code/cvx-mf-multiple-appliances-with-static.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import cvxpy as cvx\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import  os\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "from create_df_larger import read_df_larger\n",
    "df, dfc, all_homes, appliance_min, national_average = read_df_larger()\n",
    "\n",
    "df = df.rename(columns={'house_num_rooms':'num_rooms',\n",
    "                        'num_occupants':'total_occupants',\n",
    "                        'difference_ratio_min_max':'ratio_difference_min_max'})\n",
    "K_min, K_max = 1,6\n",
    "F_min, F_max=1,8\n",
    "\n",
    "from all_functions import *\n",
    "from features_larger import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "all_appliances = ['mw','oven','hvac','fridge','dw','wm']\n",
    "all_appliance_cols = []\n",
    "for appliance in all_appliances:\n",
    "    if appliance==\"hvac\":\n",
    "        #start, end=5, 11\n",
    "        start, end=1,13\n",
    "    else:\n",
    "        start, end = 1, 13\n",
    "\n",
    "    appliance_cols = ['%s_%d' %(appliance, month) for month in range(start, end)]\n",
    "    all_appliance_cols.append(appliance_cols)\n",
    "    \n",
    "aggregate_cols = ['aggregate_%d' %month for month in range(1, 13)]\n",
    "\n",
    "all_appliance_cols_flat = []\n",
    "for y in all_appliance_cols:\n",
    "    for x in y:\n",
    "        all_appliance_cols_flat.append(x)\n",
    "all_cols = deepcopy(all_appliance_cols_flat)\n",
    "all_cols.extend(aggregate_cols)\n",
    "X_matrix = dfc[all_cols]\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index([u'mw_1', u'mw_2', u'mw_3', u'mw_4', u'mw_5', u'mw_6', u'mw_7', u'mw_8',\n",
       "       u'mw_9', u'mw_10', u'mw_11', u'mw_12', u'oven_1', u'oven_2', u'oven_3',\n",
       "       u'oven_4', u'oven_5', u'oven_6', u'oven_7', u'oven_8', u'oven_9',\n",
       "       u'oven_10', u'oven_11', u'oven_12', u'hvac_1', u'hvac_2', u'hvac_3',\n",
       "       u'hvac_4', u'hvac_5', u'hvac_6', u'hvac_7', u'hvac_8', u'hvac_9',\n",
       "       u'hvac_10', u'hvac_11', u'hvac_12', u'fridge_1', u'fridge_2',\n",
       "       u'fridge_3', u'fridge_4', u'fridge_5', u'fridge_6', u'fridge_7',\n",
       "       u'fridge_8', u'fridge_9', u'fridge_10', u'fridge_11', u'fridge_12',\n",
       "       u'dw_1', u'dw_2', u'dw_3', u'dw_4', u'dw_5', u'dw_6', u'dw_7', u'dw_8',\n",
       "       u'dw_9', u'dw_10', u'dw_11', u'dw_12', u'wm_1', u'wm_2', u'wm_3',\n",
       "       u'wm_4', u'wm_5', u'wm_6', u'wm_7', u'wm_8', u'wm_9', u'wm_10',\n",
       "       u'wm_11', u'wm_12', u'aggregate_1', u'aggregate_2', u'aggregate_3',\n",
       "       u'aggregate_4', u'aggregate_5', u'aggregate_6', u'aggregate_7',\n",
       "       u'aggregate_8', u'aggregate_9', u'aggregate_10', u'aggregate_11',\n",
       "       u'aggregate_12'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_matrix.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "columns_max = {}\n",
    "columns_min = {}\n",
    "col_max = X_matrix.max()\n",
    "columns_max[appliance]=col_max\n",
    "col_min = X_matrix.min()\n",
    "columns_min[appliance]=col_min\n",
    "X_normalised = X_matrix.copy()\n",
    "#for col in X_matrix.columns:\n",
    "#    X_normalised[col] = (X_matrix[col]-col_min[col])/(col_max[col]-col_min[col])\n",
    "for col in X_matrix.columns:\n",
    "    X_normalised[col] = (X_matrix[col]-col_min.min())/(col_max.max()-col_min.min())\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mw_1</th>\n",
       "      <th>mw_2</th>\n",
       "      <th>mw_3</th>\n",
       "      <th>mw_4</th>\n",
       "      <th>mw_5</th>\n",
       "      <th>mw_6</th>\n",
       "      <th>mw_7</th>\n",
       "      <th>mw_8</th>\n",
       "      <th>mw_9</th>\n",
       "      <th>mw_10</th>\n",
       "      <th>...</th>\n",
       "      <th>aggregate_3</th>\n",
       "      <th>aggregate_4</th>\n",
       "      <th>aggregate_5</th>\n",
       "      <th>aggregate_6</th>\n",
       "      <th>aggregate_7</th>\n",
       "      <th>aggregate_8</th>\n",
       "      <th>aggregate_9</th>\n",
       "      <th>aggregate_10</th>\n",
       "      <th>aggregate_11</th>\n",
       "      <th>aggregate_12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.001233</td>\n",
       "      <td>0.000940</td>\n",
       "      <td>0.000991</td>\n",
       "      <td>0.000832</td>\n",
       "      <td>0.000833</td>\n",
       "      <td>0.000838</td>\n",
       "      <td>0.000921</td>\n",
       "      <td>0.000814</td>\n",
       "      <td>0.000793</td>\n",
       "      <td>0.000832</td>\n",
       "      <td>...</td>\n",
       "      <td>0.129283</td>\n",
       "      <td>0.169975</td>\n",
       "      <td>0.209232</td>\n",
       "      <td>0.301593</td>\n",
       "      <td>0.372234</td>\n",
       "      <td>0.412063</td>\n",
       "      <td>0.297982</td>\n",
       "      <td>0.261366</td>\n",
       "      <td>0.157718</td>\n",
       "      <td>0.141851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.335452</td>\n",
       "      <td>0.225524</td>\n",
       "      <td>0.241788</td>\n",
       "      <td>0.227818</td>\n",
       "      <td>0.308186</td>\n",
       "      <td>0.395496</td>\n",
       "      <td>0.225051</td>\n",
       "      <td>0.202733</td>\n",
       "      <td>0.231885</td>\n",
       "      <td>0.384154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.065187</td>\n",
       "      <td>0.054358</td>\n",
       "      <td>0.067508</td>\n",
       "      <td>0.079929</td>\n",
       "      <td>0.112200</td>\n",
       "      <td>0.127052</td>\n",
       "      <td>0.099792</td>\n",
       "      <td>0.075254</td>\n",
       "      <td>0.079390</td>\n",
       "      <td>0.076652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>0.003115</td>\n",
       "      <td>0.002089</td>\n",
       "      <td>0.002644</td>\n",
       "      <td>0.002881</td>\n",
       "      <td>0.002501</td>\n",
       "      <td>0.002106</td>\n",
       "      <td>0.002710</td>\n",
       "      <td>0.002734</td>\n",
       "      <td>0.002457</td>\n",
       "      <td>0.003152</td>\n",
       "      <td>...</td>\n",
       "      <td>0.062116</td>\n",
       "      <td>0.099390</td>\n",
       "      <td>0.113541</td>\n",
       "      <td>0.151897</td>\n",
       "      <td>0.192761</td>\n",
       "      <td>0.177197</td>\n",
       "      <td>0.156125</td>\n",
       "      <td>0.108503</td>\n",
       "      <td>0.075210</td>\n",
       "      <td>0.073646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>222</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.482942</td>\n",
       "      <td>0.479676</td>\n",
       "      <td>0.546716</td>\n",
       "      <td>0.641886</td>\n",
       "      <td>0.759966</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.551328</td>\n",
       "      <td>0.534909</td>\n",
       "      <td>0.410997</td>\n",
       "      <td>0.388497</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 84 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         mw_1      mw_2      mw_3      mw_4      mw_5      mw_6      mw_7  \\\n",
       "26   0.001233  0.000940  0.000991  0.000832  0.000833  0.000838  0.000921   \n",
       "59        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "94        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "101  0.003115  0.002089  0.002644  0.002881  0.002501  0.002106  0.002710   \n",
       "222       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "\n",
       "         mw_8      mw_9     mw_10      ...       aggregate_3  aggregate_4  \\\n",
       "26   0.000814  0.000793  0.000832      ...          0.129283     0.169975   \n",
       "59        NaN       NaN       NaN      ...          0.335452     0.225524   \n",
       "94        NaN       NaN       NaN      ...          0.065187     0.054358   \n",
       "101  0.002734  0.002457  0.003152      ...          0.062116     0.099390   \n",
       "222       NaN       NaN       NaN      ...          0.482942     0.479676   \n",
       "\n",
       "     aggregate_5  aggregate_6  aggregate_7  aggregate_8  aggregate_9  \\\n",
       "26      0.209232     0.301593     0.372234     0.412063     0.297982   \n",
       "59      0.241788     0.227818     0.308186     0.395496     0.225051   \n",
       "94      0.067508     0.079929     0.112200     0.127052     0.099792   \n",
       "101     0.113541     0.151897     0.192761     0.177197     0.156125   \n",
       "222     0.546716     0.641886     0.759966     1.000000     0.551328   \n",
       "\n",
       "     aggregate_10  aggregate_11  aggregate_12  \n",
       "26       0.261366      0.157718      0.141851  \n",
       "59       0.202733      0.231885      0.384154  \n",
       "94       0.075254      0.079390      0.076652  \n",
       "101      0.108503      0.075210      0.073646  \n",
       "222      0.534909      0.410997      0.388497  \n",
       "\n",
       "[5 rows x 84 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(X_normalised).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.DataFrame(X_normalised)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def transform_2(pred_df,all_appliances,  col_max, col_min):\n",
    "    pred_df_copy = pred_df.copy()\n",
    "    \n",
    "    for appliance in all_appliances:\n",
    "    \n",
    "        if appliance==\"hvac\":\n",
    "            start, stop=5, 11\n",
    "        else:\n",
    "            start, stop=1, 13\n",
    "\n",
    "        for month in range(start, stop):\n",
    "            pred_df_copy['%s_%d' %(appliance,month)] = (col_max.max()-col_min.min())*pred_df['%s_%d'%(appliance,month)] +col_min.min()\n",
    "    return pred_df_copy\n",
    "\n",
    "def transform(pred_df,appliance,  col_max, col_min):\n",
    "    pred_df_copy = pred_df.copy()\n",
    "    if appliance==\"hvac\":\n",
    "        start, stop=5, 11\n",
    "    else:\n",
    "        start, stop=1, 13\n",
    "    \n",
    "    for month in range(start, stop):\n",
    "        pred_df_copy['%s_%d' %(appliance,month)] = (col_max['%s_%d' %(appliance, month)]-col_min['%s_%d' %(appliance,month)])*pred_df['%s_%d'%(appliance,month)] +col_min['%s_%d' %(appliance,month)]\n",
    "    return pred_df_copy\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def nmf_features(A, k, f, MAX_ITERS=30):\n",
    "    np.random.seed(0)\n",
    "\n",
    "    # Generate random data matrix A.\n",
    "    m = len(A)\n",
    "    n = len(A.columns)\n",
    "    \n",
    "    \n",
    "    # Initialize Y randomly.\n",
    "    Y_init = np.random.rand(m, k)\n",
    "\n",
    "    # Ensure same initial random Y, rather than generate new one\n",
    "    # when executing this cell.\n",
    "    Y = Y_init\n",
    "    #Y[0] = f\n",
    "\n",
    "    # Perform alternating minimization.\n",
    "    \n",
    "    residual = np.zeros(MAX_ITERS)\n",
    "    for iter_num in range(1, 1+MAX_ITERS):\n",
    "        # At the beginning of an iteration, X and Y are NumPy\n",
    "        # array types, NOT CVXPY variables.\n",
    "\n",
    "        # For odd iterations, treat Y constant, optimize over X.\n",
    "        if iter_num % 2 == 1:\n",
    "            X = cvx.Variable(k, n)\n",
    "            constraint = [X >= 0]\n",
    "        # For even iterations, treat X constant, optimize over Y.\n",
    "        else:\n",
    "            Y = cvx.Variable(m, k)\n",
    "            \n",
    "            constraint = [Y >= 0, Y[:,:np.shape(f)[1]]==f]\n",
    "            \n",
    "            #Y.value[0]=f\n",
    "        Temp = Y*X\n",
    "\n",
    "        # Solve the problem.\n",
    "        obj = cvx.Minimize(cvx.norm(A.values[mask] - (Y*X)[mask], 'fro'))\n",
    "        prob = cvx.Problem(obj, constraint)\n",
    "        prob.solve(solver=cvx.SCS)\n",
    "\n",
    "        if prob.status != cvx.OPTIMAL:\n",
    "            pass\n",
    "            #return X.value, Y.value, residual\n",
    "            #raise Exception(\"Solver did not converge!\")\n",
    "\n",
    "        #print 'Iteration {}, residual norm {}'.format(iter_num, prob.value)\n",
    "        residual[iter_num-1] = prob.value\n",
    "\n",
    "        # Convert variable to NumPy array constant for next iteration.\n",
    "        if iter_num % 2 == 1:\n",
    "            X = X.value\n",
    "        else:\n",
    "            Y = Y.value\n",
    "    return X, Y, residual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def nmf(A, k, MAX_ITERS=30):\n",
    "    np.random.seed(0)\n",
    "\n",
    "    # Generate random data matrix A.\n",
    "    m = len(A)\n",
    "    n = len(A.columns)\n",
    "    \n",
    "    \n",
    "    # Initialize Y randomly.\n",
    "    Y_init = np.random.rand(m, k)\n",
    "\n",
    "    # Ensure same initial random Y, rather than generate new one\n",
    "    # when executing this cell.\n",
    "    Y = Y_init \n",
    "\n",
    "    # Perform alternating minimization.\n",
    "    \n",
    "    residual = np.zeros(MAX_ITERS)\n",
    "    for iter_num in range(1, 1+MAX_ITERS):\n",
    "        # At the beginning of an iteration, X and Y are NumPy\n",
    "        # array types, NOT CVXPY variables.\n",
    "\n",
    "        # For odd iterations, treat Y constant, optimize over X.\n",
    "        if iter_num % 2 == 1:\n",
    "            X = cvx.Variable(k, n)\n",
    "            constraint = [X >= 0]\n",
    "        # For even iterations, treat X constant, optimize over Y.\n",
    "        else:\n",
    "            Y = cvx.Variable(m, k)\n",
    "            constraint = [Y >= 0]\n",
    "        Temp = Y*X\n",
    "\n",
    "        # Solve the problem.\n",
    "        obj = cvx.Minimize(cvx.norm(A.values[mask] - (Y*X)[mask], 'fro'))\n",
    "        prob = cvx.Problem(obj, constraint)\n",
    "        prob.solve(solver=cvx.SCS)\n",
    "\n",
    "        if prob.status != cvx.OPTIMAL:\n",
    "            pass\n",
    "            #return X.value, Y.value, residual\n",
    "            #raise Exception(\"Solver did not converge!\")\n",
    "\n",
    "        #print 'Iteration {}, residual norm {}'.format(iter_num, prob.value)\n",
    "        residual[iter_num-1] = prob.value\n",
    "\n",
    "        # Convert variable to NumPy array constant for next iteration.\n",
    "        if iter_num % 2 == 1:\n",
    "            X = X.value\n",
    "        else:\n",
    "            Y = Y.value\n",
    "    return X, Y, residual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "area = dfc.ix[X_normalised.index].area.div(dfc.ix[X_normalised.index].area.max()).reshape((len(X_normalised),1))\n",
    "occ = dfc.ix[X_normalised.index].num_occupants.div(dfc.ix[X_normalised.index].num_occupants.max()).reshape((len(X_normalised),1))\n",
    "rooms = dfc.ix[X_normalised.index].house_num_rooms.div(dfc.ix[X_normalised.index].house_num_rooms.max()).reshape((len(X_normalised),1))\n",
    "\n",
    "out = {}\n",
    "for lat in range(1,10):\n",
    "    out[lat]={}\n",
    "    print lat\n",
    "    for home in X_normalised.index[:]:\n",
    "        \n",
    "        X_home = X_normalised.copy()\n",
    "        for appliance in all_appliances:\n",
    "            for month in range(start, end):\n",
    "                X_home.loc[home, '%s_%d' %(appliance, month)] = np.NAN\n",
    "        mask = X_home.notnull().values\n",
    "        # Ensure repeatably random problem data.\n",
    "        A = X_home.copy()\n",
    "        X, Y, res = nmf_features(A, lat,area, 10)\n",
    "        \n",
    "        pred_df = pd.DataFrame(Y*X)\n",
    "        pred_df.columns = X_normalised.columns\n",
    "        pred_df.index = X_normalised.index\n",
    "        #out[lat][home] = pred_df.ix[home][appliance_cols]\n",
    "        out[lat][home] = transform_2(pred_df.ix[home],all_appliances, col_max, col_min)[all_appliance_cols_flat]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dw</th>\n",
       "      <th>fridge</th>\n",
       "      <th>hvac</th>\n",
       "      <th>mw</th>\n",
       "      <th>oven</th>\n",
       "      <th>wm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>54.426397</td>\n",
       "      <td>28.125450</td>\n",
       "      <td>35.048725</td>\n",
       "      <td>45.254498</td>\n",
       "      <td>53.689221</td>\n",
       "      <td>49.480212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>53.852222</td>\n",
       "      <td>29.793324</td>\n",
       "      <td>29.166555</td>\n",
       "      <td>44.202941</td>\n",
       "      <td>53.338395</td>\n",
       "      <td>44.680635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>53.574346</td>\n",
       "      <td>31.193506</td>\n",
       "      <td>19.583177</td>\n",
       "      <td>46.041678</td>\n",
       "      <td>55.439816</td>\n",
       "      <td>41.384355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54.476665</td>\n",
       "      <td>32.468068</td>\n",
       "      <td>27.004989</td>\n",
       "      <td>47.093809</td>\n",
       "      <td>60.485085</td>\n",
       "      <td>44.590697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>54.745183</td>\n",
       "      <td>36.627401</td>\n",
       "      <td>25.480343</td>\n",
       "      <td>50.439318</td>\n",
       "      <td>58.493893</td>\n",
       "      <td>50.121264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>54.398679</td>\n",
       "      <td>32.006868</td>\n",
       "      <td>27.093455</td>\n",
       "      <td>48.194516</td>\n",
       "      <td>51.347511</td>\n",
       "      <td>48.942305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>54.719791</td>\n",
       "      <td>33.946873</td>\n",
       "      <td>28.077745</td>\n",
       "      <td>47.447438</td>\n",
       "      <td>50.193503</td>\n",
       "      <td>47.606904</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>57.253011</td>\n",
       "      <td>38.395330</td>\n",
       "      <td>32.041669</td>\n",
       "      <td>48.687325</td>\n",
       "      <td>64.692231</td>\n",
       "      <td>58.231676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>55.148274</td>\n",
       "      <td>37.753862</td>\n",
       "      <td>32.040605</td>\n",
       "      <td>48.546011</td>\n",
       "      <td>54.631151</td>\n",
       "      <td>52.616952</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          dw     fridge       hvac         mw       oven         wm\n",
       "1  54.426397  28.125450  35.048725  45.254498  53.689221  49.480212\n",
       "2  53.852222  29.793324  29.166555  44.202941  53.338395  44.680635\n",
       "3  53.574346  31.193506  19.583177  46.041678  55.439816  41.384355\n",
       "4  54.476665  32.468068  27.004989  47.093809  60.485085  44.590697\n",
       "5  54.745183  36.627401  25.480343  50.439318  58.493893  50.121264\n",
       "6  54.398679  32.006868  27.093455  48.194516  51.347511  48.942305\n",
       "7  54.719791  33.946873  28.077745  47.447438  50.193503  47.606904\n",
       "8  57.253011  38.395330  32.041669  48.687325  64.692231  58.231676\n",
       "9  55.148274  37.753862  32.040605  48.546011  54.631151  52.616952"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error_lat = {}\n",
    "for appliance in all_appliances:\n",
    "    error_lat[appliance]={}\n",
    "    if appliance==\"hvac\":\n",
    "        start, end=5, 11\n",
    "        #start, end=1,13\n",
    "    else:\n",
    "        start, end = 1, 13\n",
    "    appliance_cols = ['%s_%d' %(appliance, month) for month in range(start, end)]\n",
    "    gt = X_matrix[appliance_cols]\n",
    "    \n",
    "    for lat in range(1,10):\n",
    "\n",
    "        pr = pd.DataFrame(out[lat]).T\n",
    "\n",
    "        error = (pr-gt).abs()\n",
    "        error_lat[appliance][lat] = error.div(gt).mul(100).median().mean()\n",
    "pd.DataFrame(error_lat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dw</th>\n",
       "      <th>fridge</th>\n",
       "      <th>hvac</th>\n",
       "      <th>mw</th>\n",
       "      <th>oven</th>\n",
       "      <th>wm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>54.465959</td>\n",
       "      <td>28.472909</td>\n",
       "      <td>29.038784</td>\n",
       "      <td>45.332588</td>\n",
       "      <td>52.352397</td>\n",
       "      <td>45.292877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>54.871356</td>\n",
       "      <td>31.905234</td>\n",
       "      <td>20.143806</td>\n",
       "      <td>45.635348</td>\n",
       "      <td>53.216279</td>\n",
       "      <td>40.154435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>55.831237</td>\n",
       "      <td>32.427419</td>\n",
       "      <td>26.035662</td>\n",
       "      <td>46.863918</td>\n",
       "      <td>52.815503</td>\n",
       "      <td>46.888093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>57.890857</td>\n",
       "      <td>32.041163</td>\n",
       "      <td>26.162834</td>\n",
       "      <td>49.897327</td>\n",
       "      <td>62.546300</td>\n",
       "      <td>45.452146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>56.733842</td>\n",
       "      <td>33.280320</td>\n",
       "      <td>27.992968</td>\n",
       "      <td>49.895089</td>\n",
       "      <td>54.926144</td>\n",
       "      <td>52.994555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>56.256804</td>\n",
       "      <td>34.037190</td>\n",
       "      <td>30.537658</td>\n",
       "      <td>49.186329</td>\n",
       "      <td>51.870513</td>\n",
       "      <td>47.513372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>56.072782</td>\n",
       "      <td>38.278235</td>\n",
       "      <td>30.118350</td>\n",
       "      <td>50.792403</td>\n",
       "      <td>54.151223</td>\n",
       "      <td>46.496375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>61.484432</td>\n",
       "      <td>55.654182</td>\n",
       "      <td>36.731152</td>\n",
       "      <td>51.032149</td>\n",
       "      <td>71.381180</td>\n",
       "      <td>64.303755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>56.220968</td>\n",
       "      <td>49.183087</td>\n",
       "      <td>26.150757</td>\n",
       "      <td>50.000686</td>\n",
       "      <td>54.884808</td>\n",
       "      <td>60.188134</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          dw     fridge       hvac         mw       oven         wm\n",
       "1  54.465959  28.472909  29.038784  45.332588  52.352397  45.292877\n",
       "2  54.871356  31.905234  20.143806  45.635348  53.216279  40.154435\n",
       "3  55.831237  32.427419  26.035662  46.863918  52.815503  46.888093\n",
       "4  57.890857  32.041163  26.162834  49.897327  62.546300  45.452146\n",
       "5  56.733842  33.280320  27.992968  49.895089  54.926144  52.994555\n",
       "6  56.256804  34.037190  30.537658  49.186329  51.870513  47.513372\n",
       "7  56.072782  38.278235  30.118350  50.792403  54.151223  46.496375\n",
       "8  61.484432  55.654182  36.731152  51.032149  71.381180  64.303755\n",
       "9  56.220968  49.183087  26.150757  50.000686  54.884808  60.188134"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error_lat = {}\n",
    "for appliance in all_appliances:\n",
    "    error_lat[appliance]={}\n",
    "    if appliance==\"hvac\":\n",
    "        start, end=5, 11\n",
    "        #start, end=1,13\n",
    "    else:\n",
    "        start, end = 1, 13\n",
    "    appliance_cols = ['%s_%d' %(appliance, month) for month in range(start, end)]\n",
    "    gt = X_matrix[appliance_cols]\n",
    "    \n",
    "    for lat in range(1,10):\n",
    "\n",
    "        pr = pd.DataFrame(out[lat]).T\n",
    "\n",
    "        error = (pr-gt).abs()\n",
    "        error_lat[appliance][lat] = error.div(gt).mul(100).median().mean()\n",
    "pd.DataFrame(error_lat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>26</th>\n",
       "      <th>59</th>\n",
       "      <th>94</th>\n",
       "      <th>101</th>\n",
       "      <th>222</th>\n",
       "      <th>252</th>\n",
       "      <th>364</th>\n",
       "      <th>545</th>\n",
       "      <th>624</th>\n",
       "      <th>661</th>\n",
       "      <th>...</th>\n",
       "      <th>9484</th>\n",
       "      <th>9609</th>\n",
       "      <th>9647</th>\n",
       "      <th>9729</th>\n",
       "      <th>9912</th>\n",
       "      <th>9922</th>\n",
       "      <th>9932</th>\n",
       "      <th>9933</th>\n",
       "      <th>9971</th>\n",
       "      <th>9982</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>hvac_5</th>\n",
       "      <td>227.144895</td>\n",
       "      <td>271.152134</td>\n",
       "      <td>75.648727</td>\n",
       "      <td>109.928912</td>\n",
       "      <td>537.492011</td>\n",
       "      <td>377.805833</td>\n",
       "      <td>192.215484</td>\n",
       "      <td>255.084125</td>\n",
       "      <td>117.849722</td>\n",
       "      <td>241.472362</td>\n",
       "      <td>...</td>\n",
       "      <td>330.332732</td>\n",
       "      <td>168.258923</td>\n",
       "      <td>557.896673</td>\n",
       "      <td>200.153105</td>\n",
       "      <td>94.708261</td>\n",
       "      <td>356.649081</td>\n",
       "      <td>95.536151</td>\n",
       "      <td>166.095463</td>\n",
       "      <td>134.758764</td>\n",
       "      <td>135.492789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hvac_6</th>\n",
       "      <td>431.489754</td>\n",
       "      <td>515.439576</td>\n",
       "      <td>143.969998</td>\n",
       "      <td>209.359114</td>\n",
       "      <td>1024.077134</td>\n",
       "      <td>719.179457</td>\n",
       "      <td>365.229783</td>\n",
       "      <td>483.997778</td>\n",
       "      <td>224.186506</td>\n",
       "      <td>456.837584</td>\n",
       "      <td>...</td>\n",
       "      <td>637.103909</td>\n",
       "      <td>319.813327</td>\n",
       "      <td>1076.028903</td>\n",
       "      <td>378.854269</td>\n",
       "      <td>180.293523</td>\n",
       "      <td>676.756155</td>\n",
       "      <td>181.661806</td>\n",
       "      <td>316.568818</td>\n",
       "      <td>256.013287</td>\n",
       "      <td>257.641983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hvac_7</th>\n",
       "      <td>663.479855</td>\n",
       "      <td>789.399779</td>\n",
       "      <td>221.080822</td>\n",
       "      <td>321.629271</td>\n",
       "      <td>1590.803093</td>\n",
       "      <td>1104.508799</td>\n",
       "      <td>561.590806</td>\n",
       "      <td>745.152649</td>\n",
       "      <td>344.263019</td>\n",
       "      <td>702.282182</td>\n",
       "      <td>...</td>\n",
       "      <td>973.106295</td>\n",
       "      <td>490.733314</td>\n",
       "      <td>1655.121693</td>\n",
       "      <td>587.844264</td>\n",
       "      <td>276.877712</td>\n",
       "      <td>1036.572974</td>\n",
       "      <td>278.795550</td>\n",
       "      <td>486.188990</td>\n",
       "      <td>393.025224</td>\n",
       "      <td>395.160526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hvac_8</th>\n",
       "      <td>721.644177</td>\n",
       "      <td>856.653508</td>\n",
       "      <td>240.707317</td>\n",
       "      <td>350.259740</td>\n",
       "      <td>1734.209234</td>\n",
       "      <td>1202.661856</td>\n",
       "      <td>611.117709</td>\n",
       "      <td>811.929188</td>\n",
       "      <td>374.703400</td>\n",
       "      <td>764.151909</td>\n",
       "      <td>...</td>\n",
       "      <td>1058.539309</td>\n",
       "      <td>533.818753</td>\n",
       "      <td>1798.220732</td>\n",
       "      <td>637.364876</td>\n",
       "      <td>301.415477</td>\n",
       "      <td>1125.448539</td>\n",
       "      <td>303.965530</td>\n",
       "      <td>529.321596</td>\n",
       "      <td>427.865145</td>\n",
       "      <td>430.780081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hvac_9</th>\n",
       "      <td>516.546565</td>\n",
       "      <td>616.403290</td>\n",
       "      <td>172.187746</td>\n",
       "      <td>250.516899</td>\n",
       "      <td>1236.056344</td>\n",
       "      <td>860.212270</td>\n",
       "      <td>436.831083</td>\n",
       "      <td>580.931663</td>\n",
       "      <td>268.119246</td>\n",
       "      <td>546.670822</td>\n",
       "      <td>...</td>\n",
       "      <td>757.114330</td>\n",
       "      <td>382.466807</td>\n",
       "      <td>1283.307934</td>\n",
       "      <td>456.000613</td>\n",
       "      <td>215.500702</td>\n",
       "      <td>805.984241</td>\n",
       "      <td>217.267753</td>\n",
       "      <td>378.990370</td>\n",
       "      <td>306.118116</td>\n",
       "      <td>308.120659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hvac_10</th>\n",
       "      <td>261.854224</td>\n",
       "      <td>314.193778</td>\n",
       "      <td>87.610519</td>\n",
       "      <td>127.405452</td>\n",
       "      <td>620.765264</td>\n",
       "      <td>437.604478</td>\n",
       "      <td>221.814354</td>\n",
       "      <td>295.892361</td>\n",
       "      <td>136.677533</td>\n",
       "      <td>277.918282</td>\n",
       "      <td>...</td>\n",
       "      <td>385.253385</td>\n",
       "      <td>194.748570</td>\n",
       "      <td>650.114428</td>\n",
       "      <td>231.559569</td>\n",
       "      <td>109.578828</td>\n",
       "      <td>410.754929</td>\n",
       "      <td>110.660411</td>\n",
       "      <td>192.791765</td>\n",
       "      <td>156.815500</td>\n",
       "      <td>156.862307</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6 rows × 105 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               26          59          94          101          222   \\\n",
       "hvac_5   227.144895  271.152134   75.648727  109.928912   537.492011   \n",
       "hvac_6   431.489754  515.439576  143.969998  209.359114  1024.077134   \n",
       "hvac_7   663.479855  789.399779  221.080822  321.629271  1590.803093   \n",
       "hvac_8   721.644177  856.653508  240.707317  350.259740  1734.209234   \n",
       "hvac_9   516.546565  616.403290  172.187746  250.516899  1236.056344   \n",
       "hvac_10  261.854224  314.193778   87.610519  127.405452   620.765264   \n",
       "\n",
       "                252         364         545         624         661   \\\n",
       "hvac_5    377.805833  192.215484  255.084125  117.849722  241.472362   \n",
       "hvac_6    719.179457  365.229783  483.997778  224.186506  456.837584   \n",
       "hvac_7   1104.508799  561.590806  745.152649  344.263019  702.282182   \n",
       "hvac_8   1202.661856  611.117709  811.929188  374.703400  764.151909   \n",
       "hvac_9    860.212270  436.831083  580.931663  268.119246  546.670822   \n",
       "hvac_10   437.604478  221.814354  295.892361  136.677533  277.918282   \n",
       "\n",
       "            ...             9484        9609         9647        9729  \\\n",
       "hvac_5      ...       330.332732  168.258923   557.896673  200.153105   \n",
       "hvac_6      ...       637.103909  319.813327  1076.028903  378.854269   \n",
       "hvac_7      ...       973.106295  490.733314  1655.121693  587.844264   \n",
       "hvac_8      ...      1058.539309  533.818753  1798.220732  637.364876   \n",
       "hvac_9      ...       757.114330  382.466807  1283.307934  456.000613   \n",
       "hvac_10     ...       385.253385  194.748570   650.114428  231.559569   \n",
       "\n",
       "               9912         9922        9932        9933        9971  \\\n",
       "hvac_5    94.708261   356.649081   95.536151  166.095463  134.758764   \n",
       "hvac_6   180.293523   676.756155  181.661806  316.568818  256.013287   \n",
       "hvac_7   276.877712  1036.572974  278.795550  486.188990  393.025224   \n",
       "hvac_8   301.415477  1125.448539  303.965530  529.321596  427.865145   \n",
       "hvac_9   215.500702   805.984241  217.267753  378.990370  306.118116   \n",
       "hvac_10  109.578828   410.754929  110.660411  192.791765  156.815500   \n",
       "\n",
       "               9982  \n",
       "hvac_5   135.492789  \n",
       "hvac_6   257.641983  \n",
       "hvac_7   395.160526  \n",
       "hvac_8   430.780081  \n",
       "hvac_9   308.120659  \n",
       "hvac_10  156.862307  \n",
       "\n",
       "[6 rows x 105 columns]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(out[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>hvac_5</th>\n",
       "      <th>hvac_6</th>\n",
       "      <th>hvac_7</th>\n",
       "      <th>hvac_8</th>\n",
       "      <th>hvac_9</th>\n",
       "      <th>hvac_10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>242.395737</td>\n",
       "      <td>543.781433</td>\n",
       "      <td>761.394043</td>\n",
       "      <td>902.418823</td>\n",
       "      <td>610.035828</td>\n",
       "      <td>395.169098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>77.613205</td>\n",
       "      <td>197.951508</td>\n",
       "      <td>457.950378</td>\n",
       "      <td>700.443054</td>\n",
       "      <td>244.340973</td>\n",
       "      <td>81.064682</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>19.836948</td>\n",
       "      <td>66.621819</td>\n",
       "      <td>126.121681</td>\n",
       "      <td>155.045364</td>\n",
       "      <td>92.979385</td>\n",
       "      <td>33.392750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>191.965454</td>\n",
       "      <td>325.858032</td>\n",
       "      <td>462.708923</td>\n",
       "      <td>485.186005</td>\n",
       "      <td>350.491455</td>\n",
       "      <td>192.567566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>222</th>\n",
       "      <td>478.951691</td>\n",
       "      <td>896.467285</td>\n",
       "      <td>1077.890137</td>\n",
       "      <td>1139.740479</td>\n",
       "      <td>887.044739</td>\n",
       "      <td>584.328979</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         hvac_5      hvac_6       hvac_7       hvac_8      hvac_9     hvac_10\n",
       "26   242.395737  543.781433   761.394043   902.418823  610.035828  395.169098\n",
       "59    77.613205  197.951508   457.950378   700.443054  244.340973   81.064682\n",
       "94    19.836948   66.621819   126.121681   155.045364   92.979385   33.392750\n",
       "101  191.965454  325.858032   462.708923   485.186005  350.491455  192.567566\n",
       "222  478.951691  896.467285  1077.890137  1139.740479  887.044739  584.328979"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gt.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x117bab410>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZYAAAEPCAYAAABhkeIdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1lluAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1139b8290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(Y, pd.DataFrame(A)['fridge_7'])\n",
    "plt.xlabel(\"Latent factor for home\")\n",
    "plt.ylabel(\"Fridge energy consumption\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_m = pd.DataFrame(X)\n",
    "X_m.columns = A.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x118aa88d0>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEACAYAAABGYoqtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11883ef50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_m.values.flatten()[12:],X_m.values.flatten()[:12])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dds = [438, 579, 724, 747, 617, 376]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.06953881,  0.13357938,  0.20515153,  0.22322771,  0.15941742,\n",
       "        0.08067859])"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_m.values.flatten()[:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'dds' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-23-940acf84e2af>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_m\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Latent factor for month\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Degree days per month\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'dds' is not defined"
     ]
    }
   ],
   "source": [
    "plt.scatter(X_m.values.flatten()[:], dds)\n",
    "plt.xlabel(\"Latent factor for month\")\n",
    "plt.ylabel(\"Degree days per month\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.019238\n",
       "dtype: float64"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(Y).corrwith(pd.DataFrame(A)['hvac_10'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 26.801509765613513,\n",
       " 2: 32.16594754531535,\n",
       " 3: 32.75057009957243,\n",
       " 4: 33.608574403734316,\n",
       " 5: 35.51499390605262,\n",
       " 6: 34.5542641062825,\n",
       " 7: 29.260989092833853,\n",
       " 8: 36.03229595821327,\n",
       " 9: 23.69216706014821}"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error_lat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>hvac_5</th>\n",
       "      <th>hvac_6</th>\n",
       "      <th>hvac_7</th>\n",
       "      <th>hvac_8</th>\n",
       "      <th>hvac_9</th>\n",
       "      <th>hvac_10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>245.072444</td>\n",
       "      <td>468.099853</td>\n",
       "      <td>719.521842</td>\n",
       "      <td>780.840442</td>\n",
       "      <td>558.748129</td>\n",
       "      <td>282.693567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>213.142529</td>\n",
       "      <td>407.232402</td>\n",
       "      <td>623.663812</td>\n",
       "      <td>675.819377</td>\n",
       "      <td>485.543535</td>\n",
       "      <td>247.101512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>75.897705</td>\n",
       "      <td>143.707019</td>\n",
       "      <td>219.694360</td>\n",
       "      <td>238.534062</td>\n",
       "      <td>171.053473</td>\n",
       "      <td>87.703643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>119.326641</td>\n",
       "      <td>227.375958</td>\n",
       "      <td>348.506622</td>\n",
       "      <td>378.596035</td>\n",
       "      <td>271.048929</td>\n",
       "      <td>138.213791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>222</th>\n",
       "      <td>534.515723</td>\n",
       "      <td>1026.999975</td>\n",
       "      <td>1595.523641</td>\n",
       "      <td>1735.603353</td>\n",
       "      <td>1235.946874</td>\n",
       "      <td>618.391287</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         hvac_5       hvac_6       hvac_7       hvac_8       hvac_9  \\\n",
       "26   245.072444   468.099853   719.521842   780.840442   558.748129   \n",
       "59   213.142529   407.232402   623.663812   675.819377   485.543535   \n",
       "94    75.897705   143.707019   219.694360   238.534062   171.053473   \n",
       "101  119.326641   227.375958   348.506622   378.596035   271.048929   \n",
       "222  534.515723  1026.999975  1595.523641  1735.603353  1235.946874   \n",
       "\n",
       "        hvac_10  \n",
       "26   282.693567  \n",
       "59   247.101512  \n",
       "94    87.703643  \n",
       "101  138.213791  \n",
       "222  618.391287  "
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(out[1]).T.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>hvac_5</th>\n",
       "      <th>hvac_6</th>\n",
       "      <th>hvac_7</th>\n",
       "      <th>hvac_8</th>\n",
       "      <th>hvac_9</th>\n",
       "      <th>hvac_10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.052413</td>\n",
       "      <td>0.118235</td>\n",
       "      <td>0.165761</td>\n",
       "      <td>0.196560</td>\n",
       "      <td>0.132704</td>\n",
       "      <td>0.085778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>0.016425</td>\n",
       "      <td>0.042707</td>\n",
       "      <td>0.099490</td>\n",
       "      <td>0.152449</td>\n",
       "      <td>0.052838</td>\n",
       "      <td>0.017179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.003807</td>\n",
       "      <td>0.014025</td>\n",
       "      <td>0.027019</td>\n",
       "      <td>0.033336</td>\n",
       "      <td>0.019781</td>\n",
       "      <td>0.006768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>0.041399</td>\n",
       "      <td>0.070641</td>\n",
       "      <td>0.100529</td>\n",
       "      <td>0.105438</td>\n",
       "      <td>0.076021</td>\n",
       "      <td>0.041531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>222</th>\n",
       "      <td>0.104076</td>\n",
       "      <td>0.195260</td>\n",
       "      <td>0.234882</td>\n",
       "      <td>0.248390</td>\n",
       "      <td>0.193202</td>\n",
       "      <td>0.127090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       hvac_5    hvac_6    hvac_7    hvac_8    hvac_9   hvac_10\n",
       "26   0.052413  0.118235  0.165761  0.196560  0.132704  0.085778\n",
       "59   0.016425  0.042707  0.099490  0.152449  0.052838  0.017179\n",
       "94   0.003807  0.014025  0.027019  0.033336  0.019781  0.006768\n",
       "101  0.041399  0.070641  0.100529  0.105438  0.076021  0.041531\n",
       "222  0.104076  0.195260  0.234882  0.248390  0.193202  0.127090"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.head()[appliance_cols]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    32.570682\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(error_lat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>95.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.660303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.342348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.117898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.423632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.614642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.827686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.971936</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               0\n",
       "count  95.000000\n",
       "mean    0.660303\n",
       "std     0.342348\n",
       "min     0.117898\n",
       "25%     0.423632\n",
       "50%     0.614642\n",
       "75%     0.827686\n",
       "max     1.971936"
      ]
     },
     "execution_count": 380,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(Y).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x122dab850>"
      ]
     },
     "execution_count": 381,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEHCAYAAABRF9YCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1249bbc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(Y).plot(legend=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1249a4710>"
      ]
     },
     "execution_count": 382,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEHCAYAAACncpHfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nElPqAEREYkodgIhITP0/9JPHGIXB0R8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x123df8a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(X)[[0,1,2,3,4,5]].T.plot(legend=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.301025</td>\n",
       "      <td>0.370936</td>\n",
       "      <td>0.365748</td>\n",
       "      <td>0.456318</td>\n",
       "      <td>0.422244</td>\n",
       "      <td>0.349034</td>\n",
       "      <td>0.321586</td>\n",
       "      <td>0.447455</td>\n",
       "      <td>0.481452</td>\n",
       "      <td>0.346902</td>\n",
       "      <td>0.369798</td>\n",
       "      <td>0.324113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.191067</td>\n",
       "      <td>0.235441</td>\n",
       "      <td>0.232148</td>\n",
       "      <td>0.289636</td>\n",
       "      <td>0.268008</td>\n",
       "      <td>0.221539</td>\n",
       "      <td>0.204118</td>\n",
       "      <td>0.284010</td>\n",
       "      <td>0.305589</td>\n",
       "      <td>0.220187</td>\n",
       "      <td>0.234719</td>\n",
       "      <td>0.205722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.042508</td>\n",
       "      <td>0.052380</td>\n",
       "      <td>0.051648</td>\n",
       "      <td>0.064437</td>\n",
       "      <td>0.059626</td>\n",
       "      <td>0.049288</td>\n",
       "      <td>0.045412</td>\n",
       "      <td>0.063186</td>\n",
       "      <td>0.067987</td>\n",
       "      <td>0.048987</td>\n",
       "      <td>0.052220</td>\n",
       "      <td>0.045769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.145898</td>\n",
       "      <td>0.179781</td>\n",
       "      <td>0.177267</td>\n",
       "      <td>0.221164</td>\n",
       "      <td>0.204649</td>\n",
       "      <td>0.169166</td>\n",
       "      <td>0.155863</td>\n",
       "      <td>0.216868</td>\n",
       "      <td>0.233345</td>\n",
       "      <td>0.168133</td>\n",
       "      <td>0.179230</td>\n",
       "      <td>0.157088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.576494</td>\n",
       "      <td>0.710382</td>\n",
       "      <td>0.700446</td>\n",
       "      <td>0.873898</td>\n",
       "      <td>0.808642</td>\n",
       "      <td>0.668436</td>\n",
       "      <td>0.615872</td>\n",
       "      <td>0.856924</td>\n",
       "      <td>0.922033</td>\n",
       "      <td>0.664354</td>\n",
       "      <td>0.708202</td>\n",
       "      <td>0.620711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.277854</td>\n",
       "      <td>0.342384</td>\n",
       "      <td>0.337596</td>\n",
       "      <td>0.421195</td>\n",
       "      <td>0.389743</td>\n",
       "      <td>0.322168</td>\n",
       "      <td>0.296833</td>\n",
       "      <td>0.413013</td>\n",
       "      <td>0.444394</td>\n",
       "      <td>0.320200</td>\n",
       "      <td>0.341333</td>\n",
       "      <td>0.299166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.372349</td>\n",
       "      <td>0.458825</td>\n",
       "      <td>0.452408</td>\n",
       "      <td>0.564438</td>\n",
       "      <td>0.522290</td>\n",
       "      <td>0.431733</td>\n",
       "      <td>0.397783</td>\n",
       "      <td>0.553474</td>\n",
       "      <td>0.595527</td>\n",
       "      <td>0.429097</td>\n",
       "      <td>0.457417</td>\n",
       "      <td>0.400908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.099863</td>\n",
       "      <td>0.123055</td>\n",
       "      <td>0.121334</td>\n",
       "      <td>0.151380</td>\n",
       "      <td>0.140076</td>\n",
       "      <td>0.115789</td>\n",
       "      <td>0.106684</td>\n",
       "      <td>0.148440</td>\n",
       "      <td>0.159718</td>\n",
       "      <td>0.115082</td>\n",
       "      <td>0.122678</td>\n",
       "      <td>0.107522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.336755</td>\n",
       "      <td>0.414965</td>\n",
       "      <td>0.409161</td>\n",
       "      <td>0.510482</td>\n",
       "      <td>0.472362</td>\n",
       "      <td>0.390463</td>\n",
       "      <td>0.359758</td>\n",
       "      <td>0.500566</td>\n",
       "      <td>0.538599</td>\n",
       "      <td>0.388078</td>\n",
       "      <td>0.413691</td>\n",
       "      <td>0.362584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.141821</td>\n",
       "      <td>0.174758</td>\n",
       "      <td>0.172314</td>\n",
       "      <td>0.214984</td>\n",
       "      <td>0.198931</td>\n",
       "      <td>0.164439</td>\n",
       "      <td>0.151508</td>\n",
       "      <td>0.210808</td>\n",
       "      <td>0.226825</td>\n",
       "      <td>0.163435</td>\n",
       "      <td>0.174222</td>\n",
       "      <td>0.152699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.187937</td>\n",
       "      <td>0.231584</td>\n",
       "      <td>0.228345</td>\n",
       "      <td>0.284890</td>\n",
       "      <td>0.263617</td>\n",
       "      <td>0.217910</td>\n",
       "      <td>0.200774</td>\n",
       "      <td>0.279356</td>\n",
       "      <td>0.300582</td>\n",
       "      <td>0.216579</td>\n",
       "      <td>0.230873</td>\n",
       "      <td>0.202351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.128308</td>\n",
       "      <td>0.158107</td>\n",
       "      <td>0.155896</td>\n",
       "      <td>0.194501</td>\n",
       "      <td>0.179977</td>\n",
       "      <td>0.148772</td>\n",
       "      <td>0.137073</td>\n",
       "      <td>0.190723</td>\n",
       "      <td>0.205214</td>\n",
       "      <td>0.147863</td>\n",
       "      <td>0.157622</td>\n",
       "      <td>0.138150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.434653</td>\n",
       "      <td>0.535599</td>\n",
       "      <td>0.528108</td>\n",
       "      <td>0.658884</td>\n",
       "      <td>0.609683</td>\n",
       "      <td>0.503974</td>\n",
       "      <td>0.464343</td>\n",
       "      <td>0.646085</td>\n",
       "      <td>0.695175</td>\n",
       "      <td>0.500896</td>\n",
       "      <td>0.533955</td>\n",
       "      <td>0.467991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.133009</td>\n",
       "      <td>0.163899</td>\n",
       "      <td>0.161607</td>\n",
       "      <td>0.201626</td>\n",
       "      <td>0.186570</td>\n",
       "      <td>0.154222</td>\n",
       "      <td>0.142094</td>\n",
       "      <td>0.197709</td>\n",
       "      <td>0.212731</td>\n",
       "      <td>0.153280</td>\n",
       "      <td>0.163396</td>\n",
       "      <td>0.143211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.146398</td>\n",
       "      <td>0.180399</td>\n",
       "      <td>0.177876</td>\n",
       "      <td>0.221923</td>\n",
       "      <td>0.205351</td>\n",
       "      <td>0.169747</td>\n",
       "      <td>0.156398</td>\n",
       "      <td>0.217612</td>\n",
       "      <td>0.234146</td>\n",
       "      <td>0.168710</td>\n",
       "      <td>0.179845</td>\n",
       "      <td>0.157627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.178335</td>\n",
       "      <td>0.219753</td>\n",
       "      <td>0.216679</td>\n",
       "      <td>0.270336</td>\n",
       "      <td>0.250149</td>\n",
       "      <td>0.206777</td>\n",
       "      <td>0.190517</td>\n",
       "      <td>0.265085</td>\n",
       "      <td>0.285226</td>\n",
       "      <td>0.205514</td>\n",
       "      <td>0.219078</td>\n",
       "      <td>0.192014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.213726</td>\n",
       "      <td>0.263362</td>\n",
       "      <td>0.259679</td>\n",
       "      <td>0.323983</td>\n",
       "      <td>0.299791</td>\n",
       "      <td>0.247812</td>\n",
       "      <td>0.228324</td>\n",
       "      <td>0.317690</td>\n",
       "      <td>0.341828</td>\n",
       "      <td>0.246298</td>\n",
       "      <td>0.262554</td>\n",
       "      <td>0.230119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.052788</td>\n",
       "      <td>0.065048</td>\n",
       "      <td>0.064138</td>\n",
       "      <td>0.080020</td>\n",
       "      <td>0.074045</td>\n",
       "      <td>0.061207</td>\n",
       "      <td>0.056394</td>\n",
       "      <td>0.078466</td>\n",
       "      <td>0.084428</td>\n",
       "      <td>0.060833</td>\n",
       "      <td>0.064848</td>\n",
       "      <td>0.056837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.232142</td>\n",
       "      <td>0.286056</td>\n",
       "      <td>0.282055</td>\n",
       "      <td>0.351901</td>\n",
       "      <td>0.325623</td>\n",
       "      <td>0.269165</td>\n",
       "      <td>0.247999</td>\n",
       "      <td>0.345065</td>\n",
       "      <td>0.371283</td>\n",
       "      <td>0.267522</td>\n",
       "      <td>0.285178</td>\n",
       "      <td>0.249948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.479437</td>\n",
       "      <td>0.590784</td>\n",
       "      <td>0.582521</td>\n",
       "      <td>0.726771</td>\n",
       "      <td>0.672501</td>\n",
       "      <td>0.555900</td>\n",
       "      <td>0.512186</td>\n",
       "      <td>0.712654</td>\n",
       "      <td>0.766802</td>\n",
       "      <td>0.552505</td>\n",
       "      <td>0.588971</td>\n",
       "      <td>0.516210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.230261</td>\n",
       "      <td>0.283738</td>\n",
       "      <td>0.279769</td>\n",
       "      <td>0.349049</td>\n",
       "      <td>0.322984</td>\n",
       "      <td>0.266984</td>\n",
       "      <td>0.245989</td>\n",
       "      <td>0.342269</td>\n",
       "      <td>0.368274</td>\n",
       "      <td>0.265354</td>\n",
       "      <td>0.282867</td>\n",
       "      <td>0.247922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.387604</td>\n",
       "      <td>0.477623</td>\n",
       "      <td>0.470943</td>\n",
       "      <td>0.587563</td>\n",
       "      <td>0.543688</td>\n",
       "      <td>0.449421</td>\n",
       "      <td>0.414080</td>\n",
       "      <td>0.576150</td>\n",
       "      <td>0.619926</td>\n",
       "      <td>0.446677</td>\n",
       "      <td>0.476157</td>\n",
       "      <td>0.417333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.265118</td>\n",
       "      <td>0.326690</td>\n",
       "      <td>0.322120</td>\n",
       "      <td>0.401887</td>\n",
       "      <td>0.371877</td>\n",
       "      <td>0.307400</td>\n",
       "      <td>0.283227</td>\n",
       "      <td>0.394081</td>\n",
       "      <td>0.424023</td>\n",
       "      <td>0.305523</td>\n",
       "      <td>0.325687</td>\n",
       "      <td>0.285452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.177147</td>\n",
       "      <td>0.218288</td>\n",
       "      <td>0.215235</td>\n",
       "      <td>0.268534</td>\n",
       "      <td>0.248482</td>\n",
       "      <td>0.205399</td>\n",
       "      <td>0.189247</td>\n",
       "      <td>0.263318</td>\n",
       "      <td>0.283325</td>\n",
       "      <td>0.204145</td>\n",
       "      <td>0.217618</td>\n",
       "      <td>0.190734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.337383</td>\n",
       "      <td>0.415738</td>\n",
       "      <td>0.409924</td>\n",
       "      <td>0.511433</td>\n",
       "      <td>0.473243</td>\n",
       "      <td>0.391190</td>\n",
       "      <td>0.360428</td>\n",
       "      <td>0.501499</td>\n",
       "      <td>0.539603</td>\n",
       "      <td>0.388801</td>\n",
       "      <td>0.414462</td>\n",
       "      <td>0.363260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.233854</td>\n",
       "      <td>0.288166</td>\n",
       "      <td>0.284135</td>\n",
       "      <td>0.354496</td>\n",
       "      <td>0.328025</td>\n",
       "      <td>0.271151</td>\n",
       "      <td>0.249828</td>\n",
       "      <td>0.347610</td>\n",
       "      <td>0.374022</td>\n",
       "      <td>0.269495</td>\n",
       "      <td>0.287281</td>\n",
       "      <td>0.251791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.408952</td>\n",
       "      <td>0.503929</td>\n",
       "      <td>0.496881</td>\n",
       "      <td>0.619924</td>\n",
       "      <td>0.573632</td>\n",
       "      <td>0.474174</td>\n",
       "      <td>0.436886</td>\n",
       "      <td>0.607882</td>\n",
       "      <td>0.654069</td>\n",
       "      <td>0.471278</td>\n",
       "      <td>0.502382</td>\n",
       "      <td>0.440319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.373262</td>\n",
       "      <td>0.459950</td>\n",
       "      <td>0.453517</td>\n",
       "      <td>0.565822</td>\n",
       "      <td>0.523570</td>\n",
       "      <td>0.432792</td>\n",
       "      <td>0.398758</td>\n",
       "      <td>0.554831</td>\n",
       "      <td>0.596988</td>\n",
       "      <td>0.430149</td>\n",
       "      <td>0.458539</td>\n",
       "      <td>0.401891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.111997</td>\n",
       "      <td>0.138007</td>\n",
       "      <td>0.136077</td>\n",
       "      <td>0.169774</td>\n",
       "      <td>0.157096</td>\n",
       "      <td>0.129858</td>\n",
       "      <td>0.119647</td>\n",
       "      <td>0.166476</td>\n",
       "      <td>0.179125</td>\n",
       "      <td>0.129065</td>\n",
       "      <td>0.137584</td>\n",
       "      <td>0.120587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.242720</td>\n",
       "      <td>0.299090</td>\n",
       "      <td>0.294907</td>\n",
       "      <td>0.367935</td>\n",
       "      <td>0.340460</td>\n",
       "      <td>0.281430</td>\n",
       "      <td>0.259299</td>\n",
       "      <td>0.360788</td>\n",
       "      <td>0.388201</td>\n",
       "      <td>0.279711</td>\n",
       "      <td>0.298172</td>\n",
       "      <td>0.261336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>0.243854</td>\n",
       "      <td>0.300487</td>\n",
       "      <td>0.296285</td>\n",
       "      <td>0.369654</td>\n",
       "      <td>0.342051</td>\n",
       "      <td>0.282745</td>\n",
       "      <td>0.260510</td>\n",
       "      <td>0.362474</td>\n",
       "      <td>0.390014</td>\n",
       "      <td>0.281018</td>\n",
       "      <td>0.299565</td>\n",
       "      <td>0.262557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>0.299428</td>\n",
       "      <td>0.368969</td>\n",
       "      <td>0.363808</td>\n",
       "      <td>0.453898</td>\n",
       "      <td>0.420004</td>\n",
       "      <td>0.347183</td>\n",
       "      <td>0.319881</td>\n",
       "      <td>0.445082</td>\n",
       "      <td>0.478899</td>\n",
       "      <td>0.345062</td>\n",
       "      <td>0.367836</td>\n",
       "      <td>0.322394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>0.341297</td>\n",
       "      <td>0.420561</td>\n",
       "      <td>0.414679</td>\n",
       "      <td>0.517367</td>\n",
       "      <td>0.478733</td>\n",
       "      <td>0.395729</td>\n",
       "      <td>0.364610</td>\n",
       "      <td>0.507317</td>\n",
       "      <td>0.545863</td>\n",
       "      <td>0.393312</td>\n",
       "      <td>0.419271</td>\n",
       "      <td>0.367475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>0.111865</td>\n",
       "      <td>0.137844</td>\n",
       "      <td>0.135917</td>\n",
       "      <td>0.169574</td>\n",
       "      <td>0.156911</td>\n",
       "      <td>0.129705</td>\n",
       "      <td>0.119506</td>\n",
       "      <td>0.166280</td>\n",
       "      <td>0.178914</td>\n",
       "      <td>0.128913</td>\n",
       "      <td>0.137421</td>\n",
       "      <td>0.120445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>0.194762</td>\n",
       "      <td>0.239994</td>\n",
       "      <td>0.236637</td>\n",
       "      <td>0.295236</td>\n",
       "      <td>0.273190</td>\n",
       "      <td>0.225823</td>\n",
       "      <td>0.208065</td>\n",
       "      <td>0.289501</td>\n",
       "      <td>0.311498</td>\n",
       "      <td>0.224444</td>\n",
       "      <td>0.239257</td>\n",
       "      <td>0.209700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.262573</td>\n",
       "      <td>0.323554</td>\n",
       "      <td>0.319028</td>\n",
       "      <td>0.398030</td>\n",
       "      <td>0.368308</td>\n",
       "      <td>0.304449</td>\n",
       "      <td>0.280508</td>\n",
       "      <td>0.390298</td>\n",
       "      <td>0.419953</td>\n",
       "      <td>0.302590</td>\n",
       "      <td>0.322561</td>\n",
       "      <td>0.282712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>0.110907</td>\n",
       "      <td>0.136665</td>\n",
       "      <td>0.134754</td>\n",
       "      <td>0.168123</td>\n",
       "      <td>0.155568</td>\n",
       "      <td>0.128595</td>\n",
       "      <td>0.118483</td>\n",
       "      <td>0.164857</td>\n",
       "      <td>0.177383</td>\n",
       "      <td>0.127810</td>\n",
       "      <td>0.136246</td>\n",
       "      <td>0.119414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>0.339669</td>\n",
       "      <td>0.418554</td>\n",
       "      <td>0.412701</td>\n",
       "      <td>0.514898</td>\n",
       "      <td>0.476449</td>\n",
       "      <td>0.393840</td>\n",
       "      <td>0.362870</td>\n",
       "      <td>0.504896</td>\n",
       "      <td>0.543258</td>\n",
       "      <td>0.391435</td>\n",
       "      <td>0.417270</td>\n",
       "      <td>0.365721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>0.146232</td>\n",
       "      <td>0.180193</td>\n",
       "      <td>0.177673</td>\n",
       "      <td>0.221670</td>\n",
       "      <td>0.205118</td>\n",
       "      <td>0.169554</td>\n",
       "      <td>0.156220</td>\n",
       "      <td>0.217365</td>\n",
       "      <td>0.233880</td>\n",
       "      <td>0.168518</td>\n",
       "      <td>0.179640</td>\n",
       "      <td>0.157448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>0.339282</td>\n",
       "      <td>0.418079</td>\n",
       "      <td>0.412231</td>\n",
       "      <td>0.514312</td>\n",
       "      <td>0.475907</td>\n",
       "      <td>0.393393</td>\n",
       "      <td>0.362457</td>\n",
       "      <td>0.504322</td>\n",
       "      <td>0.542641</td>\n",
       "      <td>0.390990</td>\n",
       "      <td>0.416796</td>\n",
       "      <td>0.365305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>0.237208</td>\n",
       "      <td>0.292298</td>\n",
       "      <td>0.288210</td>\n",
       "      <td>0.359580</td>\n",
       "      <td>0.332729</td>\n",
       "      <td>0.275039</td>\n",
       "      <td>0.253411</td>\n",
       "      <td>0.352595</td>\n",
       "      <td>0.379386</td>\n",
       "      <td>0.273360</td>\n",
       "      <td>0.291401</td>\n",
       "      <td>0.255402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>0.054897</td>\n",
       "      <td>0.067647</td>\n",
       "      <td>0.066701</td>\n",
       "      <td>0.083218</td>\n",
       "      <td>0.077004</td>\n",
       "      <td>0.063653</td>\n",
       "      <td>0.058647</td>\n",
       "      <td>0.081602</td>\n",
       "      <td>0.087802</td>\n",
       "      <td>0.063264</td>\n",
       "      <td>0.067439</td>\n",
       "      <td>0.059108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>0.227789</td>\n",
       "      <td>0.280692</td>\n",
       "      <td>0.276766</td>\n",
       "      <td>0.345301</td>\n",
       "      <td>0.319517</td>\n",
       "      <td>0.264118</td>\n",
       "      <td>0.243348</td>\n",
       "      <td>0.338594</td>\n",
       "      <td>0.364321</td>\n",
       "      <td>0.262505</td>\n",
       "      <td>0.279830</td>\n",
       "      <td>0.245260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>0.220278</td>\n",
       "      <td>0.271436</td>\n",
       "      <td>0.267640</td>\n",
       "      <td>0.333915</td>\n",
       "      <td>0.308981</td>\n",
       "      <td>0.255409</td>\n",
       "      <td>0.235324</td>\n",
       "      <td>0.327429</td>\n",
       "      <td>0.352308</td>\n",
       "      <td>0.253849</td>\n",
       "      <td>0.270603</td>\n",
       "      <td>0.237173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>0.122426</td>\n",
       "      <td>0.150859</td>\n",
       "      <td>0.148749</td>\n",
       "      <td>0.185584</td>\n",
       "      <td>0.171726</td>\n",
       "      <td>0.141951</td>\n",
       "      <td>0.130788</td>\n",
       "      <td>0.181979</td>\n",
       "      <td>0.195806</td>\n",
       "      <td>0.141084</td>\n",
       "      <td>0.150396</td>\n",
       "      <td>0.131816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.225239</td>\n",
       "      <td>0.277550</td>\n",
       "      <td>0.273668</td>\n",
       "      <td>0.341436</td>\n",
       "      <td>0.315940</td>\n",
       "      <td>0.261161</td>\n",
       "      <td>0.240624</td>\n",
       "      <td>0.334804</td>\n",
       "      <td>0.360243</td>\n",
       "      <td>0.259567</td>\n",
       "      <td>0.276698</td>\n",
       "      <td>0.242515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>0.157551</td>\n",
       "      <td>0.194142</td>\n",
       "      <td>0.191426</td>\n",
       "      <td>0.238829</td>\n",
       "      <td>0.220995</td>\n",
       "      <td>0.182678</td>\n",
       "      <td>0.168313</td>\n",
       "      <td>0.234190</td>\n",
       "      <td>0.251984</td>\n",
       "      <td>0.181563</td>\n",
       "      <td>0.193546</td>\n",
       "      <td>0.169635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>0.155822</td>\n",
       "      <td>0.192011</td>\n",
       "      <td>0.189326</td>\n",
       "      <td>0.236209</td>\n",
       "      <td>0.218570</td>\n",
       "      <td>0.180674</td>\n",
       "      <td>0.166466</td>\n",
       "      <td>0.231620</td>\n",
       "      <td>0.249219</td>\n",
       "      <td>0.179570</td>\n",
       "      <td>0.191422</td>\n",
       "      <td>0.167774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>0.257327</td>\n",
       "      <td>0.317089</td>\n",
       "      <td>0.312654</td>\n",
       "      <td>0.390077</td>\n",
       "      <td>0.360949</td>\n",
       "      <td>0.298366</td>\n",
       "      <td>0.274904</td>\n",
       "      <td>0.382500</td>\n",
       "      <td>0.411563</td>\n",
       "      <td>0.296544</td>\n",
       "      <td>0.316116</td>\n",
       "      <td>0.277064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.189401</td>\n",
       "      <td>0.233388</td>\n",
       "      <td>0.230124</td>\n",
       "      <td>0.287110</td>\n",
       "      <td>0.265670</td>\n",
       "      <td>0.219608</td>\n",
       "      <td>0.202338</td>\n",
       "      <td>0.281533</td>\n",
       "      <td>0.302924</td>\n",
       "      <td>0.218266</td>\n",
       "      <td>0.232672</td>\n",
       "      <td>0.203928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>0.426909</td>\n",
       "      <td>0.526056</td>\n",
       "      <td>0.518698</td>\n",
       "      <td>0.647144</td>\n",
       "      <td>0.598820</td>\n",
       "      <td>0.494994</td>\n",
       "      <td>0.456069</td>\n",
       "      <td>0.634574</td>\n",
       "      <td>0.682788</td>\n",
       "      <td>0.491971</td>\n",
       "      <td>0.524441</td>\n",
       "      <td>0.459652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>0.166049</td>\n",
       "      <td>0.204613</td>\n",
       "      <td>0.201751</td>\n",
       "      <td>0.251711</td>\n",
       "      <td>0.232915</td>\n",
       "      <td>0.192531</td>\n",
       "      <td>0.177391</td>\n",
       "      <td>0.246821</td>\n",
       "      <td>0.265575</td>\n",
       "      <td>0.191355</td>\n",
       "      <td>0.203985</td>\n",
       "      <td>0.178785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.495837</td>\n",
       "      <td>0.610992</td>\n",
       "      <td>0.602447</td>\n",
       "      <td>0.751631</td>\n",
       "      <td>0.695504</td>\n",
       "      <td>0.574915</td>\n",
       "      <td>0.529705</td>\n",
       "      <td>0.737031</td>\n",
       "      <td>0.793031</td>\n",
       "      <td>0.571404</td>\n",
       "      <td>0.609117</td>\n",
       "      <td>0.533868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.277324</td>\n",
       "      <td>0.341731</td>\n",
       "      <td>0.336952</td>\n",
       "      <td>0.420391</td>\n",
       "      <td>0.388999</td>\n",
       "      <td>0.321553</td>\n",
       "      <td>0.296267</td>\n",
       "      <td>0.412226</td>\n",
       "      <td>0.443547</td>\n",
       "      <td>0.319590</td>\n",
       "      <td>0.340682</td>\n",
       "      <td>0.298595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>0.081497</td>\n",
       "      <td>0.100424</td>\n",
       "      <td>0.099019</td>\n",
       "      <td>0.123539</td>\n",
       "      <td>0.114314</td>\n",
       "      <td>0.094494</td>\n",
       "      <td>0.087063</td>\n",
       "      <td>0.121140</td>\n",
       "      <td>0.130344</td>\n",
       "      <td>0.093917</td>\n",
       "      <td>0.100116</td>\n",
       "      <td>0.087747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.294432</td>\n",
       "      <td>0.362813</td>\n",
       "      <td>0.357738</td>\n",
       "      <td>0.446325</td>\n",
       "      <td>0.412997</td>\n",
       "      <td>0.341390</td>\n",
       "      <td>0.314544</td>\n",
       "      <td>0.437656</td>\n",
       "      <td>0.470909</td>\n",
       "      <td>0.339305</td>\n",
       "      <td>0.361699</td>\n",
       "      <td>0.317015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>0.081543</td>\n",
       "      <td>0.100481</td>\n",
       "      <td>0.099075</td>\n",
       "      <td>0.123610</td>\n",
       "      <td>0.114379</td>\n",
       "      <td>0.094548</td>\n",
       "      <td>0.087113</td>\n",
       "      <td>0.121209</td>\n",
       "      <td>0.130418</td>\n",
       "      <td>0.093970</td>\n",
       "      <td>0.100172</td>\n",
       "      <td>0.087797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>0.167414</td>\n",
       "      <td>0.206295</td>\n",
       "      <td>0.203410</td>\n",
       "      <td>0.253780</td>\n",
       "      <td>0.234829</td>\n",
       "      <td>0.194114</td>\n",
       "      <td>0.178849</td>\n",
       "      <td>0.248851</td>\n",
       "      <td>0.267758</td>\n",
       "      <td>0.192928</td>\n",
       "      <td>0.205662</td>\n",
       "      <td>0.180255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>0.175844</td>\n",
       "      <td>0.216683</td>\n",
       "      <td>0.213652</td>\n",
       "      <td>0.266559</td>\n",
       "      <td>0.246654</td>\n",
       "      <td>0.203888</td>\n",
       "      <td>0.187855</td>\n",
       "      <td>0.261381</td>\n",
       "      <td>0.281241</td>\n",
       "      <td>0.202643</td>\n",
       "      <td>0.216018</td>\n",
       "      <td>0.189331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.152028</td>\n",
       "      <td>0.187335</td>\n",
       "      <td>0.184715</td>\n",
       "      <td>0.230456</td>\n",
       "      <td>0.213248</td>\n",
       "      <td>0.176274</td>\n",
       "      <td>0.162412</td>\n",
       "      <td>0.225980</td>\n",
       "      <td>0.243150</td>\n",
       "      <td>0.175197</td>\n",
       "      <td>0.186760</td>\n",
       "      <td>0.163688</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>95 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6   \\\n",
       "0   0.301025  0.370936  0.365748  0.456318  0.422244  0.349034  0.321586   \n",
       "1   0.191067  0.235441  0.232148  0.289636  0.268008  0.221539  0.204118   \n",
       "2   0.042508  0.052380  0.051648  0.064437  0.059626  0.049288  0.045412   \n",
       "3   0.145898  0.179781  0.177267  0.221164  0.204649  0.169166  0.155863   \n",
       "4   0.576494  0.710382  0.700446  0.873898  0.808642  0.668436  0.615872   \n",
       "5   0.277854  0.342384  0.337596  0.421195  0.389743  0.322168  0.296833   \n",
       "6   0.372349  0.458825  0.452408  0.564438  0.522290  0.431733  0.397783   \n",
       "7   0.099863  0.123055  0.121334  0.151380  0.140076  0.115789  0.106684   \n",
       "8   0.336755  0.414965  0.409161  0.510482  0.472362  0.390463  0.359758   \n",
       "9   0.141821  0.174758  0.172314  0.214984  0.198931  0.164439  0.151508   \n",
       "10  0.187937  0.231584  0.228345  0.284890  0.263617  0.217910  0.200774   \n",
       "11  0.128308  0.158107  0.155896  0.194501  0.179977  0.148772  0.137073   \n",
       "12  0.434653  0.535599  0.528108  0.658884  0.609683  0.503974  0.464343   \n",
       "13  0.133009  0.163899  0.161607  0.201626  0.186570  0.154222  0.142094   \n",
       "14  0.146398  0.180399  0.177876  0.221923  0.205351  0.169747  0.156398   \n",
       "15  0.178335  0.219753  0.216679  0.270336  0.250149  0.206777  0.190517   \n",
       "16  0.213726  0.263362  0.259679  0.323983  0.299791  0.247812  0.228324   \n",
       "17  0.052788  0.065048  0.064138  0.080020  0.074045  0.061207  0.056394   \n",
       "18  0.232142  0.286056  0.282055  0.351901  0.325623  0.269165  0.247999   \n",
       "19  0.479437  0.590784  0.582521  0.726771  0.672501  0.555900  0.512186   \n",
       "20  0.230261  0.283738  0.279769  0.349049  0.322984  0.266984  0.245989   \n",
       "21  0.387604  0.477623  0.470943  0.587563  0.543688  0.449421  0.414080   \n",
       "22  0.265118  0.326690  0.322120  0.401887  0.371877  0.307400  0.283227   \n",
       "23  0.177147  0.218288  0.215235  0.268534  0.248482  0.205399  0.189247   \n",
       "24  0.337383  0.415738  0.409924  0.511433  0.473243  0.391190  0.360428   \n",
       "25  0.233854  0.288166  0.284135  0.354496  0.328025  0.271151  0.249828   \n",
       "26  0.408952  0.503929  0.496881  0.619924  0.573632  0.474174  0.436886   \n",
       "27  0.373262  0.459950  0.453517  0.565822  0.523570  0.432792  0.398758   \n",
       "28  0.111997  0.138007  0.136077  0.169774  0.157096  0.129858  0.119647   \n",
       "29  0.242720  0.299090  0.294907  0.367935  0.340460  0.281430  0.259299   \n",
       "..       ...       ...       ...       ...       ...       ...       ...   \n",
       "65  0.243854  0.300487  0.296285  0.369654  0.342051  0.282745  0.260510   \n",
       "66  0.299428  0.368969  0.363808  0.453898  0.420004  0.347183  0.319881   \n",
       "67  0.341297  0.420561  0.414679  0.517367  0.478733  0.395729  0.364610   \n",
       "68  0.111865  0.137844  0.135917  0.169574  0.156911  0.129705  0.119506   \n",
       "69  0.194762  0.239994  0.236637  0.295236  0.273190  0.225823  0.208065   \n",
       "70  0.262573  0.323554  0.319028  0.398030  0.368308  0.304449  0.280508   \n",
       "71  0.110907  0.136665  0.134754  0.168123  0.155568  0.128595  0.118483   \n",
       "72  0.339669  0.418554  0.412701  0.514898  0.476449  0.393840  0.362870   \n",
       "73  0.146232  0.180193  0.177673  0.221670  0.205118  0.169554  0.156220   \n",
       "74  0.339282  0.418079  0.412231  0.514312  0.475907  0.393393  0.362457   \n",
       "75  0.237208  0.292298  0.288210  0.359580  0.332729  0.275039  0.253411   \n",
       "76  0.054897  0.067647  0.066701  0.083218  0.077004  0.063653  0.058647   \n",
       "77  0.227789  0.280692  0.276766  0.345301  0.319517  0.264118  0.243348   \n",
       "78  0.220278  0.271436  0.267640  0.333915  0.308981  0.255409  0.235324   \n",
       "79  0.122426  0.150859  0.148749  0.185584  0.171726  0.141951  0.130788   \n",
       "80  0.225239  0.277550  0.273668  0.341436  0.315940  0.261161  0.240624   \n",
       "81  0.157551  0.194142  0.191426  0.238829  0.220995  0.182678  0.168313   \n",
       "82  0.155822  0.192011  0.189326  0.236209  0.218570  0.180674  0.166466   \n",
       "83  0.257327  0.317089  0.312654  0.390077  0.360949  0.298366  0.274904   \n",
       "84  0.189401  0.233388  0.230124  0.287110  0.265670  0.219608  0.202338   \n",
       "85  0.426909  0.526056  0.518698  0.647144  0.598820  0.494994  0.456069   \n",
       "86  0.166049  0.204613  0.201751  0.251711  0.232915  0.192531  0.177391   \n",
       "87  0.495837  0.610992  0.602447  0.751631  0.695504  0.574915  0.529705   \n",
       "88  0.277324  0.341731  0.336952  0.420391  0.388999  0.321553  0.296267   \n",
       "89  0.081497  0.100424  0.099019  0.123539  0.114314  0.094494  0.087063   \n",
       "90  0.294432  0.362813  0.357738  0.446325  0.412997  0.341390  0.314544   \n",
       "91  0.081543  0.100481  0.099075  0.123610  0.114379  0.094548  0.087113   \n",
       "92  0.167414  0.206295  0.203410  0.253780  0.234829  0.194114  0.178849   \n",
       "93  0.175844  0.216683  0.213652  0.266559  0.246654  0.203888  0.187855   \n",
       "94  0.152028  0.187335  0.184715  0.230456  0.213248  0.176274  0.162412   \n",
       "\n",
       "          7         8         9         10        11  \n",
       "0   0.447455  0.481452  0.346902  0.369798  0.324113  \n",
       "1   0.284010  0.305589  0.220187  0.234719  0.205722  \n",
       "2   0.063186  0.067987  0.048987  0.052220  0.045769  \n",
       "3   0.216868  0.233345  0.168133  0.179230  0.157088  \n",
       "4   0.856924  0.922033  0.664354  0.708202  0.620711  \n",
       "5   0.413013  0.444394  0.320200  0.341333  0.299166  \n",
       "6   0.553474  0.595527  0.429097  0.457417  0.400908  \n",
       "7   0.148440  0.159718  0.115082  0.122678  0.107522  \n",
       "8   0.500566  0.538599  0.388078  0.413691  0.362584  \n",
       "9   0.210808  0.226825  0.163435  0.174222  0.152699  \n",
       "10  0.279356  0.300582  0.216579  0.230873  0.202351  \n",
       "11  0.190723  0.205214  0.147863  0.157622  0.138150  \n",
       "12  0.646085  0.695175  0.500896  0.533955  0.467991  \n",
       "13  0.197709  0.212731  0.153280  0.163396  0.143211  \n",
       "14  0.217612  0.234146  0.168710  0.179845  0.157627  \n",
       "15  0.265085  0.285226  0.205514  0.219078  0.192014  \n",
       "16  0.317690  0.341828  0.246298  0.262554  0.230119  \n",
       "17  0.078466  0.084428  0.060833  0.064848  0.056837  \n",
       "18  0.345065  0.371283  0.267522  0.285178  0.249948  \n",
       "19  0.712654  0.766802  0.552505  0.588971  0.516210  \n",
       "20  0.342269  0.368274  0.265354  0.282867  0.247922  \n",
       "21  0.576150  0.619926  0.446677  0.476157  0.417333  \n",
       "22  0.394081  0.424023  0.305523  0.325687  0.285452  \n",
       "23  0.263318  0.283325  0.204145  0.217618  0.190734  \n",
       "24  0.501499  0.539603  0.388801  0.414462  0.363260  \n",
       "25  0.347610  0.374022  0.269495  0.287281  0.251791  \n",
       "26  0.607882  0.654069  0.471278  0.502382  0.440319  \n",
       "27  0.554831  0.596988  0.430149  0.458539  0.401891  \n",
       "28  0.166476  0.179125  0.129065  0.137584  0.120587  \n",
       "29  0.360788  0.388201  0.279711  0.298172  0.261336  \n",
       "..       ...       ...       ...       ...       ...  \n",
       "65  0.362474  0.390014  0.281018  0.299565  0.262557  \n",
       "66  0.445082  0.478899  0.345062  0.367836  0.322394  \n",
       "67  0.507317  0.545863  0.393312  0.419271  0.367475  \n",
       "68  0.166280  0.178914  0.128913  0.137421  0.120445  \n",
       "69  0.289501  0.311498  0.224444  0.239257  0.209700  \n",
       "70  0.390298  0.419953  0.302590  0.322561  0.282712  \n",
       "71  0.164857  0.177383  0.127810  0.136246  0.119414  \n",
       "72  0.504896  0.543258  0.391435  0.417270  0.365721  \n",
       "73  0.217365  0.233880  0.168518  0.179640  0.157448  \n",
       "74  0.504322  0.542641  0.390990  0.416796  0.365305  \n",
       "75  0.352595  0.379386  0.273360  0.291401  0.255402  \n",
       "76  0.081602  0.087802  0.063264  0.067439  0.059108  \n",
       "77  0.338594  0.364321  0.262505  0.279830  0.245260  \n",
       "78  0.327429  0.352308  0.253849  0.270603  0.237173  \n",
       "79  0.181979  0.195806  0.141084  0.150396  0.131816  \n",
       "80  0.334804  0.360243  0.259567  0.276698  0.242515  \n",
       "81  0.234190  0.251984  0.181563  0.193546  0.169635  \n",
       "82  0.231620  0.249219  0.179570  0.191422  0.167774  \n",
       "83  0.382500  0.411563  0.296544  0.316116  0.277064  \n",
       "84  0.281533  0.302924  0.218266  0.232672  0.203928  \n",
       "85  0.634574  0.682788  0.491971  0.524441  0.459652  \n",
       "86  0.246821  0.265575  0.191355  0.203985  0.178785  \n",
       "87  0.737031  0.793031  0.571404  0.609117  0.533868  \n",
       "88  0.412226  0.443547  0.319590  0.340682  0.298595  \n",
       "89  0.121140  0.130344  0.093917  0.100116  0.087747  \n",
       "90  0.437656  0.470909  0.339305  0.361699  0.317015  \n",
       "91  0.121209  0.130418  0.093970  0.100172  0.087797  \n",
       "92  0.248851  0.267758  0.192928  0.205662  0.180255  \n",
       "93  0.261381  0.281241  0.202643  0.216018  0.189331  \n",
       "94  0.225980  0.243150  0.175197  0.186760  0.163688  \n",
       "\n",
       "[95 rows x 12 columns]"
      ]
     },
     "execution_count": 363,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(Y*X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x123b51850>]"
      ]
     },
     "execution_count": 348,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEHCAYAAABSjBpvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1239bf3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pd.DataFrame(Y*X)[0]-pd.DataFrame(X_normalised['hvac_5'].values)[0].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.061689182092503847"
      ]
     },
     "execution_count": 349,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "np.sqrt(mean_squared_error(Y*X, X_normalised.values))\n",
    "#pd.DataFrame(Y*X)-pd.DataFrame(X_normalised.values)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dw        68.495285\n",
       "fridge    41.210222\n",
       "hvac      23.297621\n",
       "mw        60.897398\n",
       "oven      63.322534\n",
       "wm        47.359437\n",
       "dtype: float64"
      ]
     },
     "execution_count": 289,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(results).min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>95.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>95.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2298.792724</td>\n",
       "      <td>2590.036973</td>\n",
       "      <td>2493.324328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1366.027314</td>\n",
       "      <td>1337.211355</td>\n",
       "      <td>1312.536172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>74.457818</td>\n",
       "      <td>1.682887</td>\n",
       "      <td>90.212011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1070.234162</td>\n",
       "      <td>1441.592814</td>\n",
       "      <td>1509.352575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2262.878502</td>\n",
       "      <td>2754.591065</td>\n",
       "      <td>2543.472756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3528.501643</td>\n",
       "      <td>3792.788742</td>\n",
       "      <td>3639.383733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>4573.696706</td>\n",
       "      <td>4574.483307</td>\n",
       "      <td>4572.175328</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0            1            2\n",
       "count    95.000000    95.000000    95.000000\n",
       "mean   2298.792724  2590.036973  2493.324328\n",
       "std    1366.027314  1337.211355  1312.536172\n",
       "min      74.457818     1.682887    90.212011\n",
       "25%    1070.234162  1441.592814  1509.352575\n",
       "50%    2262.878502  2754.591065  2543.472756\n",
       "75%    3528.501643  3792.788742  3639.383733\n",
       "max    4573.696706  4574.483307  4572.175328"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = len(A)\n",
    "n = len(A.columns)\n",
    "k=3\n",
    "Y_init = A.max().max()*np.random.rand(m, k)\n",
    "pd.DataFrame(Y_init).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>hvac_5</th>\n",
       "      <th>hvac_6</th>\n",
       "      <th>hvac_7</th>\n",
       "      <th>hvac_8</th>\n",
       "      <th>hvac_9</th>\n",
       "      <th>hvac_10</th>\n",
       "      <th>aggregate_5</th>\n",
       "      <th>aggregate_6</th>\n",
       "      <th>aggregate_7</th>\n",
       "      <th>aggregate_8</th>\n",
       "      <th>aggregate_9</th>\n",
       "      <th>aggregate_10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>94.000000</td>\n",
       "      <td>94.000000</td>\n",
       "      <td>94.000000</td>\n",
       "      <td>94.000000</td>\n",
       "      <td>94.000000</td>\n",
       "      <td>94.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>95.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>204.697577</td>\n",
       "      <td>410.772775</td>\n",
       "      <td>634.932650</td>\n",
       "      <td>703.427444</td>\n",
       "      <td>496.814433</td>\n",
       "      <td>243.957545</td>\n",
       "      <td>894.636166</td>\n",
       "      <td>1117.168094</td>\n",
       "      <td>1435.362421</td>\n",
       "      <td>1570.281882</td>\n",
       "      <td>1260.032510</td>\n",
       "      <td>935.727852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>152.308577</td>\n",
       "      <td>249.724508</td>\n",
       "      <td>348.390233</td>\n",
       "      <td>343.614402</td>\n",
       "      <td>252.160506</td>\n",
       "      <td>152.017218</td>\n",
       "      <td>526.052474</td>\n",
       "      <td>563.679895</td>\n",
       "      <td>699.529397</td>\n",
       "      <td>762.214791</td>\n",
       "      <td>607.968624</td>\n",
       "      <td>515.139351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>3.054133</td>\n",
       "      <td>2.404883</td>\n",
       "      <td>9.934549</td>\n",
       "      <td>21.709467</td>\n",
       "      <td>40.952965</td>\n",
       "      <td>8.885633</td>\n",
       "      <td>182.287521</td>\n",
       "      <td>41.541668</td>\n",
       "      <td>174.545334</td>\n",
       "      <td>485.617706</td>\n",
       "      <td>386.186584</td>\n",
       "      <td>178.216537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>84.733067</td>\n",
       "      <td>239.801712</td>\n",
       "      <td>409.715370</td>\n",
       "      <td>469.171234</td>\n",
       "      <td>319.873489</td>\n",
       "      <td>144.406563</td>\n",
       "      <td>538.820801</td>\n",
       "      <td>741.668213</td>\n",
       "      <td>927.531219</td>\n",
       "      <td>1050.480408</td>\n",
       "      <td>845.363953</td>\n",
       "      <td>612.034912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>177.884102</td>\n",
       "      <td>338.474533</td>\n",
       "      <td>572.622009</td>\n",
       "      <td>643.759674</td>\n",
       "      <td>460.979889</td>\n",
       "      <td>214.063858</td>\n",
       "      <td>781.487122</td>\n",
       "      <td>979.500122</td>\n",
       "      <td>1289.663940</td>\n",
       "      <td>1425.989990</td>\n",
       "      <td>1142.088135</td>\n",
       "      <td>801.091187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>289.427666</td>\n",
       "      <td>542.997314</td>\n",
       "      <td>804.441116</td>\n",
       "      <td>892.596329</td>\n",
       "      <td>617.534866</td>\n",
       "      <td>346.822327</td>\n",
       "      <td>1093.304993</td>\n",
       "      <td>1403.773315</td>\n",
       "      <td>1764.296936</td>\n",
       "      <td>1903.711792</td>\n",
       "      <td>1561.776794</td>\n",
       "      <td>1104.915527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>894.190308</td>\n",
       "      <td>1385.010742</td>\n",
       "      <td>2130.617920</td>\n",
       "      <td>1834.047852</td>\n",
       "      <td>1386.018921</td>\n",
       "      <td>876.380493</td>\n",
       "      <td>3120.817871</td>\n",
       "      <td>3010.485352</td>\n",
       "      <td>3481.583496</td>\n",
       "      <td>4581.233398</td>\n",
       "      <td>3462.281494</td>\n",
       "      <td>3176.753418</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           hvac_5       hvac_6       hvac_7       hvac_8       hvac_9  \\\n",
       "count   94.000000    94.000000    94.000000    94.000000    94.000000   \n",
       "mean   204.697577   410.772775   634.932650   703.427444   496.814433   \n",
       "std    152.308577   249.724508   348.390233   343.614402   252.160506   \n",
       "min      3.054133     2.404883     9.934549    21.709467    40.952965   \n",
       "25%     84.733067   239.801712   409.715370   469.171234   319.873489   \n",
       "50%    177.884102   338.474533   572.622009   643.759674   460.979889   \n",
       "75%    289.427666   542.997314   804.441116   892.596329   617.534866   \n",
       "max    894.190308  1385.010742  2130.617920  1834.047852  1386.018921   \n",
       "\n",
       "          hvac_10  aggregate_5  aggregate_6  aggregate_7  aggregate_8  \\\n",
       "count   94.000000    95.000000    95.000000    95.000000    95.000000   \n",
       "mean   243.957545   894.636166  1117.168094  1435.362421  1570.281882   \n",
       "std    152.017218   526.052474   563.679895   699.529397   762.214791   \n",
       "min      8.885633   182.287521    41.541668   174.545334   485.617706   \n",
       "25%    144.406563   538.820801   741.668213   927.531219  1050.480408   \n",
       "50%    214.063858   781.487122   979.500122  1289.663940  1425.989990   \n",
       "75%    346.822327  1093.304993  1403.773315  1764.296936  1903.711792   \n",
       "max    876.380493  3120.817871  3010.485352  3481.583496  4581.233398   \n",
       "\n",
       "       aggregate_9  aggregate_10  \n",
       "count    95.000000     95.000000  \n",
       "mean   1260.032510    935.727852  \n",
       "std     607.968624    515.139351  \n",
       "min     386.186584    178.216537  \n",
       "25%     845.363953    612.034912  \n",
       "50%    1142.088135    801.091187  \n",
       "75%    1561.776794   1104.915527  \n",
       "max    3462.281494   3176.753418  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'optimal'"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEbCAYAAADajfNFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBYKIiADw/1kgSqq9ZiNQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119023c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original matrix:\n",
      "        hvac_5    hvac_6    hvac_7    hvac_8    hvac_9   hvac_10  aggregate_5  \\\n",
      "26         NaN       NaN       NaN       NaN       NaN       NaN     0.264163   \n",
      "59    0.083667  0.141433  0.211260  0.374507  0.151210  0.083204     0.314919   \n",
      "94    0.018833  0.046446  0.054788  0.073571  0.038679  0.028250     0.043213   \n",
      "101   0.211989  0.233945  0.213504  0.255734  0.230129  0.211738     0.114979   \n",
      "222   0.534035  0.646650  0.503590  0.616900  0.629034  0.663339     0.790309   \n",
      "364   0.262441  0.385219  0.342594  0.457073  0.447491  0.426416     0.245914   \n",
      "545   0.389795  0.561114  0.497692  0.606508  0.555478  0.422386     0.306238   \n",
      "624   0.078196  0.136574  0.140541  0.202991  0.147672  0.015232     0.098029   \n",
      "661   0.245238  0.467515  0.439553  0.578096  0.531963  0.450393     0.266728   \n",
      "871   0.090979  0.165842  0.185541  0.272096  0.207023  0.152141     0.132008   \n",
      "946   0.240927  0.321466  0.280712  0.364962  0.305803  0.276486     0.123545   \n",
      "1169  0.020248  0.127003  0.149972  0.233702  0.178913  0.134137     0.070773   \n",
      "1283  0.572043  0.378876  0.608742  0.819876  0.934504  0.510819     0.326314   \n",
      "1310  0.257873  0.215592  0.155067  0.190282  0.208393  0.305314     0.120886   \n",
      "1334  0.046084  0.160185  0.212569  0.296099  0.289316  0.233638     0.084529   \n",
      "1415  0.197319  0.254382  0.220302  0.331535  0.288481  0.267414     0.148367   \n",
      "1463  0.040658  0.349886  0.366425  0.509810  0.412880  0.155231     0.065746   \n",
      "1500  0.094843  0.111589  0.022485  0.107882  0.098477  0.087447     0.069610   \n",
      "1642  0.175598  0.170121  0.291993  0.296486  0.332984  0.274678     0.262452   \n",
      "1697  0.593912  0.589546  0.521979  0.674317  0.669988  0.667983     0.529163   \n",
      "1700  0.128459  0.176542  0.169414  0.215692  0.253328  0.159192     0.302523   \n",
      "1790  0.233702  0.423079  0.446517  0.507357  0.440564  0.310795     0.421835   \n",
      "1800  0.285667  0.452811  0.377387  0.230390  0.410066  0.458969     0.213602   \n",
      "1953  0.086953  0.231495  0.294377  0.411857  0.307426  0.197269     0.066840   \n",
      "2129  0.375517  0.447841  0.415199  0.511974  0.470954  0.398028     0.363481   \n",
      "2156  0.359815  0.295166  0.280545  0.330379  0.383247  0.391592     0.307522   \n",
      "2233  0.545957  0.579321  0.615186  0.753994  0.663149  0.533992     0.343538   \n",
      "2242  0.324235  0.383106  0.382257  0.364164  0.398856  0.429605     0.486088   \n",
      "2365  0.021626  0.102599  0.076425  0.118553  0.114828  0.047847     0.159917   \n",
      "2378  0.428213  0.000000  0.263525  0.660409  0.430523  0.051815     0.407608   \n",
      "...        ...       ...       ...       ...       ...       ...          ...   \n",
      "6139  0.118453  0.244656  0.301981  0.392984  0.323881  0.200185     0.278008   \n",
      "6498  0.076202  0.217826  0.186081  0.243952  0.176497  0.080943     0.478367   \n",
      "6692  0.396308  0.505988  0.475855  0.578473  0.546052  0.401328     0.312528   \n",
      "6836  0.045622  0.140804  0.141072  0.169198  0.140117  0.115150     0.076577   \n",
      "6910  0.180709  0.219596  0.239040  0.300958  0.246338  0.196811     0.230417   \n",
      "7016  0.013542  0.003102  0.000000  0.000000  0.000000  0.023978     0.553151   \n",
      "7390  0.064954  0.173169  0.176549  0.217817  0.154965  0.116463     0.069039   \n",
      "7429  0.436321  0.544474  0.457485  0.597935  0.526493  0.491426     0.265819   \n",
      "7510  0.009566  0.023263  0.049726  0.082285  0.041877  0.000000     0.305359   \n",
      "7641  0.373713  0.476550  0.428024  0.501517  0.491671  0.404982     0.365437   \n",
      "7731  0.225774  0.361324  0.325870  0.455709  0.409439  0.336676     0.142046   \n",
      "7769  0.059981  0.104904  0.102002  0.133833  0.097616  0.045937     0.026070   \n",
      "7793  0.159878  0.245742  0.228014  0.299642  0.238214  0.187787     0.263086   \n",
      "7800  0.242323  0.331926  0.311883  0.423053  0.330461  0.343614     0.167055   \n",
      "7866  0.185521  0.226899  0.188048  0.263258  0.177828  0.163277     0.118543   \n",
      "8236  0.199708  0.300688  0.272043  0.403561  0.370847  0.316240     0.188411   \n",
      "8243  0.067992  0.217199  0.191815  0.312226  0.222407  0.203155     0.111199   \n",
      "8317  0.172035  0.220096  0.204707  0.256749  0.232320  0.229948     0.143242   \n",
      "9052  0.189056  0.269484  0.400027  0.544218  0.491610  0.363750     0.135462   \n",
      "9134  0.093692  0.200500  0.231806  0.312099  0.268831  0.178808     0.162163   \n",
      "9484  0.568348  0.448149  0.551623  0.721005  0.676426  0.542733     0.525413   \n",
      "9609  0.117508  0.206237  0.238633  0.347733  0.233225  0.161856     0.121775   \n",
      "9647  0.377577  0.298944  0.276376  0.381785  0.384137  0.368209     1.000000   \n",
      "9729  0.306245  0.560696  0.226274  0.458460  0.412396  0.395298     0.252849   \n",
      "9912  0.078958  0.095393  0.096514  0.137328  0.149801  0.163715     0.065631   \n",
      "9922  0.126133  0.220109  0.270342  0.410312  0.346492  0.252707     0.210120   \n",
      "9932  0.039314  0.127777  0.175550  0.100293  0.136188  0.038777     0.076250   \n",
      "9933  0.221638  0.223950  0.220813  0.282442  0.202153  0.174667     0.166210   \n",
      "9971  0.183358  0.319774  0.335846  0.434003  0.383700  0.001631     0.077466   \n",
      "9982  0.143904  0.230671  0.291574  0.294091  0.264141  0.187730     0.132651   \n",
      "\n",
      "      aggregate_6  aggregate_7  aggregate_8  aggregate_9  aggregate_10  \n",
      "26       0.451381     0.462876     0.342351     0.318240      0.339887  \n",
      "59       0.337543     0.374149     0.323820     0.209625      0.250306  \n",
      "94       0.109343     0.102650     0.023547     0.023076      0.055540  \n",
      "101      0.220393     0.214252     0.079637     0.106973      0.106339  \n",
      "222      0.976471     1.000000     1.000000     0.695549      0.757812  \n",
      "364      0.441337     0.395841     0.248856     0.275310      0.256052  \n",
      "545      0.551074     0.576684     0.414428     0.410604      0.315398  \n",
      "624      0.210571     0.180674     0.088194     0.076730      0.089123  \n",
      "661      0.493854     0.490906     0.368298     0.385970      0.340996  \n",
      "871      0.237228     0.229447     0.147799     0.148474      0.142589  \n",
      "946      0.258824     0.247945     0.142535     0.130467      0.137382  \n",
      "1169     0.244351     0.230547     0.156714     0.163431      0.180769  \n",
      "1283     0.360368     0.620634     0.483697     0.607840      0.347817  \n",
      "1310     0.189730     0.146556     0.048989     0.078821      0.138775  \n",
      "1334     0.200846     0.221218     0.123463     0.146976      0.151753  \n",
      "1415     0.261174     0.224819     0.155077     0.161658      0.185718  \n",
      "1463     0.299150     0.337196     0.245469     0.217377      0.108349  \n",
      "1500     0.138303     0.000000     0.000000     0.024267      0.053308  \n",
      "1642     0.351292     0.469912     0.267400     0.319841      0.277571  \n",
      "1697     0.668077     0.688301     0.531300     0.623415      0.580770  \n",
      "1700     0.512757     0.435641     0.498735     0.353644      0.262197  \n",
      "1790     0.679439     0.780542     0.539133     0.588292      0.431051  \n",
      "1800     0.467606     0.414230     0.134424     0.284350      0.300563  \n",
      "1953     0.243554     0.288967     0.188105     0.158250      0.125528  \n",
      "2129     0.518382     0.516489     0.354440     0.391815      0.350633  \n",
      "2156     0.298602     0.308049     0.171818     0.245734      0.223524  \n",
      "2233     0.478594     0.585107     0.408224     0.391352      0.291228  \n",
      "2242     0.689968     0.721414     0.499810     0.566147      0.410247  \n",
      "2365     0.262832     0.177596     0.182121     0.248525      0.173782  \n",
      "2378     0.174132     0.341568     0.477158     0.387582      0.051408  \n",
      "...           ...          ...          ...          ...           ...  \n",
      "6139     0.399501     0.445064     0.317884     0.343866      0.275978  \n",
      "6498     0.702644     0.704102     0.534871     0.583006      0.506783  \n",
      "6692     0.454916     0.487245     0.323645     0.389086      0.289931  \n",
      "6836     0.231661     0.211578     0.117225     0.118053      0.149268  \n",
      "6910     0.307347     0.359334     0.229409     0.242680      0.174469  \n",
      "7016     0.488929     0.658788     0.714978     0.900258      0.721040  \n",
      "7390     0.208700     0.195208     0.091698     0.077095      0.085233  \n",
      "7429     0.456750     0.438407     0.321895     0.326158      0.291024  \n",
      "7510     0.419936     0.363390     0.267583     0.329616      0.302703  \n",
      "7641     0.523947     0.518014     0.313510     0.378370      0.366901  \n",
      "7731     0.321644     0.323055     0.229605     0.235964      0.189870  \n",
      "7769     0.110387     0.086963     0.005197     0.001341      0.024274  \n",
      "7793     0.404188     0.403620     0.304141     0.367545      0.342598  \n",
      "7800     0.302936     0.310169     0.211287     0.162768      0.181822  \n",
      "7866     0.186302     0.145671     0.074715     0.038746      0.080651  \n",
      "8236     0.329378     0.297209     0.238488     0.248535      0.230899  \n",
      "8243     0.267454     0.243695     0.169684     0.136866      0.199211  \n",
      "8317     0.241801     0.232677     0.121288     0.137328      0.160988  \n",
      "9052     0.225814     0.395066     0.298317     0.307111      0.226268  \n",
      "9134     0.294498     0.294040     0.212108     0.303130      0.294566  \n",
      "9484     0.437206     0.643460     0.457206     0.492139      0.459968  \n",
      "9609     0.240246     0.280799     0.195267     0.161979      0.163218  \n",
      "9647     0.911494     0.946515     0.698748     1.000000      1.000000  \n",
      "9729     0.521295     0.225937     0.284902     0.297172      0.285073  \n",
      "9912     0.131362     0.112014     0.035487     0.061325      0.099684  \n",
      "9922     0.297783     0.656228     0.549342     0.576069      0.520165  \n",
      "9932     0.158422     0.194356     0.005245     0.062453      0.076385  \n",
      "9933     0.263300     0.258165     0.161936     0.157895      0.207726  \n",
      "9971     0.234405     0.270168     0.165000     0.157749      0.000000  \n",
      "9982     0.240191     0.298131     0.134802     0.164150      0.160963  \n",
      "\n",
      "[95 rows x 12 columns]\n",
      "Left factor Y:\n",
      "[[  1.26316302e+00   1.82612618e-01   1.15404330e+00   2.65924437e-01\n",
      "    1.67267532e+00]\n",
      " [  1.78110885e+00   2.30485773e-01   1.84098465e-01   8.29096242e-02\n",
      "    1.44146150e+00]\n",
      " [  2.78108063e-01   1.25487783e-01   6.88696759e-02   9.55551481e-06\n",
      "    1.51658624e-01]\n",
      " [  2.38592140e-06   2.98153114e-01   5.81398946e-01   2.41890949e-01\n",
      "    3.60894226e-01]\n",
      " [  4.57077824e+00   6.38968769e-01   1.59939592e+00   8.62289586e-01\n",
      "    9.17765969e-01]\n",
      " [  7.76505742e-01   1.85292956e-01   1.30448835e+00   2.64523363e-01\n",
      "    1.20388178e+00]\n",
      " [  1.04422332e+00   5.72689806e-01   1.19403718e+00   4.54645132e-01\n",
      "    1.73303992e+00]\n",
      " [  4.23748851e-01   2.56966282e-01   1.51094777e-01   1.12216175e-05\n",
      "    7.34482727e-01]\n",
      " [  1.25685047e+00   1.47575865e-01   1.43504420e+00   2.08667412e-01\n",
      "    2.10960863e+00]\n",
      " [  6.68107874e-01   9.59378786e-02   5.08244678e-01   2.19576114e-02\n",
      "    1.05772868e+00]\n",
      " [ -1.74391455e-06   2.76858862e-01   8.29318855e-01   2.20035409e-01\n",
      "    8.62540644e-01]\n",
      " [  9.06922536e-01   3.57201398e-05   4.48809120e-01   7.97457209e-06\n",
      "    1.08649387e+00]\n",
      " [ -3.00205861e-05   5.87062428e-02   1.17437908e+00   1.76013327e+00\n",
      "    3.10017048e+00]\n",
      " [  6.26234349e-05   6.92228605e-02   8.73823792e-01   2.86601338e-01\n",
      "   -4.91837269e-05]\n",
      " [  3.72691070e-01   1.50759076e-05   6.80400517e-01   3.44758725e-02\n",
      "    1.32825581e+00]\n",
      " [  3.05371765e-01   8.60382837e-02   8.67893552e-01   2.43401030e-01\n",
      "    8.20171688e-01]\n",
      " [  2.61404407e-01   1.93819379e-01   5.90155762e-01   3.15155739e-05\n",
      "    2.79114706e+00]\n",
      " [  8.26706984e-03   1.57333728e-05   4.76811280e-01   5.57498759e-06\n",
      "    5.31385905e-06]\n",
      " [  1.42228461e+00   2.20893771e-01   5.41205154e-01   4.48538392e-01\n",
      "    9.63524528e-01]\n",
      " [  1.77212299e+00   3.90288426e-01   1.75799199e+00   1.23908596e+00\n",
      "    8.36007531e-01]\n",
      " [  2.75666458e+00   1.85824364e-01   4.59111764e-01   1.44495895e-05\n",
      "    1.04482809e+00]\n",
      " [  3.19169902e+00   5.62273124e-01   7.58398569e-01   1.54305746e-01\n",
      "    1.95375137e+00]\n",
      " [  8.81147159e-01   4.45053793e-01   1.34910918e+00   1.52106921e-01\n",
      "    7.39051099e-06]\n",
      " [  3.02132916e-01   1.04447801e-01   6.16886907e-01   1.02935894e-05\n",
      "    2.03994444e+00]\n",
      " [  1.23614148e+00   4.66613329e-01   1.09202074e+00   5.85231750e-01\n",
      "    1.01274145e+00]\n",
      " [  1.11106133e-01   2.73065555e-01   9.28931380e-01   8.76929072e-01\n",
      "    3.75709541e-06]\n",
      " [ -7.27224931e-06   6.48965823e-01   1.23392451e+00   1.07173061e+00\n",
      "    1.81740396e+00]\n",
      " [  3.00056799e+00   5.91552280e-01   8.96223210e-01   4.74837168e-01\n",
      "    4.98959765e-01]\n",
      " [  1.50841527e+00   3.55801743e-03   2.86463613e-01   1.55770598e-05\n",
      "    5.00085793e-01]\n",
      " [  8.08189238e-02  -3.92137677e-04  -2.54785987e-04   1.51244230e+00\n",
      "    2.45585364e+00]\n",
      " [  4.89411905e-01   3.14476061e-01   5.90080117e-01   1.60549465e-01\n",
      "    8.53722735e-01]\n",
      " [  1.51003779e+00   2.57331911e-01   3.86479282e-01   6.71764184e-06\n",
      "    6.93498854e-01]\n",
      " [  1.01427758e+00   3.56786560e-01   9.60667773e-01   4.40156448e-01\n",
      "    1.36161063e+00]\n",
      " [ -1.16846158e-05   1.12612528e-01   1.06781923e-01  -1.50592350e-05\n",
      "    6.48594924e-01]\n",
      " [  1.41511728e-01   8.43452579e-02   4.14386189e-01   9.79153594e-06\n",
      "    5.70690920e-01]\n",
      " [  8.61720158e-01   3.59695605e-01   5.57910829e-01   2.27770593e-01\n",
      "    3.80241225e-01]\n",
      " [  9.23499876e-01   1.05270354e-01   7.38442915e-01   5.33589103e-02\n",
      "    1.10184388e+00]\n",
      " [  1.34972958e+00   5.21585740e-02   1.71579425e+00   7.74658623e-01\n",
      "    1.53785463e+00]\n",
      " [  1.20374407e-01   3.58065038e-05   7.95382329e-01   1.77212827e-01\n",
      "    1.25573923e+00]\n",
      " [  4.70441715e-01   3.70005509e-01   4.15224962e-01   7.05674069e-02\n",
      "    1.23831156e-01]\n",
      " [  9.54098746e-02   4.18859046e-01   7.64957728e-01   2.62448327e-01\n",
      "    1.18438512e+00]\n",
      " [  7.87920150e-01   2.47430541e-01   1.25008305e+00   5.11530063e-01\n",
      "    2.49523158e+00]\n",
      " [  7.21278298e-01   1.27610299e-01   1.20433267e+00   2.55074453e-01\n",
      "    1.28101227e+00]\n",
      " [  9.00532821e-01   3.42973148e-01   3.85275955e-01   2.71535741e-02\n",
      "    2.92196215e-01]\n",
      " [  5.22322205e-01   5.50659947e-02   8.93760082e-01   3.67164713e-01\n",
      "    7.47556999e-01]\n",
      " [  1.32964525e+00   3.09428737e-01   2.07263184e-01   1.55789526e-01\n",
      "    9.43911054e-01]\n",
      " [  7.09895998e-01   6.30872586e-01   8.82319564e-01   4.33779488e-01\n",
      "    7.82616759e-01]\n",
      " [ -7.61855924e-07   4.88510937e-01   7.13782543e-01   4.74340133e-01\n",
      "    6.09530730e-01]\n",
      " [  8.82171165e-02   2.30704758e-05   5.93018586e-01   2.96817392e-02\n",
      "    8.62306683e-01]\n",
      " [  3.77522139e-01   3.46795751e-01   2.05730789e-01   7.57057133e-06\n",
      "    1.91385048e-01]\n",
      " [  1.05359894e-01   4.15795937e-01   8.51532945e-01   3.09223638e-01\n",
      "    1.17096106e+00]\n",
      " [  2.08836657e-01   3.08687509e-05   2.50254023e-01   2.26456235e+00\n",
      "    5.47794145e-01]\n",
      " [  9.44850748e-01   3.33146625e-01   1.31199461e+00   6.48730988e-01\n",
      "    2.63638081e+00]\n",
      " [  1.05681086e+00   1.89476894e-01   1.44621414e+00   8.24803440e-02\n",
      "    1.30384967e+00]\n",
      " [  2.22759373e+00   1.22672622e-01   5.65359006e-01   1.51301460e-05\n",
      "    1.12531745e+00]\n",
      " [  5.40159197e+00   3.19590005e-01   5.60038358e-01   2.41910161e-01\n",
      "    1.19254505e+00]\n",
      " [  1.20105334e+00   3.65475575e-01   1.04427440e+00   7.14766754e-01\n",
      "    2.74998580e+00]\n",
      " [  6.85986042e-01   2.21434507e+00   8.22224109e-01   8.86037559e-01\n",
      "    1.67521995e-01]\n",
      " [  5.19024044e-01  -6.18398108e-06   6.15966864e-01   2.00930255e-01\n",
      "    8.87795355e-02]\n",
      " [  1.45322014e+00   1.15515877e+00   2.44758772e+00   2.11749465e+00\n",
      "    7.23761168e-02]\n",
      " [  2.85455157e-01   4.37322501e-01   8.58726370e-01   6.24489462e-01\n",
      "    8.68462335e-01]\n",
      " [  1.60926648e-01   4.20644358e-01   1.26771710e+00   8.37890305e-01\n",
      "    9.00655686e-01]\n",
      " [  6.24751331e-06   3.31336382e-01   6.28469990e-01   2.04361258e-01\n",
      "    6.20860369e-01]\n",
      " [  5.00050582e-01   1.17886424e-01   9.53242471e-01   1.45548153e-01\n",
      "    1.71677206e+00]\n",
      " [ -3.97521891e-07   3.16084469e-01   5.24840445e-01   1.27171395e-01\n",
      "    9.49745334e-01]\n",
      " [  1.76834476e+00   1.94694735e-01   5.91913979e-01   1.09526576e-01\n",
      "    1.70025831e+00]\n",
      " [  4.61219838e+00   4.19738503e-01   2.02696742e-01   3.19519263e-05\n",
      "    8.11294493e-01]\n",
      " [  5.24499457e-01   4.95976140e-01   1.11140926e+00   6.81272590e-01\n",
      "    1.43047881e+00]\n",
      " [  7.33708875e-01   1.34246356e-01   3.65103843e-01   1.75608250e-05\n",
      "    5.82486928e-01]\n",
      " [  9.58812366e-01   3.27781113e-01   4.15063855e-01   3.05460905e-01\n",
      "    8.08431314e-01]\n",
      " [  6.32220051e+00  -4.49220048e-03  -2.75883636e-03   2.15487481e-01\n",
      "   -6.71070665e-04]\n",
      " [  2.70318035e-01   2.28721347e-01   3.38862897e-01   1.45609796e-05\n",
      "    7.47923308e-01]\n",
      " [  2.16624790e-01   4.31493720e-01   1.39627362e+00   6.48169639e-01\n",
      "    1.21676561e+00]\n",
      " [  2.92571584e+00   1.56594931e-01   7.28010768e-03   2.24366586e-05\n",
      "    1.63304481e-01]\n",
      " [  1.16764301e+00   4.96518740e-01   1.17232722e+00   5.44860436e-01\n",
      "    8.94145002e-01]\n",
      " [  2.93040308e-01   1.46471070e-01   1.05884832e+00   2.33647846e-01\n",
      "    1.57899186e+00]\n",
      " [ -3.32092371e-06   1.62149309e-01   1.78848005e-01  -1.40224680e-05\n",
      "    3.49940124e-01]\n",
      " [  2.06096754e+00   1.86622268e-01   6.22297921e-01   1.26636466e-01\n",
      "    9.02821112e-01]\n",
      " [  1.49455694e-01   2.54118229e-01   9.30459181e-01   3.10981121e-01\n",
      "    1.07373564e+00]\n",
      " [  6.21107609e-06   2.64455730e-01   5.27726076e-01   9.95531865e-02\n",
      "    4.22936081e-01]\n",
      " [  6.96388084e-01   3.48170721e-02   1.04201424e+00   2.36296760e-01\n",
      "    1.32063250e+00]\n",
      " [  7.21257537e-01   2.55844297e-02   7.10421606e-01   1.75150253e-05\n",
      "    1.16719719e+00]\n",
      " [  3.44558703e-01   1.90184095e-01   6.62926271e-01   2.11680207e-01\n",
      "    4.87604403e-01]\n",
      " [  1.73112952e-01   4.91153625e-05   8.60006981e-01   5.82851344e-01\n",
      "    2.44814294e+00]\n",
      " [  1.36645407e+00   3.18684404e-05   6.79963134e-01   6.56644324e-02\n",
      "    1.31727785e+00]\n",
      " [  5.43636161e-01   4.46867425e-01   1.09206191e+00   1.69589942e+00\n",
      "    1.29222288e+00]\n",
      " [  5.99490973e-01   1.61797909e-01   4.84228105e-01   7.80300257e-02\n",
      "    1.42416033e+00]\n",
      " [  6.51497664e+00   1.81586923e-01   1.01403931e+00   9.77898774e-01\n",
      "    1.75974570e-05]\n",
      " [  1.01635076e+00   8.22301730e-02   1.74656410e+00   1.56137145e-05\n",
      "    7.51398885e-01]\n",
      " [  1.36658299e-01   1.56431828e-05   5.02802215e-01   9.65399270e-02\n",
      "    2.63307067e-01]\n",
      " [  2.76765560e+00   3.84240631e-05   4.04190655e-01   5.47251029e-01\n",
      "    2.14337379e+00]\n",
      " [  2.45061111e-01   3.51367036e-01   8.14447122e-02   8.46545824e-06\n",
      "    2.99730223e-01]\n",
      " [  5.16101206e-01   3.11531365e-01   4.86091095e-01   3.04925063e-01\n",
      "    4.28882856e-01]\n",
      " [  2.26969048e-06   4.65673443e-01   2.06492413e-01   2.41265796e-05\n",
      "    2.20984261e+00]\n",
      " [  3.60978507e-01   3.15185062e-01   4.73000219e-01   1.84689733e-01\n",
      "    9.77911277e-01]]\n",
      "Right factor X:\n",
      "[[ -1.28499234e-03  -7.70564791e-04  -1.12626668e-03  -3.32479685e-04\n",
      "   -1.68023082e-04   3.48960602e-03   9.19950368e-02   9.81737847e-02\n",
      "    1.06553522e-01   9.98926155e-02   1.14639003e-01   1.04679199e-01]\n",
      " [  2.00039032e-01   3.40702789e-01   3.33205326e-01   1.85932553e-01\n",
      "    1.30429503e-01   8.73565846e-02   1.20194868e-01   2.83441136e-01\n",
      "    3.06045576e-01   9.53299393e-02   5.83442953e-02   2.69641269e-02]\n",
      " [  1.43034074e-01   2.41435782e-01   1.17212662e-01   1.67333268e-01\n",
      "    2.06610009e-01   2.63978519e-01   7.63891896e-02   2.04353581e-01\n",
      "    7.52729199e-02   3.27594565e-02   6.25736169e-02   1.19359255e-01]\n",
      " [  1.97512580e-01   9.29639588e-06   9.77243333e-02   1.47261528e-01\n",
      "    1.64790600e-01   1.33495876e-01   1.78685875e-01   3.99888910e-06\n",
      "    1.56162361e-01   1.51377226e-01   1.86903195e-01   1.35539321e-01]\n",
      " [ -1.46846724e-04   2.81348149e-02   8.28373123e-02   1.42709114e-01\n",
      "    8.94919148e-02  -1.14495240e-05  -2.04202712e-04   3.01511012e-02\n",
      "    7.74672591e-02   6.78554283e-02   4.23135892e-02   7.38000378e-06]]\n",
      "Residual A - Y * X:\n",
      "        hvac_5    hvac_6    hvac_7    hvac_8    hvac_9   hvac_10  aggregate_5  \\\n",
      "26         NaN       NaN       NaN       NaN       NaN       NaN    -0.009322   \n",
      "59   -0.002646 -0.020725 -0.012621  0.083520 -0.059251 -0.002795     0.094779   \n",
      "94   -0.015742 -0.016988 -0.007349  0.017163 -0.005444 -0.001862    -0.002686   \n",
      "101   0.021464 -0.018163 -0.007524  0.015886 -0.001040 -0.000071    -0.008419   \n",
      "222   0.013143  0.020493 -0.051931 -0.025973 -0.008220  0.054263     0.016951   \n",
      "364  -0.012283 -0.026136  0.003249 -0.006164  0.002605  0.027864     0.005538   \n",
      "545   0.016245  0.029755 -0.019902 -0.013701  0.004243 -0.007160    -0.030756   \n",
      "624   0.005832 -0.007793 -0.023158  0.025252  0.017277 -0.048573     0.016766   \n",
      "661  -0.028833  0.012378  0.028444 -0.020845 -0.006748  0.026462    -0.013111   \n",
      "871  -0.004232 -0.018798  0.004989  0.015253 -0.008663  0.004343     0.016482   \n",
      "946   0.023590  0.002642 -0.001698  0.019217 -0.015103  0.004014    -0.012224   \n",
      "1169 -0.042631 -0.011238  0.008372  0.003843 -0.010901  0.012505    -0.046727   \n",
      "1283  0.045130 -0.011901  0.022711 -0.089174  0.116715 -0.039255    -0.084328   \n",
      "1310  0.062432 -0.018966  0.001575 -0.011007 -0.028402  0.030336    -0.005402   \n",
      "1334 -0.057375 -0.041177  0.019834 -0.012264  0.024249  0.048138    -0.007623   \n",
      "1415  0.008408 -0.007314 -0.001477  0.017522 -0.015514 -0.002756     0.000311   \n",
      "1463 -0.081786  0.063040  0.001750 -0.023220  0.015922 -0.018373    -0.026116   \n",
      "1500  0.026649 -0.003529 -0.033400  0.028094 -0.000039 -0.038452     0.032423   \n",
      "1642 -0.032623 -0.061821  0.032907 -0.038230  0.032451  0.047684    -0.016235   \n",
      "1697  0.022051  0.009965 -0.002472  0.006393 -0.022844 -0.001770    -0.036302   \n",
      "1700  0.029311 -0.024887 -0.029765 -0.043875  0.041191  0.012153    -0.008272   \n",
      "1790 -0.013340 -0.004104 -0.003058 -0.024573  0.010798  0.029761    -0.024474   \n",
      "1800 -0.025241 -0.023866  0.057087 -0.100219  0.048360  0.040575    -0.051189   \n",
      "1953 -0.021491 -0.010190  0.018623 -0.001808 -0.016161  0.024267    -0.020218   \n",
      "2129  0.012127 -0.002335 -0.007970  0.012185 -0.002394 -0.013431     0.005893   \n",
      "2156 -0.000739 -0.022068 -0.004897 -0.004935  0.011214  0.005066     0.036825   \n",
      "2233  0.028232  0.009161 -0.000968  0.009668 -0.015691  0.008520    -0.019854   \n",
      "2242 -0.012147 -0.046548 -0.004256 -0.035926  0.014134  0.067491    -0.014258   \n",
      "2365 -0.018051  0.019316  0.001934 -0.000911  0.010675 -0.033344    -0.001061   \n",
      "2378  0.130066 -0.068852 -0.087463  0.087355 -0.038375 -0.150243     0.130489   \n",
      "...        ...       ...       ...       ...       ...       ...          ...   \n",
      "6139 -0.024268 -0.011061  0.018171 -0.000446  0.006280  0.006152     0.027488   \n",
      "6498 -0.030715  0.006610 -0.039550  0.017741  0.008037 -0.025321    -0.011707   \n",
      "6692  0.004449  0.028825 -0.004161 -0.004014  0.011538 -0.028148    -0.001679   \n",
      "6836 -0.032430 -0.008906  0.006119  0.000258 -0.004834  0.004487    -0.034830   \n",
      "6910 -0.003210 -0.014300 -0.014568  0.010525 -0.004695  0.014495     0.016690   \n",
      "7016 -0.019602  0.010187 -0.012062 -0.028238 -0.033232 -0.025730    -0.066214   \n",
      "7390 -0.028814 -0.007405 -0.001034  0.011940 -0.011769  0.006094    -0.009055   \n",
      "7429  0.022726  0.026280 -0.013844  0.015041 -0.033937 -0.002124    -0.028203   \n",
      "7510 -0.019021 -0.034187 -0.013541  0.029615  0.005822 -0.025812     0.016859   \n",
      "7641  0.000722  0.000081 -0.000830  0.005578  0.015086 -0.024662     0.011611   \n",
      "7731 -0.000517  0.011576 -0.000348 -0.008352 -0.008194  0.012172    -0.024829   \n",
      "7769  0.002017 -0.003366 -0.001977  0.023819  0.008200 -0.015434    -0.007007   \n",
      "7793  0.011305  0.008101  0.008048  0.014008 -0.016018 -0.016876    -0.018924   \n",
      "7800 -0.002671 -0.009396 -0.001019  0.021130 -0.042238  0.033769    -0.003664   \n",
      "7866  0.037536 -0.002514 -0.006690  0.050764 -0.019953 -0.012418     0.028741   \n",
      "8236 -0.001883  0.000625  0.006599 -0.000308 -0.005993  0.004170    -0.001390   \n",
      "8243 -0.037645  0.004678  0.004142  0.022260 -0.032046  0.010878    -0.012262   \n",
      "8317 -0.002125 -0.018210  0.002943  0.009815 -0.007914  0.008881     0.000320   \n",
      "9052 -0.048503 -0.006919  0.039646 -0.034845 -0.001190  0.058338    -0.049813   \n",
      "9134 -0.014593  0.000313  0.038097  0.001109 -0.000137 -0.014209    -0.026954   \n",
      "9484 -0.011318 -0.003717  0.002559  0.021207 -0.002510 -0.012862     0.035498   \n",
      "9609  0.001449 -0.005405  0.003040  0.022090 -0.028134  0.007404    -0.003464   \n",
      "9647  0.011435 -0.002738  0.008784  0.036496 -0.009113 -0.068619     0.126630   \n",
      "9729  0.041391  0.090640 -0.066945  0.044016 -0.026263 -0.076481     0.016198   \n",
      "9912 -0.011817 -0.033310  0.006482  0.001442  0.006465  0.017623    -0.002548   \n",
      "9922 -0.035906  0.064334 -0.004961 -0.042878 -0.018554  0.063317    -0.172719   \n",
      "9932 -0.042265 -0.019842  0.024372 -0.021360  0.046748 -0.014270     0.005312   \n",
      "9933  0.030291 -0.011221 -0.004711  0.037241 -0.027454 -0.023367    -0.010243   \n",
      "9971  0.060990  0.049090 -0.026582 -0.002502  0.082532 -0.093536     0.006167   \n",
      "9982 -0.022671 -0.018149  0.032462 -0.010296  0.007415  0.009430    -0.007375   \n",
      "\n",
      "      aggregate_6  aggregate_7  aggregate_8  aggregate_9  aggregate_10  \n",
      "26      -0.010655     0.014420     0.007201    -0.029914      0.028935  \n",
      "59       0.016273    -0.024645     0.007535    -0.096017      0.024424  \n",
      "94       0.027825     0.017678    -0.028746    -0.026856      0.014822  \n",
      "101      0.006191     0.013508    -0.028938    -0.007284     -0.003884  \n",
      "222     -0.007887    -0.008731     0.237298    -0.165799     -0.045666  \n",
      "364      0.009709     0.023631    -0.010842    -0.006526     -0.021793  \n",
      "545     -0.010026    -0.004982     0.029988     0.024461     -0.013507  \n",
      "624      0.043113    -0.011395    -0.033422    -0.027376      0.019795  \n",
      "661     -0.028229     0.007787     0.006932     0.015214      0.005867  \n",
      "871      0.008691     0.005271    -0.019832    -0.014377      0.006417  \n",
      "946     -0.015131    -0.000392    -0.002862    -0.015202      0.001100  \n",
      "1169     0.030830     0.015948    -0.022313    -0.014598      0.032254  \n",
      "1283     0.010262    -0.000757    -0.037176     0.070779     -0.032526  \n",
      "1310    -0.008465     0.014836    -0.029624    -0.033468     -0.006243  \n",
      "1334    -0.014837     0.022006    -0.031406    -0.000971      0.026845  \n",
      "1415     0.004721    -0.000927    -0.004560    -0.012873      0.014844  \n",
      "1463     0.013794    -0.010626    -0.007853     0.021064      0.005294  \n",
      "1500     0.040049    -0.036778    -0.016449    -0.006519     -0.004470  \n",
      "1642     0.009400     0.065335    -0.046742    -0.014565     -0.002668  \n",
      "1697    -0.000986    -0.010562     0.015184     0.020522      0.006958  \n",
      "1700     0.064130    -0.030463     0.119711    -0.046160     -0.086187  \n",
      "1790    -0.007163     0.035839    -0.014072     0.030627     -0.029665  \n",
      "1800    -0.020742     0.058829    -0.063245     0.044521      0.014680  \n",
      "1953    -0.003282     0.020342    -0.010664    -0.007400      0.017437  \n",
      "2129     0.011072    -0.010076    -0.006608     0.002315     -0.001019  \n",
      "2156     0.020462     0.005773    -0.028490    -0.004962     -0.025205  \n",
      "2233    -0.012307    -0.014540     0.020380    -0.000932     -0.018825  \n",
      "2242     0.029528     0.040384     0.008586     0.021709     -0.091136  \n",
      "2365     0.040118    -0.044525    -0.012218     0.036306     -0.018411  \n",
      "2378     0.092308    -0.093339     0.073538    -0.008241     -0.162025  \n",
      "...           ...          ...          ...          ...           ...  \n",
      "6139    -0.001513     0.003682    -0.028663     0.000332      0.000111  \n",
      "6498     0.064993     0.006086    -0.027563    -0.017239     -0.011540  \n",
      "6692    -0.007410    -0.021297    -0.012634     0.042615     -0.003354  \n",
      "6836     0.029406     0.019704    -0.020353    -0.021387      0.025259  \n",
      "6910     0.011114     0.015282    -0.012310    -0.003633     -0.025687  \n",
      "7016    -0.129889    -0.046881     0.051382     0.135675      0.030481  \n",
      "7390     0.025534     0.012957    -0.018963    -0.020092      0.010315  \n",
      "7429    -0.008842    -0.017313     0.032698     0.016148      0.002194  \n",
      "7510     0.081910    -0.009482    -0.050926    -0.022291     -0.008655  \n",
      "7641     0.002050    -0.000958    -0.032019     0.002516      0.017501  \n",
      "7731    -0.012630     0.008494     0.009170     0.017087     -0.002819  \n",
      "7769     0.017328    -0.003230    -0.039862    -0.034115     -0.001446  \n",
      "7793    -0.005432    -0.009655    -0.020342     0.019579      0.030377  \n",
      "7800    -0.006283     0.014691     0.021717    -0.030971      0.006108  \n",
      "7866    -0.009251    -0.023299    -0.011553    -0.046209     -0.002966  \n",
      "8236    -0.001616    -0.005291     0.006087     0.001423      0.000652  \n",
      "8243     0.009025     0.015115    -0.007280    -0.041156      0.038214  \n",
      "8317     0.003894     0.017028    -0.018108    -0.014946      0.011971  \n",
      "9052    -0.040757     0.031200    -0.001504     0.020923      0.026478  \n",
      "9134    -0.018331    -0.015053    -0.045993     0.035919      0.061456  \n",
      "9484    -0.004961     0.001629    -0.019879    -0.036237      0.030793  \n",
      "9609    -0.006362     0.008443    -0.004354    -0.021331      0.027717  \n",
      "9647     0.013198    -0.032294    -0.150613    -0.003690      0.059542  \n",
      "9729     0.018636    -0.097205     0.067332     0.034775     -0.032011  \n",
      "9912     0.007252     0.024127    -0.027118    -0.014990      0.012277  \n",
      "9922    -0.121164     0.079387     0.031348     0.040517      0.108014  \n",
      "9932     0.009091     0.031359    -0.075738    -0.003922      0.031533  \n",
      "9933     0.012065    -0.009601    -0.010501    -0.025002      0.045949  \n",
      "9971    -0.006412    -0.059087    -0.036111     0.024147     -0.037223  \n",
      "9982    -0.010729     0.023005    -0.041113    -0.001117      0.033181  \n",
      "\n",
      "[95 rows x 12 columns]\n",
      "Residual after 30 iterations: 1.12640625307\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Show plot inline in ipython.\n",
    "%matplotlib inline\n",
    "\n",
    "# Set plot properties.\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif')\n",
    "font = {'family' : 'normal',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 16}\n",
    "plt.rc('font', **font)\n",
    "\n",
    "# Create the plot.\n",
    "plt.plot(residual)\n",
    "plt.xlabel('Iteration Number')\n",
    "plt.ylabel('Residual Norm')\n",
    "plt.show()\n",
    "\n",
    "#\n",
    "# Print results.\n",
    "#\n",
    "print 'Original matrix:'\n",
    "print A\n",
    "print 'Left factor Y:'\n",
    "print Y\n",
    "print 'Right factor X:'\n",
    "print X\n",
    "print 'Residual A - Y * X:'\n",
    "print A - Y * X\n",
    "print 'Residual after {} iterations: {}'.format(iter_num, prob.value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pred_df = pd.DataFrame(Y*X)\n",
    "pred_df.columns = X_normalised.columns\n",
    "pred_df.index = X_normalised.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "hvac_5          0.252252\n",
       "hvac_6          0.386934\n",
       "hvac_7          0.359241\n",
       "hvac_8          0.504510\n",
       "hvac_9          0.455555\n",
       "hvac_10         0.360484\n",
       "aggregate_5     0.273486\n",
       "aggregate_6     0.462036\n",
       "aggregate_7     0.448455\n",
       "aggregate_8     0.335150\n",
       "aggregate_9     0.348154\n",
       "aggregate_10    0.310952\n",
       "Name: 26, dtype: float64"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_df.ix[26]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "hvac_5          0.268580\n",
       "hvac_6          0.391562\n",
       "hvac_7          0.354348\n",
       "hvac_8          0.485952\n",
       "hvac_9          0.423089\n",
       "hvac_10         0.445286\n",
       "aggregate_5     0.264163\n",
       "aggregate_6     0.451381\n",
       "aggregate_7     0.462876\n",
       "aggregate_8     0.342351\n",
       "aggregate_9     0.318240\n",
       "aggregate_10    0.339887\n",
       "Name: 26, dtype: float64"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_normalised.ix[26]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "hvac_5           242.395737\n",
       "hvac_6           543.781433\n",
       "hvac_7           761.394043\n",
       "hvac_8           902.418823\n",
       "hvac_9           610.035828\n",
       "hvac_10          395.169098\n",
       "aggregate_5      958.539734\n",
       "aggregate_6     1381.666504\n",
       "aggregate_7     1705.293091\n",
       "aggregate_8     1887.754883\n",
       "aggregate_9     1365.123535\n",
       "aggregate_10    1197.380859\n",
       "Name: 26, dtype: float64"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_matrix.ix[26]"
   ]
  },
  {
   "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}