prediction-generation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T20:09:10.850000",
     "start_time": "2016-04-02T20:09:10.649000"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:39:55.102000",
     "start_time": "2016-04-02T22:39:53.939000"
    },
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Category plastic: Found 177 files, created 177 trajectories\n"
     ]
    }
   ],
   "source": [
    "# Read all data files of one category.\n",
    "import os\n",
    "\n",
    "category = 'plastic'\n",
    "downsample_steps = {'alive': 2, 'fibro': 5, 'plastic': 5}  # TODO: Rename var.\n",
    "\n",
    "data_dir = 'data/JulianTrajs/' + category\n",
    "trajectories = []\n",
    "filenames = os.listdir(data_dir)    \n",
    "for filename in filenames:\n",
    "    trajectory = np.genfromtxt(os.path.join(data_dir, filename))\n",
    "#     for start in range(1):\n",
    "#         end = -(downsample_steps[category] - start)\n",
    "#         sliced_trajectory = trajectory[start:end:downsample_steps[category]]\n",
    "    trajectories.append(trajectory[::downsample_steps[category]])\n",
    "trajectories = np.array(trajectories)\n",
    "\n",
    "print \"Category {}: Found {} files, created {} trajectories\".format(category, len(filenames), len(trajectories))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:39:55.109000",
     "start_time": "2016-04-02T22:39:55.104000"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This is not in um/min because no resampling was used for prediction.\n",
    "def to_velocities(x, multiple_trajectories=False):\n",
    "    return np.diff(x, axis=int(multiple_trajectories)) #/ 5.\n",
    "# TODO: Does only work for single trajectory right now, extend to multiple trajectories if needed.\n",
    "def to_positions(x):\n",
    "    return np.append(np.zeros((1, 3)), np.cumsum(x , axis=0), axis=0)#* 5., axis=0), axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:39:55.507000",
     "start_time": "2016-04-02T22:39:55.503000"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "trajectories = to_velocities(trajectories, multiple_trajectories=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:39:56.808000",
     "start_time": "2016-04-02T22:39:56.798000"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "48.116587\n"
     ]
    }
   ],
   "source": [
    "# Normalize trajectories to [-1, 1] for the LSTM network (it outputs values between -1 and 1 by default)\n",
    "# TODO: Do not use min/max values here but fixed value to generalize to other datasets.\n",
    "\n",
    "# TODO: Normalize by just dividigng through abs_max_value (i. e. not moving the mean).\n",
    "\n",
    "min_value = np.min(trajectories)\n",
    "max_value = np.max(trajectories)\n",
    "abs_max_value = max(abs(min_value), abs(max_value))\n",
    "print abs_max_value\n",
    "def normalize(x):\n",
    "    #return x / abs_max_value\n",
    "    return np.interp(x, [min_value, max_value], [-1., 1.])\n",
    "def denormalize(x):\n",
    "    #return x * abs_max_value\n",
    "    return np.interp(x, [-1., 1.], [min_value, max_value])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-03-31T01:18:07.731000",
     "start_time": "2016-03-31T01:18:07.718000"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Normalize to mean 0 and standard deviation 0.5.\n",
    "# TODO: Evaluate if this is better than normalizing to [-1, 1].\n",
    "traj_means = np.mean(trajectories, axis=(0, 1))\n",
    "traj_stds = np.std(trajectories, axis=(0, 1))\n",
    "#traj_stds[traj_stds == 0] = 1.  # Fix zero stds by setting them to 0.\n",
    "\n",
    "def normalize(x):\n",
    "    return np.nan_to_num((x - traj_means) / (3. * traj_stds))\n",
    "def denormalize(x):\n",
    "    return x * 3. * traj_stds + traj_means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:40:00.244000",
     "start_time": "2016-04-02T22:40:00.240000"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trajectories = normalize(trajectories)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:40:00.651000",
     "start_time": "2016-04-02T22:40:00.635000"
    },
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.12831537, -0.12740698, -0.1274353 ]),\n",
       " array([  6.68431155e-02,   7.43936720e-02,   2.23987495e-14]))"
      ]
     },
     "execution_count": 332,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(trajectories, axis=(0, 1)), np.std(trajectories, axis=(0, 1))\n",
    "# fibro, norm by dividing through abs_max_value: 0.0015, 0.0015, 0\n",
    "# fibro, norm to [-1, 1]: 0.12, 0.12, 0.11\n",
    "# fibro, norm to [0, 1]: 0.558, 0.558, 0.557"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:40:01.380000",
     "start_time": "2016-04-02T22:40:00.903000"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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QJDUZEpKkJkNCktRkSEiSmgwJaTmsgCQHfU1NT427M+mILMefL5X0HDB7cHl+dv5odyIN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\n2RO3ZGfUpQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a387d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, bins, patches = plt.hist(trajectories[:, :, 0].flatten(), bins=51, facecolor='green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:40:02.021000",
     "start_time": "2016-04-02T22:40:02.018000"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "batch_size = len(trajectories)\n",
    "num_timesteps = len(trajectories[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:40:03.103000",
     "start_time": "2016-04-02T22:40:03.036000"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Layer implementing a Gaussian mixture model.\n",
    "# Implementation largely follows https://github.com/fchollet/keras/issues/1061.\n",
    "# In contrast to the original code, the loss was divided by sqrt(2 pi) to use the same Gaussian as in numpy.random.norm \n",
    "\n",
    "from keras.layers import Layer\n",
    "# TODO: This is only implemented for theano, rewrite it using keras.backend (as an exercise).\n",
    "import theano\n",
    "import theano.tensor as T\n",
    "\n",
    "class GMMActivation(Layer):\n",
    "    \"\"\"\n",
    "    GMM-like activation function.\n",
    "    Assumes that input has (D+2)*M dimensions, where D is the dimensionality of the \n",
    "    target data. The first M*D features are treated as means, the next M features as \n",
    "    standard devs and the last M features as mixture components of the GMM. \n",
    "    \"\"\"\n",
    "    def __init__(self, M, **kwargs):\n",
    "        super(GMMActivation, self).__init__(**kwargs)\n",
    "        self.M = M\n",
    "\n",
    "    def get_output(self, train=False):\n",
    "        X = self.get_input(train)\n",
    "        D = T.shape(X)[1]/self.M - 2\n",
    "        # leave mu values as they are since they're unconstrained\n",
    "        # scale sigmas with exp, s.t. all values are non-negative \n",
    "        X = T.set_subtensor(X[:,D*self.M:(D+1)*self.M], T.exp(X[:,D*self.M:(D+1)*self.M]))\n",
    "        # scale alphas with softmax, s.t. that all values are between [0,1] and sum up to 1\n",
    "        X = T.set_subtensor(X[:,(D+1)*self.M:(D+2)*self.M], T.nnet.softmax(X[:,(D+1)*self.M:(D+2)*self.M]))\n",
    "        return X\n",
    "\n",
    "    def get_config(self):\n",
    "        config = {\"name\": self.__class__.__name__,\n",
    "                  \"M\": self.M}\n",
    "        base_config = super(GMMActivation, self).get_config()\n",
    "        return dict(list(base_config.items()) + list(config.items()))\n",
    "\n",
    "def gmm_loss(y_true, y_pred):\n",
    "    \"\"\"\n",
    "    GMM loss function.\n",
    "    Assumes that y_pred has (D+2)*M dimensions and y_true has D dimensions. The first \n",
    "    M*D features are treated as means, the next M features as standard devs and the last \n",
    "    M features as mixture components of the GMM. \n",
    "    \"\"\"\n",
    "    def loss(m, M, D, y_true, y_pred):\n",
    "        mu = y_pred[:,D*m:(m+1)*D]\n",
    "        sigma = y_pred[:,D*M+m]\n",
    "        alpha = y_pred[:,(D+1)*M+m]\n",
    "        return (alpha/sigma/np.sqrt(2. * np.pi)) * T.exp(-T.sum(T.sqr(mu-y_true),-1)/(2*sigma**2))\n",
    "\n",
    "    D = T.shape(y_true)[1]\n",
    "    M = T.shape(y_pred)[1]/(D+2)\n",
    "    seq = T.arange(M)\n",
    "    result, _ = theano.scan(fn=loss, outputs_info=None, \n",
    "    sequences=seq, non_sequences=[M, D, y_true, y_pred])\n",
    "    return -T.log(result.sum(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:41:06.419000",
     "start_time": "2016-04-02T22:40:05.187000"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Python\\27_32bit\\lib\\site-packages\\ipykernel\\__main__.py:23: DeprecationWarning: Division of two integer types with x / y is deprecated, please use x // y for an integer division.\n",
      "D:\\Python\\27_32bit\\lib\\site-packages\\ipykernel\\__main__.py:51: DeprecationWarning: Division of two integer types with x / y is deprecated, please use x // y for an integer division.\n"
     ]
    }
   ],
   "source": [
    "# Set up the network.\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Activation, Dropout\n",
    "from keras.layers import LSTM\n",
    "from keras.optimizers import RMSprop\n",
    "\n",
    "model = Sequential()\n",
    "model.add(LSTM(batch_input_shape=(batch_size, 1, 3), output_dim=10, return_sequences=False, stateful=True))\n",
    "# model.add(LSTM(batch_input_shape=(batch_size, 1, 3), output_dim=100, return_sequences=True, stateful=True))\n",
    "\n",
    "#model.add(LSTM(output_dim=10, return_sequences=False, stateful=True))\n",
    "#model.add(LSTM(output_dim=100, return_sequences=True, stateful=True))\n",
    "\n",
    "#model.add(LSTM(output_dim=100, return_sequences=True, stateful=True))\n",
    "#model.add(LSTM(output_dim=100, return_sequences=False, stateful=True))\n",
    "num_mixture_components = 10  # TODO: Play around with this parameter.\n",
    "model.add(Dense( (3+2) * num_mixture_components ))\n",
    "model.add(GMMActivation(num_mixture_components))\n",
    "model.compile(loss=gmm_loss, optimizer=RMSprop(lr=0.001))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:41:06.423000",
     "start_time": "2016-04-02T22:41:06.421000"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "losses = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:41:57.901000",
     "start_time": "2016-04-02T22:41:06.437000"
    },
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 - loss: 0.429314282007\n",
      "Epoch 2 - loss: -0.892840943939\n",
      "Epoch 3 - loss: -0.924454009082\n",
      "Epoch 4 - loss: -0.937840492258\n",
      "Epoch 5 - loss: -0.946719426296\n",
      "Epoch 6 - loss: -0.953109727981\n",
      "Epoch 7 - loss: -0.957881014307\n",
      "Epoch 8 - loss: -0.961565068579\n",
      "Epoch 9 - loss: -0.964437990216\n",
      "Epoch 10 - loss: -0.96674476121\n",
      "Epoch 11 - loss: -0.968820956993\n",
      "Epoch 12 - loss: -0.970644911359\n",
      "Epoch 13 - loss: -0.972300207421\n",
      "Epoch 14 - loss: -0.97381491295\n",
      "Epoch 15 - loss: -0.975175332393\n",
      "Epoch 16 - loss: -0.976385330778\n",
      "Epoch 17 - loss: -0.977497503997\n",
      "Epoch 18 - loss: -0.978531518181\n",
      "Epoch 19 - loss: -0.979483393831\n",
      "Epoch 20 - loss: -0.980301329224\n",
      "Epoch 21 - loss: -0.981093616741\n",
      "Epoch 22 - loss: -0.981851740628\n",
      "Epoch 23 - loss: -0.982472878333\n",
      "Epoch 24 - loss: -0.983139830661\n",
      "Epoch 25 - loss: -0.983779664981\n",
      "Epoch 26 - loss: -0.984331880577\n",
      "Epoch 27 - loss: -0.984877366631\n",
      "Epoch 28 - loss: -0.985416065006\n",
      "Epoch 29 - loss: -0.985920928593\n",
      "Epoch 30 - loss: -0.986425924404\n",
      "Epoch 31 - loss: -0.986891440037\n",
      "Epoch 32 - loss: -0.987342036082\n",
      "Epoch 33 - loss: -0.987753299237\n",
      "Epoch 34 - loss: -0.988175883123\n",
      "Epoch 35 - loss: -0.988575854171\n",
      "Epoch 36 - loss: -0.988981996481\n",
      "Epoch 37 - loss: -0.989366559076\n",
      "Epoch 38 - loss: -0.989735870273\n",
      "Epoch 39 - loss: -0.99009222624\n",
      "Epoch 40 - loss: -0.990443505019\n",
      "Epoch 41 - loss: -0.990748527853\n",
      "Epoch 42 - loss: -0.991067066157\n",
      "Epoch 43 - loss: -0.991391343986\n",
      "Epoch 44"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-338-5e98ff78025a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      6\u001b[0m     \u001b[0mlosses_epoch\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnum_timesteps\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 8\u001b[1;33m         \u001b[0mresults\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtrain_on_batch\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtrajectories\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrajectories\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      9\u001b[0m         \u001b[0mlosses_epoch\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     10\u001b[0m     \u001b[0mmean_loss\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlosses_epoch\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Python\\27_32bit\\lib\\site-packages\\keras\\models.pyc\u001b[0m in \u001b[0;36mtrain_on_batch\u001b[1;34m(self, X, y, accuracy, class_weight, sample_weight)\u001b[0m\n\u001b[0;32m    770\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_train_with_acc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mins\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    771\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 772\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_train\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mins\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    773\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    774\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mtest_on_batch\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maccuracy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msample_weight\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Python\\27_32bit\\lib\\site-packages\\keras\\backend\\theano_backend.pyc\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, inputs)\u001b[0m\n\u001b[0;32m    382\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minputs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    383\u001b[0m         \u001b[1;32massert\u001b[0m \u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minputs\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32min\u001b[0m \u001b[1;33m{\u001b[0m\u001b[0mlist\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtuple\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 384\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfunction\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0minputs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    385\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    386\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Python\\27_32bit\\lib\\site-packages\\theano\\compile\\function_module.pyc\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    857\u001b[0m         \u001b[0mt0_fn\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    858\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 859\u001b[1;33m             \u001b[0moutputs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    860\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    861\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'position_of_error'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Python\\27_32bit\\lib\\site-packages\\theano\\scan_module\\scan_op.pyc\u001b[0m in \u001b[0;36mrval\u001b[1;34m(p, i, o, n, allow_gc)\u001b[0m\n\u001b[0;32m    949\u001b[0m         def rval(p=p, i=node_input_storage, o=node_output_storage, n=node,\n\u001b[0;32m    950\u001b[0m                  allow_gc=allow_gc):\n\u001b[1;32m--> 951\u001b[1;33m             \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mo\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    952\u001b[0m             \u001b[1;32mfor\u001b[0m \u001b[0mo\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mnode\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0moutputs\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    953\u001b[0m                 \u001b[0mcompute_map\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mo\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Python\\27_32bit\\lib\\site-packages\\theano\\scan_module\\scan_op.pyc\u001b[0m in \u001b[0;36m<lambda>\u001b[1;34m(node, args, outs)\u001b[0m\n\u001b[0;32m    938\u001b[0m                         \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    939\u001b[0m                         \u001b[0mouts\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 940\u001b[1;33m                         self, node)\n\u001b[0m\u001b[0;32m    941\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mImportError\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtheano\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgof\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcmodule\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mMissingGXX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    942\u001b[0m             \u001b[0mp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mexecute\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mtheano/scan_module/scan_perform.pyx\u001b[0m in \u001b[0;36mtheano.scan_module.scan_perform.perform (C:\\Users\\Johannes\\AppData\\Local\\Theano\\compiledir_Windows-8-6.2.9200-Intel64_Family_6_Model_69_Stepping_1_GenuineIntel-2.7.8-32\\scan_perform\\mod.cpp:4193)\u001b[1;34m()\u001b[0m\n",
      "\u001b[1;32mD:\\Python\\27_32bit\\lib\\site-packages\\theano\\gof\\op.pyc\u001b[0m in \u001b[0;36mrval\u001b[1;34m(p, i, o, n)\u001b[0m\n\u001b[0;32m    910\u001b[0m             \u001b[1;31m# default arguments are stored in the closure of `rval`\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    911\u001b[0m             \u001b[1;32mdef\u001b[0m \u001b[0mrval\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnode_input_storage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mo\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnode_output_storage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnode\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 912\u001b[1;33m                 \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mo\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    913\u001b[0m                 \u001b[1;32mfor\u001b[0m \u001b[0mo\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mnode\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0moutputs\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    914\u001b[0m                     \u001b[0mcompute_map\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mo\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTrue\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\Python\\27_32bit\\lib\\site-packages\\theano\\tensor\\blas.pyc\u001b[0m in \u001b[0;36mperform\u001b[1;34m(self, node, inp, out)\u001b[0m\n\u001b[0;32m   1528\u001b[0m         \u001b[0mz\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mout\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1529\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1530\u001b[1;33m             \u001b[0mz\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1531\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1532\u001b[0m             \u001b[1;31m# The error raised by numpy has no shape information, we mean to\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# Train on complete trajectories.\n",
    "num_epochs = 300\n",
    "model.reset_states()\n",
    "for epoch in range(1, num_epochs+1):\n",
    "    print 'Epoch', epoch,\n",
    "    losses_epoch = []\n",
    "    for i in range(num_timesteps - 1):\n",
    "        results = model.train_on_batch(trajectories[:, i:i+1], trajectories[:, i+1])\n",
    "        losses_epoch.append(results[0])\n",
    "    mean_loss = np.mean(losses_epoch)\n",
    "    print '- loss:', mean_loss\n",
    "    losses.append(mean_loss)\n",
    "    model.reset_states()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:38:18.085000",
     "start_time": "2016-04-02T22:38:17.726000"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2dbbbb90>]"
      ]
     },
     "execution_count": 309,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x28fa39b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:42:10.964000",
     "start_time": "2016-04-02T22:42:10.462000"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Predict next timesteps using the training data as input (i. e. not the predictions themselves!).\n",
    "model.reset_states()\n",
    "predicted = []\n",
    "predicted.append(trajectories[:, 0])  # Take first timestep from training data so predicted and expected have the same dimensions.\n",
    "\n",
    "for i in range(num_timesteps - 1):\n",
    "    pred_parameters = model.predict_on_batch(trajectories[:, i:i+1])[0]\n",
    "    means = pred_parameters[:, :num_mixture_components * 3]\n",
    "    sds = pred_parameters[:, num_mixture_components * 3:num_mixture_components * (3 + 1)]\n",
    "    weights = pred_parameters[:, num_mixture_components * (3 + 1):]\n",
    "    \n",
    "    # Reshape arrays to allow broadcasting of means (3-dimensional vectors) and sds/weights (scalars).\n",
    "    means = means.reshape(-1, num_mixture_components, 3)\n",
    "    sds = sds[:, :, np.newaxis]\n",
    "    weights = weights[:, :, np.newaxis]\n",
    "    \n",
    "    pred = weights * np.random.normal(means, sds)\n",
    "    pred = np.sum(pred, axis=1)\n",
    "    predicted.append(pred)\n",
    "    \n",
    "predicted = np.array(predicted)\n",
    "predicted = predicted.transpose((1, 0, 2))\n",
    "expected = trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:42:30.406000",
     "start_time": "2016-04-02T22:42:29.855000"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mQ3Pg3YTFCsO2vcCahPY1YbuIHEVSeqRkZm+Y2UcJjyXhv+cCuPut7t4SmAhc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\nikJJRGJFoSQisfL/AT5txfqMyjLVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c974c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot single trajectory from velocities.\n",
    "i_traj = 1\n",
    "pr = to_positions(denormalize(predicted[i_traj]))\n",
    "plt.plot(pr[:, 0], pr[:, 1], label='Predicted')\n",
    "exp = to_positions(denormalize(expected[i_traj]))\n",
    "plt.plot(exp[:, 0], exp[:, 1], label='Expected')\n",
    "lim = 300#abs(max(np.min(pr), np.max(pr), np.min(exp), np.max(exp), key=abs)) + 20\n",
    "plt.xlim(-lim, lim)\n",
    "plt.ylim(-lim, lim)\n",
    "plt.xlabel(u'x (\\u00b5m)')\n",
    "plt.ylabel(u'y (\\u00b5m)')\n",
    "plt.legend(loc='lower right')\n",
    "plt.gca().set(adjustable='box-forced', aspect='equal')\n",
    "\n",
    "#plt.savefig('plots/{}-{}.png'.format(category, i_traj), dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T22:33:57.264000",
     "start_time": "2016-04-02T22:33:56.709000"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-300, 300)"
      ]
     },
     "execution_count": 307,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8OQ5/c+kLWZbZF7mPxNxEFp5dSG7Wcb4NUl5bdag54wb2Jjd1BdaXh5F48jA4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\nCCHsSGAQQghhRwKDEEIIOxIYhBBC2Pl/8D7NgZ1JCLgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bf45f70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot multiple trajectories from velocities.\n",
    "for traj in predicted:\n",
    "    pr = to_positions(denormalize(traj))\n",
    "    plt.plot(pr[:, 0], pr[:, 1], label='Predicted')\n",
    "lim = 300#abs(max(np.min(pr), np.max(pr), np.min(exp), np.max(exp), key=abs)) + 20\n",
    "plt.xlim(-lim, lim)\n",
    "plt.ylim(-lim, lim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T20:37:34.905000",
     "start_time": "2016-04-02T20:37:34.015000"
    },
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tr 0, step 0: In: [[-0.11929745 -0.16926699 -0.1274353 ]] - Out: [-0.07543063 -0.05903367 -0.07567553] --> Seed\n",
      "Tr 0, step 1: In: [[-0.1269096  -0.23584018 -0.1274353 ]] - Out: [-0.06460239 -0.10555829 -0.19765334] --> Seed\n",
      "Tr 0, step 2: In: [[-0.13533153 -0.18214361 -0.1274353 ]] - Out: [-0.11142873 -0.11718103 -0.12200553] --> Seed\n",
      "Tr 0, step 3: In: [[-0.21454122 -0.09839719 -0.1274353 ]] - Out: [-0.24823113 -0.23943736 -0.19145711] --> Seed\n",
      "Tr 0, step 4: In: [[-0.21283643 -0.04382512 -0.1274353 ]] - Out: [-0.34343137 -0.0823497  -0.09680619] --> Seed\n",
      "Tr 0, step 5: In: [[-0.17235168 -0.13002572 -0.1274353 ]] - Out: [-0.17550509 -0.1589601   0.01969278] --> Seed\n",
      "Tr 0, step 6: In: [[-0.18961012 -0.10719503 -0.1274353 ]] - Out: [-0.15862429 -0.02779072 -0.10346575] --> Seed\n",
      "Tr 0, step 7: In: [[-0.26534981 -0.05835042 -0.1274353 ]] - Out: [-0.30202523 -0.08380032 -0.23723742] --> Seed\n",
      "Tr 0, step 8: In: [[-0.16319002 -0.07215143 -0.1274353 ]] - Out: [-0.04633253 -0.21989403 -0.07649696] --> Seed\n",
      "Tr 0, step 9: In: [[-0.14190674 -0.11908445 -0.1274353 ]] - Out: [-0.13039288 -0.14185083 -0.1083584 ] --> Seed\n",
      "Tr 0, step 10: In: [[-0.12505988 -0.1123646  -0.1274353 ]] - Out: [-0.04416999 -0.07478187 -0.03667847] --> Seed\n",
      "Tr 0, step 11: In: [[-0.12986997 -0.18278158 -0.1274353 ]] - Out: [-0.13320743 -0.08336808 -0.15396872] --> Seed\n",
      "Tr 0, step 12: In: [[-0.12878494 -0.14145886 -0.1274353 ]] - Out: [-0.2687823  -0.15327557 -0.22510037] --> Seed\n",
      "Tr 0, step 13: In: [[-0.09831396 -0.12198768 -0.1274353 ]] - Out: [-0.1169703  -0.12093703 -0.15501725] --> Seed\n",
      "Tr 0, step 14: In: [[-0.09886876 -0.22198338 -0.1274353 ]] - Out: [-0.03543084 -0.15838051 -0.04373798] --> Seed\n",
      "Tr 0, step 15: In: [[-0.12514114 -0.07878254 -0.1274353 ]] - Out: [-0.12827279 -0.14875758 -0.10709481] --> Seed\n",
      "Tr 0, step 16: In: [[-0.06662042 -0.1812054  -0.1274353 ]] - Out: [-0.12919208 -0.10167708 -0.11685322] --> Seed\n",
      "Tr 0, step 17: In: [[-0.06921809 -0.08335102 -0.1274353 ]] - Out: [ 0.02646056 -0.13801211 -0.16004889] --> Seed\n",
      "Tr 0, step 18: In: [[-0.12804924 -0.14596127 -0.1274353 ]] - Out: [-0.13210628 -0.00679231 -0.12247906] --> Seed\n",
      "Tr 0, step 19: In: [[-0.12202718 -0.15219509 -0.1274353 ]] - Out: [-0.14032507 -0.15646977 -0.076869  ] --> Storing at 20\n",
      "Tr 0, step 20: In: [[-0.14032507 -0.15646977 -0.076869  ]] - Out: [-0.15495459 -0.22124943 -0.19039782] --> Storing at 21\n",
      "Tr 0, step 21: In: [[-0.15495459 -0.22124943 -0.19039782]] - Out: [-0.18163968 -0.20221076 -0.07538853] --> Storing at 22\n",
      "Tr 0, step 22: In: [[-0.18163968 -0.20221076 -0.07538853]] - Out: [-0.28028952 -0.19772323 -0.05854952] --> Storing at 23\n",
      "Tr 0, step 23: In: [[-0.28028952 -0.19772323 -0.05854952]] - Out: [-0.22630789 -0.19441285 -0.10369911] --> Storing at 24\n",
      "Tr 0, step 24: In: [[-0.22630789 -0.19441285 -0.10369911]] - Out: [-0.13682787 -0.21383631 -0.15684776] --> Storing at 25\n",
      "Tr 0, step 25: In: [[-0.13682787 -0.21383631 -0.15684776]] - Out: [-0.07726472 -0.11147884 -0.1422657 ] --> Storing at 26\n",
      "Tr 0, step 26: In: [[-0.07726472 -0.11147884 -0.1422657 ]] - Out: [-0.10477729 -0.2114985  -0.15835762] --> Storing at 27\n",
      "Tr 0, step 27: In: [[-0.10477729 -0.2114985  -0.15835762]] - Out: [-0.12584486 -0.14485479 -0.14873009] --> Storing at 28\n",
      "Tr 0, step 28: In: [[-0.12584486 -0.14485479 -0.14873009]] - Out: [-0.16851693 -0.15090314 -0.17598578] --> Storing at 29\n",
      "Tr 0, step 29: In: [[-0.16851693 -0.15090314 -0.17598578]] - Out: [-0.16971519 -0.13586636 -0.11077922] --> Storing at 30\n",
      "Tr 0, step 30: In: [[-0.16971519 -0.13586636 -0.11077922]] - Out: [-0.17099848 -0.10129228 -0.14297678] --> Storing at 31\n",
      "Tr 0, step 31: In: [[-0.17099848 -0.10129228 -0.14297678]] - Out: [ 0.01775364 -0.10552971 -0.09254654] --> Storing at 32\n",
      "Tr 0, step 32: In: [[ 0.01775364 -0.10552971 -0.09254654]] - Out: [ 0.05056456 -0.01253279 -0.07761047] --> Storing at 33\n",
      "Tr 0, step 33: In: [[ 0.05056456 -0.01253279 -0.07761047]] - Out: [-0.16020483 -0.14464242 -0.22509518] --> Storing at 34\n",
      "Tr 0, step 34: In: [[-0.16020483 -0.14464242 -0.22509518]] - Out: [-0.20355017 -0.03613841 -0.19888946] --> Storing at 35\n",
      "Tr 0, step 35: In: [[-0.20355017 -0.03613841 -0.19888946]] - Out: [-0.06010044 -0.15814206 -0.12882553] --> Storing at 36\n",
      "Tr 0, step 36: In: [[-0.06010044 -0.15814206 -0.12882553]] - Out: [-0.14238556 -0.21450315 -0.04865734] --> Storing at 37\n",
      "Tr 0, step 37: In: [[-0.14238556 -0.21450315 -0.04865734]] - Out: [-0.14343684 -0.09652818 -0.18010448] --> Storing at 38\n",
      "Tr 0, step 38: In: [[-0.14343684 -0.09652818 -0.18010448]] - Out: [-0.18189674 -0.20150811 -0.05555578] --> Storing at 39\n",
      "Tr 0, step 39: In: [[-0.18189674 -0.20150811 -0.05555578]] - Out: [-0.1750048  -0.12082915 -0.18020543] --> Storing at 40\n",
      "Tr 0, step 40: In: [[-0.1750048  -0.12082915 -0.18020543]] - Out: [-0.18177104 -0.14223685 -0.20176165] --> Storing at 41\n",
      "Tr 0, step 41: In: [[-0.18177104 -0.14223685 -0.20176165]] - Out: [-0.11863783 -0.23022421 -0.147357  ] --> Storing at 42\n",
      "Tr 0, step 42: In: [[-0.11863783 -0.23022421 -0.147357  ]] - Out: [-0.03510323 -0.10142934 -0.14126069] --> Storing at 43\n",
      "Tr 0, step 43: In: [[-0.03510323 -0.10142934 -0.14126069]] - Out: [-0.0119578  -0.19802103  0.0206829 ] --> Storing at 44\n",
      "Tr 0, step 44: In: [[-0.0119578  -0.19802103  0.0206829 ]] - Out: [-0.13068334 -0.19277122 -0.11256114] --> Storing at 45\n",
      "Tr 0, step 45: In: [[-0.13068334 -0.19277122 -0.11256114]] - Out: [-0.21402728 -0.16557898 -0.10677333] --> Storing at 46\n",
      "Tr 0, step 46: In: [[-0.21402728 -0.16557898 -0.10677333]] - Out: [-0.16556469 -0.13439834 -0.13924062] --> Storing at 47\n",
      "Tr 0, step 47: In: [[-0.16556469 -0.13439834 -0.13924062]] - Out: [-0.17366555 -0.24057872 -0.10502346] --> Storing at 48\n",
      "Tr 0, step 48: In: [[-0.17366555 -0.24057872 -0.10502346]] - Out: [-0.18214843 -0.15981703 -0.09040661] --> Storing at 49\n",
      "Tr 0, step 49: In: [[-0.18214843 -0.15981703 -0.09040661]] - Out: [-0.27314189 -0.17957027 -0.0835679 ] --> Storing at 50\n",
      "Tr 0, step 50: In: [[-0.27314189 -0.17957027 -0.0835679 ]] - Out: [-0.25036251 -0.10693775 -0.10264224] --> Storing at 51\n",
      "Tr 0, step 51: In: [[-0.25036251 -0.10693775 -0.10264224]] - Out: [-0.10210443 -0.21419061 -0.11605843] --> Storing at 52\n",
      "Tr 0, step 52: In: [[-0.10210443 -0.21419061 -0.11605843]] - Out: [-0.03190532 -0.20751053 -0.06500879] --> Storing at 53\n",
      "Tr 0, step 53: In: [[-0.03190532 -0.20751053 -0.06500879]] - Out: [-0.02473098 -0.18761041 -0.01774172] --> Storing at 54\n",
      "Tr 0, step 54: In: [[-0.02473098 -0.18761041 -0.01774172]] - Out: [-0.12013789 -0.11262364 -0.11076598] --> Storing at 55\n",
      "Tr 0, step 55: In: [[-0.12013789 -0.11262364 -0.11076598]] - Out: [-0.27806563 -0.21320735 -0.06381018] --> Storing at 56\n",
      "Tr 0, step 56: In: [[-0.27806563 -0.21320735 -0.06381018]] - Out: [-0.15623361 -0.21409789 -0.1980502 ] --> Storing at 57\n",
      "Tr 0, step 57: In: [[-0.15623361 -0.21409789 -0.1980502 ]] - Out: [-0.02011093 -0.13265609 -0.03026657] --> Storing at 58\n",
      "Tr 0, step 58: In: [[-0.02011093 -0.13265609 -0.03026657]] - Out: [-0.15292414 -0.1102126  -0.08626967] --> Storing at 59\n",
      "Tr 0, step 59: In: [[-0.15292414 -0.1102126  -0.08626967]] - Out: [-0.04236206 -0.08046436 -0.20989087] --> Storing at 60\n",
      "Tr 0, step 60: In: [[-0.04236206 -0.08046436 -0.20989087]] - Out: [-0.15518898 -0.07829856 -0.11921545] --> Storing at 61\n",
      "Tr 0, step 61: In: [[-0.15518898 -0.07829856 -0.11921545]] - Out: [-0.07082441 -0.19030153 -0.13808588] --> Storing at 62\n",
      "Tr 0, step 62: In: [[-0.07082441 -0.19030153 -0.13808588]] - Out: [-0.16872701 -0.09763125 -0.16574051] --> Storing at 63\n",
      "Tr 0, step 63: In: [[-0.16872701 -0.09763125 -0.16574051]] - Out: [-0.15163306 -0.12132127 -0.07501619] --> Storing at 64\n",
      "Tr 0, step 64: In: [[-0.15163306 -0.12132127 -0.07501619]] - Out: [-0.27341632 -0.13429725 -0.0893691 ] --> Storing at 65\n",
      "Tr 0, step 65: In: [[-0.27341632 -0.13429725 -0.0893691 ]] - Out: [-0.18981302 -0.04268481 -0.19407275] --> Storing at 66\n",
      "Tr 0, step 66: In: [[-0.18981302 -0.04268481 -0.19407275]] - Out: [-0.16150837 -0.17739583 -0.32594401] --> Storing at 67\n",
      "Tr 0, step 67: In: [[-0.16150837 -0.17739583 -0.32594401]] - Out: [-0.06782118 -0.14604171 -0.01589016] --> Storing at 68\n",
      "Tr 0, step 68: In: [[-0.06782118 -0.14604171 -0.01589016]] - Out: [-0.18510324 -0.23020932 -0.28838856] --> Storing at 69\n",
      "Tr 0, step 69: In: [[-0.18510324 -0.23020932 -0.28838856]] - Out: [-0.01705344 -0.124921   -0.19305776] --> Storing at 70\n",
      "Tr 0, step 70: In: [[-0.01705344 -0.124921   -0.19305776]] - Out: [-0.12014266 -0.09076232 -0.13924496] --> Storing at 71\n",
      "Tr 0, step 71: In: [[-0.12014266 -0.09076232 -0.13924496]] - Out: [-0.15834065 -0.15591244 -0.14921333] --> Storing at 72\n",
      "Tr 0, step 72: In: [[-0.15834065 -0.15591244 -0.14921333]] - Out: [-0.08838657 -0.18351198 -0.14704589] --> Storing at 73\n",
      "Tr 0, step 73: In: [[-0.08838657 -0.18351198 -0.14704589]] - Out: [-0.146983   -0.17359407 -0.12685096] --> Storing at 74\n",
      "Tr 0, step 74: In: [[-0.146983   -0.17359407 -0.12685096]] - Out: [-0.05788456 -0.11948598 -0.17251853] --> Storing at 75\n",
      "Tr 0, step 75: In: [[-0.05788456 -0.11948598 -0.17251853]] - Out: [-0.1477398  -0.15751775 -0.11369052] --> Storing at 76\n",
      "Tr 0, step 76: In: [[-0.1477398  -0.15751775 -0.11369052]] - Out: [-0.07837444 -0.11109349 -0.13972299] --> Storing at 77\n",
      "Tr 0, step 77: In: [[-0.07837444 -0.11109349 -0.13972299]] - Out: [-0.0742972  -0.14092236 -0.14319395] --> Storing at 78\n",
      "Tr 0, step 78: In: [[-0.0742972  -0.14092236 -0.14319395]] - Out: [-0.13664933 -0.16155937 -0.030233  ] --> Storing at 79\n",
      "Tr 0, step 79: In: [[-0.13664933 -0.16155937 -0.030233  ]] - Out: [-0.08784995 -0.08430954 -0.16889703] --> Storing at 80\n",
      "Tr 0, step 80: In: [[-0.08784995 -0.08430954 -0.16889703]] - Out: [-0.1237706  -0.13621131 -0.09133568] --> Storing at 81\n",
      "Tr 0, step 81: In: [[-0.1237706  -0.13621131 -0.09133568]] - Out: [-0.15389127 -0.10726423 -0.06584823] --> Storing at 82\n",
      "Tr 0, step 82: In: [[-0.15389127 -0.10726423 -0.06584823]] - Out: [-0.08422639 -0.17708064 -0.15387978] --> Storing at 83\n",
      "Tr 0, step 83: In: [[-0.08422639 -0.17708064 -0.15387978]] - Out: [-0.12676629 -0.19217971 -0.20984952] --> Storing at 84\n",
      "Tr 0, step 84: In: [[-0.12676629 -0.19217971 -0.20984952]] - Out: [-0.1562607  -0.16105084 -0.11230834] --> Storing at 85\n",
      "Tr 0, step 85: In: [[-0.1562607  -0.16105084 -0.11230834]] - Out: [-0.10336565 -0.15195682 -0.15068399] --> Storing at 86\n",
      "Tr 0, step 86: In: [[-0.10336565 -0.15195682 -0.15068399]] - Out: [-0.11781907 -0.18605851 -0.14301086] --> Storing at 87\n",
      "Tr 0, step 87: In: [[-0.11781907 -0.18605851 -0.14301086]] - Out: [-0.10162481 -0.18065999 -0.10769621] --> Storing at 88\n",
      "Tr 0, step 88: In: [[-0.10162481 -0.18065999 -0.10769621]] - Out: [-0.15636035 -0.19114002 -0.10598131] --> Storing at 89\n",
      "Tr 0, step 89: In: [[-0.15636035 -0.19114002 -0.10598131]] - Out: [-0.09149926 -0.09392138 -0.08231969] --> Storing at 90\n",
      "Tr 0, step 90: In: [[-0.09149926 -0.09392138 -0.08231969]] - Out: [-0.14411668 -0.15854812 -0.11483505] --> Storing at 91\n",
      "Tr 0, step 91: In: [[-0.14411668 -0.15854812 -0.11483505]] - Out: [-0.11884319 -0.11053722 -0.11807265] --> Storing at 92\n",
      "Tr 0, step 92: In: [[-0.11884319 -0.11053722 -0.11807265]] - Out: [-0.11075996 -0.09975058 -0.14768518] --> Storing at 93\n",
      "Tr 0, step 93: In: [[-0.11075996 -0.09975058 -0.14768518]] - Out: [-0.14000216 -0.15748554 -0.05465435] --> Storing at 94\n",
      "Tr 0, step 94: In: [[-0.14000216 -0.15748554 -0.05465435]] - Out: [-0.15782878 -0.10611641 -0.07369476] --> Storing at 95\n",
      "Tr 0, step 95: In: [[-0.15782878 -0.10611641 -0.07369476]] - Out: [-0.14819283 -0.06861099 -0.11377906] --> Storing at 96\n",
      "Tr 0, step 96: In: [[-0.14819283 -0.06861099 -0.11377906]] - Out: [-0.10558386 -0.12327761 -0.123761  ] --> Storing at 97\n",
      "Tr 0, step 97: In: [[-0.10558386 -0.12327761 -0.123761  ]] - Out: [-0.09800171 -0.13973979 -0.09873765] --> Storing at 98\n",
      "Tr 0, step 98: In: [[-0.09800171 -0.13973979 -0.09873765]] - Out: [-0.05652061 -0.10976055 -0.11315837] --> Storing at 99\n",
      "Tr 0, step 99: In: [[-0.05652061 -0.10976055 -0.11315837]] - Out: [-0.06466318 -0.22570425 -0.12426556] --> Storing at 100\n",
      "Tr 0, step 100: In: [[-0.06466318 -0.22570425 -0.12426556]] - Out: [-0.03816979 -0.11865276 -0.16738302] --> Storing at 101\n",
      "Tr 0, step 101: In: [[-0.03816979 -0.11865276 -0.16738302]] - Out: [-0.11107537 -0.12255718 -0.16474666] --> Storing at 102\n",
      "Tr 0, step 102: In: [[-0.11107537 -0.12255718 -0.16474666]] - Out: [-0.1627822  -0.10139529 -0.10740081] --> Storing at 103\n",
      "Tr 0, step 103: In: [[-0.1627822  -0.10139529 -0.10740081]] - Out: [-0.13518944 -0.07105141 -0.17446002] --> Storing at 104\n",
      "Tr 0, step 104: In: [[-0.13518944 -0.07105141 -0.17446002]] - Out: [-0.15990369 -0.159866   -0.16193783] --> Storing at 105\n",
      "Tr 0, step 105: In: [[-0.15990369 -0.159866   -0.16193783]] - Out: [-0.21655404 -0.09689177 -0.05020174] --> Storing at 106\n",
      "Tr 0, step 106: In: [[-0.21655404 -0.09689177 -0.05020174]] - Out: [-0.23261604 -0.08407264 -0.0782364 ] --> Storing at 107\n",
      "Tr 0, step 107: In: [[-0.23261604 -0.08407264 -0.0782364 ]] - Out: [-0.14182511 -0.15888777 -0.15328218] --> Storing at 108\n",
      "Tr 0, step 108: In: [[-0.14182511 -0.15888777 -0.15328218]] - Out: [-0.09942337 -0.03093559 -0.1203717 ] --> Storing at 109\n",
      "Tr 0, step 109: In: [[-0.09942337 -0.03093559 -0.1203717 ]] - Out: [-0.11483831 -0.0822924  -0.07416822] --> Storing at 110\n",
      "Tr 0, step 110: In: [[-0.11483831 -0.0822924  -0.07416822]] - Out: [-0.18141824 -0.0822313  -0.14244175] --> Storing at 111\n",
      "Tr 0, step 111: In: [[-0.18141824 -0.0822313  -0.14244175]] - Out: [-0.2060647  -0.09930889 -0.13401173] --> Storing at 112\n",
      "Tr 0, step 112: In: [[-0.2060647  -0.09930889 -0.13401173]] - Out: [-0.25114547  0.01680559 -0.13459336] --> Storing at 113\n",
      "Tr 0, step 113: In: [[-0.25114547  0.01680559 -0.13459336]] - Out: [-0.08016886 -0.03362698 -0.10876192] --> Storing at 114\n",
      "Tr 0, step 114: In: [[-0.08016886 -0.03362698 -0.10876192]] - Out: [-0.15248232 -0.06696347 -0.12816248] --> Storing at 115\n",
      "Tr 0, step 115: In: [[-0.15248232 -0.06696347 -0.12816248]] - Out: [-0.11178104 -0.17487349 -0.07302433] --> Storing at 116\n",
      "Tr 0, step 116: In: [[-0.11178104 -0.17487349 -0.07302433]] - Out: [-0.20117682 -0.09712119 -0.11703916] --> Storing at 117\n",
      "Tr 0, step 117: In: [[-0.20117682 -0.09712119 -0.11703916]] - Out: [-0.1459598  -0.18643426 -0.08387307] --> Storing at 118\n",
      "Tr 0, step 118: In: [[-0.1459598  -0.18643426 -0.08387307]] - Out: [-0.20985767 -0.24897427 -0.06552764] --> Storing at 119\n",
      "Tr 0, step 119: In: [[-0.20985767 -0.24897427 -0.06552764]] - Out: [-0.24933487 -0.16559037 -0.08377312] --> Storing at 120\n",
      "Tr 0, step 120: In: [[-0.24933487 -0.16559037 -0.08377312]] - Out: [-0.27597756 -0.224461   -0.0726153 ] --> Storing at 121\n",
      "Tr 0, step 121: In: [[-0.27597756 -0.224461   -0.0726153 ]] - Out: [-0.23384057 -0.2445118  -0.22254736] --> Storing at 122\n",
      "Tr 0, step 122: In: [[-0.23384057 -0.2445118  -0.22254736]] - Out: [-0.07841939 -0.23413135 -0.15437638] --> Storing at 123\n",
      "Tr 0, step 123: In: [[-0.07841939 -0.23413135 -0.15437638]] - Out: [-0.10274656 -0.1134072  -0.0804391 ] --> Storing at 124\n",
      "Tr 0, step 124: In: [[-0.10274656 -0.1134072  -0.0804391 ]] - Out: [-0.11205979 -0.20695914 -0.11064028] --> Storing at 125\n",
      "Tr 0, step 125: In: [[-0.11205979 -0.20695914 -0.11064028]] - Out: [-0.16604652 -0.17210805 -0.12894391] --> Storing at 126\n",
      "Tr 0, step 126: In: [[-0.16604652 -0.17210805 -0.12894391]] - Out: [-0.14895925 -0.14963504 -0.15032446] --> Storing at 127\n",
      "Tr 0, step 127: In: [[-0.14895925 -0.14963504 -0.15032446]] - Out: [-0.15076955 -0.07937174 -0.11560928] --> Storing at 128\n",
      "Tr 0, step 128: In: [[-0.15076955 -0.07937174 -0.11560928]] - Out: [-0.1548608  -0.18284566 -0.22445238] --> Storing at 129\n",
      "Tr 0, step 129: In: [[-0.1548608  -0.18284566 -0.22445238]] - Out: [-0.05853693 -0.12170891 -0.11952084] --> Storing at 130\n",
      "Tr 0, step 130: In: [[-0.05853693 -0.12170891 -0.11952084]] - Out: [-0.06412266 -0.16037879 -0.16302976] --> Storing at 131\n",
      "Tr 0, step 131: In: [[-0.06412266 -0.16037879 -0.16302976]] - Out: [-0.09113373 -0.16618297 -0.16095094] --> Storing at 132\n",
      "Tr 0, step 132: In: [[-0.09113373 -0.16618297 -0.16095094]] - Out: [-0.14392652 -0.08772087 -0.122186  ] --> Storing at 133\n",
      "Tr 0, step 133: In: [[-0.14392652 -0.08772087 -0.122186  ]] - Out: [-0.09144017 -0.15047259 -0.17900979] --> Storing at 134\n",
      "Tr 0, step 134: In: [[-0.09144017 -0.15047259 -0.17900979]] - Out: [-0.06759741 -0.18900292 -0.00460925] --> Storing at 135\n",
      "Tr 0, step 135: In: [[-0.06759741 -0.18900292 -0.00460925]] - Out: [-0.04584725 -0.11586125 -0.17816443] --> Storing at 136\n",
      "Tr 0, step 136: In: [[-0.04584725 -0.11586125 -0.17816443]] - Out: [-0.08868845 -0.14077461 -0.13579976] --> Storing at 137\n",
      "Tr 0, step 137: In: [[-0.08868845 -0.14077461 -0.13579976]] - Out: [-0.11182893 -0.07487559 -0.14140781] --> Storing at 138\n",
      "Tr 0, step 138: In: [[-0.11182893 -0.07487559 -0.14140781]] - Out: [-0.15915612 -0.12006235 -0.14343353] --> Storing at 139\n",
      "Tr 0, step 139: In: [[-0.15915612 -0.12006235 -0.14343353]] - Out: [-0.188472   -0.02282452 -0.08691905] --> Storing at 140\n",
      "Tr 0, step 140: In: [[-0.188472   -0.02282452 -0.08691905]] - Out: [-0.10737495 -0.15603401 -0.11728695] --> Storing at 141\n",
      "Tr 0, step 141: In: [[-0.10737495 -0.15603401 -0.11728695]] - Out: [-0.03675622 -0.14516488 -0.08632543] --> Storing at 142\n",
      "Tr 0, step 142: In: [[-0.03675622 -0.14516488 -0.08632543]] - Out: [-0.25364304 -0.07736982 -0.15715799] --> Storing at 143\n",
      "Tr 0, step 143: In: [[-0.25364304 -0.07736982 -0.15715799]] - Out: [-0.10579321 -0.10459047 -0.02951062] --> Storing at 144\n",
      "Tr 0, step 144: In: [[-0.10579321 -0.10459047 -0.02951062]] - Out: [-0.17066242 -0.06850665 -0.02136443] --> Storing at 145\n",
      "Tr 0, step 145: In: [[-0.17066242 -0.06850665 -0.02136443]] - Out: [-0.20313435 -0.10733571 -0.08531596] --> Storing at 146\n",
      "Tr 0, step 146: In: [[-0.20313435 -0.10733571 -0.08531596]] - Out: [-0.27993122 -0.16526515 -0.08606276] --> Storing at 147\n",
      "Tr 0, step 147: In: [[-0.27993122 -0.16526515 -0.08606276]] - Out: [-0.27184334 -0.06786075 -0.10536147] --> Storing at 148\n",
      "Tr 0, step 148: In: [[-0.27184334 -0.06786075 -0.10536147]] - Out: [-0.1813421 -0.1125584 -0.0505083] --> Storing at 149\n",
      "Tr 0, step 149: In: [[-0.1813421 -0.1125584 -0.0505083]] - Out: [-0.04515492 -0.13084091 -0.13112162] --> Storing at 150\n",
      "Tr 0, step 150: In: [[-0.04515492 -0.13084091 -0.13112162]] - Out: [-0.0549345  -0.22116827 -0.10698769] --> Storing at 151\n",
      "Tr 0, step 151: In: [[-0.0549345  -0.22116827 -0.10698769]] - Out: [-0.08319836 -0.15173028 -0.24420455] --> Storing at 152\n",
      "Tr 0, step 152: In: [[-0.08319836 -0.15173028 -0.24420455]] - Out: [-0.16295566 -0.12196546 -0.11322584] --> Storing at 153\n",
      "Tr 0, step 153: In: [[-0.16295566 -0.12196546 -0.11322584]] - Out: [-0.12897898 -0.17169158 -0.11631564] --> Storing at 154\n",
      "Tr 0, step 154: In: [[-0.12897898 -0.17169158 -0.11631564]] - Out: [-0.24074003 -0.13014656 -0.08297681] --> Storing at 155\n",
      "Tr 0, step 155: In: [[-0.24074003 -0.13014656 -0.08297681]] - Out: [-0.16154482 -0.05607195 -0.1664746 ] --> Storing at 156\n",
      "Tr 0, step 156: In: [[-0.16154482 -0.05607195 -0.1664746 ]] - Out: [-0.13126298 -0.17345342 -0.06927448] --> Storing at 157\n",
      "Tr 0, step 157: In: [[-0.13126298 -0.17345342 -0.06927448]] - Out: [-0.05718631 -0.10049591 -0.0991006 ] --> Storing at 158\n",
      "Tr 0, step 158: In: [[-0.05718631 -0.10049591 -0.0991006 ]] - Out: [-0.21060081 -0.0918901  -0.06707749] --> Storing at 159\n",
      "Tr 0, step 159: In: [[-0.21060081 -0.0918901  -0.06707749]] - Out: [-0.05722532  0.00069161 -0.11383914] --> Storing at 160\n",
      "Tr 0, step 160: In: [[-0.05722532  0.00069161 -0.11383914]] - Out: [-0.01457814 -0.1290962  -0.08820828] --> Storing at 161\n",
      "Tr 0, step 161: In: [[-0.01457814 -0.1290962  -0.08820828]] - Out: [-0.08530144 -0.03891568 -0.10528107] --> Storing at 162\n",
      "Tr 0, step 162: In: [[-0.08530144 -0.03891568 -0.10528107]] - Out: [-0.24618629 -0.14352911 -0.11102895] --> Storing at 163\n",
      "Tr 0, step 163: In: [[-0.24618629 -0.14352911 -0.11102895]] - Out: [-0.00696751 -0.14857478 -0.01187503] --> Storing at 164\n",
      "Tr 0, step 164: In: [[-0.00696751 -0.14857478 -0.01187503]] - Out: [-0.05012168 -0.20205054 -0.16349298] --> Storing at 165\n",
      "Tr 0, step 165: In: [[-0.05012168 -0.20205054 -0.16349298]] - Out: [-0.08855283 -0.05268433 -0.14672654] --> Storing at 166\n",
      "Tr 0, step 166: In: [[-0.08855283 -0.05268433 -0.14672654]] - Out: [-0.03641064 -0.16326692 -0.13793463] --> Storing at 167\n",
      "Tr 0, step 167: In: [[-0.03641064 -0.16326692 -0.13793463]] - Out: [-0.16674503 -0.17745732 -0.09332786] --> Storing at 168\n",
      "Tr 0, step 168: In: [[-0.16674503 -0.17745732 -0.09332786]] - Out: [-0.09093255 -0.22342205 -0.14046006] --> Storing at 169\n",
      "Tr 0, step 169: In: [[-0.09093255 -0.22342205 -0.14046006]] - Out: [-0.1517302  -0.08142912 -0.14809895] --> Storing at 170\n",
      "Tr 0, step 170: In: [[-0.1517302  -0.08142912 -0.14809895]] - Out: [-0.12053214 -0.12337722 -0.2124188 ] --> Storing at 171\n",
      "Tr 0, step 171: In: [[-0.12053214 -0.12337722 -0.2124188 ]] - Out: [-0.11911967 -0.14923083 -0.10536711] --> Storing at 172\n",
      "Tr 0, step 172: In: [[-0.11911967 -0.14923083 -0.10536711]] - Out: [-0.06424804 -0.10029231 -0.0222668 ] --> Storing at 173\n",
      "Tr 0, step 173: In: [[-0.06424804 -0.10029231 -0.0222668 ]] - Out: [-0.13779434 -0.06326842 -0.06932715] --> Storing at 174\n",
      "Tr 0, step 174: In: [[-0.13779434 -0.06326842 -0.06932715]] - Out: [-0.07688045 -0.06342172 -0.08134625] --> Storing at 175\n",
      "Tr 0, step 175: In: [[-0.07688045 -0.06342172 -0.08134625]] - Out: [-0.08024657 -0.14939883 -0.11648726] --> Storing at 176\n",
      "Tr 0, step 176: In: [[-0.08024657 -0.14939883 -0.11648726]] - Out: [-0.06131727 -0.2368125  -0.10857386] --> Storing at 177\n",
      "Tr 0, step 177: In: [[-0.06131727 -0.2368125  -0.10857386]] - Out: [-0.0055288  -0.19787483 -0.1125895 ] --> Storing at 178\n",
      "Tr 0, step 178: In: [[-0.0055288  -0.19787483 -0.1125895 ]] - Out: [ 0.07069886 -0.13239053 -0.20849533] --> Storing at 179\n",
      "Tr 0, step 179: In: [[ 0.07069886 -0.13239053 -0.20849533]] - Out: [ 0.03733934 -0.12204005 -0.11644788] --> Storing at 180\n",
      "Tr 0, step 180: In: [[ 0.03733934 -0.12204005 -0.11644788]] - Out: [-0.08750368 -0.09858812 -0.05245641] --> Storing at 181\n",
      "Tr 0, step 181: In: [[-0.08750368 -0.09858812 -0.05245641]] - Out: [ 0.00894424 -0.20701083 -0.11736264] --> Storing at 182\n",
      "Tr 0, step 182: In: [[ 0.00894424 -0.20701083 -0.11736264]] - Out: [-0.14195721 -0.15134503 -0.11512418] --> Storing at 183\n",
      "Tr 0, step 183: In: [[-0.14195721 -0.15134503 -0.11512418]] - Out: [ 0.03746802 -0.10823006 -0.15600209] --> Storing at 184\n",
      "Tr 0, step 184: In: [[ 0.03746802 -0.10823006 -0.15600209]] - Out: [-0.13399178 -0.24192349 -0.19616652] --> Storing at 185\n",
      "Tr 0, step 185: In: [[-0.13399178 -0.24192349 -0.19616652]] - Out: [-0.25055719 -0.14151617 -0.1910863 ] --> Storing at 186\n",
      "Tr 0, step 186: In: [[-0.25055719 -0.14151617 -0.1910863 ]] - Out: [-0.13312429 -0.30352658 -0.0847089 ] --> Storing at 187\n",
      "Tr 0, step 187: In: [[-0.13312429 -0.30352658 -0.0847089 ]] - Out: [-0.14416925 -0.17541557 -0.13711262] --> Storing at 188\n",
      "Tr 0, step 188: In: [[-0.14416925 -0.17541557 -0.13711262]] - Out: [-0.17392641 -0.14326535 -0.13458904] --> Storing at 189\n",
      "Tr 0, step 189: In: [[-0.17392641 -0.14326535 -0.13458904]] - Out: [-0.01647797 -0.14205507 -0.22247847] --> Storing at 190\n",
      "Tr 0, step 190: In: [[-0.01647797 -0.14205507 -0.22247847]] - Out: [-0.16356364 -0.10471899 -0.12364639] --> Storing at 191\n",
      "Tr 0, step 191: In: [[-0.16356364 -0.10471899 -0.12364639]] - Out: [-0.24494056 -0.16291747 -0.09271288] --> Storing at 192\n",
      "Tr 0, step 192: In: [[-0.24494056 -0.16291747 -0.09271288]] - Out: [-0.27174367 -0.19303139 -0.0814265 ] --> Storing at 193\n",
      "Tr 0, step 193: In: [[-0.27174367 -0.19303139 -0.0814265 ]] - Out: [-0.24476815 -0.12272819 -0.15729676] --> Storing at 194\n",
      "Tr 0, step 194: In: [[-0.24476815 -0.12272819 -0.15729676]] - Out: [-0.12358109 -0.08147435 -0.23466376] --> Storing at 195\n",
      "Tr 0, step 195: In: [[-0.12358109 -0.08147435 -0.23466376]] - Out: [-0.08036447 -0.1006645  -0.14732859] --> Storing at 196\n",
      "Tr 0, step 196: In: [[-0.08036447 -0.1006645  -0.14732859]] - Out: [-0.02808906 -0.19463258 -0.16375296] --> Storing at 197\n",
      "Tr 0, step 197: In: [[-0.02808906 -0.19463258 -0.16375296]] - Out: [-0.02510694 -0.16986878 -0.06838761] --> Storing at 198\n"
     ]
    }
   ],
   "source": [
    "# Predict new trajectories one timestep after another using a seed.\n",
    "\n",
    "len_seed = 20  # TODO: Play around with seed size.\n",
    "predicted = np.zeros((batch_size, num_timesteps, 3))\n",
    "\n",
    "# Take starts of training trajectories as seed.\n",
    "predicted[:, :len_seed] = trajectories[:, :len_seed]\n",
    "\n",
    "# Take random values as seed.\n",
    "#predicted[:, :len_seed] = 2. * (np.random.rand(batch_size, len_seed, 3) - 0.5)\n",
    "\n",
    "# Disable both lines above to take 0 values as seed.\n",
    "\n",
    "model.reset_states()\n",
    "\n",
    "log_traj = 0\n",
    "    \n",
    "for i in range(num_timesteps - 1):\n",
    "    model_input = predicted[:, i:i+1]\n",
    "    pred_parameters = model.predict_on_batch(model_input)[0]\n",
    "    \n",
    "    means = pred_parameters[:, :num_mixture_components * 3]\n",
    "    sds = pred_parameters[:, num_mixture_components * 3:num_mixture_components * (3 + 1)]\n",
    "    weights = pred_parameters[:, num_mixture_components * (3 + 1):]\n",
    "        \n",
    "    # Reshape arrays to allow broadcasting of means (3-dimensional vectors) and sds/weights (scalars).\n",
    "    means = means.reshape(-1, num_mixture_components, 3)\n",
    "    sds = sds[:, :, np.newaxis]\n",
    "    weights = weights[:, :, np.newaxis]\n",
    "    \n",
    "    pred = weights * np.random.normal(means, sds)\n",
    "    pred = np.sum(pred, axis=1)    \n",
    "    model_output = pred\n",
    "    \n",
    "    # Add random noise to the output values.\n",
    "    #model_output += 0.25 * (np.random.rand(batch_size, 3) - 0.5)\n",
    "    \n",
    "    print 'Tr {}, step {}: In: {} - Out: {}'.format(log_traj, i, model_input[log_traj], model_output[log_traj]), \n",
    "    \n",
    "    if i+1 >= len_seed:\n",
    "        predicted[:, i+1] = model_output\n",
    "        print '--> Storing at {}'.format(i+1)\n",
    "    else:\n",
    "        print '--> Seed'\n",
    "\n",
    "expected = trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T20:37:34.917000",
     "start_time": "2016-04-02T20:37:34.907000"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.13174982, -0.13735447, -0.12737937])"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(predicted, axis=(0, 1))\n",
    "# fibro, norm to 0.33 std, 100 epochs: 0.10, 0.035, 0\n",
    "# fibro, norm by dividing through abs_max_value, 100 epochs: 0.009, -0.015, -0.002\n",
    "# fibro, norm by dividing through abs_max_value, 100 epochs: 0.017, -0.008, -0.002\n",
    "# fibro, norm to [-1, 1], 100 epochs: 0.135, 0.115, 0.115 (minus default ca. 0.02, 0, 0)\n",
    "# fibro, norm to [-1, 1], 200 epochs: 0.125, 0.110, 0.113 (minus default ca. 0.01, -0.006, -0.003)\n",
    "# fibro, norm to [-1, 1], 500 epochs: 0.135, 0.115, 0.115 (minus default ca. 0.02, 0, 0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T20:37:35.479000",
     "start_time": "2016-04-02T20:37:35.144000"
    },
    "collapsed": false,
    "run_control": {
     "marked": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1f3c5db0>"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ttHdvqF0bKlWyS7VqsHQpPPGE7aUEsH27Df133rG9cwDOnLHDSjRr5ppB5VTh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21f5db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot single trajectory from velocities.\n",
    "i_traj = 3\n",
    "pr = to_positions(denormalize(predicted[i_traj]))\n",
    "plt.plot(pr[:, 0], pr[:, 1], label='Predicted')\n",
    "exp = to_positions(denormalize(expected[i_traj]))\n",
    "plt.plot(exp[:, 0], exp[:, 1], label='Expected')\n",
    "lim = abs(max(np.min(pr), np.max(pr), np.min(exp), np.max(exp), key=abs)) + 20\n",
    "plt.xlim(-lim, lim)\n",
    "plt.ylim(-lim, lim)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T20:37:36.887000",
     "start_time": "2016-04-02T20:37:36.060000"
    },
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-300, 300)"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Xa1gpioK/vz8rV66kV69ev/l9+D0ZFRVoVSqcLCx+M93u3FzWZmbS3M4OP62W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\nDTOj2lBNgFULXAtULO756lrJs2fGyJK/oUMHGDtEiX/zGso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nTGWmnC0pweOTNmz73JQ+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\nTQxKKaW8aGJQSinl5f8BjIHYXqr7m4cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x246d3cb0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot multiple trajectories from velocities.\n",
    "for traj in predicted:\n",
    "    pr = to_positions(denormalize(traj))\n",
    "    plt.plot(pr[:, 0], pr[:, 1], label='Predicted')\n",
    "lim = 300#abs(max(np.min(pr), np.max(pr), np.min(exp), np.max(exp), key=abs)) + 20\n",
    "plt.xlim(-lim, lim)\n",
    "plt.ylim(-lim, lim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T20:33:14.483000",
     "start_time": "2016-04-02T20:33:13.655000"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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97SYmAlevAvfvY+7679FrWH3U65iMW21+WzYbmBQI89A4OCS8wZK0NAxw24Kn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Kvr\nAnpP3Y5s8xKkm9ayYHwiZvGLMdw1gu1jl/LwoYCFxSfGjRtHamoqCoXiX7J9/tGCryiKOmAR8ARI\nBK78d+H/v4XOHdeCXMP51gJzmhRUmxbQT5yHRUA7JF83UNDGl90jNSidWmPXajWCtAxN9BJ4tBg8\navHMuYONtBLd3/toeDGZaH01T+K6oVVpGeQk4ckTcP2jHMlJdxqDaskuTcA+r47At5doHVkA37bS\nxyqCC1lOWMgbKZIoCBb1PNaVUSR0xeCHYAxH9YRHV4gpe89U+znkL1rCvqpU9pmXIU+7QHLzZ3oO\nN6F7oYI0xxTCDx8i6sBrnipFQkdb8cWtCWdTS06eKOW42XYMPtTRf+P3VP06H2WaGd9H1dLkB5vU\nIg9aGnL/mcCGfR9xfDmaXzYEEJuqY4zHGHS1U2lDBSEsJIK7uMgNeIcL607vp8DSjgYTOeKWH9EY\nNNOLPtxouI41hiRxgzGNrciu78zvZ/ewae0d/vzrO3q0uY8svD/3KOFOkZ7rR7bwMuAxj9rFkaQK\npfmWMZmHevPh5R0qancydepuyopaogz6TN20L3SwPo3VuHp2Vcm4kTEB69ze5M3oQYuAz5wp7oL4\n3T2sbjnThB02ttdwlW1HtWInla3/IIAYLOoryTEYTnrXzszzn06RTwQHKx4RbZiLZYt6JA12PI6Y\ny5PeOjZIF1Bklg+Vr1B+WolJTTM/nNWT6xfPLwprXHIyuRETTsfgV+w4ewwK7SDDB2HuWVRDvqBZ\ncImMw8eZ8SSODYfu4PQglyZ/R5xXXiF683CsWhqzK8wQF5yRGVhgpjQg4PpxEDKxqQ5C4lwOAx5j\nc34VzwzcEcZfx/hjL1ixjy89ytn5cylNygYWO96lg+sNQgzMSUvQY2bxE5ZTNiFznkyba51oq3Cm\nanoVju09ias24NnqH+mcNBTPnCR2FmyhLFlB+20FCOlSltQ+ou/DfoiZg/Eo/A6FgQFHg5KQSY0o\nKdZTb+eBrKyOywXd8dOosLg1BPvXWoz3h7N0xG4iPgxher2O1Hwnfvi8jwbLNEys/TjU+gs3ujVi\nYVdHQak7RU1DoJs1HeWT+HHnNXZ++oBrVh4zQn7lkHw2y2uW4PnnHxh068KmY4Yo88vZNKiZ/udH\nk9pKwNssgKb422iHT2J1mB2DH2Xw6YwBu+6oiTxtwvg0DU9cTfnDPIuufTxRxr1Ad0rEMNAUo8UC\nFnUimS52bF01mzFWlgx5fg6pkTMP/f2RpRwFRAyayqlTNPGw00TOW1qz0NGR1/J8gm3MSNiwnvDS\nBfg+P0LSiKEIfVfzuLIE0a4AHFV8079jR9cT8PQZDpXNXGon54MeDg44yHmHvTTWtGLA+PnkDbuA\n9sw1msP6se1GXzZK65ix8SEhgSouX4ZOnToRFxeHXC7/l3XvH+/zF0XxkSiKvqIoeouiuPufjvc/\nYdh3rflUKCdD20DXAaV8L21H8IvB5LrNYYGbIdWlp4kyr8TIaAq+pV74B6zH94UpgslXOl/4jUqO\n0fPeeATtNMxKxoEgIrFOxvBpE8UZvfmWfgRV/WYUFU8Yk90B8bGMthFtScy9ytcTIwjkHH3ykqkY\neJnp2jL2C62ZU/E9H41/pWpcA+VVeWTnZcDkWhpDy4j8IRZ/u0p0B4oQlAsxLknmdMdH6D9vovTs\nY9RVfXjX5MplaRYmlW4ciGvL+ocrWZa1l4KkDqxoSGGK9DET07ZwsTAZj11m/Gkp8H64jA7fyTjX\n/Av5hQrq9TBBmEjSlzo6deiKU603B1o0ECfrQnteU0wxkyy7YW2XRkKFE++z77Fot56iSDWgpbXB\nLDrKlpLvY0lXw5t0MvzEWNdltLGZyx7JFiJq+7A5czdLw/KwrvUkp17gbedoHgTfY/+1AJqfT6V9\nqwmsKztIfFIrlIpgOnWMxCPwLfpPHSk39sOjMJv9EU+pNDVg7P3J+FTepSFfoKB3Z4zaHUfm9RWL\nplTWr5uMXX4mkiYrLN8KDIp5wROngegUckqGPqFtVT7XbDqhXnQD42mRRO6cjqJ7OkJqO4aGhxAQ\n2Iwy/UdqCo4xLasHgz5HUiczQ922gM1Fo7H2vETemqnopu9EtX07iZMcyY4ZhWbTdlTmTVRtPoRK\nIaVDQxyjax/xQrKQFbo1tB10iqJvodRJliK9uwuheyRanySa7AwpD7RCWi+hfeMaGHob3YLfkWhN\n0Cb5UeqUjrGPmkYDPajldFC+JcPKESGkGoVoxrv+FoT0TGThkmjsl46CD7e4NasffmtyiQ7/hJCu\nx93cHfPb4+ljr+Wz7gvf/TUdK9etPDH9irdYT3R9GB3jlCT6X2ZsmRX+Ic8wbpRR3uksZu5VrM21\nQhF/G3muBforAWRMimSS1QJ+sG/D740Hia3wwTjoEsVtr7DDo5DEKS2Ysvkgc9ooeFfgxNyXt9h0\n5GeyjiaCby2bb07lxIkL+MZ4MDxC4HTTPFQ7PHmY/RR3QwOW37nP5BNa/D7p+V37C9/FnmXjkwzS\nW6tYH3EN88wgrtttJezlOjKch7De1oMQlTm3S3pybEhHlowtJvBdDhqXRGQFhShnL0BjLBBib0fT\nUAjbsZBqL1cubB3OifC7/LL8Gt5LF2PeUI1g6EylXE+TQkHVjz/ScPcurhs28G7hMAZv7M4IP5Hn\nm1awf8EobLJzWFv4BFGQwacIaCrH0Gcq3/b70efXG2zpIeWvEfvQyaS8Tkrn2phr2EcdJytLwHZF\nMAnmRwjLu4ijvpDZAVF8LbPjinIm4eFQWwvm5ub/Ft37z/MOgI2NkpPH72DfuhCZCookNQQke9Ik\nr2WS300Sa6WUqC05u20mQbGGjD3rxPeF3egV15vz3c+h1mvIzynFpUaLb3A4luXWFNw7jchgslKn\nkJ3TwB+nB1FakkBExF+4tIznQ/I96GaHTYkS6+qnPJXc43zFaxwbqzEWj1FAMdo2zVgHfcHuEZiV\n6VBWiph11iBzrCIgUUZc1EQ0Lw7QnLAWk/d7UJV3xBANTaUC89xiic8NokehHeGD95AkysmTf8M5\nU8FQk6/41Su44N2EjVkmAwurGd8gZULtci7k7qH5mwQM2mNrHIltsyNViyrYHL6BV663eZ63iFZu\nmf+Lvbd8jgJr33WvlnTS6bi7hyghIYGEQLBAgCDBBtcBBh1kBgbXQQYGGBwGd3d3Dx4ikBB3d+10\np+18+X06VbtqV737nNof3usvWJ+ueupe93oWutpX1CHiWssX+hif45Iihh/yYZQmuXH35RqCA09T\nU5rDz4IIfmu+zJ9tSqZ07kJ5/22kP0/BobWIDuvOkJqaxzOvNMaUhRAiVrK13QumfrbEKsOND9hh\nYNgDT8+HOIo2EFBphv/DztzOjSL2QSkN07/gelaEfNZXDPo8RSlrIipYziR/NU1ffEnu9oiuhR44\n1Nag3wn0E9XoCdq4LGlgfkRHvksasXGAsBEJ2K/9mV3zJNxf+SutUfspVgoZH5uE+uYw8r9HovKq\nRR6cRLxcgUNhDjdzE5lbNYT1JeE0i3WEBm6iS2QL2w4Ox/yzKePKkjB/FkPSqGxOmwylX1INeu1T\nEB+bjHLmfQzjB1A3cTd2ET8wXrKcc+0vEX63HcWdv2AS8QntteE0ethQWx6Ha/NNirN/g4nX4Wlv\nmHaMsPFnsE01Q5EWQqFrOdKhN+GdCR8m2fC4tw49PRlRFjnI5Tb0s0rm+vEajI1sCLDO5/FDHVat\nFvSMrMT//AzMfrnFzVonxk4+S4G8hV5OTrgMlqCxd+eYYRNWYa+ZG16GxdkRxL0YxrOwl9QECWlR\nihFoklAlK9H13Iey9ASiRmuSKotI0RcwasQ9XhncQ5M2FBv/L7j2/khM7As8yGbbeymVF/+kpJMt\nAsckFly9QnztSAINZSSaDOZ8ywg6adwIlx0gyOkRkhoL/FpbiCsv5IfuDYJZftx9kIoyWY5+1SUG\nN8iJN1jLtMX1DNTIMRqczb8lxkh6iLlTvow9kYeQGwloMNHj9EM1JmtDeN0+Fg9BFttvCalrNCdJ\n/yFlTc9425SEfpsYlWktdk0p9CrSZ9uBXBrOneLAtXps6xX0Wz4HQ0c9kmoPIDZxp0xSwRntC7IE\nH8g3jWXr6yyODk1A4dwZsmrpmqZi362JbPEXcqOHEUeHH+Vo4ktelt1nsa892SmBWFkZoOuk5uH5\nKs6l+2JhJSQ9Q8AL/QGsaVlKa2BnvtWJccsYj1HwCDZs+O9it/8YgQDWLDRiSNx1TCRCXFwrUYW/\noVOGBr3164hUWBL1tR8aUxVGfy1C1/0krjnxLKyNw9PkKhYmnmSGZCDLl2Ce4s2SuQVk3v9Eu5Zo\nSkSzMTc9RoVGSZ9OzbjYNpOctAqNszOWBbHo99nNssQdfOjdSO3wbzS0tTKv3Izb2sdoYhX0fFzN\nuyINwYfhp74Q56cjSCzjz71KHMy6IG8chJd6OTphLC0CY352PsKT2n48EfqSUefIk1YzzBIHUR5+\nA4NKS86XvWeygQ+hCkdcGuqZWtnG2jALkgtbCBUsRVbiTbZlPX6Ng3Dt1UygsSWSRn065gVx3rKY\nGqk9H0x2U11ewTqxAcl66zCddJ95GecJbcujXZ0/Mp0Em/Kp/C5WYexggI9pKlZGhlwOyaDaooGm\najMKaqI5aqfkVmgzUfchRNKOBTdTyHDSsP1BM15txTRhzTfrUHzbS3j5fBrTVKVkaUzpbBZPr6I9\ntErMaZDboEhpR73ch2mn63gau5NxsisEtG/kfJmcIVfMaHC3odrahBp7LTqJgpnd6qgwnUJE9R02\ndGzEtMQd75cDuWJqg+HgK1ir4ykTmmFRFIr/1WFYySUkfe3CzZ7HCa5r5f0tE1a5r+FN01tSjDvg\n75eAt/cV0rN7klU2CoPIbfS4v4xS+698CnXgZ9PtKIzkSNPaIbSoQfc1FO2MQxi3L0D0sjt86Ern\nUmeeLlnON9MC2rk2Iy23R/gsBmFIPnbl8WiD42nsJEYT8oXPp39Fz6UI3BLRfe+EduJ5pEb1+Ht+\nQaiUkJX7mNV7Kgjp/Y6l6n10a75BXY0Cp0oVB0+qWDYIdNZtJKc0oa8zoi7amv6d7iLKtcN21VGU\n4y9j5FCJ1CSHgCHPCXNQkJlmTXvLIiJfppNmMwjzAgGlF24gqg3GzPAk6rZqtDblaMOqsLUXIk/M\n56MwD7nWnAA9czYOfMW364NIeBpBTrU+icZv4Mnv2Dq/597Vg7gIS9lUs4XezaasldnhZigkL+xn\nYpNmEVKXygdFMfX+0zHrk4K73nf8sr/ztNKNcE0X+hvF88atJ3e7aajzaWWS8T7sfNN5020lZtLb\nPLq7gwDnNgy8WihzlDPYXUa/w61cMquhk8qNuAsvmP3rGIIkfixJrERibkPZ6Ckc0TflQYiSfx4q\ncK2rZ8j1L8wfHsxv02LIqz1NRfFdpJ7L+Ls1gIanpVTWtNDa0YWGgcsZ8OgRbXrZJHhVoZeVwt3b\nN1nQpRu5fbrSsVMfFMaB9G26xCjzy3ytSyO84z+8KA1kQV0Dn1TmGH83o2dfET9+KGgXUEH34fl0\nebyWoIKdGH9uQn/KPNZv2vQfyf+/n7n8DxqxC4+OdSTzkwklTwMR5jkhjrvNx9DtGFTY4SFrxm39\nXEylZejfn0jK6mLWnRpD3HA9hN0mI9yUQUGBnHi9T/yySEGduoS3DGGldgh2Ukfu3W3lobicEeP/\nJtL9A5qsWcxPNcGx1oH9s6dT3vUM2/x0VIZls6DXC4Z0tgKTAu5l/cR7ewidK6BiNwhEOlaubGak\nmR07Sq/QFTU/GIadqBCR9VleWuvTg1doyvQ4Y+bKUPV56luN4PkGcrq8plJfxdv642wkhunqFtra\n7LmZ0A+BniGnNfZ8xpIR1T5s4iuLHvbDTenI/JezuK65Q07uBEyCHyC3+E6BiQGGm81QBJSS1cGS\n1XP00HO/z1TjHiz8I5wbxpZUy9ph03CY2BYlDeWm9kFXvwAAIABJREFUpDk18fsrH5KDNVT3uEGl\neTJn9pxhWtZ5/q00p//fy9hVKEAi92ETepRKIvA3S+LqmT/Q0yjQCK/QXVvBoMxTnIvuheMDFQ2h\nDTg25XE8NYX+djl0bknj4fUFHNKbx2CJjg922Wz5sRlxu3wu1E/mzOgKetcaYhgRwdbXpogvXuZI\nUwVvrRrhrRRF2wMs9LohVcpoeeCDotGQAzEH2D5yCfX5IcyLNmBgpz9wrfHhjdMdmpou8PHVQCK6\nlhDvGEtebj8uVkzgOgbsL39BwT/7UU3fium2lWgbjdHZl9P0pCsi2yokBmoePTenbc98jk5Yg5NH\nE9O9VUj1W5nf7iNNYhW1ma5UelvgkF+EpsCZxCcDWPfoN67t30QFDmgX7eLu/g3kVXZBmuVMjyf5\n6BclEGwViDLdhqlvTnFWNZA/YoQceKlgjisseyBk94Y5vHjxmuA1IdyQ9sWmWU7lzmq+RuxDZ1iN\n6R8uvJF2YvYbM1Zs38xfB++h7J3HHP9aXk8Ip7JmKjpdIh5F69DLzWOaQwWHe0Fwoz7FTi2Yj2sl\nztaIvgkK1sU+Zc8PHbdeX+Hlj6c8O34QUdJEBEaluJiNxb0whZWj8/C0eccOUylFMwO5OrkjKz4U\n8LfDNgpaNhIv7o7HxHeUibqzetB0HFp1XOhXS4/hFnRv0PFsfj+yQ814PGc92tAyNEopcZ9KqU2y\nRTZsDOk31tLhWy/SKuBvxU6Uq1fwePcD1my/yXmvX9i1LY6FG3piYO7IsCGr+BavQye4S3Otjvmz\nF1Jz8CLNt57yKO53msz9GP/hHxDewr7EmpbaWiorK3HNM0Hz0YeOw0bwsrKKRe9lYBrMotY21BJo\n38Wad5YTeC7ry76T+zBqPsL8nyWszJvJfuF0YrxHYX7vPq0v61Com5m3YCZCkQq5vIDLYglaw3q+\nKYLomHYU1f8Bdf9f0fP/vwFfHwGZpVPoN3wRq2bU8u8xFZn5ElrDvyAI+444uSNIFSjfRdJyO4bT\nHwfzw2YHhcMT+eOpLZ3t6rhaE0xJxxy8GqzRFDkjbovn+dRBrP8xiOmfK3n2tpr5rsbM3DCRwtcW\npBgJaSs1Jscml+VecGWjIYuHydntoU+8rJiwL6FkGP3BZvU95rjVY7oQ4t9CfRlMty7DQ/SK14Kz\n6AT+4BUGxZV8SklgE0MpMWqij+QJnc2HQt1IyPdH1WbBIVdHyHTlIUF8ZiBLcUOrXI3YsgzrGgfS\ntHrcwhGsE2hq8MfOuoSQH7co9nRAnRWG4u0cJPqGSP0smK+rZv3vR5DciyPBNZMOq5ORJ0HQ/jKS\nhR3Qa4SHwsGsb1zG2PbT0a8wwehTHJ+6beazo47Ph9s4KTqBnagTW1NHMr+qAoFQQGqAiH3ZEiSa\nERh9kGNGCypkuGjTiBQfRWCuQtfSA11zGgbOzVjfUvEsR8QB9xX0XroHo4pmGjJV1BRDtzhwS5Vx\nas4BlGprPthb8Wt4Me6lR5kWcxCDex3xRYZq0UjmNThzpKGE78Hn6Hr6Ap+9vvDJ8zP6an0mpsdg\nkNOTh7KPxE6+wavj3uR9uYNA0JXgUC1CiYiFr904alNGwOcJHF3YgvbecZyao0lsW8nSVhUvr3sh\nChqMydDHGB6RYG7fxpqUK3x4IcRH2p+OtR+xSRNQ1gf2jnhN67B3iGkjKcGBPltAG5zE5V+e0LXH\nbNJcU2iutYJie8prO1D25BbOo19h6pSB530puYNPY5lThvXDTyR224jQ+SqbHH9HMuMeOcdraJ7T\nyAPbZKqF3wnvIkBYZ0LfpkrK+zxAc1vCFteDXCk3QqDti6IxhgV/zeZHfijD1+bj9f4++1J24+cZ\niF25E9s2ldIsU/KwwZM57eVITyr4ZXUdV9KUzFkJzy6b807bDkKsEN5/iZ/eYxJuHyfGMoGd1wyZ\n4tRC3j4NezS1TJbaIf6wgMGqPA62efC+5hRW+hXkak6isO1M62k9JlzrQYlWRED1YYzM95BjK2P5\nrL+oE3uwzfgIUZ+PITMQEtaQSt2hZIbe6UqB/hLefYpAb6CSozW7CW8/i7cTDBlyfyZW9eH8M1eA\ny+0bTD69gJm62TRWK8FNR1TbSl4GBPLT79NJP6XCdrgAG3kSN78eQuhQRL6blkOHN/LmzRsCAgL4\nfv48r0suoQt3pO/hNi5sruZi7j8Ur56Gf9BTJtzuQLS4PemVO7n++jCCsg7ozYvlaycp9zvqmOS2\nn+1n5jBzfi9uxHvRaiQiOS2KlNRubPFcytogC1yLtOj4z3f7/Df2+R+ysuo4c9aTSVNOYps8Dadz\nM+BZNMbDnmJmDAKPPCpKOlD2uQMJhqYEGcsYVejFjEe/YNKgYcOhVqZl5RFfEUJF7AMqnbOJcf2b\nORNK0Ua8wyurJ59elXJDIyDUTcjYoAa8Bab0CS2klw3UXLVF+nwEeYbfmPNlMUn6ufwWP4s6/To+\nty0iYsl1jIzl7L8GdSWgHx7OwdBaygvH0z3yLz58fcnaDra8KlrHF10Wr9q2cUUWSlr9fHQCbxy6\nBUH2AjI6P8csOZo6unKK0TQzDwOBBVr5ZGpxoyPxGHkVkqXx5YvSjsRFKXjX63M17wy2C64TKflO\nYUo5e0pPcN+7ikT9DILOjiPRrzsJd8dSKtUxtSYdkb4+JS6duRKVS5VVEV8tDGmnL6anRQMJRvlo\naxRE1AtxqqlhtvgmDp2k9E9oJSIpgTNBago1Y9DohHRpe02CLgYpcIrx9DKoodHOH/1+eQjtS5F+\na8RApULmp2ZoeT1t1frcHxKFV2UmVVJ7CgMaSfK6zLyGCwxTXeRMxzqmn/kLm17xxPTexZjRO3HT\nGvFnmYJUpZw13hKECn+KrAaQId5HhXk5+47voX2hN3mGlpyZbcIMk338e2I5niFpVNZD16jDCJoc\neaxrZPUbVzy0Tdj/aCa+xh/tqChiX18nU12HqcYBWeEkGqz3E/a2hbRuVtxw6EfctSz0p/wgbIMa\n25cCctw6oih2RmuqJv2cP42uOWhmaLB8r2XJ4+M4tSZjYBtJecYHyk/9hb6ohPfWd0gpVdLXQUk/\nGzXGDjo6/NPK2tpWenqL0bkJeNrXh87noxGapFHVLOF8h0Ae+u1mfsBnEDhT1MGFpvAyRm8bROnY\naIRvUlBoS7h5+wwJ3xv56v0TpooW9u/ZzdJFPzPt16/0GFuCpNIBzZbVBNdDSoSGOK9ciksgzBvq\nnwrZZK0B0zIEJiUs/fg7t1uWE+jtR3+je/QqTGdJgxCp2pgHY66jDr6HwZULJFvU8LnyBmPaZnBb\nNQ6RRQ3WeaW41p+kX8UNbDVfKe8LZSPUZF6ezyb9jZzSTsEr/B0Hb24iO8eHLuEPEYjWonehIyEv\nQomoM6DbXD/uN13gbkkKA75MoK3WlYcr0qhr1BJ/SoRHN0NmpUYjm3gTD5ma0/OWc++1DUkhBRDQ\niPEVQ1KVe/FumsuJTWmcN5Cw2r+ViPAgXiTkkJieSmZgOqVVQg6M8uPNu5OUqT3IEfhw8tI9Fs75\ngsTgPGmpizh1bTH1GgdM1CMws3zFz1PXUFku5OvHgXTq94Sd6zti4exIa7kVnXSn0HQ3ZuLLTMY2\n/o3N0kH8ueU/y/z/P+35/28d4P+Cnj/A69cV9Ohhy6VL3egR+gcZIWZomzS0GNUhG3UF3ehrXF51\nmg71NmydW8XBJRYUh77A5WsUxS7fmLGmGHNhOE0nOtHWIZTQ+1rW/a1g7lctXBbwz0YB63+3xi+v\nJyG2gYS5CRGuXwciNQ8/Q9mqsXzRfMFIaMw4wzg2iP7mV/9IvN6P40VcCZ9ygvl9yXi0khZ2bTYi\nrKM1cQZKtnw4wJpNI5g06S7zmu5zUjWPMtEAlmuaCUTJWHYxlwrW8RszRMe588dMzr70ZsmkrWyc\nY8Z03SGUPEBIESYo+S7xRiXUx9fgO0rJO3C7Dfn9MJadQ1t4HYWlGcOlY2gY4Ejurb40jRyG7Ttv\n4grWsbGmOzLJB3x/O0xO3mka9QwIUARTa1lKsXUZs1uDGRLzmbR6EQFmOoyqRXSeJKRbiBJpkykP\nM0Tcaj+Axfl30cheUy34CzO358wzcMDo9V6WqMMxs/7KtoUzuHarlNTvzXxsVVAbAp55UNVdxI/8\ntWROuYe7zzc+TOtN3yP3ydyh40yYkPdGGqZ/EjDq3m2UGJHYpY2gFCixkHNx3x041Y0vTwdzUfCW\nP5cYk2C0me7vmhj4eAZe9T68sjUibVoRMxVHeap0xVxUg0foF6yss7m9K5YCyxZ+v7WCqhg5TY/1\neW1izo1pJry9MJmNxTMoVw9hleAFAzTj2L8skMbPTjiOyke2zIu41rvc1NPHSBOB25jPzGz6hR6Z\npmzO3o+mpZoZM6P589pHomf0IfKxjCEl+UTXfEKkglx64SR+jlyiRhUIWicoMOqCIr6QfsVlHBod\njNHYSvJqDDE75MMLm1e8HrwUg6zdbA1v5Fqxhkflas62B/FXG/YmKUgYtZW2UydpNAjA9dkFng+V\no/9Nn287BOh/M8AjvoHshSB8bII8VJ+ySVG4i8bRtGEbiz2nsKTuABWybNZkConJ34Rt1TdeuD5m\naOER9pueR5eczHIDY+QfK7lpUId4jIxco3zshRac3jeJwa5htFV2wdj/MdHOVwlwc2bLtUkwvg+9\nDycTocvF8I+vVBaUc+zEDoyj15H8ag+JV9TsOjuB++rVyO6bMdgvncIBbRS3adm5pR5b+8dcizPm\n3Pcgen/sxNMOSirz/DBU1tPa8gOhlw3nGr9heGQqCrWCu2aLiREvZeL1Wr7/5k7fNZWU2rbnF9/J\nhErvslJ+Eru2LLy9vvK0rTtNGgnSF4dxvf8LBdbtsVXZcnXvX/TpMx8Dzyaqkscg0J3FzdYFXYUK\nX/1m7sltkaFCaa5B3CJEKFHAjArabknRy/+AWhuDgJX4CuayRpDJhVh3Lt4IQk9P8B/1/P87+f8P\n9vYyPn0qYurUCnR6NTj3HkRjchMCVRUS3iJstSDIIQmjR714MEzKgPsqlJIWCq0L8S0JYHTtPmqU\nP1GvL0OZW0zs5BTkDQJcHsqIdtei/vQTYbM/sutRGsGNHfFsCOW54R3+PSDm4zVLvml+0GxUSbDU\nk5Pq8/xzSMXF91k4O0rpndQZTb9ltJQO4s81jzEVGqNvehUPEy+G//Y3SR+1tLyw4kLbBk6KJvPJ\nIonH8iZWIqYf5zjRK5fr+efozhNetpMzOjONbud+wVRSiFh0jiRNCYP0jIkS/eDu8OtYqlpwlL4i\nvugTlNaB7DWBzV94plAiGDqZ0IIu7Ou2mEh1OZ4VXcnyTqbp3UxahXepE0RgbHmB/pX+5JiquX2t\nlTBXuJUazJLkebQGJ3Dr9FYaX0bjJZGj11hOvyQVP1cpOGoQSF1lN16KVCjVUwmYM5VKqYBsPzGj\nE7qQpRZSovEiesJaThxQs3SdO1nNMThUaTjf6xCPqnrjMHcXzh6ZJD8N48Djk4ztvp9+p9ScT7Bn\naGUYi5TlVJXJkdqXQKMXSzdLCEqSYp/rxeTGdjjmNuCuURLZ7m9OR0xk2Dtv/L4FU2NSR+c6HZ0/\nirEp+477b6cRFkkxeWmK6pE9ZWlziPk6DM3IK9g+9SYhajt9SvyIpz1LMteSqhhAB50paeEZLFUu\n5rLXU+wf/USXGRdJ/NaZz4VaFistyFMVMTipjgft5byJLsHvRSY7DIXo+eRSN1rC2L/y+LXmCMFN\nlWCrw7yxgaZOUiZGGOBbVo9/pg5hqwmq7jmcKLXli6WM3MXT0Kj1iDV8TYNxMZUuLSSVv2WKYSPu\nphC+Rs1tHyE9LukozjXnSFQNnZNfkSUzQJzZHnMDHZEbSqiO1iKWqDBqbqMuWEh1pY5BK9zpFtpG\ntOgTJpmltPiZM8hvPwqpgo1VP9Hz2GZ+fiHFuSWX576JvNdcQvYkEWVRHQ21laTowGqEAen+IrRJ\noYhMavAUPCXb8zqxs//FUviMKRMyuKxKI//OVjRaA+obonlf6YtVk5SLj37ixm8/sybzGuWjJOhE\nOpbZzkLbSc4k+zW8uROHfGIKOa52FH435VHZCK4nDya80J7WXqZ8aweDfR5SmX2JgB4nKEnoxVf3\nKoZ1+EBBpZyrB2NJ12ZSuasn2tZDFLUzpO7cONTOuziaV0/gRzfUz3yRJBrh9vkq2TUJqC9cos3E\nnTaZkF37NJgqZhEZMZyLRzwRMBEHtQFFTVKCg3R8bjAhWphNqtoaD+NyqgylqOpkHJgt48EpU+zF\nTvhoSmmTlFOq6cstmRPe/v8SE9uJbVv++u+F7/8JJBIBjx65YGPTj9LSwxhE1dBudzsM1JaEOdvh\nm5aLJjoBPd9UfK8eRv+3f3DevZrAXevQ63oPSYwp8w4I2Xq6EaNnBxjuYEB8chA/mo4R8nIfHn0S\nqL45kik/69htuJ2tLfs4sFeEfp4PPsFy5s22Qe2rYvbFV/Qb3MaiBToSkuCxzQU+2L8kpqOGPs63\n2e5+n7y6sbyNj4CoSrRaEXml3XgnWIWX2XyaHF/zpVVGoNCU4dRjiZD7r7IYwVwkuteosgZyzwss\n7GcToD8FH4s6BAhYbraSX6wW4C2LJn+uHr4F77HTfcdQd4Phof1ZHBxAs317frrQkY0jVhP8YRIP\nwp5wa6Y/NSYKPglc+UfrwmCVnE53N1FmosInfQCuwhJScnxRzZjKvtG2yKdc4PXzMZz4PI7mkDQK\nJprxRtsJHxH8qfvOZtUOmlo309xiim+VF4rLLcy8oMTMSEFk9BuUCkO2r9xCe3NffH2LEJkp0em1\noWq5ztmEWDSqYgRiNYKLc3AzLSL+8kgqzSxQNNWSmKbmoV8EntoEttuF4Ll5AL3elbDjD9g+3ZDb\nBlWEqRrQGhZjNSCVn6Q5WBYEk2mtoHjHHE7/3Ea5fSmeZVcRHnGm485grB/NRCe0Ymb1R1zb/2Dx\nm4Xkm0jpmm+GEWocXrUgbW1FpO2EjUEpN5oiaQzIYlzzBD6qu1NRKeF2zXlWad2IFAXxllqUIlsc\nb6fSK6uMwzoBQhdXJpwSIXukQbtCwRZlZyZymJHFthSaathb8JW3rtlkK7ToxCKK+ymRXDDmQnoO\n7X6bzJ+6ZYw9cQ+bS3p88jCmv78ht6os6NtBn/WbniCP6MeRRwZM7ytmab9GjO03kWyjRO2Rjbi6\nmLHjJZy8vopX2RFotRIaXaUoHXUYXRKi08UiuVxG4Xh4t7SUxsAE1BuWYTX8NH/OmsC0DD2MovM4\nv8CPV6ebUYjlmMdJkIqEjJDLKbLUkRKo49fQP4gttEHwVszKflDTEe5XtTGml4Yb1SG8a2wjOvoS\ngrcrsBzbh4VTt3L6Q1emxjxAL/I++WObKe/Uys/avegcrJlzQUqzxyOMbMoxPO+KxVwvPri44mNS\ny7+Cz+gtTiRx0SdMh6VyL1ROVV0CyeFlWP58nKqS7ly9M49b127QWDaEt1tG4uiUzqv4UHLeOaAN\nMCNLsYegl5dR53XEKPwpyeaNvM7ZA8eOMXTEXaziqlgw/xoBmiEY6HlStlFCB1U9UpWIcoEROgG0\nyvS5dE1Ah6klSNzrqKq2ZuyoRMTtGtm9FGy1rZTZ6Yj2e4Fn51GMm/YL02bE8rQuBgMD4//Yef+V\n//8Lc/NeuLmtJTk5GoXvDaTjCklpaaV6ySjc/zFDsHEli/uloXPO5fqOXgQvFKOefomqhFhAgKOu\ngYiuT9Hl+/DH4Z0sSbRCVeeDwKIFB2ModTCne2cxT3TPmKPfjnVLpcxZoaTnyEy6x0mxWyakm6UI\nL3cN7hHw8SUY6yuROpbx8q0FF30v0SY/SF3ddF49G8KXe/5cvnyBYw5jOSd4wMp6IR//rcPLR0UG\nOmLNxpOtFTCVXF6TBXmeXHczpWtVOk2eIgb3DGS0cRiXF1ixbpYN3U72pT7VnSVSIZv0gvlFeIyq\nJx0Z+iqbgvrVbI/bTEBVEaWPNmCY143o52sxiV+Gu/9dsn3fM8Y4ga9tbrx2ysGixILizlKsm6fz\nl8lAUrvpc2VkCENH78Cn0xsOHzuGatMunFiBl1TGir06RExArOeDcUgSNZWzUbU3Y3XuMRaX2fH0\nYz8EAi35RTMw9G+Hrk2IwdRkMv2saJdSRYqqI1b6Ih7c7c2u4h4EdH9Puy/lnGqdQqa4mADjZSy/\ncQKZrAGnry3o5nZi1FVzgg/J2PSHgGPT9Fg50IKN9d6UN3whIrkF/3w4gSuVsl58H1OGYynEtxtO\nW5mYGvUgLnV0wSRlHo1CPzpVrODkzk5Ifl1OnbsVFb3uMrM1mXeiDbSXVPCpzyJq8/2ZlZPIG0Uo\nP9Zp+ZakpEeEjkrucUt3kZ+MjPhVF8p2uT5dTvSkQi+Q0ZXviNBdJOyRIaYFhvwuVLEoyJNGw0pO\na5oYZGQGVi700OiT4KhBkibBNqeZbWNkvLj4Jx7bhATfUpGWNodLeXVsVs2ivjd8S42i2vQrikdG\nmPo5g31v9C0CCPKV09G4HaJma3qMuEqXbvG0nAik8rd/mDUyh8SHo9GqhXR5A6dF1YzLMqTICJz7\n5PP+4RaWBf2g9doE7vutY4HLOmZ96c2XYk+SDa2Y/CSAXGNDvHbsICAykl1eMvSrlcyXdWdKTS9a\nMiqZ9kDG6Y5gUGfCBu0KXgmGME4wlPaD9vLnhpEUW2Sj6f8Xke138TSoio2nO5Ft5sipijXkNuuw\nkBnSfuRtsoQRTP11GUmP+jKi/ipWUe15O3YUhyPTkLwt58zG1cy4ewPBpg1gkIi4opZq9xesWD+M\nYw/n89YykOpDZbj8NIXiEnvSM8PQvLID8TXa3prRghF/9djFvIRAqqa4obf/E2bnUlFWaBFebKCf\n8XwUzbVUztzO5kJXIk0bcB/YgCD0DRqdK6lueYyqSmT3SDEivaO0CCRcMDJDsymV7w16lEY30XYi\nmY9DBCQkWuEdeJ1bz/tj/K4zBtr/3HX/zfz/F1RVXaeq6jqt8hwUdwWoQlIRPh+M8/VmCoYJ+Hi3\nLwdH7sJ7/x6WrNiCJNcVzYNYcp2zsV50iK/7VtE53p+PYlPCnL5hHP0Adakdw0IOcqq2B6n+T5Hl\nqfEfADsz4HdfaFaBVA0aoKoZtIYirs32pcEsjz9+NiN9+a9sNdmKias7xYkvmDt3GSePLKBD+2M0\nZp4jI8CVBfJWojYkk5YMKzfI0OouYioazgmVijnIKBfFwh/3+FhtQcilEoStOpR6MCHYiu8ldZQV\na9BpoFUIW0aG8+83BfnRctzVZaBnhFpYy/ED3ZigPkGT05/IRx5DcvdfLGM2UWZZxKh3oxj1ZgKj\nfx+F7K9c1v/+Mxb/rGYq4UjNtMgVajwcHfHz8WTU7d3kDFyD0asofILhuKURj59PQGbYjMmgFCqu\nRmKgX0Cd4TtkZRmEhwkRVoTyILsbenoOgBCRWEUH93iyM4M42TcGSbYxwyvO8iQ2BgOnRlx3NZA7\nSsIX82FsOrgNict7TnefR7sLKiJU13AyEdMc10jQawGX9opRx1uh3e6PhyaPrYIvXB3vRE5dDp/H\nt2PPpRNMvPuUb5rtiGjhstSKfw5aEZtTidgzgyNL/sRI0ML9XyRMNLfDrsmfv9fNIT7kJid7PsFW\nU4Tq8V5y06cjXPsDbVQtYRu3s3LSZz43RXFc2pdHv8whmG/0pJSrjKK74RMsNVXER++j39cw7pRv\nIH2qPk9qrFmeUsrYhS5sX5rPo44yhrzXECgQ81HYTIm/CO8aDQkuOkRSAerBOiqcDJiRpaK54Svt\nzzThocpH1KuYAze30vPIdiY5HiBMkMD7FxHcubmZ3qYX+NXwOMdD9Fj8t4hqkSlvFthg2T+Tr0l2\nuKx0psVpCPGTEnFu/4hIawMm1p2mWawgrvkdE6z2cuDdeB6u2YdEdJZQ0VSumFoTOcuUwt4HGZ36\nkviE9bhKLVlv74tw8xoWmU7CKbiGydHu5FhWc0LuQK4sEm/bYVToNzDAoIwIqS0rD0yn8b4WcZUV\nUoNSuq5YyfvOvVAuXox65w6cyKNE4MHRlvE4/urIt0g/Zp48jmDGFCIdU0ls9xtioT5aW3Ms7t5F\nmP2Kyg/pDBi1AOnwZl5njEdPpsJSew8TS2PeTSgC5T4wb2RswACuv33I4d3RZKXMoKDFlbf9Uxj0\nsZnT9v3R6WnYYz2XY0e2YVzqRFO1DR4+BvwqycD8SQe8o2MIN/Dg/fAosPZHL9kC7d8u2HjUUrEz\nF12CObpWEHSu5efWM9y1jUEwOwizbpVkVrkz18OKPbulCAT/Web/38n/f4G19XD8/c8SGvaezo7z\nsfwgQhBzDs34Joi7jb3Gg/ojqYjbOrDlwHYYegPhwh14LdmF6vQUDsZP4ovgBW3tkjCpsKDlVS+e\nlA6mW3oMuwuNKKmAgIFQ1Aj9raC6WMLJXBGTkpy4VW+Ipx1Y6WvoaO2EXCvn5qtm/PHgpOE6jhjG\n8KvzI4rOzaRX23lmJXRgZ9thOnh48rAhl7kTTbDWOnFxvxUGet35a4MFaw3FyFFgqCmAojCWiwyQ\nW+hxTiXEu9Wcum91bLLTkKAPTsYCppgJWaf/CXn/UkY9+onie7NxelWFYK+WGNUbKnSBiIri0b0I\nQhDzO1KtigFZkdzpcpV1Y1fhVe7OGFJ48HQNH9SWdPNvo3uoFk2zHgUlf5JyZxuT6MyGx5vJ65WE\n4mMUt2/Nw86+lA6d79AnaiTOgan4SmoYEvkc2bRbTJ9zCCvPvYQET8TIqJEVB8eyd19nvmb1pFZj\nx7HWOYRlp3NgxiiknYvxO1jP8PFqlgj88I1+zKdwDzT2d9irnM0vqm3oMOF1Y2fSLkXwJbYF14Vm\nqI744LX0Ns5iQ/RFZqS6VTBW/y5dM98x6O49PmvdmBbcjtcBZuyfJAMrJc9MrbEyD6HT0VNsbZXS\n7i8FbS3FFKjecnLgBo53v0n9rU8UPD9CXsy31923AAAgAElEQVQOmBuLNqQRQU4rifq7EdsoOO8T\ni4t7K9e7zESHF28d6rHp+ZVUTTCvfbSY+T3h/uQ/8be6xVarY+xuK0I3UUuWwoTeY0S0VjZzzysK\nDd6c8BMQ/E1NfaOYu/njUQz1Z95ZMdczVJgIxqKNaqAsRJ+NyjW8ujuJLroPZG8ZTLumQkCEtbOS\nnIIgohecxvqNgHFH2vhZbzfflokZeDSdheuecOBoJZ/7TOCTbTjnlffQVW1hVMVpah864fLRhN5r\nenGhdiUTnN/i51yOvm4UUX1PkFYXjl1LJGbVBbx186LUTkpn2xqEnb7wzU+NtUZOXaMaW/29RJgb\noFY3YPf4B1mD+9Hhsi2vcuTMX3OF5lOmiIVT0SyoQ24LDw+doWHFCnx790ajUZGPO0d9fHkrjqZu\nQAY3mkzx81vMXv8slFmAsxNqUynaVauojYlB078LpmIPck0rqTTqy7Z6FVs2qLFIcCPZJBgn10sY\nmDQT3eEapdo/iAi9hviZO4esi7k/2BCNQRCnE35GsT0IjY+Co+nzePM2lse57UluMeXyNzHnOp3j\n5sHRkJFF0m+x4OGAaN4N1B7NCCZlUNb+KOKvFuhO5EBEA2GlN/gl/RoWDQZUb64ht70MbbIF77rm\n/x9x3H8vfP83EIUGYuLXh+KmEzS3K4MCT0wbpLj17cHq6a2sOevAlEo/VPpF8KYbsvv9GRI7jaXZ\nu5jWKMdUp0avygbHVhXtClw5NHQvzY8P88PxBl8yLGjct4vJNY9xj1Ex1KUJiUaFrRT0hQLafPK5\ndlnHH0U7kR3/A7vCFsxLNVgZG+LcVIC+TM61wI90xZMBAWn0+y0Ns8vj2fjmE/266PHu4WCyy8rw\nq3OjUFeGj24EpbIK8pxL+EvVwj13M5ThLphElHHaB3ZGCqnpoiO1E0hS9dBeU/O96hXCxkYqG4bT\npvqHXvRGj4HE4U9i+Uosk09y+uNRCl0vkGjXQrnClu41FYzK68uNYkNakRBY0cjdPD10BovwlHQl\nSGFLR9lakhUZZFWvI7hFi0voLZ6lDcA6ag93NCnMHJnEHN89yPS8aWf1g0ePFbz/UcW6TRWkNnej\nNHUZ6RUqZBodTo6pJP3ohkfvT4y68w7LhxJ2B4fx3rUDJT86ce3uUHotv09jfDPX3x6m14gL9Mv+\nyswjU7h8Zwm/51YSJv0MP39k5sd79Mn25FQXFcOaT3EidgAPVi0BqZa/lsfx0v8oT8sGo0vqgK5f\nFTYHzSn/1wlBt2SyNBr8mgp44a1G9WYD6d1PIH29CUVjZ9SFpfBpLYw4jcCwN7rLAYiGZuBRWos2\nzZIhppcJ6vuMTykDqJ5iizi8AW2iDKLmEepojLmDK6nKApLv96ah7xke3RIQHncWN5tw5ty7xyMb\na3q078+Ixa/5/mYMnrUpCJpXU1BpRaGtHXfLcmh2X4LO1RC5REpX7rMvbQNFg8WIxG2cPPEnNVWO\nnD27hmGjd+HRZoCRQQGlVR6k/aLDMKYC+3tibpSPJK8ymfObF3OycBU55j68L56KalMQ0aYWfL9o\ny5DyetJ9bAnzPMobLxM0X8IJ+yZhpf44cuIcMGjcS5VDD2RKPRaHpqOoteFT7Xu8wwq58UiPk0O7\nc8u8H3VqS+qbitG8j6es1Yy6mo+QlISuLRFz03cI80YjnZqCstAO08xM6oqK0GRl4hDVib6WduR8\nfs+qtfEYCtOJG/yF06cbEDeUoKoSonRyhC8lSAOCaHTzxqPWj4zYMFbduE/IgRU4mNjRog2jqUcR\n3aNVDOt4krK6CNQhPVDVJZEuCeO7ZRP2EntsPllQ/NQL17WPKb8cSqG3FQE5rbTTr6XnmENEjPqH\n/fs28fjuZEy9OtGk9xYjYSvam+uRfJ6FalY5dHZBs98S8s8ifjmOfeNG8epwHM+7RxJ3VsY3VxE6\nQw3VoRksdHFmy8b/7IXvf+X/v4meiQNqdT0tLal4hq5Arv+a8JYoXBY6k3KvEL8PLVi0FtI64SHc\ni0Oj8Ca/1Q50Kga0beKx50gsrb9xd5oFBlm5OPV+iHdhO7LkK3g/242k14Pon3SbkQp9HhdLmL5z\nGKqeOZhYt1GYakir13uKGMgs3WZS/MWIFX4YNemzaspvKO0qECgkuGaH8qmblu7nfsFcG8Da+GtI\nRHfJKftGuiaVdgIfJokC8Cpy4mPFdEIs6xDp7PC3MyK6rYShx9TcfzMAlzeGmMaX0z0vhkpNFqeG\nejI4fRvP1FOZSgL9uckcwSmGcJG6/mb453VEp6nDr1DIHWEf2gJvsPJ9C5rmOJ4qd/GVe3TGg1cC\nXzSaCPy7z+fXIk/WKNZiYaWmpmYRpSjxa1aTZmRIRb0RP8lSSDPJoEuAmh1H2rh3px5FkBeTZllT\nZezOzBNDuJZpx5eEbixeN4awDie4fXshb7qYMbT4A1Gb93Dd8jbqQ7exbLMmr7oT5t7vkeb15nte\nI9HKg/SwKKDwSzkZdf0ZrWzBTS3FJ6cN84zeuGnvM7VwOclSK07/NJjeSd+oNzZjReG/eKZNo7lK\nisnOL4g/G9KQ7URLaSEtGetQ/D4f9x9PEGgUBBX0ZnJRKk891sPqNLTW8aD9Du6+oCiDKyZoJ4oQ\nZOozN3IjCoURD59NYvTo7Typ6opGGYckaDcaDQwJcaN9YyXfg4LR3plC1II4Jn1LxeH1Hu7r5RNZ\nXcaqRcUEBMdj8a8Nq1KrcBbYkIkrz4dGEq8ejML1HLoOE4n4kEVJR2P0b/fBW/yRvDhzpo5fxcsP\n81BletI19gS9o67xLLsX9kO+kxZmi4vfOzbVdsaq0QE7VSaf6v7ASu8I100T0F6/hU2hNa8fiVg8\nqw2TvSfIV6Rz680gLIIz6W36ifpyU0RlGXQ2SuXrDBNsk3eitQ1heoOWQJvXVBSI6NCtABc7Iy53\nOY5yzUacby8kIqEd6b5/Q1MNmrSHGGRm4Ce/RHOUhHCvFtI/TkYRuYGoIB9+mvIbr2xnon1zCtf8\nbPI9JPxYtxnPPmG0FvlT8FiIS6/huDtCWftAFKaOGHXvwTlPuF/2GHnPDgTW5HBh2WYuSaUIqpPo\nLx/L0WEGxIsieG7cmbIIW9yD1TS1GFDrbUpFqBtDnguoPu9KZVwLos7J6D9U0Tpaw7pbDeQtesfT\nI3MZN/Aqj+9NoU3vJoqiMASxjYit3OjWlEFmUhJ6CX3xD8vGLbkG1/YlCBWm1JpmcrDRBY3eDhqM\nrlBf6QwBeoxPFjO6vzfr16//b9vn/y+8vHZgZBSETqdE7f6RkkNF1D2vY6yNgGqBIR1WDWLFjgzq\nwox54+tKq6mKz22OKILNmf3YE1GWByvUm/jZcBKv2zIw+jqA3y+4c3xBOXWpIRh/GET05/6Mjo9C\nnj4c0cUhtKlEOEe08rG+hhu3ZqO44c67WG/2rxbzY+QjAoWmzBHM5GbX80hSA/HcNJcfLkL6a4NZ\n1bsHO7xnEcNBtPpCUoXfeaAZgbUuGkF+Kokvf8KsTcjyGncS7gpY0CpCpx5GsWYAB0PGsEA0EbVA\nRE10GVkmbZRhhpgsLjOeIl0Qt2y30GfUadq3DeKm3mumqn3Zq7oJgM1gA0rcXtLTIBANnuxBiFD4\nknaWKUx4Oo+jFndowwWhVI5YlE21WMNnRSAmLldp/hGN4tN43lfqcTNDn8AZRSj+kDBySCFO0gy2\nVgzjjsk3es7PRDwpiyOOU/m7vg+q8f2pvNKXgK69EP2YhcWpXYxVXMJlynFEXa5w9OkW7tSNZYrZ\nfWJEJmTZROGh6sBQ81auKhvQzf8dXeAP1N4nOT1TjpGgkSZ9N8QaLU/ad2VC7Fa0H0yoTalDGltA\ng4EO3xfjMPsqxFZ6G5PQDOplBjzuHEVZ+UBG577lW8JmTAZmEZ5wBCMXf0RT7RB4+CFoLIB/8hGo\ndDQVOdPWZMi2Vae5eGopzpICbkX140nXOu6FtjLPrTMFlwbQK96ayHvxCHrXEJbYAY8HTzEXm/Fb\nxVfiNkLdJUOi5uhzVinnrVEhzwcI6G13mQexYtrGF4EsGJFOQca+dHSGWr5F5tJt/QEO7fuTv48d\nwGpIIb/s0hD30wmuXZ/LttrPFLyJ5FNKDMslaxFXfOG57gXROWdRS/RZXilDcu0Jw2wF9K58iP/s\naHRGRkyq3c40kxuk6LpTKXHH1DuX7u73KF4iJ2WpkPZ5RVw6pWVcbSLfA4Xs3PUnpo6QU9iJXU+2\nIvdygKWbKK6azG2lDkGSEr0eGuym3kFm8paibnvwd/6Vj2OsMLJSgtadN/JHbE+9jGpzJ1Ddpy2j\ngEcjfker8+XTg+eELRnM5rntqKqo4YX9Clo6hjLN4CzddOtpqx/GZuMziGklJqwH9RUVnL92jfdW\neogamgj/ZIxQKcZh7ka2Vmyn9kc5k9coqVn4AqsRtlw8EkJDgwipeiflue1p/8MZ0wwhGxa/4VUH\nd+wW/z/svWdU1c225vtbkQWLnHMUERQVQVERREwYMbxmUDHn/JpzzjnnHDDnnCNKEkEEBEmS4yLD\nCvfD3uf07tGnR98+b4+++9yxn09Vc84x6/+lnppj/ms89ZBZi65QZ9AAywsgIhNNyybUrvHjXe49\nBG7ZCPLsKFwSQElxV/TVbVGEDCOzPh6JQIH545XMjZ0O4vPQvJY7tStpUNb9ZT77V+X/vwmx2Jic\nnL0IRVLsQ4JJGVSKvKqOiXXtiFZ58C1FxO7rhmjtKcS2roaz6qZsMthI6Xg5xVmvaXYyFtn0J9ip\nYIv+J/yTPGlRJMPKrIjy323pmatgRvp5jhh1ZX9MGLrCHDoE/eDYUSHFhbvQt6+itlSHaV11iaqZ\ni2FeGwR5o9AI3+JWZ4HsexNeqi2xoRrXpI5oGSg4WbKRSvEqRGJnsqWxfDfypcJ4HlQcoKA4kyi9\nUn4k/8CB5RQzBghGWNQMz0FXKclIoahel/Sq0WRVWBErbodLh2fsyF5NoUBKkFE6ptEtCVSf5z4P\nMM8spb8v6CqU7Hpcw0Qm8da8OVXVnRGou/NnnRPF6jpO1wgxsxJTmDsNRHIQOJHXqMfxolwyzJN5\nXmKKKu86RfVmzOtSzx82YCSCux8bSC/4ybt21nyx/YZINQ6zp9mk2WVi2tQZTRtb1NcnUf1mNo1y\nM3SnnOdV0EiUtvk0HOtLQ40+JstS6fcwC3FJOzyKXiNThLBL7crtX1toOeozupdcOeI9gsYUIx7l\nDaKp7nfUrpX8PN6Ddh0e8D21PRYDo6iLe0b17Re0tk8lRjyCGgMR6kgPfg9pTu17e+4r+vFZpwua\n4TlsMVvLoLXvuCaRI/Rtg/rHITAehdlRQzLCoX6rIT9+dWH9lv7MNlvF1bhH6PwZhlOsDQ5hT7h/\ndjrS1/WcSLyMkTqFmJe2hIeU8a2NiJIWLzCrWsKwba/ZpJnPJ0U6Wkf30GPYH3wx0KelgZwoZSYS\nkz74JWgwfeZKfl8Rec11cX20Afm2tijM6zFuKibRXpuSZ3KuXZmCZPwDthzbgXabTDa5ryD0sxM7\nz2WwTQlqk0DefJ2Kl309hyq3MLRwLT9KArCs/0KxqCMZWmuR1uUx4vUJxoxcS7SJHcqil4hEanrH\nX6O9bibP5FXctZxJ8T5XBoZc4sL2JTz394HXumCvR+NoXxiixCizgAbzGOqa/0bUNxpv9484t3Ij\nJnET9Q7FCISfwaE/KrtAGN+IsG8JRV37Iug9kKLYoUj61JNtfYqTddfIa1pDtXdrBEWRtKy4i6+0\nkB3JdZxJHEJjk47EVdTSOj8fvw4dmLd2LZMbJWjnNkXVXIe4hEc8uJnGqmtd2Fx/lt+cxlVdi7M6\nku2YUPRNQsbTQNrqVNBqzD5Uzl3JqNUQ3rIEhXMheaMKEf78iY6nEUKpilZlVmS/NsZ9vYxKAznl\nH1rQdsxKYtNcETW7TKu6AJJsu+JbLMA65DCCr2aU2gaiinFm6ZB2rF371yr/f5H//ya0tV3JzFyH\ngYEfIvNa7Hv1xXamDd2GyzAwyGLs2O+4tXPGJtSSxOxiXpSb00HvNeVeB5Fol/J72i/0ftTgvcWf\n2tqOPBlxny5vQjAslVOpKyNANY9aHSmXrixEcU7I7fQBxHkepuK1OY0Ngajr7CHRCO2U1ySYXaAh\n9SxPvWVoVdbw2/UKDlY6+CSYcW6DPiO6WnOSPyn4bk5T1RqyVN0QiIajG/4KcZo5DspcKhs9KMic\nQmu5goTGprR2+kanDi+5n9yXVEkW/v3vcfm5IclVS5BoNFSLRHh2uEZNrRGlpZZ4xAlw1fvKrQ4t\nEP4egVLzjAOf1DyOl1KunkiXBi8KG0QYSqo5rPTH0LyO19Ud8OzfSJ9ln3lxeRYatT0mxiU0r2lg\ngCaVIFUZUQ292KKrYuRnXySD3qOIcSH9ThcyKlJJNy6jsU04pGzBvMyAdLtkRI21VLfejm9ZEuYB\n6dT4R1Lfficbhoyk+eteSF5pkyZ5RkejNObdciVH4odOmTUFDcMwMX3Agfr+zK0L5k60DofLDqBO\nMqRlm9eYL36F5oILr4e5UPewjgy/0wgs21IR3IDH9o1M1W/kSPE9sHuLJmgtduVVKGyqMfVrwPTL\nNIw8oqkSCrCtfE95M3Mi3yq48/Yl55pkIbgyFkmcAS1bfeZFgA/rW82k+JcjyeJXlMsssQ1uwpDL\nT8nuoYWdJovlX44TZHGLpKxA6us0nLlQSkCXaXxJ6MqQNG2GCgU80k/HbP488qpa8kojIMrRDr/d\nW3mrnYuypR8zLnzjafpA2iqfUupmQUG1kuItW5DZ2vDi2DEmajT0efOWb8V1nLy7ihrlB1J/rMMh\nWYFuJwV6D9X4a9zRFtvzzeUjXTPm0KsomgvdNyEXvEBY5I2F8DXRtSE0itpwaqkZJZXaPFk9k8GN\nP/Ac8ZGgD7m8rwhiy63n4FRJTYA2rRVxxGV3JmeQEM1dJyxLb1B1oxe67+dROSyM0/Y3eW2+gHKD\nDuhZdmZ+cz/uyIKh/gXKLAPwnQjf3yARielhGEt5oTsm0VY4DxTRqfVTviSfZ+Gz43waHAT5uagN\njDkXeIny9KW8z1BSdGEk6soK6o1yuXryJG3MrLka/Zn2eg00SQnAN1rJpazdOFQaEVcTSTI/8LTy\nIFPxCvMpZXgUjyKi3BI9wvEd8oPWPRw5r3JHS6GgsFTMDxc9VIcOIPZqRj/TNHR/VvJdSx+HDDH9\nkrJoH/adSNPb5LpaoSh9whDndJKd5+FruJ9wv+tYmJRilLue5JovlAl/MCewB5v+orzDX2r7CASC\nrQKBIEkgEMQJBILrAoFA/x98SwQCQerf/T3+yjr/TBAIhJiY9EEsNiQ7ezt5ZrMpFO5BLh+Hs7MX\nUmk/FIovSE2l9D7kSVWbIi56dMLxiSVNlzrxa8pFdN6tIqt8Ju9C7IiR5vNzbzWV+kJa3nVFv3Vz\nfrV3507xeRwkYuor7UlJ8aZO1oKBIX9grF9IWy8lTduforbBgKQIX3oJTUgJ6clzeRZmvS6hfWs8\n7b1n88XlHqdu6+Nu3YXewjxEaj3cu3hRqJdMWEgNCuuDTJq1CjTziWycjIpejFuwn+FhOxk9ZhUx\npePY9+YLGYWxlChMKWnURawScidiA6mZTbBtH8sK5ViOGEp4/S2T1jOfsKWHko/h+gS7H8a5qSEb\nmcT7BjdM6q5TOvgoxk2K6Np/E2OmzeTWul8Y8xaZIIbWvrMZK0zDSW8xJWNj2CBMpKCsK+LxVyj4\nZc+sHY9Z9uQkefKBaOOMKHI2snwFefo5NEnVZs2V5SzbOohzm1fj+0xOuac1XfTEtLnahuarolh4\np4rp4gSmpRtSP3cbm1aH8XzSGMxn9cLWajfSEbvZoGnL19xtjBfNp7jSjAZtCWMMT9JgnYis7geh\ng24g7D4R7e5fEWywIbX7VNYG9wZpDcLOx+HrBH47vUU77Rh1MndKpgwnxb8jDl+/8v6iJ56tSjAs\nmcnq6U1BbohGN5KqgCqSlGsQmGew26SS/Q6J1BbEQPQarjv14sjIYOTP9Dj7agFT/U8TXeLLOUah\nZfwVLX0lo8clsWndOVrsnci8qMVc0dSQ1sSB7l/cuWnnhds7fXY2LaP3DUNmRJxFJnhJvlib3lM/\nM2VDAfqeXdBfvhyLO3ew/viR/mvWkOfvz+Oyw1RXf6C23yuiXJxZ9lZM8MJKpnuboRLro6M6ysIy\nB1bW5nPQoBfrRxvTIekzP3X+oFhlQ71jBnmdLnCsjS/hv7fyfogFxt/FyH5KKYxpze3UMJ55tmGC\n2RcMvX5zq2kvXPq9RatEhWBaMupuIgQJBdR/kiCoqSVCvh6pVI8ZolMkKQ0Z+VOBRmDB6or1DBHv\nBEUK5h8k9KpdxztBF6Q2MOZ3EfX2FTz5vBqR21p2LDRGLDQjzL0jwnwpFrq1DB3aSOHJw/wx6T3c\n6s6KZsHUz5tH4joh3Upb8rlED9QazsvPo5reiHJYI98ECVjqL6CPoRMjhcMov/ubm4OKSBMeRc+k\nkv0Rl5HluDLXzg5TCwsSTEyRx8QhfHgfXTM/niz5k6TjQdQ3e4o0pBW7fJdzJWYurVscwjpuLbje\nx6JKQ7tPqwg1SmTxci3iYwN4nbMS8fvnKD1b83/g/fa/3PN/AjTXaDStgVRgCYBAIPAAhgLuQC/g\noEAg+E/fR/1ng4lJb6qrv+Pr+xO53BOlshS53JN27X7g5naUxMTB1NcXoF0XzWj/V7yL74TNyRKM\nWqlxzDEn+WUQLlssSPLxRde6F+Pqt1I4TMjLdVf4w9yI5RZydjS4811lzW5mI4gLRdsznd85OQQF\nncfB4Qg3vtvRkNSHggIBEdMsOVythSRfizh5OB39LvD190QmjOsLxBG6Zx9tVWWskCTQqyCE+kRT\nJLaZFKcrOHqmHFGYFCT5yLQLsas3om7ufuSuWezd4E19sREigQShMJu+A2YgVAsRakTIdHKpeOvL\nQPV3jmbP44dgBDv2B9D/7VYqLrkTldiVbz9e4NbNCVvXdLpsXI9t8AOKpqzFeeZ13l/UYqBtETIL\nHxxCk3n/+jb5jhEc7u9ExeBnVE88QXW5NQUXd7Bw6TssAxOxtyhh4Nk5HDu8De0GDTp3lcjOgtRp\nOWHZVxn9pS/3dZbjFJ/H8vWGTF40g7dvXrNS5MH+Hbdx/92UZy0ecdFYzhJ7DT6DKzho0QKddDF7\n/U9iMzqU5e790ZX/QiAs4WeBB5fPLSPx2XR6f/hFpKcz2qtcaYhag1bMeWpSPKiNHoy8byZCvUQ8\nigxpZVlB21wxlyfuptTCCWHbttx6GcmBmDoS8kzwav+dD6k3EGSaQ4eFKGOhclsiwg9e5Oj3pLLu\nK08fu7DueRwykYQCc2PC220jNaMNzSde55LPH4ToP8Ik8AOGZlmMGzGfwboRlIgNeWjrS9CSdZge\n02JyFwW8mUdOozcOTcsJ89Fj59GzxOOO0C2TNZKRFIbFs2dWNYrKKmKHDMHkxAkUQ4Zgt3o1SuEv\nekx9wOl7V2iVlkaCnj39dUDbuAKRUyQ+il8MKhhLhnQQjsr+HFp1n3KBD6IVa1mxN5xFOyw4NtST\nodWHwaUpPpaPKfXRRv+cMVaZ+QyakoBMJaQ4L59jxmY4ZBVwt2Ugi+xOMargKoXWbrQxy0Hc5iID\nxBLuanVkeF0GgWUfsduxmhKVnGpFA5a1kbwZVoA8IxZvLSGvs+Usv6HhyPhGtIpUpFRW0j1nAEYl\nLijrJYy9KsSswZjmajU7d+7kwYMHNGvWjAPzQxEFPGXjJhWTnkrw+qqhQ15zPlTkcK77bi71uUTA\n7QBqTWtp4raXOePG0Vc1FqsmRuT/hoidD1GpL7Fh0xYWyRYxJ2wOLm/e8byVGyOFech3HqCNqxea\nKe0wKNDj2Jl0ZClrCWqmpnXKVWZe3MCzB9bIqh2wLvNBSzORAQOK0dODQX8YcvdBNn8MVOP8uQA9\nLREC2V8XZP5LGTQazbN/mH4CBv993J+/vderBDIEAkEq0A6I/Cvr/bPA0LArSUmhCARS7O0X/Hc+\nM7NBVFXFERXVCo2mgQFNGjmRXMKVw8cY7mSKc7obgXMMWd+3imaVKeQVPMQYIdMsgzDUM6KrRRCO\nGfasSFhFuZMzJlMX0OnBd6I884g7CKGDDxJTGECB9Cmd0ueyc+FnXiXNITbuK2r3vWwS7WZpyHxS\nL3ti0nE7hmUqSoytyen5jEhJPmNe9MP+lzF6Q0ahMlyDaTsDKsP6UG1xFjf5d8o++XFkmh6RXsOQ\nFo7CXFaJ0MCEeW3+5OS766gMl1FfYYycGcy3nMvtajdOHO5K3OeOJP0wJCrSh25l9wEZcr0qPsef\nZeywP1m/XIizGtpad6DP+nj8B9WgKGjFvrGduarfn2HXhZyuukHlzQpaNpqyT/6A52PsaXzZlSN5\nn1nWS8jUDhZ8vSJlWMZWZC2ucmD7MmZq4ni6fxuvXMOwig/BQV3PhtkFaKnh5vh6UvMXUxO8k9SC\nDHop9+H1y4vZpRdxPzSLqB6XuW0SSzNPIV1fZrIuLJO+D+GPEbo0HpFSkO5IaZIVgYGXMa8xYHb1\ne2bGdUZi/pXa0AK4lIREpUH4x0yE7xs50nw3R7JCifg1gpclUXQ9/IiPVimEV0Zz1KITFVkltOt1\nmrvnp6CdMInGyc1hWjtcHn+l5L2covadETVcYoiTPh9S9vHK4CaaOjEWd6VY+udj7lLK9g0bkB45\nwrHqPQxKimFy5UDEwQXcH2VKrcYA9UEfDJ6ImHzbmcZxDdjoWRN+yRCf3BtEObSne2QKR+dX4VDz\ng1E6F/Ev2YdP5HbumhbR7NYtxixcSNC7l0yav5iglSs5pVRyb942Li2/h5HAk2/PxnHpj9GET4GO\nq0s5tLORD7rp3A67z8GgcWy3tMOowZo3E6bxe2sOxQ1ymie8RxxezHeNEZ4ra9AXKDAL2IHxIw9m\n3//MHjMzdl04y8x5e3G3P8o9szlcuHw5mMUAACAASURBVFDE1zl/ojwn4m1+e6RPSthx/zh7mjii\nyWoCY8oRmuixooceNWo1s+/accbnLDIF/EyKwEfeEiNlJZoKQ9ziBnE90RCm1LF0SFNCfiQwzaQT\nS1Z3w9PTk/DwcMTvxVxNMCA00xzXuCweda/lQfxZ0rv8RGVgj/RoI4NqR1MSLyKpyya87rdGy9iY\npYOtqF0ynk2qnQhFZrykjOAqf1ydXBl/ZjySbAkyqYx6x3pWRq7gg2A515XOjFs0nzr9egqzdFg/\n5yyjR2yj6hUUaE9j176W2Nh84G6iF3FfRrC600tq6tVIBB8JWGVJaO5OROpxf5nH/k/e9hkHPPj7\n2AbI/gff77/b/n8BsVgXff0OlJX97exraCgmIWEgNTU/0Wg0NDQUAWrU6jqcHYfS1CORibkO7HNy\nIqO/hMHjJWz6XMhoSxsu9r9Byfb7mHzZS8XuAuZ0vMKhvYfwq1+EoO1xmgb048CeI4R3H0lDc5i9\n7jfnT13G/FV3muZksPP8cLJ/tsPUtBWbwoxQqyU4hswj85M29ZovlDgKOJmUzUK/Leh0fsIXpQOh\nVmGsHb0WmUyGILWWwINnGSiV8ksSzd4QJ3555SGQ6dDyblO0HRKIuGpL0hQnlrQNpIPFOuTG5/nD\nW4KlSkSacyYPb4VSVGjGkNDWNAybyqAB4xEJxSgbbzNyynlGfczkgdETThhdJT33FEXnN+E2x4hR\ns16QWRTKROEZgg8L2LDUlQWWR/n4ooAb5Ya86+/M82XJHJ2oy9bFOvR3reLpL2NW7OhOz18fKGg1\nH2MdMwKnTSdCHo5GI+LCJDm/00x47S8gzrKKOotJyEqz8f/eHmfnJjiWu9IrZiBngx5zWx0EIj0O\nt1JhdkeA80QQF0GzNo0g0kFTW4fKdwdvcu5z7moIj5+1QSS4iFesFlhVIXP/iZ5VNpV1tzHK9YRe\nSqJfeyJK8mfP9SAyvJeidLiK8fIVrHOzJ/SOKa0t82iV1AfPGVsY4zUJaz0rfnT3oMhuOoJiQ4b2\n3EDq2ImMWz0Hu4IC7gUH8/N5AIUdKjBtTGCAaxP8Zs7ExqcM/c6fWOx/hMlTZ1OpK0OjgYanVujJ\nH1GorqLrB10qREX0Lq1lZ3g4ja360736Jc42T9B5sJSAldVcCgnC6eRSZp+/SN8OHRiamEjm4jEo\n791l+ZIlRM9awIRVS7grfczYsyO56n8diV8/lG5VpPUx5M9zV3AuKeRoWGf2zvSiVUY64/MPkHJO\nwf2UPzC0bqAw8wZJ8fNYeuAZNTIx2XoN9OkJG4VGOKd/4cTyteiEHaHeDCTH3vFwjzPtquOwciiD\nDDlFZ23Qf+GHxYA36G/eCNfGIMrNRqxUUdUoJ6j0K+0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sqNSipDCb9Xc20OqbB4cXXebB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0JiIpuuLWVrM3uO9QhgwKkBzDo2yigJvHOHdHVdUpWNSTv3kQjHCK7UvoeLiS8ajYYms5qg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\nQv4POCj6eHX4a9gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1688c630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for traj in predicted:\n",
    "    pr = to_positions(denormalize(traj))\n",
    "    plt.plot(pr[:, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-03-31T01:18:52.223000",
     "start_time": "2016-03-31T01:18:52.191000"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "to_positions(denormalize(predicted[0]))[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-04-02T20:33:11.980000",
     "start_time": "2016-04-02T20:33:11.567000"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Save generated trajectories to file.\n",
    "for i, trajectory in enumerate(predicted):\n",
    "    np.savetxt('data/generated/{}/cell{:03d}.dat'.format(category, i+1), to_positions(denormalize(trajectory)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-03-30T20:58:50.248000",
     "start_time": "2016-03-30T20:58:50.243000"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "len(predicted[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}