M8\nkQdkKpvKzN5pd8ucc85tJ5EcedFDi7I+T0tOjlzuOSQzyfYnQB1hkMjHCSMXE+/bYm2c1znnXB4k\nMXrqaKafP51X73s1TNJO+l9ZFaKqZwhso6eORsptfbdylC0ITSV8bOtT3jvnnCuSyupKTpx4Ikse\nXcLAzwzkjcfeoLmhmapeVd0uOXI2GYObmV2Q7b1zzrniWHDXAv5p3D9x6q9ObbtwN+Xdh845VySZ\nsvsPGjWIkZeNpP+w/jt0LVqr8crUV/jytC8XqdVdgwc355wrgpamlq1JkJu3NG8d3t+0uYmF0xay\n5JElDD49PDurrK7cWu/tOW/TY6ce7DN0n2I1vUvINloyNfVWrszMvpZnXeecK3up2f13ON5qNG3a\nlt1/zB/GbL2De2XKKwy9YGi3HiySi2x3bhfkeU4DPLg551wG+WT3H3D0AD7a+BGLpi/i5J+f3Ekt\n7bqyBbcDsxxzzjmXpzjZ/Zs2NXH7yNuxVqOyupJee/Zi/dvr6bN3H797yyLbaMnuOfPPOec6WJzs\n/gDWEsq2fNTCxpUbufOkO9M+j3PbFHqxUuecc22Im91/O8Z2z+O682rb2Xj6Leec62Rxs/unk/o8\nzm0v251bHWFl7INS3rf1tbRjmuqcc+Vh0KhBqKL9z8sSq227HXn6Leec62QjJowIk7Y3te/uLbHa\nttuRp99yzrlOlsju/9r9r9Ha3Nquc3Xn1baz8QwlzjnXgTKl2BrwqQFQAVW9q2jZ0hJr9GSy7rza\ndjZ5fSqS9geOBHYldFvON7NlhWyYc851ddlSbNU9WUdFjwoOOOYAanap2ZrdH20b+t+W7r7adjax\ngpukQcB/ASelOTYT+I6ZeQewc67bayvFFkDrR6288/Q7DDljCD/68EdIYvlzy5l68tScnsd199W2\ns8l5npukg4G5wMmEEZFTgf+Mtkuj/U9H5ZxzrlvLJ8UWbHse11Z3Y/Jq225HcSZx/wzYE/hXYLCZ\nXWhmPzKzC4HBwKVAX+C6wjfTOee6ljgptpKH9CdW2x5yxhCq+1TvMGVAFaK6dzVDzhjS7VfbziZO\nt+TJwCNmdnPqATNrBX4l6fPAZwrVOOec66ripNhKHdJfWV3JmD+MYcW8FcydNJcljyzx1bZjihPc\negAvt1FmPnBs/s1xzrnyEDfFVupdniQGHD2As+47q5DN6jbidEu+ArT1PO1gYEH+zXHOufJQ3as6\nVnkf0l9YcYLbdcAYSaemOyhpFPAl4NpCNMw557qyOCm2fEh/4WVLnHx+mt2PAg9LegKYDawC+gHH\nE6YHzCAMKnHOuW4tTootH9JfeNnug6ewYy7JxJ8hnyH9wJEvAqcTpgc451y3lRjSv+ihRVlHTfqQ\n/o6RLbhd2BkNkLQnoTtzFHA4MAD4CPg7cAdwRzQaM1G+lrD6QCb3mtk5Ga41DvgOcCjQQhgAM8nM\nHs5QvhL4HuGzGAQ0AH8DJprZ3Ax1egH/DpwDfAzYAMwCrjSzhVna7ZwrI4kh/Q+e9yCv3vcqkrYb\nPakKUdUzBDYf0l942RIn39lJbTgL+A3wLvAk8A6hq3MM8FvgVEln2Y4r8r0CTE9zvn+ku4ikScAE\nYDlwG2H05znADEmXmNktKeUF3AOMBRYDtwB7AGcDsyWdaWYPpdSpAR4HjgFeAH4F7B99j6MknWRm\nz7X5iTjnykJldSWHnnUoaxauoe/gvj6kvxOVwvCc1wndmX9JuUO7HHgeOJMQ6Kal1HvZzK7K5QKS\nRhIC25vAMDN7P9p/PfAiMEnSw2ZWl1TtHEJgmwucbGZbojq3Ak8Dt0maaWYfJtX5PiGw3Q+cnfh+\nJN1LCMS/k3R48vfpnCtvL976Isf88BiO+Jcjit2UbiXOaMkOYWYzzWxG6n/4ZrYSuDV6e0I7L/Ot\naHttIrBF16gDfg3UsGM37Lej7RWJwBbVmQfcC+xFCH7A1ju9xHV+mPz9RHd4cwjdoce383txznUR\n7y15j5WvrOTQsYcWuyndTsbgJmmppDclHZj0PpevNwvYvsQwo3RPY/tL+qaky6Nttj+LEomeH0tz\n7NGUMkjqCYwENhOCUpt1CCuWHwC8bmbpngmmq+OcK2Mv3PoCQy8cSlVNKXSSdS/ZPvEKth8tmfo+\nk4I8FZVUBSSmI6QLSp+NvpLrzALGmdk7Sfv6EAapbDSzd9OcZ0m0TZ5kchBQCSw1s3SBNV2dwdE2\n06oI6eo457qITOuyDRo1iJGXjaT/sP7bDQppamjilTtf4eLnLy5iq7uvbANKarO97wQ/Bz5ByGf5\nv0n7NwP/QXiGtTTadwRwFXAi8ISkoWa2KTq2a7Rdn+E6if27Je3rrDrbGT9+/NbXw4cPZ/jw4ZmK\ndhsrV64sdhNKzrp166ipqemQc9fW1rJ2bV1BzrVhA9QV5lQ5yfdnpba2lro2Gtra1MqcCXNY9tdl\ntDS2QPTQoWlzE69Ne43FMxaz91F7U71TNfVP1dOypYWKqgp67NqDNxa8QV/1LdpoyO76O1SS98qS\nvkcYALIIOC/5mJmtBn6aUmW2pM8RBnp8Cvg6YaRilzJ58uRiN6Ek1dbWFrsJJaW+vp7+/TtmTlRd\nXR19+9YW5Fxm0Nn/dPn8rNTV1WWtZ2Y88JUHqH+inpaGlh0LtELLlhbefXr7jqHWpla2vLeFx7/6\nOINPD8P9K6srY7evELrj71Cc9dxmZshaklzmq9GipXmT9F1CYHoNONHM1uVSL+o+/G309rikQ4k7\npl1JL7H/gyLUcc6VuFzXZUvLoGlTE4seWsT086ez44wm11HijJY8Aahto8zHaMdoQEnjgZsJc9VO\njEZMxrEm2vZJ7Ii6J+uBnSTtm6bOoGib/KzsTcIk74HRs79c6iyOtpmeqaWr45wrcXHWZcskdUFS\n1/EKPRWgF+lHNrZJ0r8BNxKW1Tkx6n6MK/GQamnK/sTd5Clp6pyaUoZo6P9coDfpl/DZoQ4hIL4D\nHJIYYZpDHedciYuzLls2yQuSuo4XN7il/RdW8DHgC8CyuI2Q9BPCAJIXCROm12Yp+0lJO7Rb0smE\n1cAB7k45nJgv92NJuyfVqSWgXT6AAAAgAElEQVSk42okpPpK9ptoOzGaGpCoM4yQpWQNSRPLowwq\niev8Z3IbJZ1BCJKvAU9l+t6cc6Un7rpsmaQuSOo6VtYBJZJa2T6gXSXpqmxVCEvj5CzK93gNoRtw\nDvC9NKOK6sxsSvT6BmCQpLmEVFoQRksm5o/9JDXvo5nNlXQDIYPIAkn3E9JvnU1IqXVJSnYSCKm3\nxhAmas+XNAPYM6pTCVxsZhtS6twAnBbVeS5aPeEAQvqtzcBFnp3Eua6luld1fs/b0mhv96bLXVuj\nJWezLbgdR+h2q0tTrgV4D3iCbYM6cpXowqsExmco8xRhlQKAuwiJlocRuvqqCUvv3AfcYmbpJl1j\nZhMk/Z1wp/YNwmDel4Dr0yVONjOTdC6he/Ii4BJgC+EzSZs42cwaJX2WkDj5XMKd5AbCtIUrzey1\nzB+Dc64UDRo1iIXTFhaka9IXJO08WT9pMzsh8Tq6i7vDzK4pZAOi/JBXxSh/O3B7nteawrYgmUv5\nZsJzwBtj1NlMmKqQOl3BOdcFxVmXLRtfkLRzxfkz4kB8GLtzroyly0JS1bOK3n1709LYQmtz/k8V\nfEHSzpVzcDOztxOvJVUDHyfM3VoPLDSzwnRKO+dcEbQ0tTD9/Oks/vNimrc0b+2GbG5oZsPyDWCg\nSoERu4vSFyTtfLFGS0raU9JthDu4+YRFOOcDH0i6TVLfwjfROec6lpltDWxNm5t2DF7R24qqCnYe\nsDPVvatRhajuU82hYw9l4OcGUt0n7EumClHdu5ohZwzxBUk7Wc53bpL6Ac8AAwl3a88DK4F9gKHA\n14ATJR1jZqs6oK3OOdchcs1C0tLYQsO6BsY9OY4BR29bZNTMWDFvBXMnzfUFSUtEnGdu1xEC22Tg\nquRh8JJ2Aa4G/hW4lpDb0TnnuoQ4WUgSk7HH3rt1OUckMeDoAZx131kd1UQXU5zgdhowx8y+n3og\nCnSXSjoKOL1QjXPOuc4QJwuJT8buGuI8c9uZkHU/mznATvk3xznnOl/cLCQ+Gbv0xQlui4B0iYeT\n7cu2BMLOOdclVPeqjlXeJ2OXvjjB7VfA2ZKOSHdQ0lDgy4Rncs4512UMGjVoh5GOmfhk7K4hzp8f\nbwGPA89LmkpIQ7UK6EdY5uY84FGgTlLyemqY2ezCNNc55wovThYSn4zdNcQJbrMIsz1EGA35taRj\niT95vhh9pSrO8rPOOZeDAUcPYPDpg1k0fRHNWzI/T/PJ2F1HnOB2DRmWvHHOua5MEqOnjuamg29i\n47sbsRbbbvSkKkRVzxDYfDJ21xAn/dZVHdgO55zrFKn5I6/kSq7rcx37HrUvLU0tnPf4ecz79Tyf\njN3F+ZAf51y3kS5/pBBNm5t4Z/Y7VNZU8uKtLzLm92OorPanKV1Z3JW4kVQt6RRJl0YraCf295S0\nd7pVsp1zrtjazB9JSK+16KFFTD9/Omb+FKYri5s4+RTCYqV/AX7J9uuwDQXeJaxU7ZxzJSXX/JHN\nDc0snrGYFfNWdFLLXEfIObhFqbWmEwaVXAr8Ifm4mf2NMF3gS4VsoHPOFUI++SNd1xXnzu0nwGbg\nKDO7CViSpsw84J8K0TDnnCskzx/ZvcQJbscA081sZZYyy2g7RZdzznU6zx/ZvcQJbjsBa9so0zvm\nOZ1zrlN4/sjuJU4gqgcOa6PMUGBp/s1xzrmO4fkju5c4we1R4POSPp3uoKRTgZHAw4VomHPOFdKI\nCSNyvhvz/JFdX5z77p8B5wD/J+lmoBZA0ijgOOA7hKkANxS4jc45F0tqFpKmhiaqelbRu2/vMHm7\nJfPAEs8fWR7ipN+ql/Q54D7gB0mH/kxInPwmMMbM2nou55xzHSZdFhIIA0Q2LNsAgCoFhuePLGOx\nnpia2UuSBgOjgBHAnsB64G/AQ2bmw4ucc0WTmoUkk4qqCvrs3YeG9xpo3NxITZ8azx9ZZmIPBzKz\nFsLd2p8L3xznnMtfrllIWhpbaFjXwLgnx7Hfp/bDNnqqrXLjw/adc2XDs5C4hDjpt66Q1CQp7VNW\nSQMkfSTp3wrXPOecy51nIXEJce7cTgdmmVnabKJmVg88CYwuRMOccy4uz0LiEuIEt4OB19oo81pU\nLmeS9pT0dUkPSnpDUoOk9ZKelvS1TEvoSBop6RFJ66I6CySNl5RxESZJp0maFZ1/o6TnJI1ro33j\nJD0flV8f1T8tS/nKaDmgBVG71kXtHJn7p+Kca4uZsfy55fzprD9xXZ/ruHPgnSGtewyehaR8xfmX\n7UVInJzNFmDnmG04C/gNYY7ck8A7QD9gDPBb4FRJZ1nS4kqSzgCmRde7F1hHuLO8kZAD86zUi0j6\nLnAz8B5wN/ARMBaYIulwM7ssTZ1JwARgOXAb0IMw12+GpEvM7JaU8gLuic67GLgF2IOwDNBsSWea\n2UMxPx/nXIpMw/3j2JqF5L4OaKArujjBbTkwvI0ywwlpuuJ4Hfgi8Bcza03slHQ58DxwJiHQTYv2\n70IINC3ACWb2QrT/J8BMYKykc8zsnqRz1QKTCEHwKDOri/ZfQ1jJYIKkaWb2bFKdkYTA9iYwzMze\nj/ZfD7wITJL0cOJckXMIgW0ucLKZbYnq3Ao8DdwmaaaZfRjzM3KuW8o2GXvT6k20NLbkfe6tWUg8\nuJWlON2SjwHHSUq7GKmkc4DjCWm6cmZmM81sRnJgi/avBG6N3p6QdGgssBdwTyKwReW3AFdEb7+d\ncpmLgBrgluRgFAWs66K330qpk3h/bSKwRXXqgF9H57swpU7iulckAltUZx7hDnOvqP3OuTa0NLXw\nwFceYOpJU1n4wMIwvN+2TcZuV2DzLCRlL05w+wXwAfAHSQ9I+oakUdH2QeD3hDujnxewfYmnw8lP\nfU+Kto+lKT+b0HU6UlJNjnUeTSmTVx1JPQm5NTcDc2JcxzmXInUydj7djumoQlT3rmbIGUM8C0mZ\ni5t+6/PAnwgjIs9IOiygDjjLzJYXomGSqoDzo7fJAWZwtN1hDK+ZNUt6i7B6wUBgYQ513pW0CdhP\nUm8z2yypDzAA2Ghm76ZpXmKh1uS04QcBlcDSDJla0tVxzqWR62TsXKlCVPWq8iwk3Ujc9FsvSDqE\nMHhjOLAb4W7ub8AMMyvMT2Lwc+ATwCNm9r9J+3eNtusz1Evs3y1mnT5Ruc0deI3UOtsZP3781tfD\nhw9n+PC2HnGWv5Urs62N2z2tW7eOmpqatgvmoba2lrVr6wpyrg0boC7PU826ZlbsYf0ZCc5/8/yt\nb5tooi6pYbW1tdu9Lzfd9Xcon/RbTcAD0VeHkPQ9wmCORcB5HXWdUjN58uRiN6Ek1dbWFrsJJaW+\nvp7+/TvmWVFdXR19+9YW5FxmkO8/3YpZK6C17XK5qO5dnfVnqK6urux/xsr9+0un3em3JFVLOjJK\nqNxu0ZD9XxHmzJ1oZutSiiTugHYlvcT+D/Kosz5l2xHX+CDDcedcpFB3bb7oaPcVJ/3WlyXdJ2mP\npH0HAa8CLwCvRQNN8p4VKWk8YS7aPwiBLd399OJou8NPbHTtAwkDUJbmWGdfQpfkcjPbDGBmmwhT\nGnaKjqcaFG2Tn+G9SZieMDDDZ5CujnMujepe1QU5jy862n3FuXO7CBiScif1S0JGkieBBYRBJqnD\n43MS5aS8EXiZENhWZyg6M9qekubYcUBvYK6ZNeZY59SUMnnViYb+z42uf2yM6zjnUgwaNQhVtG8k\now/3797iBLdDCROega2Tqb8A3GdmnwGOJjwjix3cognYPydMjj65jQVP7wfWAudIOirpHD2BidHb\n36TUuQNoBL4bTehO1NkduDx6e2tKncT7H0flEnVqCauON0bnTZa47sSoPYk6wwhZStYQTUZ3zmU2\nYsKIvFNj+XB/B/EGlOxFSJGVMCKqfw+EgSaSHgfOjdOAKLfjNYQuvTnA99L8MNaZ2ZToOhskXUwI\ncrMk3UOYX/dFwpD/+wkTprcys7ck/QC4CXhB0r1sS7+1H/DL5OwkUZ25km4Avg8skHQ/If3W2YSU\nWpekZCch+izGROedL2kGYUHXswnTBC42sw1xPh/nuqMBRw9g8OmDWfTQoqzJjStrKrcuOtrU0ER1\n72of7u+AeMHtQ7YfLHE8IU3p00n78skteWC0rQTGZyjzFDAl8cbMpks6HvgxIT1XT+ANQiC6KTkP\nZVKdmyXVAZcR5s9VEAatXGFmd6a7qJlNkPR3wp3aNwjjt14Crjezh9OUN0nnEronLwIuIXwms4GJ\nZjY388fgnEuQxOipo5l+/nQWPrhwh2wkqhBVPUO34+ipo6msruwWox5d7uIEtyWEJMY1hKD2ZWBB\nShfix4BMz8rSMrOrgKvi1InqPUPoFo1TZwYwI2adKSQF1hzKNxOeHd4Y5zrOue1VVlcy5g9jmHLC\nFJo2N7F24VqaG5p9MrbLSZzg9j+EZ0xLCGmxaoFLU8r8M2H0pHPOtdvGlRtZvWA1ly67lB479Sh2\nc1wXkvOAkqjr7ueE0YC7EpZzuTlxPMqinxg56Zxz7fbK1Ff4+NiPe2BzscVNv3U520YXpnoB2B3Y\n1N5GOeecmTH/t/P50l1fKnZTXBdUsGVozewjwghE55xrt7dnv01lTSUDPuXP1Vx87U6/5ZxzHWH+\nb+fzya9/0uepubzkfOcmqZUwSrItZmYFuyN0zpW3TKtttza1csR5R2BmHuBcbHGC0GzSB7fdCDkb\newGv4ImBnXMp0gWw6l7VHHzqwTRuaGTZM8to3tK8dVHSxMTte8fcy+DTt81lcy5XcRYrPSHTMUk7\nE+Z1jSRk6HDOOQBamlq2rqqdHMCaNjexcNrCrHWbNjWx6KFFTD9/OmP+MMbv4FzOCvLMzcw+JGTw\naAauLcQ5nXNdn5ltDWxNm5u2BrY4mhuaWTxjMSvmreiAFrpyVbABJWbWSpjjNrpQ53TOdW31z9ez\neEYIbO3R3NDMs798tu2CzkUKPfCjJ2Gum3OumzEzPni1nqV3PcvqZ5bQ0tjE81Jed2s7nLvVeP0v\nvhSiy13BgpukIcBZhATGzrlupLW5hZevnM6qpxbT0tgMUe7yNDnM85ZtdQDnUsWZCvC7LOfYHziG\nkNl/QgHa5ZzrIsyMl6+czsqnFtO6pX3dj9nku76b657i/LRc0MbxRYSlYFIX8HTOlbEPXq1nVQcH\nNlWIQ0Yd0mHnd+UnTnA7MMP+VuB9M9tYgPY457qYpXc/G7oiO1BVzypGTBjRoddw5SXOPLe3O7Ih\nzrmuafXTS7Y+Y+sIVb3CoqT9h/XvsGu48lOQTmxJuwMfmZmvCOBcN9PS2DHdkamrbfsEbhdHzvPc\nJJ0s6T+jQJbYt7ekp4C1wDpJN3REI51zpauypjrvuqoQVb2qGPjZgXz8zI9T3acaVYjqPtUcOvZQ\nxs0ax5l/PNNTb7nY4ty5XQJ8wsx+mLRvEnAsYfj/TsC/Svqbmd1XwDY650rY3p8exLtPLMy5a1KV\nAgvdjYeMOoQRl41gwDBf1sYVVpzg9k/AU4k3knoBY4HHzezzUX7JvwPfAjy4OddNDPzqCFY/vYSW\nHEZLVveuZtyT4xhwtAcz17HipN/aG0hO7vYpQkaSKbA1v+TDwOBCNc45V/p2O2wA/Y4fTEXP7H8r\n+8AQ15niBLdGwrI2CccSlsCZnbRvA7BHAdrlnOsiJDH06tHsc/wQKtI8G1OFqO5dzZAzhvjAENdp\n4nRLvgWclPT+TGCJmdUn7dufMLjEOdeNVFRVcuTEMcw57zYqqiv5cMkqWhqbqe7tz9VcccQJbncC\nkyU9B3wEHA5cnVLmCGBxgdrmnOtCNte/z5ZV6zn5L5dS2aOKNWvglFOK3SrXXcXplvwNcA9wFCGP\n5MPALxIHJX2CEPBmFbB9zrkuYtlD8xlwyuFU9vAckK74cg5uZtZkZl8hLGmzq5mdYWaNSUVWAkcC\nNxe4jc65Etfa3Mqyh19h/zM+WeymOAfkkaHEzDZk2L8Wf97mXLe05m9v0GvvXdjl4L2L3RTngAKu\nxO2c676WPTSf/c84stjNcG4r7xx3zuUs3WrbFT2qsOZWPvblozEzH+rvSkJJ3LlJGivpZklzJG2Q\nZJLuzlC2Njqe6eueLNcZJ+l5SRslrZc0S9JpWcpXSrpU0gJJDZLWSXpE0sgsdXpJulrSYklbJK2W\ndJ+kj8f7VJwrLa3NLcy/4gH+9q2pvDtzYchIYtDa2Iy1tPLCpX9k/hUP0NrcUuymOlcyd25XENJ7\nbQSWA0NyqPMKMD3N/n+kKyxpEmGV8OXAbUAP4BxghqRLzOyWlPIijA4dS5jecAthgvrZwGxJZ5rZ\nQyl1aoDHCaNJXwB+RZj7dxYwStJJZvZcDt+bcyUll9W2W7Y0sfKpRbx85XSOnDgG8Ds4VzylEtwu\nJQSdN4DjgSdzqPOymV2Vy8mjO60JwJvAMDN7P9p/PfAiMEnSw2ZWl1TtHEJgmwucbGZbojq3Ak8D\nt0maGaUdS/g+IbDdD5xtZq1RnXsJgfh3kg5P7Heuq8h1te3WLc2semoxH7y6Avr5pG1XPCXRLWlm\nT5rZErMOW/HwW9H22kRgi65bB/waqAEuTKnz7Wh7RSKwRXXmAfcCexGCH7D1Ti9xnR8mB7DoDm8O\ncCgheDvXpcRZbbulsZmlv3+2g1vkXHYlEdzy1F/SNyVdHm2PyFI2kTbssTTHHk0pg6SewEhgMyEo\ntVkHOAg4AHjdzN7KsY5zXUKs1bbNWD3n9Y5tkHNtyNgtKemneZ7TzOw/8qwbx2ejr60kzQLGmdk7\nSfv6AAOAjWb2bprzLIm2hyTtOwioBJaaWbo/V9PVSayGkOm3Ol0d57qEuKtt53qX51xHyfbM7ao8\nz2lARwa3zdH5pwNLo31HENp7IvCEpKFmtik6tmu0XZ/hfIn9uyXt66w62xk/fvzW18OHD2f48OGZ\ninYbK1euLHYTSs66deuoqanpkHPX1taydm3dDvsrelTS2pj7KMiKHpVs2FBH3Y6n6jD5/qzU1tZS\n15kN7WTd9XcoW3A7sdNaEYOZrQZS7ypnS/ocYaDHp4CvE0YqdimTJ08udhNKUm1tbbGbUFLq6+vp\n379j1kSrq6ujb9/aHfb3O3Zw7qttS/Q7bjC77FJLZ//T5fOzUldXV/Y/Y+X+/aWTMbiZ2VOZjpUi\nM2uW9FtCcDuObcEtcce0a9qK2/Z/kLSvs+o41yXEWW27sqaKgf8yAu+YdMXUlQeUpLMm2vZJ7Ii6\nJ+uBnSTtm6bOoGib/KzsTaAFGCgp3R8A6eoklvrJ9EwtXR3nuoStq23XZJ89VNGzin7HD2a3w3y1\nbVdcpTLPrVASD6mWpuyfCZwHnALckXLs1KQyAJjZFklzCauNH8uO8+52qEMIiO8Ah0g6MM2IyXR1\nnCs56VJsVdZUs9fIg+mxSy8a123CWm37LkqJypoQ2IZe7attu+KLdecmaV9Jv5b0RpSOqiXNV4f2\nRkj6pKQd2i3pZMJkcIDU1F23RtsfS9o9qU4t8B2gkR2D3m+i7cRoakCizjBClpI1wLTE/miOXuI6\n/5ncRklnEILka0CX6u513UsFFWlTbLVsaWLlkwvZsuZDdj/yAPY5cQiVPatDUOtZzb6fOZQR/z2O\nT157JhVVlcX+NpzL/c5N0gDgeaAf8Cph4vPbhMAwMDrXy2QeLZjt3KOB0dHbfaLtCElTotdrzeyy\n6PUNwKDozmp5tO8Its0f+4mZzU0+v5nNlXQDIYPIAkn3E9JvnU1IqXVJSnYSCKm3xhAmas+XNAPY\nM6pTCVycZvmfG4DTojrPSXqCMPftLMIoz4s8O4krVWbGl/hS5hRb0Y3aB/9Yzj7HD+GUOT/yOzRX\nsuJ0S/6UEHg+b2Z/ldQK3GFm10jaj5CvsRY4OY92DAXGpewbGH1BCKKJ4HYX8CVgGKGrrxpYBdwH\n3GJm6SZdY2YTJP2dcKf2DaAVeAm43sweTlPeJJ1LSL91EXAJsAWYDUxMDaBRnUZJnwX+HTiXcCe5\ngTBt4Uoze63tj8K54lgzfw2DGRwrxdbun/AUW640xQlunwceM7O/ph4ws+WSziIkLb4a+F6cRkQ5\nIq/KseztwO1xzp9UdwowJUb5ZuDG6CvXOpsJfwjkOwneuaJY8N8LqMrxv4REiq1//tnYtgs7VwRx\nnrntQ+iOTGgBeiXemNlGQkb8MwrTNOdcZ1r2xDIqcv0vwVNsuRIXJ7htIDynSnifkNYq2XpCQmHn\nXBfTvCXeWDBPseVKWZzg9jZhbbKEV4CTJPUGiEYHfo5tgzycc11IVc94M4Mq25jz5lwxxQluTwAn\nSqqO3t8J9AfmRuuiPQMcRlgOxjnXxex/8v60kuNgXom9j/Uc4K50xfnT63ZCV2Rf4F0zu1vSPxNG\nESaWm7kHuLawTXTOdYYjvnkEix9eTI/tnj6kl0ix5VypyvnOLVpM9BfJy8aY2aXAvsAIYF8z+0ry\nwp7Oua5jryP3YjGLqWije9JTbLmuoN25Jc1sjZk9Z2arCtEg51xxSOJBHmSf47dlH0kpQGXPavY5\nfoin2HIlz58IO+e2aqWVIyeO4YNXV7DwpsdZ9/I7YKEbcu9jD+Ggr45gt8N84rYrfbGCm6Q9CNk6\njgZ2J6ShSmVmlk+WEudcCZDE7p8YwD4nDGHng/bm8H/7QrGb5FxscXJLDgFmEeaxZeuPyGE1Q+dc\nqduwZBW7H75fsZvhXF7iPHObBOwN/IKQ87HazCrSfHlKcOfKwIdLVrHLIf2K3Qzn8hKnW/JY4C9m\ndnlHNcY5Vxpam1v58K017HzQ3sVuinN5iXPnJsJ6ZM65Mrfpnffo1W8Xqnq1PefNuVIUJ7i9CAzu\nqIY450rHhiWr2Plg75J0XVec4HYN8AVJJ3RQW5xzJWLDkpXsMsiDm+u64jxz2x94CPg/SX8k3Ml9\nkK6gmU0tQNucc0Xy4ZLVHPClTxa7Gc7lLU5wm0IY5i/gvOgrddi/on0e3JzrwvzOzXV1cYLbhR3W\nCudcyfjog800b2qk1767FbspzuUt5+BmZnd2ZEOcc6Vhwxur2fngfqjCc0e6rqvdiZOdc+XFuyRd\nOYidODlaeXsMcCSwG7AeeAl40Mw2FbZ5zrnO9uGSVZ4c2XV5cRMnf4GwAvcebJ9f0oAbJV1oZg8X\nsH3OuU62YckqDhjtIyVd1xYncfIngQcIKwH8HpgJvEtYrPQk4FzgfknHmNmLHdBW51wHq6CCD5d6\n2i3X9cW5c/sx4Q7tWDP7W8qxKZJ+TVg14HLgzMI0zznXmfZgD3rutTNVfWqK3RTn2iXOgJJjgT+l\nCWwAmNlzwP1ROedcF9SPfj6YxJWFOMFtV2BZG2XeAXbJvznOuWLqRz/PKenKQpzgtoKwAnc2RxGe\nwznnuqB92MfXcHNlIU5wewQ4SdK/S9puQVJJFZImAJ+JyjnnuiDvlnTlIs6Akv8ARgPXAt+UNIdw\nl7YP8GmgFlgJTCxwG51znaDxg0Z60pPe/XcvdlOca7ec79zMbCVwDPBX4GPAV4EfEBIoHxjt/7SZ\nxeqWlDRW0s2S5kjaIMkk3d1GnZGSHpG0TlKDpAWSxqfeUabUOU3SLEnrJW2U9JykcW1cZ5yk56Py\n66P6p2UpXynp0qg9DVH7HpE0su1PwrniWrdwHatZ7Wm3XFmINYnbzOqAz0saQMhQsishQ8l8M6vP\nsw1XAP8EbASWA0OyFZZ0BjAN2ALcC6wDTgduJATfs9LU+S5wM/AecDfwETCWMIXhcDO7LE2dScCE\nqE23AT2Ac4AZki4xs1tSygu4JzrvYuAWwmT3s4HZks40s4dy+DycK4r3Fr7HKlYVuxnOFUTs9FsA\nUSDLN5ilupQQQN4AjgeezFRQ0i6EQNMCnGBmL0T7f0KYVD5W0jlmdk9SnVpgEiEIHhUFaCRdA8wD\nJkiaZmbPJtUZSQhsbwLDzOz9aP/1hHXsJkl6OHGuyDmEwDYXONnMtkR1bgWeBm6TNNPMPszjM3Ku\nw617bR0rWVnsZjhXEEVPnGxmT5rZEjNLXRsunbHAXsA9icAWnWML4Q4Q4NspdS4CaoBbkoNRFLCu\ni95+K6VO4v21icAW1akDfh2dL3UJoMR1r0gEtqjOPMId5l5R+50rSesWrvM7N1c2Mt65SfodISPJ\n5Wa2KnqfCzOzrxWkdTs6Kdo+lubYbGAzMFJSjZk15lDn0ZQyuVznUeAnUZkrAST1BEZG15+Toc55\nUZ070hx3rqhaW1p5f/H7rGZ1sZviXEFk65a8gBDcfgGsit7nwoCOCm6Do+3rO1zUrFnSW8BhwEBg\nYQ513pW0CdhPUm8z2yypDzAA2JhhcMySaHtI0r6DCDk3l5pZc451nCsaM2PN/DUsuHUBy2Yuo3lL\n+LE9ndN5/x/17HZYf8JjZOe6pmzB7cBoW5/yvph2jbbrMxxP7E9eQjiXOn2icps78BqpdXYwfvz4\nra+HDx/O8OHDsxXvFlau9GdAqdatW0dNTf65H1ubW3n5ypdZPXs1LY0t4c/RyKEcyrPfnMLuI/bj\noMuOpaIq/ycXGzZAXV3e1WPL92eltraWus5saCfrrr9DGYObmb2d7b0rvMmTJxe7CSWptra22E0o\nKfX19fTv3z+vumbGk995MgS2LS07HK+ggtbGZt7/23KW3zyfIyeOyfsOzgw6+58un5+Vurq6sv8Z\nK/fvL52c/yyT9FNJx7VR5lhJP21/szJK3AHtmuF4Yv8HedRZn7LtiGt8kOG4c51izfw1vP1/b6cN\nbMlatzSz6qnFfPDqik5qmXOFFafP4SrghDbKHEc0yKKDLI62Ozy7klRF6DptBpbmWGdfQpfkcjPb\nDBCtJl4P7BQdTzUo2iY/w3uTMD1hYNSOXOo41+kW/PcCmhvTPRbeUUtjM0t//2zbBZ0rQYWeClAN\ntBb4nMlmRttT0hw7DugNzE0aKdlWnVNTyuRVJxr6Pze6frolfzJdx7lOteyJZbn/hpqxeo7/Pea6\npkIHt08Cawt8zmT3R5IwCfQAABmUSURBVOc/R9JRiZ3RUPxETsvfpNS5A2gEvhtN6E7U2Z2wsCrA\nrSl1Eu9/HJVL1KkFvhOdL3VIf+K6E6P2JOoMI2QpWUPIrOJc0SRGReaqJce7POdKTdYMJZJS7zQu\nkHRCmqKVwP6EnJN/jNMASaMJCZkhJGEGGCFpSvR6bSI9lpltkHQxIcjNknQPIfPIFwlD/u8nTJje\nyszekvQD4CbgBUn3si391n7AL5Ozk0R15kq6Afg+sEDS/YT0W2cTUmpdkpKdBELqrTHReedLmgHs\nGdWpBC42sw1xPhvnCq2qZxXNDbkHrMqavJIYOVd0bf3knpD02giZ/2vTlGsl5G28l5BOK46hQGoC\n44HRF8DbwNbcj2Y2XdLxwI+BM4GehNRd3wduSpfpxMxullQXned8wh3ra4RsInema5SZTZD0d8Kd\n2jei7/El4HozezhNeZN0LqF78iLgEkL+y9nARDOb2/ZH4VzH2v/k/Xnrkbdy65qU2PtYn5rpuqas\nwc3MtnZbSmoFrjKzawrZADO7ijBYJU6dZ4AvxKwzA5gRs84UYEqM8s2EBM43xrmOc53liG8ewbIn\nluV091ZZU8XAfxnRCa1yrvDiPHO7EJjeUQ1xznW8vY7ci4997mNU9sy4OhQAFT2r6Hf8YHY7LL/5\ndM4VW5z13O40swUd2RjnXMeSxAm/OoHaz9dS1asKUuZnt9JKZc9q9jl+CEOvHu0puFyXlS1xcmLC\n9vNmtqWtCdzJzGx2u1vmnOsQFdUVnPjrE1nz8hpmfmcmm1ZsorW5laqeVbzc8DLf+u/J7HbYgGI3\n07l2yfbMbRZhEMnHCZOPE+9zkb3PwzlXVJLY+8i96bFzD068/0T6HdUP4P+3d+dRclZlHse/Ty90\nSICwJGHIWgQIe9hEGlBJgBNxcBhUGDOO4igj4gElY3CGQWcGPIPLIUgQnUFRQOE4rAoi67AEFQhL\nEgg7iaZjaBI6IYSQle70M3/ct6BSqaquqn6r3lp+n3PqvF3vVrdu3aqn3+U+lzFjxnDBgbckXDqR\nwSsU3L5NCGarsp6LSAPo3dDLmsVr2O2g3ZIuikjsCiVOvqjQcxGpb6sWrmLX/XelbYj6sknjSXwk\nbhFJRs/8HkYdPirpYohURCmjArSa2dAc8483syvM7LtmVgtjvolIEd6Y9wa7H7F70sUQqYhSjtxm\nAavN7L1hXcxsOvB/hGwc/wo8aWbj4i2iiMTN3XXkJg2tlOD2EeBhd88cbfo/CWOUnQH8C2Gk6a/H\nVzwRqYR13evAYYexOyRdFJGKKCW4jSPkcATAzCYSkhVf6e43uPss4B5yDxMjIjWkZ144alMnbWlU\npQS3nYDMrPbHEroG3Jsx7wVCpn0RqWE983oYdYROSUrjKiW4LSeMdJ12IrARmJcxbwfCSNgiUsN6\n5vew++G6mUQaVykdXOYCp5jZxwlDuZwGPOjuvRnr7Al0x1g+EYnZls1bWP3yakYcMiLpoohUTClH\nbt+J1r8DuI8weOcl6YXR6NMfBp6Is4AiEq9Vz69i+F7DaR/annRRRCqm6CM3d3/OzI7i/YFFb3L3\npzJWOQx4iBJH4haR6krfTCLSyErKu+Puz5ExKnbWsseBT8RRKBGpnJ75PYw7Qd1RpbGVnX7LzHY0\ns3FmtlOcBRKRylLnbWkGJQU3M2szswvMbDGh83YX8JaZLY7mKwOrSA1bv2I9vet7GT5x+MAri9Sx\nooORmW1H6NN2HKF/2zJC94A9gBTh5pKTzGyau78bf1FFZLDSR23qvC2NrpQjt68DU4C7gP3dPeXu\nR7t7ipCp5E7C3ZJKvyVSo3RKUppFKcHtM8DzwKnuvihzgbv/CfgkIUPJP8RXPBGJU8/8Ho0EIE2h\nlGtkexPySPbnWuju/WZ2D2GEABFJmLuzcsFKFl61kGUPLaNvUx84vPCLF2jfsZ2Rh47U6UlpWKUE\nt3cJ6bUKGQb0DrCOiFRYf28/c86bw9L7l9K3uQ8y/iVdev9Suh/pZsK0CUy5Ygot7RqzWBpPKa16\nIXCamY3MtdDMRhBScj0bR8FEpDzuzpzz5tB1Xxd9G7cObAD0Q9/GPrru62LOeXNw90TKKVJJpQS3\nHwEjCQOSnmlmE81sezPb08y+QEi7NTJaT0QSsnLBSpbev5Qtm7YUXG/Lpi0svX8pK59ZWaWSiVRP\n0cHN3W8GvgdMAH4KLALWEcZ4+xkhafKl0XoikpCFP1kYTkUWoW9zH8/95LkKl0ik+kpNv3Whmf0W\nOJOQS3I48DawALgmSsElIgla9uCybU9F5tMPf3ngLxUtj0gSSs4o4u5zCcPfiEgN6ttU2pCKpa4v\nUg+KOi1pZuPN7FNm9kkzq4mMq2bWZWae57EizzbHmNndZrbazDaa2UIzm2FmrQVe5+NmNsfM3jaz\ndWb2hJl9Pt/60TafN7Mno/Xfjrb/+GDfs0gx2oaU9j9rqeuL1IMBW7WZzQJmAOkOMW5ml7v7Nypa\nsuK8DczOMX9d9gwz+1vgNsJAqzcBq4G/AS4HjgVOz7HNucCVwJvADYTuEKcB15nZwe6+zQgJUX3N\nBF4DriaMezcduNPMvuruuuFGKmrcCeNYcveS4k5NtsD4E8dXvEwi1VYwuJnZ3xPSaTnwMiHA7Qt8\n3czmu3vSY7etcfeLBlopGrngamALMMXdn47m/zthDLrTzGy6u9+YsU0KmEUIgh9w965o/reBp4CZ\nZnZb5nVGMzuGENj+BBzp7m9F8y8F5gGzzOx36X2JVMLkL09m2YPLQjeAAbR1tHHwlw+uQqlEqmug\n05L/BPQBJ7r7ge5+APBRwv+EZ1a6cDE6jdBN4cZ0YANw903At6KnX8na5otAB/CjzGAUBazvRE/P\nztom/fySdGCLtukCfhzt7wuDeSMiAxl52EgmTJtA65C8Z9sBaB3SyoRpExh5aM6uqyJ1baDgNhm4\nw90fTs9w9weAO4BDK1mwInWY2WfN7EIzO8/Mpua5fnZ8NL03x7LfAxuAY8yso8ht7slaZzDbiMTK\nzJhyxRRSH03Rsl2Or3gLtG3fRuqjKaZcMUUpuKQhDXTNbRfC6chsLwOnxl+ckv0VcH3WvCVm9gV3\nfyRj3r7R9NXsHbh7n5ktAQ4EJgIvFbHNcjNbD4w1s6HuvsHMhgFjgHXuvjxHWdPJpicV88ZEBqOl\nvYWpP57K6hNXs92O2/Hm82/St6mPtiFtjD9xPJPPnqwjNmloAwW3FnLniuzl/RtMknIt8AfCSATv\nEALTucBZwD1mdrS7p1OBpUdmfDvPvtLzd86YV8w2w6L1NpT5GluZMWPGe393dnbS2dmZb9WmsWJF\nzhtfm9rq1avp6OgYcL13lrzDhpUb6Ly2k5a2rY/geunl9ddf32abVCrFqlVdsZRz7VroimdXRSm3\nraRSKbqqWdAqa9bvUDH3ANdk4jl3vzhr1vPA2Wa2jnBTx0XAJ6pdrsGYPTvXjZ+SSqWSLkJN6e7u\nZvTo0QOu98TPn2C/6fsxdvzYovfd1dXFiBGpQZTufe5Q7Y+unLbS1dXV8G2s0d9fLsX0c7vIzLZk\nPoD/AMieHz2S7hF6VTT9SMa89FHTcHJLz19TxjZvZ01LeQ2Riujv7WfRrYuY9Hc6Cy7NqZjgZiU+\nkh4/I50FdljGvFei6TbfdDNrI+TF7AP+XOQ2e0T7f83dNwC4+3qgG9ghWp5tn2i6zTU8kbgtfWAp\nO03ciZ33znsWXKShFQxE7t5SzqNahc8jfaEqM1A9FE1PyrH+R4ChwGPuvrnIbT6Wtc5gthGJ3as3\nvsp+0/dLuhgiiUk6EJXFzPaP7k7Mnp/i/SF3bshYdCuwCphuZh/IWH8I8F/R0//J2t21wGbg3Gi/\n6W12AS6Mnl6VtU36+Tej9TLLdU60v2sLvDWRkrg7PfN7eOCsB7h272u5euzVXLPXNSybs4wdxu+g\nsdqkadVrUrlPEzKE/B5YSrhbci/gZGAIcDchuwgA7r7WzL5ECHJzzOxGQuaRUwi3/N9KSMlFxjZL\nzOwbwA+Bp83sJt5PvzUWuCx7FAR3f8zMfkDI6rLQzG4lpN/6NLAr8FVlJ5G45BttOz2O232fu0+j\nbUvTqtfg9jAhKB1GyAs5jHCjxh8J/d6u96x/Wd39djM7Dvgm8ClCEFxMCEQ/zF4/2uZKM+sCzgfO\nIBzpvgh8y91/katg7j7TzJ4jHKmdRfjJmU8Y6+53g3zfIsDWo23nG5Q0c7TtqT+eqs7a0lTqMrhF\nHbQfGXDFbbd7FPjrEre5E7izxG2uA64rZRuRUpQz2vaow0ZVqXQiydO5CpE6pNG2RQpTcBOpQxpt\nW6QwBTeROqTRtkUKU3ATqUMabVukMAU3kTo07oRxxX97Ndq2NCEFN5E6NPnLk2nrKO5oTKNtSzPS\nuQqRGufudD/ZzeOzHmfR3Yvo3dhLa0crQ3YdQn9vP/19+e8s0Wjb0qwU3ERq2JbeLdx+xu288ttX\n6NvUh/eHXANbNm1h/fL14GAthuNb3z3ZEo7Y0hlK1IFbmo2Cm0iNcvf3AlvvhhxjBkc5dazNGDpi\nKJvf2qzRtkUiCm4iNar7yW5euTNPYMvQ/24/m9/azMm3nKwsJCIR3VAiUqMev+xx+jYqC4lIORTc\nRGrUorsWvXeNbUDKQiKyFZ2WFKkBue6IpMSh2JSFROR9Cm4iCct3R2SplIVE5H36NohU0TZHaBt6\nsdZwm75vGcSo2cpCIrIVBTeRMuQ6jdi+fTv7nLwPR888Gndn7mVzt1q298f2ZvPazSx7dNlWR2iD\nCmoRZSER2ZqCm0ge+QJYviDVu6GXF299kZd+/VK0A7Za9tJtL1WknMpCIrItBTdpCOUcSZVzlDVg\nkPJ4jsSKoiwkInmZe5W+iFKQmXktfhaFgsYx5x/D6CNH5/xRjTvYlBOIALCQnioUiuKX1TKjYllI\nxowZw9NPx1MPK1fCSSfFsquidHV1kUqlSt7OzKjF715cyq2XehF9ftv8CCm41Qgz80uGXlKRH/9K\nBA1rMVqHtDL+2PF07NjB4nsXVzbY1Gsgiln7sHaOu+849txzz4rsX8Gt8Si4SaLMzC/iosr8+Cto\nNARrMQ447QD2+NoeCm45KLjl1qzBTRlKak10zca3+LaBptrLpKa0DWnj6JlHJ10Mkbqg4CZSB9q2\nb2PfU/Zl9JGjky6KSF3Q3ZIiNcxajLYhIbCd+stTdUekSJEU3ERqiLUYGODhaG3SyZM4+vyjGXPk\nmKSLJlJXFNxEakD2EVpre2vSRRKpawpuInEqcPeptRitHa2M/9B4OnYK3Sf6NvbpCE2kAhTcREo0\nUJDqnNmJYTw26zEW3b1IAUwkAQpu0tjK7OMXx1HW6TefHve7EZEiKbhVgJmNBb4NnATsBiwHbgcu\ndve3kixb4irQ2XwwR1I6yhJpTApuMTOzvYDHgFHAHcDLwAeB84CTzOxYd38z/w5qJ0NJoaCxz8f2\nYdPaTSHF1sYcqbliCja9G3ppH9oeSyAqdCSloyyRxqLgFr//JgS2r7n7lemZZvYD4J+BS4Czc23Y\nPmzgH/FqLysUNNyd1596vaLBJlfqIAUiERmIckvGKDpqWwx0AXu5e3/Gsh0JpycNGOXu67O2rclR\nAZLW6HnxyvHoo48qt2QOyi2ZW6N/h5RbsjqmRtP7MwMbgLu/AzwKDAU6q10wEZFmouAWr32j6at5\nli+KppOqUBYRkaala27xGh5N386zPD1/51wLZ8yY8d7fnZ2ddHbqAG/FihVJF6HmrF69mo6Ojors\nO5VKsWpVVyz7WrsWuuLZVVHKbSupVIquaha0ypr1O6TgVkNmz56ddBFqUiNfLyhHd3c3o0dXZnSA\nrq4uRoxIxbIvd6j2R1dOW2n0a1LQnN8hnZaMV/rIbHie5en5a6pQloYwd+7cpItQc+bPn590EWqS\n2kpuzVovCm7xeiWa5rumtk80zXdNTrI06xezkAULFiRdhJqktpJbs9aLglu8Ho6m08xsq7qNugIc\nC2wAmrO1iYhUiYJbjNz9T8D9QAo4J2vxxcAw4PrsPm4iIhIvdeKOWY70Wy8BRxH6wL0KHJMr/ZaZ\n6YMQESlDrk7cCm4VYGbj2DZx8m9Q4mQRkapQcBMRkYaja24iItJwFNxERKThKLgNgpmNNbNrzOx1\nM9tsZl1mNtvMdiljX4eb2a/M7LVoX2+Y2SNmdkae9Q8ws5vNrMfMNpnZK2Z2sZltP/h3NjhJ1YuZ\neYFHot0vBlsnZjZlgPeXfozLsW3DtpVy66WW20pUvli+Q2b2ITO7I9p+k5n9xczuNrO84zXUcnsp\nha65lSnHXZHpQUmnEjpzFx6UdOt9nQtcAbwF3AV0A7sCBwGvufv0rPWPAh4C2oFbgWXA8cAHCCMP\nnODumwf5FsuScL04sBS4LsfuXnP3n5XxlgYtjjoxsxTwj3kWHwx8Enje3Q/O2q6h28og6qUm2wrE\n9x0ys68QxpdcT7ih7TVgLKFOhgLfcvdLsrap2fZSMnfXo4wHcB/gwFez5v8gmn9VkfuZBvRH+9sx\nx/L2rOetwIvRa5ySMb+F0BgduKDZ6iWa58CcpNtGpeqkwP7/N9rP15qxrZRaL7XcVuKqF0JwWgNs\nBPbNWrY/sImQUKKjXtpLyfWYdAHq8QHsFX3QS4CWrGU7AusI/y0NK2Jfz0br7lbkax8fvfYjOZZN\njJZ1ER2VN0u9RNvU3A9WnHWSZ/8jMn6odm7GtlJqvdRqW4mzXoDdo/08m2f5wmj5bhnzara9lPPQ\nNbfyxDIoqZkdBEwmZDVZbWZTzex8M5tpZidYVgqvyPHR9N7sBe7+Z0JH8QmExlhtSdZL2s5m9kUz\nu9DMzjGzpMcNqvQAtp8HOoBb3D07IXfDt5UCCtVLWq21FYivXnqAlcAkM9snc4GZTSLkuX3Gtz69\nWcvtpWQKbuWJa1DSI6NpDzCHcK77UmAW8ADwjJntXaHXroQk6yXtEODnwCXAj4DHzewZMzs4z/qV\nVunP60vR9CcJvPZgJFkvabXWViCmevFwuHUO4Td+npn9wsy+a2a/BOYBLwCnV+K1a4WCW3kGNShp\nhlHR9ExCPsqTo31PAm4gXBC/y8y2q8BrV0KS9QLhmsSxwEjCKZwjCdcKDgEeMrMxRb2LeFXs8zKz\n4wg/SM+7+2PVfO0YJFkvUJttBWKsF3e/hXA0tgY4A7gA+BzhtOa1wJ8r9dq1QMEtWen6bwWmu/vd\n7r7W3RcRGuPThB/0TyVVwISUVS/uPtPdH3P3Ve6+zt2fdvfTgdsI12DOr+J7qIazoulPEy1F7Rmw\nXpqhrZjZZwlnOv5AuIlkaDR9kHCkemNypas8BbfyxDUoaXr5Cnd/PHNBdFrhjujpByvw2pWQZL0U\nclU0/UiR68epIp+Xme1KCO4bgeur+doxSbJeCkmyrUBM9RJdV7uGcPrxc+7+srtvdPeXCUdv84DT\nzWxK3K9dKxTcyhPXoKTp/eRrLOkky5mdJ2t5QNQk66WQldF0WJHrx6lSn1f6hombC9ww0QxtJVsx\n9VJIkm0F4quXaYTuAI/kuDGlH/h99PSICrx2TVBwK09cg5LOJZz/TplZri/TQdF0Sca8h6LpNhkG\nzGwioWEuZdvz6dWQZL0Ukr6zrJ7rJFv6holCpySboa1kK6ZeCkmyrUB89dIRTUfmWZ6e/27GvFpu\nL6VLui9CvT4osaMlsB+wX479XBGtfzkZ/UcIN01sBHqBvTLmF+poeQt11jE3xnqZTO6O3ZOBVdG+\nPlPPdZKx/MPRds8N8LpN0VbKqJeabStx1QvhlL0TAuHkrGWHRt+hfuDAemkvJddj0gWo1wehs+Ub\n0Qd+O/Bdwn8+Tji83y1rfSe6ZJQ1fydgQbR8LnAZ4Y7ADdG883JscxThyOZd4FfA94CnovX/SEbW\ngWapF0IapTej17yS0G3gd0BftP5PSajzaVx1krH8+lw/fnnWbfi2Umq91HJbibNeCNfcHNhMuHnk\n+8BN0XMHLq+n9lJyPSZdgHp+AOMIt9QujxrDUmA2sEuOdfN+MYEdCH1tXo0a3hpCB+ZpBV77AMJ/\nU6uibV4FLga2b8Z6AU4Ffg0sBtZGr7scuJOM/0IboE52IfzXnTPzRhO3laLrpdbbSlz1Ahgh7+Yc\nwnXqPmA14W7J6fXYXkp5KHGyiIg0HN1QIiIiDUfBTUREGo6Cm4iINBwFNxERaTgKbiIi0nAU3ERE\npOEouImISMNRcBMRkYaj4CYiIg1HwU1EtmFmL5jZBjMbamb/ZmYvmtkmM1tuZpeaWWvSZRQpROm3\nRGQrZrY98A4hn+EqYAhhNOftgM8Qxjqb4e5XJFZIkQHoyE1Esh1CGP5kIiHB8KHufq67nwWcFa1z\nfFKFEylGW9IFEJGac1g0/Y27fz9r2fxoqn+MpaapgYpItsOjaa7RrEdF0/oYjVmaloKbiGQ7DNgC\nPJJj2SHRdEH1iiNSOgU3EXmPmbUDBwEvufvGHKscEU3nVa9UIqVTcBORTAcAHeQPXkcQRrx+sWol\nEimDgpuIZEpfb5ufvcDMhgL7A8+6+5aqlkqkRApuIpIpfadkriO3dBcBnZKUmqfgJiKZDgP6gWdy\nLEsf1Sm4Sc1TPzcReY+7f7jAYt1MInVDR24iUqwjgE3oZhKpAwpuIjIgMxtCuJPyWXfvS7o8IgNR\ncBORYhxCuIyhU5JSFzQqgIiINBwduYmISMNRcBMRkYaj4CYiIg1HwU1ERBqOgpuIiDQcBTcREWk4\nCm4iItJwFNxERKTh/D/TUmkp2xB0ygAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f13046610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "plt.axvspan(0.76, 0.76001, alpha=1, color='black')\n",
    "\n",
    "#plt.axvspan(0.72, 0.72001, alpha=10, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "\n",
    "plt.plot(etas, Xs, marker='o', linewidth = 1.0, markersize=12, color = colors[i])\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "plt.xlim(0.60, 0.84)\n",
    "#plt.ylim(-0.1,0.1)\n",
    "\n",
    "#plt.ylim(-0.1,0.1)\n",
    "#plt.yscale('log')\n",
    "\n",
    "#plt.yscale('log')\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'Positional susceptibility', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('Hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#comps_ig = incpca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:22: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n"
     ]
    },
    {
     "data": {
      "image/png": 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jxcOJMlRTFGyJ5XEnBmOwuaKCQFLEiuROXG6X2nK6Mm2GjVt+/RYAGl/ZyL2P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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe9999d8a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "#plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "#plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "#plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "#plt.axvspan(0.781, 0.781001, alpha=1, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "for i in range(0,5):\n",
    "    p_data = incpca.components_[i]\n",
    "    plt.plot(range(len(incpca.components_[0])), p_data, marker='o', linewidth = 1.0, markersize=5, color = colors[i])\n",
    "    #p_data = comps_ig[i]\n",
    "    #plt.plot(range(len(incpca.components_[0])), p_data, marker='o', linewidth = 3.0, markersize=0, color = colors[i])\n",
    "    #p_data = incpca.components_[i] - comps_ig[i]\n",
    "    #plt.plot(range(len(incpca.components_[0])), p_data, marker='o', linewidth = 3.0, markersize=0, color = colors[i])\n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 2.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "#plt.xlim(0.1,3000)\n",
    "#plt.ylim(-1,0)\n",
    "#plt.ylim(0,0.5)\n",
    "#plt.ylim(-2,1.5)\n",
    "#plt.ylim(5, 13)\n",
    "#plt.ylim(1, 0.001)\n",
    "#plt.ylim(-2000.0, 2000)\n",
    "\n",
    "#plt.xscale('log')\n",
    "plt.xlabel(r'$n$th nerest neighbor', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'$P_{i}$ weight', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA feature weights', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import gsd.hoomd\n",
    "from numpy import mean, array\n",
    "\n",
    "def ColorParticlesPCA(filename_gsd, filename_xyz, pca):\n",
    "    frames = []\n",
    "    traj = gsd.hoomd.open(name=filename, mode='rb')\n",
    "    \n",
    "    #static quantities\n",
    "    box = traj[0].configuration.box\n",
    "    D = traj[0].configuration.dimensions\n",
    "    \n",
    "    #loop over the configurations and stor in new format\n",
    "    for snap in traj:\n",
    "        #dynamic quantities\n",
    "        diameters = snap.particles.diameter\n",
    "        coords = snap.particles.position\n",
    "        \n",
    "        #check for a square box\n",
    "        if (max(box[0:D]) - min(box[0:D]))/mean(box[0:D]) > 0.000000000001:\n",
    "            raise Exception('Not a rectangle or square!!!')\n",
    "            \n",
    "        L = box[0]\n",
    "        \n",
    "        #get the particle types\n",
    "        possible_types = snap.particles.types\n",
    "        types = array([possible_types[type_id] for type_id in snap.particles.typeid])\n",
    "        \n",
    "        #create our new data structure\n",
    "        frames.append({'coords': (coords[:,0:D]+L/2.0), 'diameters': diameters, 'types': types, 'L': L, 'D': D})\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "frames = ReadGSD('../hoomd_disks/trajectories_4000p_longer/trajectory_0.1000.gsd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "frames = ReadGSD('../hoomd_disks/trajectories_ww_4000p/trajectory_2.1800.gsd', randomize = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pc = 0\n",
    "xyz_file_stream = open('op_labeled/feature_labeled_particles_2.1800_P{}.xyz'.format(pc), 'w')\n",
    "for frame in frames[0:40]:\n",
    "    coords = frame['coords']\n",
    "    N = len(coords)\n",
    "    L = frame['L']\n",
    "    types = frame['types']\n",
    "    \n",
    "    #create header\n",
    "    xyz_file_stream.write('{}\\n'.format(N))\n",
    "    xyz_file_stream.write(' L={}\\n'.format(L))\n",
    "    features = FrameToFeatures(frame, N_nn, ['distance'], particle_inc=1, nn_inc=nn_inc)\n",
    "    \n",
    "    #transform the data to features\n",
    "    ops = (incpca.transform(features)[:,pc])\n",
    "    #ops = types\n",
    "    #print len(ops)\n",
    "    \n",
    "    #joint data\n",
    "    coords_ops_types = zip(coords, ops, types)\n",
    "    for coord, op, type_ in coords_ops_types:\n",
    "        xyz_file_stream.write('  {}    {}    {}    0.0    {}\\n'.format(type_, coord[0], coord[1], op))\n",
    "xyz_file_stream.close()\n",
    "                                 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'D': 2, 'L': 38.414631, 'coords': array([[ 11.06319141,  37.75015259],\n",
       "        [  8.64294338,   4.37904453],\n",
       "        [ 38.39389038,   1.4232254 ],\n",
       "        ..., \n",
       "        [ 16.68315125,  22.83090782],\n",
       "        [ 23.82643127,   7.47303104],\n",
       "        [ 11.08653927,   9.76377487]], dtype=float32), 'diameters': array([ 1.,  1.,  1., ...,  1.,  1.,  1.], dtype=float32), 'types': array([u'A', u'A', u'A', ..., u'B', u'B', u'B'],\n",
       "       dtype='<U1')}"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frames[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.55\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.555\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.56\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.565\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.57\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.575\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.58\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.585\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.59\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.595\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.6\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.605\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.61\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.615\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.62\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.625\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.63\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.635\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.64\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.645\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.65\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.655\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.66\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.665\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.67\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.675\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.68\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.685\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.69\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.695\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.7\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.705\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.71\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.715\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.72\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.725\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.73\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.735\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.74\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.745\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.75\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.755\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.76\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.765\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.77\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.775\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.78\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.785\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.79\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.795\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.8\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "incpca_small = IncrementalPCA(n_components=16, whiten=True)\n",
    "\n",
    "frames = None\n",
    "features = None\n",
    "split_features = None\n",
    "\n",
    "for etas, file_base in file_data:\n",
    "    for eta in etas:\n",
    "        print 'eta={}\\n'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeatures(frames_partial, N_nn=N_nn, method='distance', step=step)\n",
    "            incpca_small.partial_fit(features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "        frames_split = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.55\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.555\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.56\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.565\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.57\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.575\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.58\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.585\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.59\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.595\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.6\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.605\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.61\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.615\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.62\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.625\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.63\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.635\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.64\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.645\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.65\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.655\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.66\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.665\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.67\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.675\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.68\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.685\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.69\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.695\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.7\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.705\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.71\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.715\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.72\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.725\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.73\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.735\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.74\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.745\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.75\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.755\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.76\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.765\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.77\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.775\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.78\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.785\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.79\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.795\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "eta=0.8\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "OPs_small = []\n",
    "frames = None\n",
    "features = None\n",
    "raw_OPs_small = []\n",
    "\n",
    "for etas, file_base in file_data:\n",
    "    for eta in etas:\n",
    "        print 'eta={}\\n'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        means = []\n",
    "        raw_OPs_single = []\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeatures(frames_partial, N_nn=N_nn, method='distance', step=step)\n",
    "            transformed_features_partial = incpca_small.transform(features_partial)\n",
    "            means.append(mean(transformed_features_partial, axis=0))\n",
    "            raw_OPs_single.append(transformed_features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "            \n",
    "        means = array(means)\n",
    "        op = mean(means, axis=0)\n",
    "        OPs_small.append(op)\n",
    "        raw_OPs_small.append(raw_OPs_single)\n",
    "    \n",
    "OPs_small = array(OPs_small)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import std, abs, power\n",
    "\n",
    "OPs_small_std = []\n",
    "OPs_small_abs = []\n",
    "for single_eta in raw_OPs_small:\n",
    "    merged_data = []\n",
    "    for split in single_eta:\n",
    "        merged_data.extend(split)\n",
    "        \n",
    "    OPs_small_std.append(std(split, axis=0))\n",
    "    OPs_small_abs.append(mean(abs(split), axis=0))\n",
    "    \n",
    "OPs_small_std = array(OPs_small_std)\n",
    "OPs_small_abs = array(OPs_small_abs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'OPs_small_abs' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mNameError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-292-601acafa28a3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     13\u001b[0m     \u001b[0;31m#p_data = OPs_small[:,i]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;31m#plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i], markerfacecolor='None')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m     \u001b[0mp_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mOPs_small_abs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     16\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0metas\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mp_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmarker\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'o'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmarkersize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcolors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'OPs_small_abs' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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tE27O6v39ZpKjY4yT58F7xNf6urx4jHGqqp6d5KNV9Zkxxk46uTjNdp+Bz/Ie84ccyun/\n1Hk0v3e7bGZ/O92m9lZVT0nygSSvH2PcviUTbtxcPm+TM+/PJvnZuU63eZvZ388kuaaqvpTkzUle\nWVVv3IohN2hTn7sxxqnJryeSfCzJC+c/4hxt8wsOu7Ly4uMleeQFhx9fY92PZeXFoJo69vQkX8zK\nC5gXTq4/fbtfVJjX/qbuuyw780XMzXzudif5SJLf2e59bMHe9ib53sn1C7PyLofnbfee5rW/Vfdf\nnZ33IuZmPncX5pEXoC/KyrvbzvgC6E64bOsZ+Fj5f1Meeo/53UluHpP3mFfVFVNLDyU5PCZ/spPf\n+/Ukb8jKDxodS3L95NiOsZn9JUlV/WuS92TlPwc7WVW/cK5mX88m9/aKJD+X5Oqq+tTk8oJzNvw6\nNrm35ya5o6o+neRfkrx5jPGZczX7LDb7dbmTzeFztzT53N2W5I1jjLvO1ewbUY0+NwBM2e7nwAHY\nIAEHaErAAZoScICmBBygKQEHaErAAZoScICm/h/XYwu27VMDXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4f05a17210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "plt.axvspan(0.755, 0.755001, alpha=1, color='black')\n",
    "\n",
    "#plt.axvspan(0.72, 0.72001, alpha=10, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "for i in range(0,4): #16,17\n",
    "    #p_data = OPs_small[:,i]\n",
    "    #plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i], markerfacecolor='None')\n",
    "    p_data = OPs_small_abs[:,i]\n",
    "    plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i])\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "plt.xlim(0.60, 0.84)\n",
    "#plt.ylim(-0.1,0.1)\n",
    "\n",
    "#plt.ylim(0.01,0.6)\n",
    "#plt.yscale('log')\n",
    "\n",
    "#plt.yscale('log')\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'$\\langle P_{i} \\rangle$ and $\\langle |P_{i}| \\rangle$', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1600"
      ]
     },
     "execution_count": 257,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "40*40"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing WR mixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The history saving thread hit an unexpected error (DatabaseError('database disk image is malformed',)).History will not be written to the database.\n"
     ]
    }
   ],
   "source": [
    "import hoomd\n",
    "import hoomd.hpmc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HOOMD-blue v2.1.7 CUDA (7.5) DOUBLE HPMC_MIXED MPI SSE SSE2 SSE3 \n",
      "Compiled: 05/11/2017\n",
      "Copyright 2009-2016 The Regents of the University of Michigan.\n",
      "-----\n",
      "You are using HOOMD-blue. Please cite the following:\n",
      "* J A Anderson, C D Lorenz, and A Travesset. \"General purpose molecular dynamics\n",
      "  simulations fully implemented on graphics processing units\", Journal of\n",
      "  Computational Physics 227 (2008) 5342--5359\n",
      "* J Glaser, T D Nguyen, J A Anderson, P Liu, F Spiga, J A Millan, D C Morse, and\n",
      "  S C Glotzer. \"Strong scaling of general-purpose molecular dynamics simulations\n",
      "  on GPUs\", Computer Physics Communications 192 (2015) 97--107\n",
      "-----\n",
      "-----\n",
      "You are using HPMC. Please cite the following:\n",
      "* J A Anderson, M E Irrgang, and S C Glotzer. \"Scalable Metropolis Monte Carlo\n",
      "  for simulation of hard shapes\", Computer Physics Communications 204 (2016) 21\n",
      "  --30\n",
      "-----\n",
      "notice(2): NVIDIA driver not installed or is too old, ignoring any GPUs in the system.\n",
      "HOOMD-blue is running on the CPU\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<hoomd.context.SimulationContext at 0x7f4f3ffe7350>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hoomd.context.initialize(\"--mode=cpu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import pi, arange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d = 1.0\n",
    "#etas = arange(0.65, 0.75, 0.002)\n",
    "eta_init = 0.3\n",
    "a = (((pi*d**2.0)/4.0)/eta_init)**(1.0/2.0)\n",
    "n = 64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "notice(2): Group \"all\" created containing 4096 particles\n"
     ]
    }
   ],
   "source": [
    "system = hoomd.init.create_lattice(unitcell=hoomd.lattice.sq(a=a), n=n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mc = hoomd.hpmc.integrate.sphere(d=0.2, seed=1)\n",
    "mc.shape_param.set('A', diameter=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "system.particles.types.add('B')\n",
    "for i in range(n*n/2, n*n):\n",
    "    system.particles[i].type = 'B'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mc.shape_param.set('A', diameter=1.0)\n",
    "mc.shape_param.set('B', diameter=1.0)\n",
    "mc.overlap_checks.set('A', 'A', enable=False)\n",
    "mc.overlap_checks.set('A', 'B', enable=True)\n",
    "mc.overlap_checks.set('B', 'B', enable=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(arange(0.48, 0.75001, 0.005))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "** starting run **\n",
      "Time 00:00:41 | Step 1000 / 1000 | TPS 222.192 | ETA 00:00:00\n",
      "Average TPS: 222.071\n",
      "---------\n",
      "notice(2): -- HPMC stats:\n",
      "notice(2): Average translate acceptance: 0.996867\n",
      "notice(2): Trial moves per second:        3.63535e+06\n",
      "notice(2): Overlap checks per second:     6.50141e+07\n",
      "notice(2): Overlap checks per trial move: 17.8839\n",
      "notice(2): Number of overlap errors:      0\n",
      "** run complete **\n"
     ]
    }
   ],
   "source": [
    "hoomd.run(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Compress(eta_tgt, scale=0.9):\n",
    "    #get current state\n",
    "    snap = system.take_snapshot()\n",
    "    N = len(snap.particles.diameter)\n",
    "    Vp = sum(pi*(snap.particles.diameter**2.0)/4.0)\n",
    "    Vb = system.box.get_volume()\n",
    "    eta = Vp/Vb\n",
    "    eta_init = eta\n",
    "    \n",
    "    print '\\nStarting from eta={}\\n'.format(eta)\n",
    "    \n",
    "    #calculate new quantities\n",
    "    Vb_tgt = Vp/eta_tgt\n",
    "    \n",
    "    #box compression loop\n",
    "    while Vb > Vb_tgt:\n",
    "        Vb = max(Vb*scale, Vb_tgt)\n",
    "        eta = Vp/Vb\n",
    "        new_box = system.box.set_volume(Vb)\n",
    "        hoomd.update.box_resize(Lx=new_box.Lx, Ly=new_box.Ly, Lz=new_box.Lz, period=None)\n",
    "        overlaps = mc.count_overlaps()\n",
    "        \n",
    "        #run until all overlaps are removed\n",
    "        while overlaps > 0:\n",
    "            hoomd.run(100, quiet=True)\n",
    "            overlaps = mc.count_overlaps()\n",
    "            \n",
    "        print \"Compressed to eta={}\\n\".format(eta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Starting from eta=0.333333342609\n",
      "\n",
      "Compressed to eta=0.370370380677\n",
      "\n",
      "Compressed to eta=0.411522645197\n",
      "\n",
      "Compressed to eta=0.457247383552\n",
      "\n",
      "Compressed to eta=0.508052648391\n",
      "\n",
      "Compressed to eta=0.564502942656\n",
      "\n",
      "Compressed to eta=0.62722549184\n",
      "\n",
      "Compressed to eta=0.696917213156\n",
      "\n",
      "Compressed to eta=0.774352459062\n",
      "\n",
      "Compressed to eta=0.8\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Compress(0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "** starting run **\n",
      "Time 00:01:10 | Step 3805 / 11900 | TPS 190.42 | ETA 00:00:42\n",
      "Time 00:01:20 | Step 5694 / 11900 | TPS 188.836 | ETA 00:00:32\n",
      "Time 00:01:30 | Step 7574 / 11900 | TPS 187.922 | ETA 00:00:23\n",
      "Time 00:01:40 | Step 9445 / 11900 | TPS 187.018 | ETA 00:00:13\n",
      "Time 00:01:50 | Step 11308 / 11900 | TPS 186.263 | ETA 00:00:03\n",
      "Time 00:01:54 | Step 11900 / 11900 | TPS 185.272 | ETA 00:00:00\n",
      "Average TPS: 187.915\n",
      "---------\n",
      "notice(2): -- HPMC stats:\n",
      "notice(2): Average translate acceptance: 0.988187\n",
      "notice(2): Trial moves per second:        3.07858e+06\n",
      "notice(2): Overlap checks per second:     7.58691e+07\n",
      "notice(2): Overlap checks per trial move: 24.6442\n",
      "notice(2): Number of overlap errors:      0\n",
      "** run complete **\n",
      "** starting run **\n",
      "Time 00:02:04 | Step 13754 / 21900 | TPS 185.343 | ETA 00:00:43\n",
      "Time 00:02:14 | Step 15603 / 21900 | TPS 184.845 | ETA 00:00:34\n",
      "Time 00:02:24 | Step 17446 / 21900 | TPS 184.278 | ETA 00:00:24\n",
      "Time 00:02:34 | Step 19280 / 21900 | TPS 183.358 | ETA 00:00:14\n",
      "Time 00:02:44 | Step 21109 / 21900 | TPS 182.851 | ETA 00:00:04\n",
      "Time 00:02:48 | Step 21900 / 21900 | TPS 181.764 | ETA 00:00:00\n",
      "Average TPS: 183.938\n",
      "---------\n",
      "notice(2): -- HPMC stats:\n",
      "notice(2): Average translate acceptance: 0.983622\n",
      "notice(2): Trial moves per second:        3.01343e+06\n",
      "notice(2): Overlap checks per second:     7.40972e+07\n",
      "notice(2): Overlap checks per trial move: 24.589\n",
      "notice(2): Number of overlap errors:      0\n",
      "** run complete **\n"
     ]
    }
   ],
   "source": [
    "eta=0.80\n",
    "\n",
    "hoomd.run(10000)\n",
    "    \n",
    "#set up the file writer and run the production version\n",
    "d = hoomd.dump.gsd(\"./trajectories/trajectory_{:.4f}.gsd\".format(eta), period=1000, group=hoomd.group.all(), overwrite=True)\n",
    "hoomd.run(10000)\n",
    "    \n",
    "#diable old file writer\n",
    "d.disable()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in power\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power(-2.0,3.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for single_eta in raw_OPs:\n",
    "    merged_data = []\n",
    "    for split in single_eta:\n",
    "        merged_data.extend(split)\n",
    "    plt.plot(merged_data[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(arange(0.60, 0.85001, 0.005))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.special import j0\n",
    "from numpy import histogram, pi, power, rint\n",
    "from numpy.linalg import norm\n",
    "from numpy import trapz\n",
    "\n",
    "#function for calculating the rdf\n",
    "def RDF2D(frames, dr):\n",
    "    M = len(frames)\n",
    "    N = float(len(frames[0]['coords']))\n",
    "    L = frames[0]['L']\n",
    "    rho = float((N-1))/power(L, 2)\n",
    "    r_edg = arange(0.0, L/2.0, dr)\n",
    "    r = (r_edg[:-1] + r_edg[1:])/2.0\n",
    "    hist = 0.0*r\n",
    "    \n",
    "    #loop over the frames\n",
    "    for frame in frames:\n",
    "        coords = frame['coords']\n",
    "\n",
    "        #loop over each particle\n",
    "        for coord in coords:\n",
    "            #nearest neighbor coordinate wrapping\n",
    "            Rpj = coord - coords\n",
    "            Rpj = Rpj - rint(Rpj/L)*L\n",
    "            Rpj = norm(Rpj, axis=1)\n",
    "            \n",
    "            #calculate the histogram\n",
    "            hist = hist + histogram(Rpj, bins=r_edg)[0]\n",
    "    \n",
    "    #normalize out the number of frames and \n",
    "    hist = hist/float(M*(N-1))\n",
    "    gr = hist/((2.0*pi*r*dr)*rho)\n",
    "    \n",
    "    return r, gr\n",
    "\n",
    "#function for calculating the integral of h(r)\n",
    "def PositionalSuceptibility2D(frames, dr, k):\n",
    "    N = float(len(frames[0]['coords']))\n",
    "    L = frames[0]['L']\n",
    "    rho = float(N)/power(L, 2)\n",
    "    \n",
    "    d = float(L)/rint(L)\n",
    "    k = 2.0*pi/d\n",
    "    \n",
    "    #compute the rdfs and calculate S(k0)\n",
    "    r, gr = RDF2D(frames, dr)\n",
    "    #Sk0 = 1.0 + 2.0*pi*rho*trapz(r*(gr-1.0)*j0(k*r))\n",
    "    Sk0 = 1.0 + 2.0*pi*rho*trapz(r*abs(gr-1.0))\n",
    "    \n",
    "    return (Sk0, r, gr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.special import j0\n",
    "from numpy import sin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f4eeebe4390>]"
      ]
     },
     "execution_count": 401,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Sh0BAiDz0JIQwha8J5ygEEs/5PKH2tXMVACu01lXAbqXUDoyEv+r8k61e7Zk3GfunRTF1\n/X6qaqz4+dTzc9UvENKvhm3fwzWvga+/Y4MUQngUM67gVwFpSqm2Sil/YCww9bxjvsO4ekcpFYVR\nsskzYW23MSA1ilMVF9nl6YxON0B5MeTNc0xgQgiPZXOC11pXA48CM4FtwFda6y1KqeeUUiNqD5sJ\nFCmltgLzgKe01kW2ru1O+qYYYwsu2S6ZPBACw6RMI4Swmbpo656DKaW0K8VjtpETluBrUXzzcN+L\nHzj1Mdj8LTy1E/yCHBOcEMJtKaXQWqvzX5cnWR1oQGoU6/edoKS86uIHZlwPlSdh5yzHBCaE8EiS\n4B2of1oUNVbN8l2XqE61GQDNomHLFMcEJoTwSJLgHah763CC/X0u3S7p4wsdR0LODKg45ZjghBAe\nRxK8A/n7WujdNoLFl7rRCkY3TfVp2DHD/oEJITySJHgH658WTd7RUgpPnL74gYnZ0CIOtnzrmMCE\nEB5HEryD9U+NAhowtsBigYzRsPMnoy9eCCEaSRK8g7WLbU50iwCWXupGK0Cn66GmErb/aP/AhBAe\nRxK8gylljA9euqvo4uODAeJ7QFhreehJCNEkkuCdoG9KJEdOVrDryCU6ZJQyeuLz5kHZMccEJ4Tw\nGJLgnaBvilGHb3CZxloN284f7yOEEBcnCd4JEiOCSQgPYmluAxJ8yy4QmWpsBCKEEI0gCd5J+qZE\nsiyvCKv1EnV4paDjKMhfBKUN6J8XQohakuCdpE9KJMWnq9h6oOTSB2eMAm015sQLIUQDSYJ3kj7J\nRh1+WUPq8LGdICIFtn5n56iEEJ5EEryTtAwNJDm6GcvyGpDglTIeetq9CEq9aoy+EMIGkuCdqG9K\nJCvyiqiqsV764IxRoGtgu5RphBANIwneifqmRFFaWcOmwgaMIjhTptkiZRohRMNIgnei7ORIoIF1\neKWMq/jdC6VMI4RoEEnwThTRzJ8OrUJYuquB7Y8dz5Rpptk3MCGER5AE72R9kiNZnX+c8qqaSx/c\nsjNEJEs3jRCiQSTBO1nflEgqqq2s23vi0gefeegpb4HMphFCXJIkeCfrlRyBRcGyhpZpMqRMI4Ro\nGEnwThYS6EfnhLCGDR4DYzZNeFvpphFCXJIkeBfQNyWS9ftOUFZZfemDz3bTSJlGCHFxkuBdQN+U\nSKqtmlX5xxv2BR1HGSOEt/9g38CEEG5NErwLyEqKwM9HNbxdslUmhLeRbhohxEVJgncBQf4+dEsM\nb9gDT3BON818KdMIIeolCd5FZCdHsLmwmJPlVQ37ggwp0wghLk4SvIvITo7EqmF1Q+vwrbpCWJKU\naYQQ9ZIE7yK6tQ7H38fC8oaMD4afu2mkTCOEqIckeBcR5O9D18Qwlu9uRLI+002T86P9AhNCuC1J\n8C6kd2Pr8HHdIKy1PPQkhKiTJHgXkp0cSY1Vs3pPA+vw53bTnG7g1wghvIYpCV4pNUwplaOUylVK\njb/IcTcopbRSKsuMdT1N99bh+Pmohtfhobabpgq2S5lGCPFLNid4pZQPMAEYDnQEblFKdazjuBbA\nr4EVtq7pqc7W4fMaUYeP626UaaSbRghxHjOu4HsBuVrrPK11JfAFMLKO454HXgLKTVjTY2UnR7K5\nsJhTFQ2YSwO1ZZqRsGsenG7AyGEhhNcwI8HHA/vO+byg9rWzlFLdgUSttTyVcwln6/D5jemmGW2U\naaSbRghxDrvfZFVKWYB/Ak825PisrKyzHxMnTrRvcC7o5zp8IxJ8fHcIlW4aIcQv+ZpwjkIg8ZzP\nE2pfO6MF0AmYr5QCaAlMVUqN0FqvPv9kq1df8JJXCfL3ITMhrHE3WpWCjiNgxdtGmSYozH4BCiHc\nhhlX8KuANKVUW6WUPzAWmHrmTa11sdY6SmvdRmvdBlgO1JnchSE7OZJNjanDA2ScKdNMt19gQgi3\nYnOC11pXA48CM4FtwFda6y1KqeeUUiNsPb83alIdPr4HhCZKN40Q4iwzSjRorX8EfjzvtWfrOXag\nGWt6su5JYfj5KFbsPsbA9JiGfdGZbpqVE6VMI4QA5ElWlxTs70uXxtbhATKuh5pKKdMIIQBJ8C4r\nOzmCjQXFlDamDn+2m+Zb+wUmhHAbkuBdVKPn0sDPI4R3zZXZNEIISfCuqkdSOL6WRs6lgZ+7aWSn\nJyG8niR4FxXs70tmYhgrGpvg47oZOz1JmUYIrycJ3oU1qQ6vlHEVLzs9CeH1JMG7sN5tI6m2atY0\npg4PtWWaatg+zT6BCSHcgiR4F9bkOnyrTAhvK2UaIbycJHgX1izAly4JoY1P8GfLNAugtJFfK4Tw\nGJLgXVx2ciQbC4opq2xEHR6MBK9rYPv39glMCOHyJMG7uOzkJtbhW3aGiBQp0wjhxSTBu7geSeH4\nNKUOf6ZMs3shlB61T3BCCJcmCd7F/VyHb0LLY8Zo0FbYNvXSxwohPI4keDeQnRzJhn0nGl+Hj82A\nyDQp0wjhpSTBu4Ezdfi1exq5qfaZMk3+Yjh12D7BCSFclinz4IV9ZZ1Th++fFtW4L84YDQtfNso0\nPe+3T4DC7VmtmnX7TrBy9zE27y/mUHE5xaer8POxEBLkS0p0czrGhXB5u2gSwoOdHa5oIKW1dnYM\nZymltCvF40pGv7kEH6X4+uG+jftCrWFCb2geA3fLk63ilw6VlPPh0nymrC3gUEkFAAnhQSSGBxMa\n5Ee11crxsip2HDrJyXKjRNg5PpTberdmZNd4gvx9nBm+qKWUQmutzn9druDdRO+2kby3OI+yymqC\n/Rvxf9uZMs2Cl+DkIWgRa78ghdsoLqviX3N28MnyPdRYNYPax/CH4XFc3i6a8Gb+FxyvtWbXkVLm\nbj/ElLWFjJ+yiVd/2sHjg1MZ27M1/r5S7XVFcgXvJubnHObuD1bxyX29G1+mObwN3syGq1+FXg/Y\nJ0DhNqZvOsAz323mRFklN2Ul8vDAFJIimzX467XWrNh9jH/O2sHK3cdo37IFr4zJpHNCqB2jFhdT\n3xW8/Nh1E1ltIprWDw8Q0wGiO0g3jZcrq6zm919v4OFP15IYHsT3j/XnHzd0aVRyByOZZCdH8uW4\nbCbe0YPjZZWMenMJ/5y1gxqrXKC5EinRuInmtf3wy5qS4MEo08z/O5QcgJBW5gYnXN6hknLum7SK\nLftLePSKVH49JA0/H9uu75RSDM1oSe/kSP76/RbemLOTDftO8PrYroQFX1jmEY4nV/BupMn98GBs\n5YeWh568UM7Bk4yasITdR0p5/66e/O6qdJuT+7lCg/z4vxsz+dvozizddZRRE5awt6jMtPOLppME\n70aaPJcGIDodYjpKmcbLbN1fwtiJy9AaJj/Ulyvax9hlHaUUt/ZuzRfjsjlxuoob3lrK1v0ldllL\nNJwkeDeSVTsfftkuG8o0e5dByX5zAxMuaev+Em57dzmBfj58+WA2HeNC7L5mj6QIJj/YB1+L4uaJ\ny9hcWGz3NUX9JMG7kSbPhz8jY7TxX7mK93j7jpVx5/srCfTz4Ytx2Y2+kWqLtNgWTH6oDyGBftzx\n3gpyDp502NrilyTBu5k+KZGN36f1jKg0Y7enTV+bH5hwGcVlVdzz4Soqq2v46N5eDk3uZySEB/PZ\nA73x97Vw27sr2H201OExCEnwbudMHX51U+rwAJ3GwP61ULTL3MCES6istvLgJ6vZW1TGxDuzSItt\n4bRYkiKb8en92Vi15p4PVnK8tNJpsXgrSfBupkdSOH4+TeyHB+h0A6DkKt5D/X36NpbnHePlMV3I\nTo50djikxjTnnTt7sL+4nAc/XkNFdY2zQ/IqkuDdTLC/L5kJYU2/0RoaD0n9YNNkY06N8BjTNu7n\ngyX53NOvDaO6xTs7nLN6JEXw6o2ZrMw/xh++2YQ8re44kuDdUHZyJJsKiznVlDo8QOcxULQTDm40\nNzDhNLmHT/H01xvp3jqMPwzv4OxwLjAiM47fDEljyrpCPlm+x9nheA1J8G4oOzmSGqtmdX4TdnkC\n6DgSLL7GVbxwe5XVVn79xToC/HyYcFt3lx389figNK5Ij+a5aVtZt7eJ95BEo7jmd4K4qDN1+CaP\nLQiOgNQhsHkKWK3mBicc7o05O9myv4S/X9+ZVqFBzg6nXhaL4rWbuxIbEsivPl1L0akKZ4fk8STB\nu6Egfx+6JoY1bZ/WMzrfCCWFxoNPwm2t3XucN+fnMqZHAldltHR2OJcUFuzPW7f3oKi0kt9N3iD1\neDszJcErpYYppXKUUrlKqfF1vP9bpdRWpdRGpdQcpVSSGet6s+zkSDYXFnOyvKppJ0gfDn7BUqZx\nY2WV1Tz51QZahQbx5+s6OjucBusUH8ofh7dnXs4Rqcfbmc0JXinlA0wAhgMdgVuUUud/t60DsrTW\nXYCvgZdtXdfb9Tlbh29iLdO/GaRfDVu/g2rpT3ZH/5q9k91HS3n1xkxaBPo5O5xGuatvGy5rF80L\nP2wj97A86WovZlzB9wJytdZ5WutK4Atg5LkHaK3naa3PjJdbDiSYsK5X69Y6HH8fS9P74cEo05w+\nDnnzzAtMOMTW/SW8t3g3Y3sm0ifF+f3ujaWU4tUxXQj29+E3X66nslruBdmDGQk+Hth3zucFta/V\n5z5gugnrerUzdfgm32gFSBkEgWHy0JObsVo1f/x2E2FBfowf3t7Z4TRZTEggf7++C5sLS3h9zg5n\nh+ORHHqTVSl1O5AFvFLfMVlZWWc/Jk6c6Ljg3FB2ilGHL2lqHd7X35gTv/0HqJRZIe7i05V7Wb/v\nBH+6toPbb6wxrFNLbuiewFsL8mTypB2YkeALgcRzPk+ofe0XlFJDgGeAEVrrevujVq9effZj3Lhx\nJoTnubKTI7Bqmt4PD0aZpqoUcuSXKndw9FQFL8/YTr/USEZ1dZ2nVW3x/67tQHiwP+OnbKS6Rko1\nZjIjwa8C0pRSbZVS/sBY4BfbBimlugFvYyT3wyasKYDurcPx97U0fWwBQOu+0CJOyjRu4rVZOyir\nrOGvIzqh1AV7LLulsGB/nhuZwebCEt5dvNvZ4XgUmxO81roaeBSYCWwDvtJab1FKPaeUGlF72CtA\nc2CyUmq9Ukr2jTNBoJ8P3Wzth7dYoPMNkDsLSm34QSHsbvvBEj5fuZc7spNIjWnu7HBMNbxTS67K\niOW1WTtktLCJTKnBa61/1Fq301qnaK1frH3tWa311No/D9Fax2qtu9Z+jLj4GUVDZSdHsmV/McWn\nm1iHB8i8BazVsPkb8wITptJa88K0bbQI9OM3Q9KcHY7plFI8N7IT/r4Wxn+zUR6AMok8yerm+qRE\nYtWwarcNV/GxGdCyM2z43LzAhKnmbj/M4tyj/GZImtvfWK1PbEggf7y6Ayt2H+O79RfcxhNNIAne\nzXVNDMPf18Z+eIDMW42NQI7kmBOYME1VjZUXf9hGcnQzbs/27IfAb85KJDMxjBd/2N707jBxliR4\nNxfo50P31jb2w4MxQlj5wIYvzAlMmGby6gLyjpbyx+Ed8PPx7H+yFovihZGdKCqt4LVZ0htvK8/+\nbvESfZKj2HqghOIyG654mscYEyY3fglW2XXHVZRX1fDGnJ30SApncIcYZ4fjEJ0TQrmtd2smLc1n\n6/4SZ4fj1iTBe4Ds5Ai0hpW29MMDZI41JkzmLzInMGGzT5bv4WBJOU9dle4xbZEN8buh6YQF+/Ps\n/zbLDVcbSIL3AF1bhxFgaz88GBMmA0KlTOMiTpZXMWFeLgPSolxif1VHCgv2Z/yw9qzec5xv1soN\n16aSBO8BAnx96JEUbvuNVr8gY3TB1qlQccqc4ESTvbd4N8fLqnjqqnRnh+IUY3ok0DUxjJdmbKe0\nqdtTejlJ8B4iOzmSbQdLOFFm4+jfzFuM0QXbp5kTmGiSY6WVvLtoN8MyWtIlIczZ4TiFxaJ49rqO\nHDlZwVsLdjk7HLckCd5DZCdHojWssKUfHqB1NoQlSU+8k72zKI/Symp+O7Sds0Nxqu6twxmRGcfE\nhXkUnjjt7HDcjq+zAxDmyEwMJdDPqMPbtHWbUsZV/IKXoLgQQj1joJU7OVFWyUdL87mmcyvaxbZw\ndjhNV1UORTuN76OT+6GsyNhcpqYCLH4Q0ML4CImH8CTjwsI/+ILTPD28PTO3HOTlGdt5fWw3J/xF\n3JckeA8R4OtDzzYRLMk9avvJMm+GBf+AjV/AgCdtP59olA+W5FNaWcOjg1KdHUrjnDpibB6TNx/2\nrzMemtN1tNz6BIC1CvT5kyOedPGUAAAgAElEQVQVRKdDfA/jI2UQRLQlPiyI+we0ZcK8Xdzdtw3d\nWoc74m/jEZQrtSAppbQrxeNu3lqwi39M387KPw4mJiTQtpN9cI3RMvn4OuOqXjjEyfIq+v1jLtnJ\nkUy8M8vZ4VzaqcPGDKNNk6FwjfFaUDjEZ0GrLhDbCcJaQ4tW0CwKfPyN7yetoeo0lBcb32fH8+Ho\nTuMHQ+EaKKu9UIlMhbShlLUbyeWfnSQxIphvHu7rVS2jDaGUQmt9wf8ocgXvQfqnRgGwdFcRo7rZ\nWFrpfgd8+yDkL4a2A0yITjTER8v2UFJezWODXHigmNawZwks/y/k/GhcibfsAoP+BCmDoVUmWHwu\nfg6ljHKMfzCEtIKEc36YaQ3H8iB3Nuz8CVa9R/DyN5nTrA3vFGYxa0UzhmZ3te/f0UPIFbwHsVo1\n3V+YxZAOsbx6Y6ZtJ6ssg/9rD+nD4HrZWcsRyiqr6f/SPLokhPLhPb2cHc6FtDa6qxa8DAc3QlAE\n9LgLuoyFGDtuHVheDFunojd8gdqzmGp8UBmj8enzK0joYb913Uh9V/DSReNBLBZFn+RIluYetf3p\nP/9gYz7N1v/B6RPmBCgu6rMVezlWWul6V+9aw6658M4V8OXtUFUG170Ov90KQ/5i3+QOEBgK3e9A\n3fMDq0fMZVL1UGq2T4d3B8H7w2G3PHldH0nwHqZfahT7i8vJLyqz/WTd74TqcqO+KuyqvKqGtxfm\n0S81kh5JLnQT8fge+HwsfDwaSo/CyAnwqxXQ427jwTgHy+reg/ltn+AK65uUD34Rju+GSdfCh9fC\nnqUOj8fVSYL3MP1q6/CLzeimietqzIlf+5Ht5xIX9e26Qo6crOCRgS7SOVNdCQtfhQm9jSvkK5+H\nx9ZAt9vBx7m37p4e1p7C0378u2yI0QQw7B9wdAd8MBw+vwWK5KGoMyTBe5g2kcHEhQay1IwED9D9\nLqPeun+9OecTF7BaNe8syqNTfAh9Ulxg5szh7fDuYJj7PKRdCY+uhH6Pg2+AsyMDoFN8KCO7xvHe\n4t0cOq0g+2F4fL1RLtq90Pih9NOfjNq9l5ME72GUUvRLjWJZXhFWqwk3rDuPMfqW131s+7lEneZs\nP0zekVLGXZbi3PY/qxWWvwUTLzdaF8d+Bjd/DKEJzoupHk9emU6NVfOv2bUz4/2Dof8T8Nha4zmO\npf+BN7rDxq+MewheShK8B+qXGsWJsiq2HjBhlnZQOHQcARsnG33LwnQTF+4iPiyIqzvZ8ASyrcqO\nwWc3woynoe3l8Kvl0P4a58VzCa0jg7mtdxJfrtpH7uFzBuO1iDXuE4ybB+FtYMoD8MkNxr0ELyQJ\n3gP1rf0135Q6PBg3WyuMVjVhrrV7j7Mq/zj39W+Lr7N2azqwwbhq370Qrn4Vbv3S2ADGxT02KJVg\nf19embn9wjfjusF9P8Hwl2HfCngz27iqr/GuqZSS4D1QTEgg7WKbmzO2ACCpP4S3hTUfmnM+cdY7\nC/MIDfLj5p6Jzglg/Wfw3lBjF697ZkCvB9zmyeXI5gE8eFkyM7ccYs2e4xceYPGB3g/CIyug7WXw\n0zPw/lVedRNWEryH6psSxar8Y1RUm7D9nsUCWffA3qVwaKvt5xMA5B8tZcaWg9ye3ZpmAQ7uTLFa\nYdaf4buHIaEnjFvglg8N3TegLVHNA3hp+vb6n/0ITYBbvoAb3oOiXHirP6x61ytq85LgPVS/1CjK\nq6ys22vSQ0pdbzdutq5+z5zzCd5dnIefxcJdfds4duGqcvjmPljyL8i6F+74DppHOzYGkwT7+/Kb\nIWmszD/GnG2H6z9QKaNh4FfLjJHYPzwJn46BkgOOC9YJJMF7qN7JEfhYlHllmmaR0Ol6Yzu/ipPm\nnNOLFZ2qYPLqAkZ3iyemhY2D4Rqj7Bh8PAq2TIErn4Nr/un0vnZb3dwzkbZRzXhpxnZqLtU5FhIH\nt08x7jXkL4H/9oEt3zkmUCeQBO+hQgL96JIQal6CB+h5P1Sego1fmndOL/XZir1UVFt54LK2jlu0\nZL9Rgy5cC2M+gH6/dpt6+8X4+Vj43dB0dh4+xZS1BZf+AqWMew0PLYaIZJh8F3z/G4/sEpME78H6\npUSxoaCYk+VV5pwwvge06gqr3vOK+qW9VNVY+XTFXgakRZEa46ANPY7nw/vDjJLEHd8av415kKs7\nt6RLQiivzdpBeVUD7ztFpcK9M6Hfb2DNB/DOIOMhLw8iCd6D9UuNosaqWZFn4zZ+ZyhlXMUf3gp7\nl5lzTi80a+shDpaUc1efNo5Z8EiOkdwrSuCuqdCmn2PWdSClFOOHtWd/cTmfLG9Ez7uPH1z5V7j9\nG2O2/cSBxmgOD7mAkQTvwbonhRHoZ2HJLhPLNJ1uMKb7rXzHvHN6mQ+X5pMYEcQV7R3Qa35gI3xw\ntdEGefePEN/d/ms6Sd/UKAakRfGfebmUNPa31tQh8PASSOwFUx8zbkKXm/CgoJNJgvdgZ7bxW7TT\nxATvH2x01GybCicPmXdeL7HtQAkrdx/jjuwkfCx2rn8f3AQfjQDfQLh3BsR2tO96LuDpYe05UVbF\nxAV5jf/iFi2N8tWg/2fceH17gHG/wo1Jgvdwl7eLJvfwKfabuSN91r1grYa1k8w7p5f4aFk+gX4W\nbsqy84NNh7fDR6PALxjungaRKfZdz0V0ig/lukxjENnhkvLGn8DiA5f9Du750Xjq9b2hsGyC25Zs\nJMF7uMvaGf3NC3ccMe+kUanG1myr3oXqCvPO6+GKy6r4dl0ho7rGExbsb7+FjuYaV+4WH7jre4hw\nYKeOC3jyynZU1Vh5Y+7Opp+kdTY8tAjShsLMPxpjiMtMupflQJLgPVxaTHNahgSycKeJCR6gz6/g\n1CHYPMXc83qwyWv2UV5l5U573lw9thsmXWfU3O+c6jVX7udqE9WMW3q15ouV+8g/Wtr0EwVHwNhP\nYdhLsGuO8QTsHvdqLjAlwSulhimlcpRSuUqp8XW8H6CU+rL2/RVKqTZmrCsuTSnFZe2iWLzzKNU1\nVvNOnDIYotu79a+vjlRj1Xy0bA+92kTQMS7EPosUF8CkEVB9Gu78n/230nNhjw1Oxc/Hwqs/5dh2\nIqUg+yFjcJmPP3x4jbERitXEf0t2ZHOCV0r5ABOA4UBH4Bal1Pl3c+4DjmutU4HXgJdsXVc03GXt\noikpr2ZDgYkbICgFfR6BQ5sgX/bEvJQFOw6z91gZd/ZNss8Cp0/ApzdC+Qlj9EDLTvZZx03EtAjk\n/gFtmbbxAJvM+L6P6wYPLoSMUcZGKJ9cb7RVujgzruB7Abla6zytdSXwBTDyvGNGAmfuyH0NDFZO\n3dnAu/RPjcKiTK7DA3S+CYKjjKt4cVEfLt1DbEgAV2XYYeZ7dSV8dYexbd3NHxtbLQrGXZZMeLAf\nL80w6eGlwBBjYNl1bxjPgfy3H+yaZ8657cSMBB8P7Dvn84La1+o8RmtdDRQDLrA3mXcIC/anS0KY\n+XV4v0Djke8dM+CoDTe0PFzekVMs3HGE23on4Wf2zHetjb7t3QthxH8geaC553djLQL9eOSKVBbn\nHmWxWa3CSkGPu+CBeUaN/uPRMOd5l50z73I3WbOyss5+TJw40dnheIzL2kWzYd8JTpRVmnvirPuM\nKZPL3zT3vB7k4+V78PNRjO1lh9bIuS/Axi/gij9B11vMP7+buz07ifiwIF6asd2cLSzPiO0ID8yF\nbrfBoldh0rVQXGje+U1iRoIvBM79zk2ofa3OY5RSvkAoUFTXyVavXn32Y9y4cSaEJwAubxeFVZu4\ny9MZzaOhy02w/nMorfP/Uq9WWlHN16sLuKZzK/OnRq7+wEgu3e80erfFBQL9fHjiynZsKizmx80m\njwb2b2ZsD3j9O8ZDZW/1h5wZ5q5hIzMS/CogTSnVVinlD4wFzt/bbSpwV+2fxwBzdb3T+YU9ZCaE\n0SLQ1/w6PBg3W6tPw0r5jet8U9YVcrKimjvNnvm+4ydjpnnqELjmNY+YCmkvo7vFkx7bgldn5lBl\nZifZGV1uMjZMCY2Hz2+GGX90medDbE7wtTX1R4GZwDbgK631FqXUc0qpEbWHvQdEKqVygd8CF7RS\nCvvy9bHQPzWKhTuO1r/zTVPFdID0a2DFWzIr/hxaaz5amk/n+FC6JYaZd+L962Dy3RCbATd+6Pbz\n3O3Nx6J46qp08ovK+HLVvkt/QVNEpcJ9s6HXOFg+wRhadmCjfdZqBFNq8FrrH7XW7bTWKVrrF2tf\ne1ZrPbX2z+Va6xu11qla615a6yYMihC2uqxdNAdLytl57i70ZhnwpNGit0p2fDpj2a4idh4+xV19\n22Ba09jxPfDpTRAcCbdNhgAHjRt2c4M7xJCVFM7rc3ZSVmmnG6J+gXD1K3DrZOOp13eugAWvOPUG\nrMvdZBX2Y5exBWck9DA6OJZN8MiNE5riw6X5hAf7cW2XVuacsOyYsc1cTQXc/rUxHEs0iFKK8cPb\nc+RkBR8sybfvYu2GGlsDdhwF816A94fCkR32XbMekuC9SHxYECnRzVhgjwQPMOB3UHoY1n1in/O7\nkYLjZczedoixvVoT6Odj+wmryuGL24yNO8Z+DtHptp/Ty2S1iWBIhxjemr+L46Umd5OdLzgCxrxn\nlNCO7TYmUy79t8Ov5iXBe5nL28WwYvcx+/ya2qY/JPaGJa9DjUm7SLmpT1fsBYw2PZtZrfDdw7B3\nKYz6r0du2OEoT13VnlOV1bw5P9cxC2aMhl8th5RB8NOf4J2BULjGMWsjCd7rXNE+mspqK0tz7dDS\nqJRRiy/e59X7tpZX1fDFyr1c2TGW+LAg2084+8/GJtlD/gqdx9h+Pi+W3rIF13dLYNKyPRSaOUL7\nYlrEwtjP4KaPoPQovDMYfvy9QzYUkQTvZXq1jaCZvw9zc+w0RyNtKLTsAgtf8dqr+O837Od4WRV3\nmdEaufIdWPqGsVViv1/bfj7Bb4e2A+C1WQ6siysFHUfCIyuNTpuVE2FCL9j4lV2H9UmC9zIBvj70\nT4ti3vbD5rdLgvGNfMUzRq3YC2vxWmsmLcsnLaY5fZJtnMax/QeY/ntIvxqGvyy97iaJDwvizuwk\npqwtYMchB7f1BobA1S/D/XOgeSxMeQDeuxIKVttlOUnwXmhw+1gOFJez7YCdvrnbXQUJPY2r+Kom\n7KrjxtbuPcHmwhLutLU1smA1fH2fMcXwhveMzTuEaR65IpVm/r68PMPGccJNldDDmGcz6r9wYh+8\nOxi2nv98qO0kwXuhge2Ndsm52+20p6pSxr6WJYWw+n37rOGiPlqWT4sAX67vdv68vUY4lgef3WzU\nbm/50tgHV5gqvJk/D16ezOxth1iR56QRGxYLdL0VHltj/HtJHWL+EqafUbi8mBaBdEkIZe52O86z\nTr4c2l4Gi/4PKuzwYJULOnyynB83HWBMVgLNApr4dGlpEXwyBrQVbvvGmPUj7OK+/snEhQby3LSt\n1Jg5iKyxApobs4Ts8INcEryXuiI9hnX7TlB0yo4zMwY9C2VHjREGXuDzFfuoqtFN35Kv6jR8Ptb4\nzeeWL4zH34XdBPn78PTw9mzZX8LXa+w0wsDJJMF7qcEdYtAa+z30BJDY07hBuPhfcMqO67iAymor\nn67Yw+Xtomkb1azxJ7DWwDf3Q8EqYzph697mBykuMCIzjh5J4bwyM4eT5Z7X9SUJ3kt1igslqnkA\nc+xZpgG48jlj0uS8F+27jpPN3HKQwycruKupW/LNfAa2T4Nhf4eOIy59vDCFUopnr+3I0VOV/Gee\ngx5+ciBJ8F7KYlEMah/Nwh1H7DNC9YyoNGNTkLWT4NBW+63jZB8ty6d1RDAD28U0/ouXTYAV/4Xs\nX0H2w6bHJi4uMzGMG7on8MHifPYUlTo7HFNJgvdig9rHcLK8mtX5x+270MDxEBACPz1j14c6nGXL\n/mJW5R/nzj5JWCyNbI3c8q1x9d5hBAz17N9yXNnvh6Xj66N48Ydtzg7FVJLgvVj/tGj8fJT92iXP\nCI6Ay5+GXXMhd7Z913KCj5buIcjPhxt7NHJLvvzFMGWcMb/n+olG25xwitiQQB65IpWfth5iqdm7\nnjmRfEd5seYBvvRJieKnrYfs81TruXreDxEpMGO8y+x2Y4bjpZV8t76QUd3iCQ32a/gXHtoKn98K\n4W3hls/Bz4SZNcIm9/VvS0J4EH+euoXKajuWLR1IEryXG9oxlj1FZew4ZOdedV9/4xHtolyjq8ZD\nfLV6HxXV1sbdXC0ugE9uMPqeb//G+A1HOF2gnw9/uS6DnYdP8d7i3c4OxxSS4L3c0I6xKGV0gdhd\n6hDIuN54+Klol/3Xs7Maq+bj5Xvo3TaC9i1DGvZFp08YDzJVnoLbvoawRpZ1hF0N6RjLlR1jeWPO\nTgqOlzk7HJtJgvdyMSGBdEsM46etDkjwYLQB+gbAD791+xuuc7cfpuD46YY/2FRVDl/cavwWc/Mn\n0LKTXeMTTfOXERnGf6e6f9eXJHjB0IyWbC4sccwVS4uWMPhZyJtvjEp1Yx8u3U2r0ECGZsRe+uCa\namNy4J4lMPotY5SDcEnxYUH8Zkgas7cdYtZWOzcg2JkkeMFVGcbeng77Zs6615g2Of33UHLAMWua\nbOehkyzJLeL27CT8fC7xz8hqhe8fh21T4aq/yaYdbuDe/m1Jj23BX6Zusd8m3Q4gCV7QNqoZ7WKb\nO6YOD8bo29FvG900Ux91y1LNpGX5+PtaGNvzEjV0rWHmH2D9pzDwD9DnEYfEJ2zj52PhhdGdKDxx\nmv/7yTkbZptBErwAYGjHlqzcfYxj9t6M+IzIFGOMQe5sWPOhY9Y0SfHpKr5ZU8iIzDgimwdc/OB5\nLxrD1rIfMZ4FEG6jZ5sIbs9uzftLdrNmzzFnh9MkkuAFYJRprBrmbHNgzbHn/dD2cuNJTjfqqpm8\neh+nq2q4+1Jb8i153dj0pPudcNWLsiOTGxo/vANxoUE8NXkj5VU1zg6n0STBCwA6xYcQFxrIzC0O\nTPAWC4ycAD5+MPkuY1yui6uxaj5atoespHA6xYfWf+DSf8OsZ4220Gv/JcndTTUP8OWlG7qQd7TU\nsXu4mkQSvACMqXpDM1qyaOcRTlU48KZSWKLxmP7BTTDd9UsY83MOs/dYGXf3a1P/QYv+CT/9CTJG\n144gkO323Fn/tChu6dWadxblsW6vnec2mUwSvDjrmi6tqKi2OrZMA8Yerv2fMCZOrv/csWs30odL\n82kZEni28+gCC16BOX+FTmPg+neN306E2/vj1e1pGRLIk19tcKuuGknw4qwercNpGRLI9xuc0Lp4\nxZ8gqT9MewIK1zh+/QbIPXyKRTuPclvv1he2RmoNc1+AeS9Al7HGlbtPE7ftEy6nRaAfr96Uye6i\nUv7qRg9ASYIXZ1ksiqs7t2LhjiMUn3bw7jY+vnDjh8YepJ+NhRN7Hbt+A3y0LB9/Hwu39G79yzdq\nqmHab4wbqt1uh1FvSlnGA/VNieLhy1P4cvU+ftjoHs9vSIIXv3BtZisqa6zOeYKveTTcOtnoj//0\nJigvdnwM9Sgpr+LrNQVcm9mKqHNbI6tOw1d3Gq2eA56EEf+R5O7BnriyHZmJYfxhykYKT7h+U4Ak\nePEL3RLDiA8L4oeN+50TQEx7uPkjKNppJPkKO0+5bKCvVxdQVlnDPX3b/vxi6VH4eDTk/AjDXzZG\nMEi3jEfz87Hwxtiu1Fg1j3++zuXHCkuCF7+glOKaLq1YtPMoJ8oc9NDT+ZIHwg3vQsFK+HwsVDp3\nql+NVTNpWT7dW4fROaG2NfLARpg4EPavgzHvQ+8HnRmicKCkyGb8/YYurNlznBd/cO16vCR4cYFr\nu7Si2qodN7qgLhmjYfREY9ejz8dCxUmnhTJr6yH2FJVxX/9k44Ut38L7V4G1Bu6ZDp2ud1pswjlG\nZMZxf/+2TFq2h2/WFDg7nHpJghcX6BwfSuuIYKY5+0ZSlxuNyYv5i+GDq+Gkcyb7vbsoj4TwIK5q\nFwI//A4m3w2xnWDcPIjv7pSYhPONH96e7OQI/vjtJjYVuM79onPZlOCVUhFKqVlKqZ21/w2v45iu\nSqllSqktSqmNSqmbbVlT2J9Simu7tGLpriKOnHTy9nqZY+HWL41RBu8NgUNbHLr8ur3HWb3nOL/N\nrMH3/Sth1TvGXJm7pxmjj4XX8vWx8J9buxPVPID7Jq1yyZuutl7BjwfmaK3TgDm1n5+vDLhTa50B\nDAP+pZQKs3FdYWeju8VTY9VM3eCkm63nSrvSSKjVFfDOYFj/mcOW/nBBDr8PnMLoVbfCqUNGl8+w\nvxmblgivF9U8gA/u6cnpqhru+WCl49uLL0HZstmyUioHGKi1PqCUagXM11qnX+JrNgBjtNY763hP\n233zZ9FgI/6zmBqr5ofHBzg7FMPJQ/DNfZC/yJjxMvwlaB5jt+UOr59OyZTfkmrZbzyZOuzvdl1P\nuK+luUe564OV9EgKZ9K9vQjwdWyrrFIKrfUFLVy2XsHHaq3PFGoPAhfd2kYp1QvwB9xndKAXu75b\nPFv2l7D9YImzQzG0iIU7vjOeet0+Df7TE1a9CzUmXzUVroWPRhLz3Vj8VTXHRn8GY96T5C7q1Tc1\nipfHdGF53jEe+XSty7RPXjLBK6VmK6U21/Ex8tzjai+96738rr3C/xi4R2td798+Kyvr7MfEiRMb\n8VcRZrsuMw5fi+LbtYXODuVnPr5w+VPw0GKIzYAfnoT/ZMGaSba1U9ZUw7Zp8ME18M4VWA9s5B/W\nO/l3+0+JyLzGvPiFxxrdLYHnR3Vi9rbDPPKZayR5h5RolFIhwHzgb1rrry9yPinRuJj7J61mY8EJ\nlv1hMD4WF3uIR2vYOQvmPg8HN0JAqNGymH41tB0AfkEX//ryYti30vhtYNv3UFYEoYnQ+0HeO30Z\nz88q4MfHB9AxLsQxfx/hET5als+z/9vCkA4x/PuW7gT5279cU1+JxtYE/wpQpLX+h1JqPBChtf79\necf4A9OB77XW/7rE+STBu5jpmw7w8Kdr+ejeXlzWLtrZ4dRNa9i7DFa9BznToaoULL4Q1Q6i06FZ\nNASGGqWcqjIoLoBjeXAkB9Dg1wzShxl1/XbDqNQWLnt5Hikxzfj0/mxn/+2EG/p4+R6e/d9muiaG\n8d5dPYlo5m/X9eyV4COBr4DWwB7gJq31MaVUFvCQ1vp+pdTtwAfAuf1td2ut19dxPknwLqaiuoae\nL8xmUPsY/jW2m7PDubTqCqNvfs8SOLjZGHlQVgTlJeDjD36BEBIP4W2gVSa0zobE3r+42v9q1T5+\n/81GPrynJwPTpe4ummbG5gP8+ov1xIUFMfGOHqTFtrDbWnZJ8GaTBO+anvl2E9+sLWDlM0MICXTT\n+eZaN2hOTI1VM+SfC2gW4MP3j/ZHyWwZYYPV+cd46JM1lFbU8LfrOzG6W4Jd1rFXF43wAjdlJVJe\nZeV/612gJ76pGpiof9x0gN1HS3lkYKokd2GzrDYR/Pj4ADonhPLElxt44sv1jtvYHknwogG6JISS\nERfCZyv24sm/YWmtmTAvl5ToZvXv2CREI8WEBPLZ/b359eA0pm3cz+D/m88XK/dSXWP/LhtJ8OKS\nlFLc2rs12w6UsH7fCWeHYzfzcg6z/eBJfjUwFYurdQwJt+brY+GJK9sx7bEBJEc3Z/yUTVz52kK+\nXlNAeVWN3daVGrxokFMV1fR6cTbXdG7FKzdmOjsc02mtueG/SzlUUsH8pwZeuCWfECbRWjNr6yH+\nOWsH2w+eJCTQl1Hd4rm7bxuSo5s36ZxSgxc2aR7gy8iucXy/cb/Lzdsww/K8Y6zde4KHLk+W5C7s\nSinF0IyWTP/1AD5/IJuB6TF8uWqfXWrzsiuwaLBbeyXx+cp9fLeukLv6tnF2OKb699ydRDUP4Mas\nRGeHIryEUoo+KZH0SYmktKKaID/zH4iSSxXRYJ0TQukcH8ony/d41M3WZbuKWLqriIcuTybQDv/I\nhLiUZgG+drnvIwleNMpdfduw8/ApFucedXYoptBa889ZOcSGBHB7dpKzwxHCVJLgRaNcl9mKqOYB\nvLd4t7NDMcXCnUdZlX+cR69Ilat34XEkwYtGCfD14Y7sJObnHCH3sPP2STWD1pp//pRDfFgQN/WU\n2rvwPJLgRaPdlt0af18LHyzJd3YoNpmz7TAbCop5fHCqwzdoEMIRJMGLRotqHsDorvF8s7aA4w58\n7NpMNVbNqz/lkBQZzPXd7TMfRAhnkwQvmuS+AW0pr7LywdJ8Z4fSJN+sLWD7wZM8dVW69L0LjyXf\n2aJJ2sW2YGjHWD5cspuScvd68KmssppXZ+bQNTGMazq3cnY4QtiNJHjRZI8NSqOkvJqPl+1xdiiN\n8s7C3Rw+WcGfrukgEyOFR5MEL5qsc0IoA9OjeXdRHmWV1c4Op0EOl5Tz9sJdDO/Ukqw2Ec4ORwi7\nkgQvbPLYoFSOl1Xx6fK9zg6lQV6emUNltZWnh7V3dihC2J0keGGTHkkR9E+N4r8LdnHSxWvxq/KP\n8fWaAu4fkEybqGbODkcIu5MEL2z29LD2HCut5O0Fec4OpV7VNVb+33ebiQsN5PHBqc4ORwiHkAQv\nbNY5IZTrMuN4d3Eeh0rKnR1OnT5cms/2gyd59roMgv1liKrwDpLghSmeGppOjVXzr9k7nB3KBQ4W\nl/ParB0MTI/mqoxYZ4cjhMNIghemaB0ZzG29k/hy1T62HShxdjhnaa0ZP2UjNVrz1xEZ0hYpvIok\neGGa3wxJIyzYn2e+3YTV6hrz4ievLmB+zhHGD2tPUqTcWBXeRRK8ME1YsD9/vLoDa/ee4KvV+5wd\nDoUnTvP8tK30bhvBnX3aODscIRxOErww1Q3d4+nVNoJ/zNjO0VMVToujxqr53VcbqNGaV8Zk2mW3\nHCFcnSR4YSqlFC+O6kRZRQ1/mLLJaVv7/XvuTpblFfGXERm0jgx2SgxCOJskeGG6tNgW/H5YOrO2\nHnJKqWZp7lFen7OTG1In3BwAAAbLSURBVLoncJNsoi28mCR4YRf39mtL35RI/vr9VvKPljps3X3H\nynjs83WkRDfn+VEZDltXCFckCV7YhcWiePXGTPx9LTz48RpKK+w/jKz4dBX3fLiKaqtm4h095IEm\n4fUkwQu7iQsL4t+3dGPn4ZP8bvIGu9bjK6preOTTteQfLeW/t3cnObq53dYSwl1Ighd2NSAtmj8M\n78D0zQd58YdtdknyldVWHvl0LYtzj/L36zvTNyXK9DWEcEfyO6ywu/sHtKXwxGneXbybkCA/Hh+c\nZtq5K6prePzzdczedpjnR2Zwo9xUFeIsSfDC7pRSPHttR0rKq/jnrB2UVlTz9LD2NvemnyirZNzH\na1i5+xh/vq4jd8jDTEL8gk0JXikVAXwJtAHygZu01sfrOTYE2Ap8p7V+1JZ1hfuxWBSvjMmkmb8v\nby/MY39xOX+/vjPNA5r2LbipoJjHPl/L/hPlvD62KyO7xpscsRDuT9lSE1VKvQwc01r/Qyk1HgjX\nWj9dz7GvA9G1x9eZ4JVS2lkPxgjH0Frz1oI8Xpm5ncSIYP55UyY9khq+dV55VQ3vLMzjjbk7iWwW\nwL9v7UZP2XpPeDmlFFrrC34ltjXB5wADtdYHlFKtgPla6/Q6jusBPAXMALIkwYuVu4/xxJfrKTxx\nmusy43jo8mQy4kLrPb6ssprv1u1nwrxcCk+c5pourXhxVCfCgv0dGLUQrsleCf6E1jqs9s8KOH7m\n83OOsQBzgduBIUiCF7VOVVTz9oJdvLtoN6eraujQKoQBaVGkxjQnPNifqhor+46VsXbvcZbkFnGq\noprO8aH84er20ikjxDmanOCVUrOBlnW89Qww6dyErpQ6rrUOP+/rHwWCtdYvK6Xu5hIJvkePHmc/\nHzduHOPGjbtofML9FZdV8fXaAn7acpC1e49TVfPL78n4sCAuaxfNDd3j6ZEULjPdhTiP00o0SqlP\ngQGAFWgO+ANvaq3H13E+uYL3cpXVVvafOE1JeRW+FgvxYUGEBvs5OywhXJq9EvwrQNE5N1kj9P9v\n7+5CrCgDMI7/H9yiNOiDQGpX0AspliCMCEuIyAKjaLuKgsKiy0qLQKqbbvcioi4iWMwSEiM2IYno\nAwu6k0iD1C0UK11bWyH6oBsTni5mFpYFxZid8+6Z8/xuzsywzDwve/bZOe85Z8bedoGff4JM0URE\nLKrzFXzTb7KOA/dKOko1vz5eH+xWSdsb7jsiIhpodAa/2HIGHxHx/7V1Bh8REUtUCj4ioqNS8BER\nHZWCj4joqBR8RERHpeAjIjoqBR8R0VGdKfiJiYnSEXouYx4MGfNgaGPMKfg+ljEPhox5MKTgIyLi\noi25SxWUzhAR0Y8W/WqSERGxdGWKJiKio1LwEREd1fcFL2mTpB8lHatvOtJpklZJ+krSEUmHJW0t\nnalXJC2TdFDSx6Wz9IKkqyRNSvpB0pSk20tnapuk5+vn9SFJuyVdVjpTGyTtkDQr6dC8bddI+kLS\n0frx6gvt42L0dcFLWga8CdwHjAKPShotm6p154AXbI8C64GnB2DMc7YCU6VD9NAbwKe2bwRupuNj\nlzQMbKG669tNwDLgkbKpWvMusGnBtheBfbbXAvvq9Ub6uuCB24Bjto/bPgu8D4wVztQq2zO2D9TL\nf1P90Q+XTdU+SSPA/cBA3ClM0pXAncDbALbP2v6jbKqeGAIulzQELAd+LZynFba/Bn5fsHkM2Fkv\n7wQeanqcfi/4YeDkvPVpBqDs5khaDawD9pdN0hOvA9uobt4+CNYAZ4B36mmp7ZJWlA7VJtungFeB\nE8AM8Kftz8um6qmVtmfq5dPAyqY77PeCH1iSrgA+BJ6z/VfpPG2S9AAwa/vb0ll6aAi4BXjL9jrg\nHxbhJftSVs85j1H9c7seWCHpsbKpyqjvXdr4M+z9XvCngFXz1kfqbZ0m6RKqct9le0/pPD2wAXhQ\n0s9U03B3S3qvbKTWTQPTtudenU1SFX6X3QP8ZPuM7X+BPcAdhTP10m+SrgOoH2eb7rDfC/4bYK2k\nNZIupXpDZm/hTK2SJKp52Snbr5XO0wu2X7I9Yns11e/4S9udPrOzfRo4KemGetNG4EjBSL1wAlgv\naXn9PN9Ix99YXmAvsLle3gx81HSHQ013UJLtc5KeAT6jesd9h+3DhWO1bQPwOPC9pO/qbS/b/qRg\npmjHs8Cu+uTlOPBk4Tytsr1f0iRwgOrTYgeBTl51TNJu4C7gWknTwCvAOPCBpKeAX4CHGx8nlyqI\niOimfp+iiYiI80jBR0R0VAo+IqKjUvARER2Vgo+I6KgUfERER6XgIyI6KgUfEdFR/wFaeZovUlXO\n8gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4eeebe4850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = arange(0.01,10,0.01)\n",
    "plt.plot(x, j0(x))\n",
    "plt.plot(x, sin(x)/x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x, r, gr = PositionalSuceptibility2D(frames[0::100], 0.025, 2.0*pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 6)"
      ]
     },
     "execution_count": 431,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Uv6m75NOWygOPhusrAi8mdpV44C0NwQXZEO1RU/zH49544Nb+QlELJexf1hG4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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4eecd13850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r[1:], (gr[1:]-1.0))\n",
    "plt.plot(r[1:], 1/power(r[1:], 1.0/3.0))\n",
    "plt.xlim(0,6)\n",
    "#plt.ylim(0.001,10.0)\n",
    "#plt.xscale('log')\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yAnJeP4BYw/g9Xq6AygmQou1Ifjni5BmJzEot+XhDjJWCFyoot+SXkgwFcJp/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4eeeb1d750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r[1:], abs(gr[1:]-1.0))\n",
    "plt.plot(r[1:], 1/power(r[1:], 1.0/3.0))\n",
    "plt.xlim(1,35)\n",
    "plt.ylim(0.001,5.0)\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:12: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
      "image/png": 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AzYHTgV/WTHI18BQwvV3BmZnZ+FFkD+kUYDKwU0ScCPwxPzIiAvg9sGP7wjMzs/GiSELa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\nBSckMzMrhf8PJtu2oyRDCs8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4eeea26890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "\n",
    "for r_gr in r_grs:\n",
    "    plt.plot(r_grs[0][0], r_grs[0][1], marker='o', linewidth = 2.0, markersize=2, color = 'red', markerfacecolor='None')\n",
    "    \n",
    "#plt.plot([sum(incpca.explained_variance_ratio_[:i]) for i in range(1,len(incpca.explained_variance_ratio_))], marker='o', linewidth = 1.0, markersize=12, color = 'red')\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "plt.xlim(20,30)\n",
    "plt.ylim(0.6,1.4)\n",
    "#plt.yscale('log')\n",
    "\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'Explained variance', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import trapz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1062.9743662982394"
      ]
     },
     "execution_count": 266,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho = float(len(frames[0]['coords']))/frames[0]['L']\n",
    "trapz(2.0*pi*rho*(gr-1.0), r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "510.23707895340073"
      ]
     },
     "execution_count": 277,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho = float(len(frames[0]['coords']))/frames[0]['L']\n",
    "trapz(2.0*pi*rho*r*(gr-1.0), r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.55\n",
      "\n",
      "eta=0.555\n",
      "\n",
      "eta=0.56\n",
      "\n",
      "eta=0.565\n",
      "\n",
      "eta=0.57\n",
      "\n",
      "eta=0.575\n",
      "\n",
      "eta=0.58\n",
      "\n",
      "eta=0.585\n",
      "\n",
      "eta=0.59\n",
      "\n",
      "eta=0.595\n",
      "\n",
      "eta=0.6\n",
      "\n",
      "eta=0.605\n",
      "\n",
      "eta=0.61\n",
      "\n",
      "eta=0.615\n",
      "\n",
      "eta=0.62\n",
      "\n",
      "eta=0.625\n",
      "\n",
      "eta=0.63\n",
      "\n",
      "eta=0.635\n",
      "\n",
      "eta=0.64\n",
      "\n",
      "eta=0.645\n",
      "\n",
      "eta=0.65\n",
      "\n",
      "eta=0.655\n",
      "\n",
      "eta=0.66\n",
      "\n",
      "eta=0.665\n",
      "\n",
      "eta=0.67\n",
      "\n",
      "eta=0.675\n",
      "\n",
      "eta=0.68\n",
      "\n",
      "eta=0.685\n",
      "\n",
      "eta=0.69\n",
      "\n",
      "eta=0.695\n",
      "\n",
      "eta=0.7\n",
      "\n",
      "eta=0.705\n",
      "\n",
      "eta=0.71\n",
      "\n",
      "eta=0.715\n",
      "\n",
      "eta=0.72\n",
      "\n",
      "eta=0.725\n",
      "\n",
      "eta=0.73\n",
      "\n",
      "eta=0.735\n",
      "\n",
      "eta=0.74\n",
      "\n",
      "eta=0.745\n",
      "\n",
      "eta=0.75\n",
      "\n",
      "eta=0.755\n",
      "\n",
      "eta=0.76\n",
      "\n",
      "eta=0.765\n",
      "\n",
      "eta=0.77\n",
      "\n",
      "eta=0.775\n",
      "\n",
      "eta=0.78\n",
      "\n",
      "eta=0.785\n",
      "\n",
      "eta=0.79\n",
      "\n",
      "eta=0.795\n",
      "\n",
      "eta=0.8\n",
      "\n",
      "eta=0.805\n",
      "\n",
      "eta=0.81\n",
      "\n",
      "eta=0.815\n",
      "\n",
      "eta=0.82\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r_grs = []\n",
    "Xs = []\n",
    "\n",
    "for etas, file_base in file_data:\n",
    "    for eta in etas:\n",
    "        print 'eta={}\\n'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True)\n",
    "        \n",
    "        X, r, gr = PositionalSuceptibility2D(frames[0::200], 0.025, k=2.0*pi/1.0)\n",
    "        Xs.append(X)\n",
    "        r_grs.append([r, gr])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (52,) and (55,)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mValueError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-54-397daf70341c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0mcolors\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m200\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'green'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'purple'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'orange'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'teal'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'black'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'red'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0metas\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mXs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmarker\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'o'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmarkersize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcolors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;31m#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/ryanj/.local/lib/python2.7/site-packages/matplotlib/pyplot.pyc\u001b[0m in \u001b[0;36mplot\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   3259\u001b[0m                       mplDeprecation)\n\u001b[1;32m   3260\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3261\u001b[0;31m         \u001b[0mret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3262\u001b[0m     \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3263\u001b[0m         \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_hold\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwashold\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/ryanj/.local/lib/python2.7/site-packages/matplotlib/__init__.pyc\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1715\u001b[0m                     warnings.warn(msg % (label_namer, func.__name__),\n\u001b[1;32m   1716\u001b[0m                                   RuntimeWarning, stacklevel=2)\n\u001b[0;32m-> 1717\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1718\u001b[0m         \u001b[0mpre_doc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minner\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1719\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/ryanj/.local/lib/python2.7/site-packages/matplotlib/axes/_axes.pyc\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1370\u001b[0m         \u001b[0mkwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_alias_map\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1371\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1372\u001b[0;31m         \u001b[0;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1373\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1374\u001b[0m             \u001b[0mlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/ryanj/.local/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_grab_next_args\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    402\u001b[0m                 \u001b[0mthis\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    403\u001b[0m                 \u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 404\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    405\u001b[0m                 \u001b[0;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    406\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/ryanj/.local/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_plot_args\u001b[0;34m(self, tup, kwargs)\u001b[0m\n\u001b[1;32m    382\u001b[0m             \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    383\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 384\u001b[0;31m         \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    385\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    386\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'plot'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/ryanj/.local/lib/python2.7/site-packages/matplotlib/axes/_base.pyc\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[0;34m(self, x, y)\u001b[0m\n\u001b[1;32m    241\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    242\u001b[0m             raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[0;32m--> 243\u001b[0;31m                              \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[1;32m    244\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    245\u001b[0m             raise ValueError(\"x and y can be no greater than 2-D, but have \"\n",
      "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (52,) and (55,)"
     ]
    },
    {
     "data": {
      "image/png": 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iC3DKr6Wqnpjk7UleMcb4v6XM7Ph931rGGLeNMZ6V5GlJXl5VT1ja7OY3u47fSnJ4jHFk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\nKQEHaErAAZr6f89e5ubNhb1XAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f132ad710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "plt.axvspan(0.76, 0.76001, alpha=1, color='black')\n",
    "\n",
    "#plt.axvspan(0.72, 0.72001, alpha=10, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "\n",
    "plt.plot(etas, Xs, marker='o', linewidth = 1.0, markersize=12, color = colors[i])\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "plt.xlim(0.60, 0.84)\n",
    "#plt.ylim(-0.1,0.1)\n",
    "\n",
    "#plt.ylim(-0.1,0.1)\n",
    "#plt.yscale('log')\n",
    "\n",
    "#plt.yscale('log')\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'Positional susceptibility', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.74165739,  3.46410162])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm([[1,2,3],[2,2,2]], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.  ,   0.02,   0.04,   0.06,   0.08,   0.1 ,   0.12,   0.14,\n",
       "         0.16,   0.18,   0.2 ,   0.22,   0.24,   0.26,   0.28,   0.3 ,\n",
       "         0.32,   0.34,   0.36,   0.38,   0.4 ,   0.42,   0.44,   0.46,\n",
       "         0.48,   0.5 ,   0.52,   0.54,   0.56,   0.58,   0.6 ,   0.62,\n",
       "         0.64,   0.66,   0.68,   0.7 ,   0.72,   0.74,   0.76,   0.78,\n",
       "         0.8 ,   0.82,   0.84,   0.86,   0.88,   0.9 ,   0.92,   0.94,\n",
       "         0.96,   0.98,   1.  ,   1.02,   1.04,   1.06,   1.08,   1.1 ,\n",
       "         1.12,   1.14,   1.16,   1.18,   1.2 ,   1.22,   1.24,   1.26,\n",
       "         1.28,   1.3 ,   1.32,   1.34,   1.36,   1.38,   1.4 ,   1.42,\n",
       "         1.44,   1.46,   1.48,   1.5 ,   1.52,   1.54,   1.56,   1.58,\n",
       "         1.6 ,   1.62,   1.64,   1.66,   1.68,   1.7 ,   1.72,   1.74,\n",
       "         1.76,   1.78,   1.8 ,   1.82,   1.84,   1.86,   1.88,   1.9 ,\n",
       "         1.92,   1.94,   1.96,   1.98,   2.  ,   2.02,   2.04,   2.06,\n",
       "         2.08,   2.1 ,   2.12,   2.14,   2.16,   2.18,   2.2 ,   2.22,\n",
       "         2.24,   2.26,   2.28,   2.3 ,   2.32,   2.34,   2.36,   2.38,\n",
       "         2.4 ,   2.42,   2.44,   2.46,   2.48,   2.5 ,   2.52,   2.54,\n",
       "         2.56,   2.58,   2.6 ,   2.62,   2.64,   2.66,   2.68,   2.7 ,\n",
       "         2.72,   2.74,   2.76,   2.78,   2.8 ,   2.82,   2.84,   2.86,\n",
       "         2.88,   2.9 ,   2.92,   2.94,   2.96,   2.98,   3.  ,   3.02,\n",
       "         3.04,   3.06,   3.08,   3.1 ,   3.12,   3.14,   3.16,   3.18,\n",
       "         3.2 ,   3.22,   3.24,   3.26,   3.28,   3.3 ,   3.32,   3.34,\n",
       "         3.36,   3.38,   3.4 ,   3.42,   3.44,   3.46,   3.48,   3.5 ,\n",
       "         3.52,   3.54,   3.56,   3.58,   3.6 ,   3.62,   3.64,   3.66,\n",
       "         3.68,   3.7 ,   3.72,   3.74,   3.76,   3.78,   3.8 ,   3.82,\n",
       "         3.84,   3.86,   3.88,   3.9 ,   3.92,   3.94,   3.96,   3.98,\n",
       "         4.  ,   4.02,   4.04,   4.06,   4.08,   4.1 ,   4.12,   4.14,\n",
       "         4.16,   4.18,   4.2 ,   4.22,   4.24,   4.26,   4.28,   4.3 ,\n",
       "         4.32,   4.34,   4.36,   4.38,   4.4 ,   4.42,   4.44,   4.46,\n",
       "         4.48,   4.5 ,   4.52,   4.54,   4.56,   4.58,   4.6 ,   4.62,\n",
       "         4.64,   4.66,   4.68,   4.7 ,   4.72,   4.74,   4.76,   4.78,\n",
       "         4.8 ,   4.82,   4.84,   4.86,   4.88,   4.9 ,   4.92,   4.94,\n",
       "         4.96,   4.98,   5.  ,   5.02,   5.04,   5.06,   5.08,   5.1 ,\n",
       "         5.12,   5.14,   5.16,   5.18,   5.2 ,   5.22,   5.24,   5.26,\n",
       "         5.28,   5.3 ,   5.32,   5.34,   5.36,   5.38,   5.4 ,   5.42,\n",
       "         5.44,   5.46,   5.48,   5.5 ,   5.52,   5.54,   5.56,   5.58,\n",
       "         5.6 ,   5.62,   5.64,   5.66,   5.68,   5.7 ,   5.72,   5.74,\n",
       "         5.76,   5.78,   5.8 ,   5.82,   5.84,   5.86,   5.88,   5.9 ,\n",
       "         5.92,   5.94,   5.96,   5.98,   6.  ,   6.02,   6.04,   6.06,\n",
       "         6.08,   6.1 ,   6.12,   6.14,   6.16,   6.18,   6.2 ,   6.22,\n",
       "         6.24,   6.26,   6.28,   6.3 ,   6.32,   6.34,   6.36,   6.38,\n",
       "         6.4 ,   6.42,   6.44,   6.46,   6.48,   6.5 ,   6.52,   6.54,\n",
       "         6.56,   6.58,   6.6 ,   6.62,   6.64,   6.66,   6.68,   6.7 ,\n",
       "         6.72,   6.74,   6.76,   6.78,   6.8 ,   6.82,   6.84,   6.86,\n",
       "         6.88,   6.9 ,   6.92,   6.94,   6.96,   6.98,   7.  ,   7.02,\n",
       "         7.04,   7.06,   7.08,   7.1 ,   7.12,   7.14,   7.16,   7.18,\n",
       "         7.2 ,   7.22,   7.24,   7.26,   7.28,   7.3 ,   7.32,   7.34,\n",
       "         7.36,   7.38,   7.4 ,   7.42,   7.44,   7.46,   7.48,   7.5 ,\n",
       "         7.52,   7.54,   7.56,   7.58,   7.6 ,   7.62,   7.64,   7.66,\n",
       "         7.68,   7.7 ,   7.72,   7.74,   7.76,   7.78,   7.8 ,   7.82,\n",
       "         7.84,   7.86,   7.88,   7.9 ,   7.92,   7.94,   7.96,   7.98,\n",
       "         8.  ,   8.02,   8.04,   8.06,   8.08,   8.1 ,   8.12,   8.14,\n",
       "         8.16,   8.18,   8.2 ,   8.22,   8.24,   8.26,   8.28,   8.3 ,\n",
       "         8.32,   8.34,   8.36,   8.38,   8.4 ,   8.42,   8.44,   8.46,\n",
       "         8.48,   8.5 ,   8.52,   8.54,   8.56,   8.58,   8.6 ,   8.62,\n",
       "         8.64,   8.66,   8.68,   8.7 ,   8.72,   8.74,   8.76,   8.78,\n",
       "         8.8 ,   8.82,   8.84,   8.86,   8.88,   8.9 ,   8.92,   8.94,\n",
       "         8.96,   8.98,   9.  ,   9.02,   9.04,   9.06,   9.08,   9.1 ,\n",
       "         9.12,   9.14,   9.16,   9.18,   9.2 ,   9.22,   9.24,   9.26,\n",
       "         9.28,   9.3 ,   9.32,   9.34,   9.36,   9.38,   9.4 ,   9.42,\n",
       "         9.44,   9.46,   9.48,   9.5 ,   9.52,   9.54,   9.56,   9.58,\n",
       "         9.6 ,   9.62,   9.64,   9.66,   9.68,   9.7 ,   9.72,   9.74,\n",
       "         9.76,   9.78,   9.8 ,   9.82,   9.84,   9.86,   9.88,   9.9 ,\n",
       "         9.92,   9.94,   9.96,   9.98,  10.  ,  10.02,  10.04,  10.06,\n",
       "        10.08,  10.1 ,  10.12,  10.14,  10.16,  10.18,  10.2 ,  10.22,\n",
       "        10.24,  10.26,  10.28,  10.3 ,  10.32,  10.34,  10.36,  10.38,\n",
       "        10.4 ,  10.42,  10.44,  10.46,  10.48,  10.5 ,  10.52,  10.54,\n",
       "        10.56,  10.58,  10.6 ,  10.62,  10.64,  10.66,  10.68,  10.7 ,\n",
       "        10.72,  10.74,  10.76,  10.78,  10.8 ,  10.82,  10.84,  10.86,\n",
       "        10.88,  10.9 ,  10.92,  10.94,  10.96,  10.98,  11.  ,  11.02,\n",
       "        11.04,  11.06,  11.08,  11.1 ,  11.12,  11.14,  11.16,  11.18,\n",
       "        11.2 ,  11.22,  11.24,  11.26,  11.28,  11.3 ,  11.32,  11.34,\n",
       "        11.36,  11.38,  11.4 ,  11.42,  11.44,  11.46,  11.48])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arange(0.0, 23./2.0, 0.02)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.96"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "11.48*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import save, load"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "numpy.save(file, arr, allow_pickle=True, fix_imports=True)[source]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file = open(\".testfile.txt\",\"r\") "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "save(file, [[1,2],[3,43],[9.0,7]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = array([[1,2,3],[4,5,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with open('./data.pickle', 'wb') as handle:\n",
    "    pickle.dump(a, handle, protocol=pickle.HIGHEST_PROTOCOL)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with open('./processed_data/raw_OPs.pickle', 'rb') as handle:\n",
    "    raw_OPs = pickle.load(handle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "frames = ReadGSD('../hoomd_disks/trajectories_ww_4000p/trajectory_1.5000.gsd', shuffle_data=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "r, gr = RDF2D(frames[0::10], 0.15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bDPId+q23XoP//o4bAABvesVa73YvyPvq7V962tmMdHRqEYZlYyZvYM2QMwMnyJKNWnhd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f1307b590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(r[1:], gr[1:]-1)\n",
    "#plt.plot(r, 1/power(r, 1.0/3.0))\n",
    "#plt.xlim(1,35)\n",
    "#plt.ylim(0.001,5.0)\n",
    "#plt.xscale('log')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'D': 2, 'L': 46.310482, 'coords': array([[ 17.61962891,  20.17847633],\n",
       "        [ 17.09300041,  17.70657349],\n",
       "        [  5.15569687,   3.58562469],\n",
       "        ..., \n",
       "        [ 30.17601585,   2.96033478],\n",
       "        [ 32.05548096,   2.4064827 ],\n",
       "        [ 39.42152786,  18.0430069 ]], dtype=float32), 'diameters': array([ 1.,  1.,  1., ...,  1.,  1.,  1.], dtype=float32), 'types': array([u'A', u'A', u'A', ..., u'B', u'B', u'B'],\n",
       "       dtype='<U1')}"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frames[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'unique' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mNameError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-111-04fbbc13f2aa>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0munique\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mframes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'types'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'unique' is not defined"
     ]
    }
   ],
   "source": [
    "frames[0]['types']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import unique, place, transpose\n",
    "from copy import deepcopy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "particle_types = deepcopy(frames[0]['types'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([u'A', u'B'],\n",
       "      dtype='<U1')"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unique(particle_types)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True, ..., False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "particle_types == 'A'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#place(particle_types, particle_types=='A', [[1,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([u'A', u'A', u'A', ..., u'B', u'B', u'B'],\n",
       "      dtype='<U1')"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "particle_types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "NumPy boolean array indexing assignment cannot assign 2 input values to the 2048 output values where the mask is true",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mValueError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-150-de5caf0ceff3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mparticle_types\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mparticle_types\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'A'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: NumPy boolean array indexing assignment cannot assign 2 input values to the 2048 output values where the mask is true"
     ]
    }
   ],
   "source": [
    "particle_types[particle_types == 'A'] = (1,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([u'5', u'5', u'5', ..., u'B', u'B', u'B'],\n",
       "      dtype='<U1')"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "particle_types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LabelBinarizer(neg_label=0, pos_label=1, sparse_output=False)"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lb = preprocessing.LabelBinarizer()\n",
    "lb.fit(['A','B', 'C'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, ..., 0, 1, 0])"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lb.transform(particle_types).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lb.transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "frames = ReadGSD('../hoomd_disks/trajectories_ww_4000p/trajectory_1.0000.gsd', shuffle_data=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features = FrameToFeatures(frames[0], 50, ['composition'], 10, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0,\n",
       "       0, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 307,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy\n",
    "from numpy import power, rint, sqrt, sum, unique, repeat, arccos, dot, transpose, append, cos, sin, hstack, maximum, minimum, pi, array\n",
    "from numpy.linalg import norm\n",
    "from numpy.random import shuffle\n",
    "from sklearn import preprocessing\n",
    "\n",
    "#this generates NN features for the PCA analysis (or some other machine learning method as well)\n",
    "def FrameToFeatures(frame, N_nn, method, particle_inc, nn_inc):\n",
    "    #extract some relevant frames level details\n",
    "    coords = deepcopy(frame['coords'])\n",
    "    p_types = deepcopy(frame['types'])\n",
    "    D = float(frame['D'])\n",
    "    N = float(len(coords))\n",
    "    V = power(frame['L'], D)\n",
    "    normalizing_distance = power(V/N, 1.0/D)\n",
    "    diameters = frame['diameters']\n",
    "    diameters_scaled = frame['diameters']/frame['diameters'][0]\n",
    "    \n",
    "    frame_features = []\n",
    "    combined_data = zip(coords, p_types)\n",
    "    for particle, p_type in combined_data[0::particle_inc]:\n",
    "        #nearest neighbor coordinate wrapping\n",
    "        Rpj_v = particle - coords\n",
    "        Rpj_v = Rpj_v - rint(Rpj_v/frame['L'])*frame['L']\n",
    "        Rpj = (sqrt(sum(power(Rpj_v, 2.0), axis=1)))     \n",
    "        \n",
    "        #generate statistics for various nearest neighbors\n",
    "        sorter = Rpj.argsort()\n",
    "        Rpj = Rpj[sorter[::1]]\n",
    "        \n",
    "        #for composition calculations (the identity of the tagged particle is automatically included via the 0th entry)\n",
    "        if 'composition' in method:\n",
    "            p_types_one_hot = p_types[sorter[::1]]\n",
    "            lb = preprocessing.LabelBinarizer()\n",
    "            lb.fit(unique(p_types_one_hot))\n",
    "            p_types_one_hot = lb.transform(p_types_one_hot).flatten()\n",
    "        \n",
    "        #chosen axis for measuring angles based on nearest neighbor\n",
    "        if 'angular' in method:\n",
    "            #sort the particle-particle vectors according to distance\n",
    "            Rpj_v = Rpj_v[sorter[::1]]\n",
    "            \n",
    "            #normalize all of the vectors\n",
    "            Rpj_v = Rpj_v/maximum(norm(Rpj_v, axis=1), 1.0e-10)[:,None]\n",
    "            \n",
    "            #find the unit x and y axis to base all angular details on using the 1st and 2nd nearest neighbors\n",
    "            x_axis = Rpj_v[1] #this specifies the x direction to measure the angular elevation from\n",
    "            y_axis = Rpj_v[2] - array([dot(Rpj_v[2], Rpj_v[1]), 0.0]) #this specifies the upper two quadrants\n",
    "            y_axis = y_axis/norm(y_axis)\n",
    "            \n",
    "            #compute the raw angle between 0-pi that has unresolved upper and lower quadrants\n",
    "            x_axis_T = transpose(x_axis)\n",
    "            y_axis_T = transpose(y_axis)\n",
    "            Tpj = arccos(minimum(maximum(dot(Rpj_v, x_axis_T), -0.9999999), 0.9999999))\n",
    "            \n",
    "            #determine if the vector points into the upper quadrant defined by the second nearest neighbor\n",
    "            LQ = arccos(minimum(maximum(dot(Rpj_v, y_axis_T), -0.9999999), 0.9999999)) > pi/2.0\n",
    "            \n",
    "            #adjust the angle to upper or lower quadrants \n",
    "            Tpj[LQ] = 2.0*pi - Tpj[LQ]\n",
    "        \n",
    "        #possible feature options\n",
    "        feature_batch = []\n",
    "        if 'distance' in method:\n",
    "            feature_batch.extend((Rpj[1:N_nn+1]/normalizing_distance)[0::nn_inc])\n",
    "        if 'composition' in method:\n",
    "            feature_batch.extend(p_types_one_hot[0:N_nn+1][0::nn_inc])\n",
    "        if 'angular' in method:\n",
    "            feature_batch.extend(append(cos(Tpj[2:N_nn+1])[0::nn_inc], \n",
    "                                        sin(Tpj[2:N_nn+1])[0::nn_inc], axis=0))\n",
    "            \n",
    "        frame_features.append(feature_batch)\n",
    "\n",
    "    return array(frame_features)\n",
    "\n",
    "#this converts an entire trajectory into features\n",
    "def TrajectoryToFeatures(frames, N_nn, method, particle_inc, nn_inc):\n",
    "    #print filename\n",
    "    features = []\n",
    "    for frame in frames:        \n",
    "        features_sp = FrameToFeatures(frame, N_nn, method, particle_inc, nn_inc)\n",
    "        for feature in features_sp:\n",
    "            features.append(feature)\n",
    "    return features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### WR mixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy\n",
    "from numpy import power, rint, sqrt, sum, unique, repeat, arccos, dot, transpose, append, cos, sin, hstack, maximum, minimum, pi, array\n",
    "from numpy.linalg import norm\n",
    "from numpy.random import shuffle\n",
    "from sklearn import preprocessing\n",
    "\n",
    "#this generates NN features for the PCA analysis (or some other machine learning method as well)\n",
    "def FrameToFeaturesComposition(frame, probe_particle_indicies):\n",
    "    #extract some relevant frames level details\n",
    "    coords = deepcopy(frame['coords'])\n",
    "    p_types = deepcopy(frame['types'])\n",
    "    D = float(frame['D'])\n",
    "    N = float(len(coords))\n",
    "    V = power(frame['L'], D)\n",
    "    normalizing_distance = power(V/N, 1.0/D)\n",
    "    diameters = frame['diameters']\n",
    "    diameters_scaled = frame['diameters']/frame['diameters'][0]\n",
    "    \n",
    "    #reduce the coords down to only those we care about\n",
    "    coords = coords[probe_particle_indicies]\n",
    "\n",
    "    #build up the features considering only the probes\n",
    "    frame_features = []\n",
    "    for particle in coords:\n",
    "        #nearest neighbor coordinate wrapping\n",
    "        Rpj_v = particle - coords\n",
    "        Rpj_v = Rpj_v - rint(Rpj_v/frame['L'])*frame['L']\n",
    "        Rpj = (sqrt(sum(power(Rpj_v, 2.0), axis=1)))     \n",
    "        \n",
    "        #extend the feature vector stacking the particle side by side\n",
    "        frame_features.extend(Rpj/normalizing_distance)\n",
    "\n",
    "    return array(frame_features)\n",
    "\n",
    "#this converts an entire trajectory into features\n",
    "def TrajectoryToFeaturesComposition(frames, probe_particle_indicies):\n",
    "    features = []\n",
    "    for frame in frames:        \n",
    "        features.append(FrameToFeaturesComposition(frame, probe_particle_indicies))\n",
    "    return features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "103"
      ]
     },
     "execution_count": 418,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(arange(0,4096,1)[0::40])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#specify what data to read in and process\n",
    "file_data = [(arange(0.100, 2.06001, 0.04), '../hoomd_disks/trajectories_ww_4000p')]\n",
    "probe_particle_indicies = arange(0,4096,1)[0::40]\n",
    "split=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 484,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.1\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.14\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.18\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.22\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.26\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.3\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.34\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.38\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.42\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.46\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.5\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.54\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.58\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.62\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.66\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.7\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.74\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.78\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.82\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.86\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.9\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.94\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.98\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.02\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.06\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.1\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.14\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.18\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.22\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.26\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.3\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.34\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.38\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.42\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.46\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.5\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.54\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.58\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.62\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.66\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.7\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.74\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.78\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.82\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.86\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.9\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.94\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.98\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=2.02\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=2.06\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "incpca = IncrementalPCA(n_components=16, whiten=True)\n",
    "\n",
    "frames = None\n",
    "features = None\n",
    "split_features = None\n",
    "\n",
    "for etas, file_base in file_data:\n",
    "    for eta in etas:\n",
    "        print 'eta={}\\n'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeaturesComposition(frames_partial, probe_particle_indicies=probe_particle_indicies)\n",
    "            incpca.partial_fit(features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "        frames_split = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:20: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n"
     ]
    },
    {
     "data": {
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D33D4WutP3WkqU/ed2pK2taLt1dZ5aOFDdKiDlbGSzpGdACxYsmCN/s7zjB0zttvyq7Un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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f305d1d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "#plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "#plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "#plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "#plt.axvspan(0.781, 0.781001, alpha=1, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "for i in range(0,1):\n",
    "    p_data = incpca.components_[i]\n",
    "    plt.plot(range(len(incpca.components_[0])), p_data, marker='o', linewidth = 0.0, markersize=6, color = colors[i])\n",
    "    #p_data = OPs_non_abs[:,i]\n",
    "    #plt.plot(etas, (p_data), marker='o', linewidth = 2.0, markersize=10, color = colors[i])\n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 2.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "#plt.xlim(0,103)\n",
    "#plt.ylim(-1,0)\n",
    "#plt.ylim(0,0.5)\n",
    "#plt.ylim(-2,1.5)\n",
    "#plt.ylim(5, 13)\n",
    "#plt.ylim(1, 0.001)\n",
    "#plt.ylim(-2000.0, 2000)\n",
    "\n",
    "#plt.xscale('log')\n",
    "plt.xlabel(r'$n$th nerest neighbor', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'$P_{i}$ weight', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA feature weights', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eta=0.1\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.14\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.18\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.22\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.26\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.3\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.34\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.38\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.42\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.46\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.5\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.54\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.58\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.62\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.66\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.7\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.74\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.78\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.82\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.86\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.9\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.94\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=0.98\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.02\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.06\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.1\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.14\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.18\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.22\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.26\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.3\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.34\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.38\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.42\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.46\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.5\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.54\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.58\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.62\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.66\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.7\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.74\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.78\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.82\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.86\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.9\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.94\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=1.98\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=2.02\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "eta=2.06\n",
      "\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "OPs = []\n",
    "frames = None\n",
    "features = None\n",
    "raw_OPs = []\n",
    "\n",
    "for etas, file_base in file_data:\n",
    "    for eta in etas:\n",
    "        print 'eta={}\\n'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        means = []\n",
    "        raw_OPs_single = []\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeaturesComposition(frames_partial, probe_particle_indicies=probe_particle_indicies)\n",
    "            transformed_features_partial = incpca.transform(features_partial)\n",
    "            means.append(mean(transformed_features_partial, axis=0))\n",
    "            raw_OPs_single.append(transformed_features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "            \n",
    "        means = array(means)\n",
    "        op = mean(means, axis=0)\n",
    "        OPs.append(op)\n",
    "        raw_OPs.append(raw_OPs_single)\n",
    "    \n",
    "OPs = array(OPs)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import std, abs, power\n",
    "from scipy.stats import moment\n",
    "\n",
    "OPs = []\n",
    "OPs_std = []\n",
    "OPs_abs = []\n",
    "OPs_third = []\n",
    "for single_eta in raw_OPs:\n",
    "    merged_data = []\n",
    "    for split in single_eta:\n",
    "        merged_data.extend(split)\n",
    "    \n",
    "    OPs.append(mean((split), axis=0))\n",
    "    OPs_std.append(std(split, axis=0))\n",
    "    OPs_abs.append(mean(abs(split), axis=0))\n",
    "    OPs_third.append(moment(split, 4, axis=0))\n",
    "\n",
    "OPs = array(OPs)\n",
    "OPs_std = array(OPs_std)\n",
    "OPs_abs = array(OPs_abs)\n",
    "OPs_third = array(OPs_third)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:23: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n"
     ]
    },
    {
     "data": {
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+fYCxp4ylrKKM35zxG/71xb+qlf+7qxgBNu/fzJ/e/RNv/PoNPt/6OYfLD3sd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\nIWjAUkopVSFowFJKKVUh/D+vqwblnSo9tgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f2e371ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#highlight the transition region if found\n",
    "plt.axvspan(0.700, 0.716, alpha=0.2, color='grey')\n",
    "plt.axvspan(0.716, 0.730, alpha=0.2, color='blue')\n",
    "\n",
    "plt.axvspan(0.716, 0.716001, alpha=1, color='black')\n",
    "plt.axvspan(0.76, 0.76001, alpha=1, color='black')\n",
    "\n",
    "#plt.axvspan(0.72, 0.72001, alpha=10, color='black')\n",
    "\n",
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "for i in range(0,1): #12,13\n",
    "    p_data = OPs[:,i]\n",
    "    plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i], markerfacecolor='None')\n",
    "    p_data = OPs_abs[:,i]\n",
    "    #plt.plot(etas, (p_data), marker='o', linewidth = 1.0, markersize=12, color = colors[i])\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#axis range and labels (also specify if log or not)\n",
    "plt.xlim(0.10, 2.1)\n",
    "#plt.ylim(-0.1,0.1)\n",
    "\n",
    "#plt.ylim(-0.1,0.1)\n",
    "#plt.yscale('log')\n",
    "\n",
    "#plt.yscale('log')\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'$\\langle P_{i} \\rangle$ and $\\langle |P_{i}| \\rangle$', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ryanj/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:12: MatplotlibDeprecationWarning: The set_axis_bgcolor function was deprecated in version 2.0. Use set_facecolor instead.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
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RYlJPT6OaYw3Q4+PRknxcWk8zjkkrXBMr9VzGVykvrR/oTt+GxImIpyPiKtIpzC2A7zZj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\nAJAsQgwAkKwfL7S5l9QEVuQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0f1374bf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the principal components\n",
    "colors = 200*['green', 'purple', 'orange', 'teal', 'black', 'red']\n",
    "\n",
    "plt.plot(incpca.explained_variance_ratio_, marker='o', linewidth = 1.0, markersize=12, color = 'red', markerfacecolor='None')\n",
    "#plt.plot([sum(incpca.explained_variance_ratio_[:i]) for i in range(1,len(incpca.explained_variance_ratio_))], marker='o', linewidth = 1.0, markersize=12, color = 'red')\n",
    "    \n",
    "#plt.plot(etas, num_defects, marker='o', linewidth = 1.0, markersize=10, color = 'black')    \n",
    "\n",
    "#backround grid details\n",
    "axes = plt.gca()\n",
    "axes.grid(b = True, which = 'both', axis = 'both', color = 'gray', linestyle = '-', alpha = 0.5, linewidth = 0.5) \n",
    "axes.set_axis_bgcolor('white')  \n",
    "\n",
    "#font scpecifications\n",
    "title_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'heavy','size': 20}\n",
    "axis_label_font = {'family' : 'arial', 'color'  : 'black', 'weight' : 'normal','size': 20}                                                   \n",
    "\n",
    "#figure size and tick style\n",
    "plt.rcParams[\"figure.figsize\"] = [6,6]\n",
    "plt.rc('axes',edgecolor='black',linewidth=1)\n",
    "plt.tick_params(which='both', axis='both', color='black', length=4, width=0.5)\n",
    "plt.rcParams['xtick.direction'] = 'in'\n",
    "plt.rcParams['ytick.direction'] = 'in'\n",
    "\n",
    "#plt.ylim(0.0,0.8)\n",
    "#plt.yscale('log')\n",
    "\n",
    "plt.xlabel(r'$\\eta$', y=3, fontsize=20, fontdict = axis_label_font)\n",
    "plt.ylabel(r'Explained variance', fontsize=20, fontdict = axis_label_font)\n",
    "\n",
    "#title and axis labels\n",
    "plt.tick_params(axis='both', labelsize=20)\n",
    "plt.title('PCA hard disks', y=1.05, fontdict = title_font)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Old stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "OPs = []\n",
    "frames = None\n",
    "features = None\n",
    "raw_OPs = []\n",
    "\n",
    "for etas, file_base in file_data:\n",
    "    for eta in etas:\n",
    "        print 'eta={}\\n'.format(eta)\n",
    "        filename = \"{}/trajectory_{:.4f}.gsd\".format(file_base, eta)\n",
    "        frames = ReadGSD(filename, shuffle_data=True, randomize=randomize)\n",
    "        \n",
    "        frames_split = array_split(frames, split)\n",
    "        frames = None\n",
    "        count = 0\n",
    "        means = []\n",
    "        raw_OPs_single = []\n",
    "        for frames_partial in frames_split:\n",
    "            features_partial = TrajectoryToFeatures(frames_partial, \n",
    "                                                    N_nn=N_nn, \n",
    "                                                    method=method, \n",
    "                                                    particle_inc=particle_inc, \n",
    "                                                    nn_inc=nn_inc)\n",
    "            features_partial_ig_projection = incpca_ig.inverse_transform(incpca_ig.transform(features_partial))\n",
    "            transformed_features_partial = incpca.transform(features_partial - features_partial_ig_projection)\n",
    "            means.append(mean(transformed_features_partial, axis=0))\n",
    "            raw_OPs_single.append(transformed_features_partial)\n",
    "            count = count + 1\n",
    "            print count\n",
    "            \n",
    "        means = array(means)\n",
    "        op = mean(means, axis=0)\n",
    "        OPs.append(op)\n",
    "        raw_OPs.append(raw_OPs_single)\n",
    "    \n",
    "OPs = array(OPs)        "
   ]
  }
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