code/cvx-mf-nuclear.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": [
    "appliance=\"hvac\"\n",
    "if appliance==\"hvac\":\n",
    "    start, end=5, 11\n",
    "else:\n",
    "    start, end = 1, 13\n",
    "\n",
    "appliance_cols = ['%s_%d' %(appliance, month) for month in range(start, end)]\n",
    "aggregate_cols = ['aggregate_%d' %month for month in range(start, end)]\n",
    "\n",
    "all_cols = deepcopy(appliance_cols)\n",
    "all_cols.extend(aggregate_cols)\n",
    "X_matrix = dfc[all_cols].dropna()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<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>26</th>\n",
       "      <td>0.268580</td>\n",
       "      <td>0.391562</td>\n",
       "      <td>0.354348</td>\n",
       "      <td>0.485952</td>\n",
       "      <td>0.423089</td>\n",
       "      <td>0.445286</td>\n",
       "      <td>0.264163</td>\n",
       "      <td>0.451381</td>\n",
       "      <td>0.462876</td>\n",
       "      <td>0.342351</td>\n",
       "      <td>0.318240</td>\n",
       "      <td>0.339887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>0.083667</td>\n",
       "      <td>0.141433</td>\n",
       "      <td>0.211260</td>\n",
       "      <td>0.374507</td>\n",
       "      <td>0.151210</td>\n",
       "      <td>0.083204</td>\n",
       "      <td>0.314919</td>\n",
       "      <td>0.337543</td>\n",
       "      <td>0.374149</td>\n",
       "      <td>0.323820</td>\n",
       "      <td>0.209625</td>\n",
       "      <td>0.250306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.018833</td>\n",
       "      <td>0.046446</td>\n",
       "      <td>0.054788</td>\n",
       "      <td>0.073571</td>\n",
       "      <td>0.038679</td>\n",
       "      <td>0.028250</td>\n",
       "      <td>0.043213</td>\n",
       "      <td>0.109343</td>\n",
       "      <td>0.102650</td>\n",
       "      <td>0.023547</td>\n",
       "      <td>0.023076</td>\n",
       "      <td>0.055540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>0.211989</td>\n",
       "      <td>0.233945</td>\n",
       "      <td>0.213504</td>\n",
       "      <td>0.255734</td>\n",
       "      <td>0.230129</td>\n",
       "      <td>0.211738</td>\n",
       "      <td>0.114979</td>\n",
       "      <td>0.220393</td>\n",
       "      <td>0.214252</td>\n",
       "      <td>0.079637</td>\n",
       "      <td>0.106973</td>\n",
       "      <td>0.106339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>222</th>\n",
       "      <td>0.534035</td>\n",
       "      <td>0.646650</td>\n",
       "      <td>0.503590</td>\n",
       "      <td>0.616900</td>\n",
       "      <td>0.629034</td>\n",
       "      <td>0.663339</td>\n",
       "      <td>0.790309</td>\n",
       "      <td>0.976471</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.695549</td>\n",
       "      <td>0.757812</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       hvac_5    hvac_6    hvac_7    hvac_8    hvac_9   hvac_10  aggregate_5  \\\n",
       "26   0.268580  0.391562  0.354348  0.485952  0.423089  0.445286     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",
       "\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  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(X_normalised).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.DataFrame(X_normalised)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<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>26</th>\n",
       "      <td>0.268580</td>\n",
       "      <td>0.391562</td>\n",
       "      <td>0.354348</td>\n",
       "      <td>0.485952</td>\n",
       "      <td>0.423089</td>\n",
       "      <td>0.445286</td>\n",
       "      <td>0.264163</td>\n",
       "      <td>0.451381</td>\n",
       "      <td>0.462876</td>\n",
       "      <td>0.342351</td>\n",
       "      <td>0.318240</td>\n",
       "      <td>0.339887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>0.083667</td>\n",
       "      <td>0.141433</td>\n",
       "      <td>0.211260</td>\n",
       "      <td>0.374507</td>\n",
       "      <td>0.151210</td>\n",
       "      <td>0.083204</td>\n",
       "      <td>0.314919</td>\n",
       "      <td>0.337543</td>\n",
       "      <td>0.374149</td>\n",
       "      <td>0.323820</td>\n",
       "      <td>0.209625</td>\n",
       "      <td>0.250306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.018833</td>\n",
       "      <td>0.046446</td>\n",
       "      <td>0.054788</td>\n",
       "      <td>0.073571</td>\n",
       "      <td>0.038679</td>\n",
       "      <td>0.028250</td>\n",
       "      <td>0.043213</td>\n",
       "      <td>0.109343</td>\n",
       "      <td>0.102650</td>\n",
       "      <td>0.023547</td>\n",
       "      <td>0.023076</td>\n",
       "      <td>0.055540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>0.211989</td>\n",
       "      <td>0.233945</td>\n",
       "      <td>0.213504</td>\n",
       "      <td>0.255734</td>\n",
       "      <td>0.230129</td>\n",
       "      <td>0.211738</td>\n",
       "      <td>0.114979</td>\n",
       "      <td>0.220393</td>\n",
       "      <td>0.214252</td>\n",
       "      <td>0.079637</td>\n",
       "      <td>0.106973</td>\n",
       "      <td>0.106339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>222</th>\n",
       "      <td>0.534035</td>\n",
       "      <td>0.646650</td>\n",
       "      <td>0.503590</td>\n",
       "      <td>0.616900</td>\n",
       "      <td>0.629034</td>\n",
       "      <td>0.663339</td>\n",
       "      <td>0.790309</td>\n",
       "      <td>0.976471</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.695549</td>\n",
       "      <td>0.757812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>364</th>\n",
       "      <td>0.262441</td>\n",
       "      <td>0.385219</td>\n",
       "      <td>0.342594</td>\n",
       "      <td>0.457073</td>\n",
       "      <td>0.447491</td>\n",
       "      <td>0.426416</td>\n",
       "      <td>0.245914</td>\n",
       "      <td>0.441337</td>\n",
       "      <td>0.395841</td>\n",
       "      <td>0.248856</td>\n",
       "      <td>0.275310</td>\n",
       "      <td>0.256052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>545</th>\n",
       "      <td>0.389795</td>\n",
       "      <td>0.561114</td>\n",
       "      <td>0.497692</td>\n",
       "      <td>0.606508</td>\n",
       "      <td>0.555478</td>\n",
       "      <td>0.422386</td>\n",
       "      <td>0.306238</td>\n",
       "      <td>0.551074</td>\n",
       "      <td>0.576684</td>\n",
       "      <td>0.414428</td>\n",
       "      <td>0.410604</td>\n",
       "      <td>0.315398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>624</th>\n",
       "      <td>0.078196</td>\n",
       "      <td>0.136574</td>\n",
       "      <td>0.140541</td>\n",
       "      <td>0.202991</td>\n",
       "      <td>0.147672</td>\n",
       "      <td>0.015232</td>\n",
       "      <td>0.098029</td>\n",
       "      <td>0.210571</td>\n",
       "      <td>0.180674</td>\n",
       "      <td>0.088194</td>\n",
       "      <td>0.076730</td>\n",
       "      <td>0.089123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>661</th>\n",
       "      <td>0.245238</td>\n",
       "      <td>0.467515</td>\n",
       "      <td>0.439553</td>\n",
       "      <td>0.578096</td>\n",
       "      <td>0.531963</td>\n",
       "      <td>0.450393</td>\n",
       "      <td>0.266728</td>\n",
       "      <td>0.493854</td>\n",
       "      <td>0.490906</td>\n",
       "      <td>0.368298</td>\n",
       "      <td>0.385970</td>\n",
       "      <td>0.340996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>871</th>\n",
       "      <td>0.090979</td>\n",
       "      <td>0.165842</td>\n",
       "      <td>0.185541</td>\n",
       "      <td>0.272096</td>\n",
       "      <td>0.207023</td>\n",
       "      <td>0.152141</td>\n",
       "      <td>0.132008</td>\n",
       "      <td>0.237228</td>\n",
       "      <td>0.229447</td>\n",
       "      <td>0.147799</td>\n",
       "      <td>0.148474</td>\n",
       "      <td>0.142589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>946</th>\n",
       "      <td>0.240927</td>\n",
       "      <td>0.321466</td>\n",
       "      <td>0.280712</td>\n",
       "      <td>0.364962</td>\n",
       "      <td>0.305803</td>\n",
       "      <td>0.276486</td>\n",
       "      <td>0.123545</td>\n",
       "      <td>0.258824</td>\n",
       "      <td>0.247945</td>\n",
       "      <td>0.142535</td>\n",
       "      <td>0.130467</td>\n",
       "      <td>0.137382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1169</th>\n",
       "      <td>0.020248</td>\n",
       "      <td>0.127003</td>\n",
       "      <td>0.149972</td>\n",
       "      <td>0.233702</td>\n",
       "      <td>0.178913</td>\n",
       "      <td>0.134137</td>\n",
       "      <td>0.070773</td>\n",
       "      <td>0.244351</td>\n",
       "      <td>0.230547</td>\n",
       "      <td>0.156714</td>\n",
       "      <td>0.163431</td>\n",
       "      <td>0.180769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1283</th>\n",
       "      <td>0.572043</td>\n",
       "      <td>0.378876</td>\n",
       "      <td>0.608742</td>\n",
       "      <td>0.819876</td>\n",
       "      <td>0.934504</td>\n",
       "      <td>0.510819</td>\n",
       "      <td>0.326314</td>\n",
       "      <td>0.360368</td>\n",
       "      <td>0.620634</td>\n",
       "      <td>0.483697</td>\n",
       "      <td>0.607840</td>\n",
       "      <td>0.347817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1310</th>\n",
       "      <td>0.257873</td>\n",
       "      <td>0.215592</td>\n",
       "      <td>0.155067</td>\n",
       "      <td>0.190282</td>\n",
       "      <td>0.208393</td>\n",
       "      <td>0.305314</td>\n",
       "      <td>0.120886</td>\n",
       "      <td>0.189730</td>\n",
       "      <td>0.146556</td>\n",
       "      <td>0.048989</td>\n",
       "      <td>0.078821</td>\n",
       "      <td>0.138775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1334</th>\n",
       "      <td>0.046084</td>\n",
       "      <td>0.160185</td>\n",
       "      <td>0.212569</td>\n",
       "      <td>0.296099</td>\n",
       "      <td>0.289316</td>\n",
       "      <td>0.233638</td>\n",
       "      <td>0.084529</td>\n",
       "      <td>0.200846</td>\n",
       "      <td>0.221218</td>\n",
       "      <td>0.123463</td>\n",
       "      <td>0.146976</td>\n",
       "      <td>0.151753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1415</th>\n",
       "      <td>0.197319</td>\n",
       "      <td>0.254382</td>\n",
       "      <td>0.220302</td>\n",
       "      <td>0.331535</td>\n",
       "      <td>0.288481</td>\n",
       "      <td>0.267414</td>\n",
       "      <td>0.148367</td>\n",
       "      <td>0.261174</td>\n",
       "      <td>0.224819</td>\n",
       "      <td>0.155077</td>\n",
       "      <td>0.161658</td>\n",
       "      <td>0.185718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1463</th>\n",
       "      <td>0.040658</td>\n",
       "      <td>0.349886</td>\n",
       "      <td>0.366425</td>\n",
       "      <td>0.509810</td>\n",
       "      <td>0.412880</td>\n",
       "      <td>0.155231</td>\n",
       "      <td>0.065746</td>\n",
       "      <td>0.299150</td>\n",
       "      <td>0.337196</td>\n",
       "      <td>0.245469</td>\n",
       "      <td>0.217377</td>\n",
       "      <td>0.108349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1500</th>\n",
       "      <td>0.094843</td>\n",
       "      <td>0.111589</td>\n",
       "      <td>0.022485</td>\n",
       "      <td>0.107882</td>\n",
       "      <td>0.098477</td>\n",
       "      <td>0.087447</td>\n",
       "      <td>0.069610</td>\n",
       "      <td>0.138303</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.024267</td>\n",
       "      <td>0.053308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1642</th>\n",
       "      <td>0.175598</td>\n",
       "      <td>0.170121</td>\n",
       "      <td>0.291993</td>\n",
       "      <td>0.296486</td>\n",
       "      <td>0.332984</td>\n",
       "      <td>0.274678</td>\n",
       "      <td>0.262452</td>\n",
       "      <td>0.351292</td>\n",
       "      <td>0.469912</td>\n",
       "      <td>0.267400</td>\n",
       "      <td>0.319841</td>\n",
       "      <td>0.277571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1697</th>\n",
       "      <td>0.593912</td>\n",
       "      <td>0.589546</td>\n",
       "      <td>0.521979</td>\n",
       "      <td>0.674317</td>\n",
       "      <td>0.669988</td>\n",
       "      <td>0.667983</td>\n",
       "      <td>0.529163</td>\n",
       "      <td>0.668077</td>\n",
       "      <td>0.688301</td>\n",
       "      <td>0.531300</td>\n",
       "      <td>0.623415</td>\n",
       "      <td>0.580770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1700</th>\n",
       "      <td>0.128459</td>\n",
       "      <td>0.176542</td>\n",
       "      <td>0.169414</td>\n",
       "      <td>0.215692</td>\n",
       "      <td>0.253328</td>\n",
       "      <td>0.159192</td>\n",
       "      <td>0.302523</td>\n",
       "      <td>0.512757</td>\n",
       "      <td>0.435641</td>\n",
       "      <td>0.498735</td>\n",
       "      <td>0.353644</td>\n",
       "      <td>0.262197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1790</th>\n",
       "      <td>0.233702</td>\n",
       "      <td>0.423079</td>\n",
       "      <td>0.446517</td>\n",
       "      <td>0.507357</td>\n",
       "      <td>0.440564</td>\n",
       "      <td>0.310795</td>\n",
       "      <td>0.421835</td>\n",
       "      <td>0.679439</td>\n",
       "      <td>0.780542</td>\n",
       "      <td>0.539133</td>\n",
       "      <td>0.588292</td>\n",
       "      <td>0.431051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1800</th>\n",
       "      <td>0.285667</td>\n",
       "      <td>0.452811</td>\n",
       "      <td>0.377387</td>\n",
       "      <td>0.230390</td>\n",
       "      <td>0.410066</td>\n",
       "      <td>0.458969</td>\n",
       "      <td>0.213602</td>\n",
       "      <td>0.467606</td>\n",
       "      <td>0.414230</td>\n",
       "      <td>0.134424</td>\n",
       "      <td>0.284350</td>\n",
       "      <td>0.300563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1953</th>\n",
       "      <td>0.086953</td>\n",
       "      <td>0.231495</td>\n",
       "      <td>0.294377</td>\n",
       "      <td>0.411857</td>\n",
       "      <td>0.307426</td>\n",
       "      <td>0.197269</td>\n",
       "      <td>0.066840</td>\n",
       "      <td>0.243554</td>\n",
       "      <td>0.288967</td>\n",
       "      <td>0.188105</td>\n",
       "      <td>0.158250</td>\n",
       "      <td>0.125528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2129</th>\n",
       "      <td>0.375517</td>\n",
       "      <td>0.447841</td>\n",
       "      <td>0.415199</td>\n",
       "      <td>0.511974</td>\n",
       "      <td>0.470954</td>\n",
       "      <td>0.398028</td>\n",
       "      <td>0.363481</td>\n",
       "      <td>0.518382</td>\n",
       "      <td>0.516489</td>\n",
       "      <td>0.354440</td>\n",
       "      <td>0.391815</td>\n",
       "      <td>0.350633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2156</th>\n",
       "      <td>0.359815</td>\n",
       "      <td>0.295166</td>\n",
       "      <td>0.280545</td>\n",
       "      <td>0.330379</td>\n",
       "      <td>0.383247</td>\n",
       "      <td>0.391592</td>\n",
       "      <td>0.307522</td>\n",
       "      <td>0.298602</td>\n",
       "      <td>0.308049</td>\n",
       "      <td>0.171818</td>\n",
       "      <td>0.245734</td>\n",
       "      <td>0.223524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2233</th>\n",
       "      <td>0.545957</td>\n",
       "      <td>0.579321</td>\n",
       "      <td>0.615186</td>\n",
       "      <td>0.753994</td>\n",
       "      <td>0.663149</td>\n",
       "      <td>0.533992</td>\n",
       "      <td>0.343538</td>\n",
       "      <td>0.478594</td>\n",
       "      <td>0.585107</td>\n",
       "      <td>0.408224</td>\n",
       "      <td>0.391352</td>\n",
       "      <td>0.291228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2242</th>\n",
       "      <td>0.324235</td>\n",
       "      <td>0.383106</td>\n",
       "      <td>0.382257</td>\n",
       "      <td>0.364164</td>\n",
       "      <td>0.398856</td>\n",
       "      <td>0.429605</td>\n",
       "      <td>0.486088</td>\n",
       "      <td>0.689968</td>\n",
       "      <td>0.721414</td>\n",
       "      <td>0.499810</td>\n",
       "      <td>0.566147</td>\n",
       "      <td>0.410247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2365</th>\n",
       "      <td>0.021626</td>\n",
       "      <td>0.102599</td>\n",
       "      <td>0.076425</td>\n",
       "      <td>0.118553</td>\n",
       "      <td>0.114828</td>\n",
       "      <td>0.047847</td>\n",
       "      <td>0.159917</td>\n",
       "      <td>0.262832</td>\n",
       "      <td>0.177596</td>\n",
       "      <td>0.182121</td>\n",
       "      <td>0.248525</td>\n",
       "      <td>0.173782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2378</th>\n",
       "      <td>0.428213</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.263525</td>\n",
       "      <td>0.660409</td>\n",
       "      <td>0.430523</td>\n",
       "      <td>0.051815</td>\n",
       "      <td>0.407608</td>\n",
       "      <td>0.174132</td>\n",
       "      <td>0.341568</td>\n",
       "      <td>0.477158</td>\n",
       "      <td>0.387582</td>\n",
       "      <td>0.051408</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>6139</th>\n",
       "      <td>0.118453</td>\n",
       "      <td>0.244656</td>\n",
       "      <td>0.301981</td>\n",
       "      <td>0.392984</td>\n",
       "      <td>0.323881</td>\n",
       "      <td>0.200185</td>\n",
       "      <td>0.278008</td>\n",
       "      <td>0.399501</td>\n",
       "      <td>0.445064</td>\n",
       "      <td>0.317884</td>\n",
       "      <td>0.343866</td>\n",
       "      <td>0.275978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6498</th>\n",
       "      <td>0.076202</td>\n",
       "      <td>0.217826</td>\n",
       "      <td>0.186081</td>\n",
       "      <td>0.243952</td>\n",
       "      <td>0.176497</td>\n",
       "      <td>0.080943</td>\n",
       "      <td>0.478367</td>\n",
       "      <td>0.702644</td>\n",
       "      <td>0.704102</td>\n",
       "      <td>0.534871</td>\n",
       "      <td>0.583006</td>\n",
       "      <td>0.506783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6692</th>\n",
       "      <td>0.396308</td>\n",
       "      <td>0.505988</td>\n",
       "      <td>0.475855</td>\n",
       "      <td>0.578473</td>\n",
       "      <td>0.546052</td>\n",
       "      <td>0.401328</td>\n",
       "      <td>0.312528</td>\n",
       "      <td>0.454916</td>\n",
       "      <td>0.487245</td>\n",
       "      <td>0.323645</td>\n",
       "      <td>0.389086</td>\n",
       "      <td>0.289931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6836</th>\n",
       "      <td>0.045622</td>\n",
       "      <td>0.140804</td>\n",
       "      <td>0.141072</td>\n",
       "      <td>0.169198</td>\n",
       "      <td>0.140117</td>\n",
       "      <td>0.115150</td>\n",
       "      <td>0.076577</td>\n",
       "      <td>0.231661</td>\n",
       "      <td>0.211578</td>\n",
       "      <td>0.117225</td>\n",
       "      <td>0.118053</td>\n",
       "      <td>0.149268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6910</th>\n",
       "      <td>0.180709</td>\n",
       "      <td>0.219596</td>\n",
       "      <td>0.239040</td>\n",
       "      <td>0.300958</td>\n",
       "      <td>0.246338</td>\n",
       "      <td>0.196811</td>\n",
       "      <td>0.230417</td>\n",
       "      <td>0.307347</td>\n",
       "      <td>0.359334</td>\n",
       "      <td>0.229409</td>\n",
       "      <td>0.242680</td>\n",
       "      <td>0.174469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7016</th>\n",
       "      <td>0.013542</td>\n",
       "      <td>0.003102</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.023978</td>\n",
       "      <td>0.553151</td>\n",
       "      <td>0.488929</td>\n",
       "      <td>0.658788</td>\n",
       "      <td>0.714978</td>\n",
       "      <td>0.900258</td>\n",
       "      <td>0.721040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7390</th>\n",
       "      <td>0.064954</td>\n",
       "      <td>0.173169</td>\n",
       "      <td>0.176549</td>\n",
       "      <td>0.217817</td>\n",
       "      <td>0.154965</td>\n",
       "      <td>0.116463</td>\n",
       "      <td>0.069039</td>\n",
       "      <td>0.208700</td>\n",
       "      <td>0.195208</td>\n",
       "      <td>0.091698</td>\n",
       "      <td>0.077095</td>\n",
       "      <td>0.085233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7429</th>\n",
       "      <td>0.436321</td>\n",
       "      <td>0.544474</td>\n",
       "      <td>0.457485</td>\n",
       "      <td>0.597935</td>\n",
       "      <td>0.526493</td>\n",
       "      <td>0.491426</td>\n",
       "      <td>0.265819</td>\n",
       "      <td>0.456750</td>\n",
       "      <td>0.438407</td>\n",
       "      <td>0.321895</td>\n",
       "      <td>0.326158</td>\n",
       "      <td>0.291024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7510</th>\n",
       "      <td>0.009566</td>\n",
       "      <td>0.023263</td>\n",
       "      <td>0.049726</td>\n",
       "      <td>0.082285</td>\n",
       "      <td>0.041877</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.305359</td>\n",
       "      <td>0.419936</td>\n",
       "      <td>0.363390</td>\n",
       "      <td>0.267583</td>\n",
       "      <td>0.329616</td>\n",
       "      <td>0.302703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7641</th>\n",
       "      <td>0.373713</td>\n",
       "      <td>0.476550</td>\n",
       "      <td>0.428024</td>\n",
       "      <td>0.501517</td>\n",
       "      <td>0.491671</td>\n",
       "      <td>0.404982</td>\n",
       "      <td>0.365437</td>\n",
       "      <td>0.523947</td>\n",
       "      <td>0.518014</td>\n",
       "      <td>0.313510</td>\n",
       "      <td>0.378370</td>\n",
       "      <td>0.366901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7731</th>\n",
       "      <td>0.225774</td>\n",
       "      <td>0.361324</td>\n",
       "      <td>0.325870</td>\n",
       "      <td>0.455709</td>\n",
       "      <td>0.409439</td>\n",
       "      <td>0.336676</td>\n",
       "      <td>0.142046</td>\n",
       "      <td>0.321644</td>\n",
       "      <td>0.323055</td>\n",
       "      <td>0.229605</td>\n",
       "      <td>0.235964</td>\n",
       "      <td>0.189870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7769</th>\n",
       "      <td>0.059981</td>\n",
       "      <td>0.104904</td>\n",
       "      <td>0.102002</td>\n",
       "      <td>0.133833</td>\n",
       "      <td>0.097616</td>\n",
       "      <td>0.045937</td>\n",
       "      <td>0.026070</td>\n",
       "      <td>0.110387</td>\n",
       "      <td>0.086963</td>\n",
       "      <td>0.005197</td>\n",
       "      <td>0.001341</td>\n",
       "      <td>0.024274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7793</th>\n",
       "      <td>0.159878</td>\n",
       "      <td>0.245742</td>\n",
       "      <td>0.228014</td>\n",
       "      <td>0.299642</td>\n",
       "      <td>0.238214</td>\n",
       "      <td>0.187787</td>\n",
       "      <td>0.263086</td>\n",
       "      <td>0.404188</td>\n",
       "      <td>0.403620</td>\n",
       "      <td>0.304141</td>\n",
       "      <td>0.367545</td>\n",
       "      <td>0.342598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7800</th>\n",
       "      <td>0.242323</td>\n",
       "      <td>0.331926</td>\n",
       "      <td>0.311883</td>\n",
       "      <td>0.423053</td>\n",
       "      <td>0.330461</td>\n",
       "      <td>0.343614</td>\n",
       "      <td>0.167055</td>\n",
       "      <td>0.302936</td>\n",
       "      <td>0.310169</td>\n",
       "      <td>0.211287</td>\n",
       "      <td>0.162768</td>\n",
       "      <td>0.181822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7866</th>\n",
       "      <td>0.185521</td>\n",
       "      <td>0.226899</td>\n",
       "      <td>0.188048</td>\n",
       "      <td>0.263258</td>\n",
       "      <td>0.177828</td>\n",
       "      <td>0.163277</td>\n",
       "      <td>0.118543</td>\n",
       "      <td>0.186302</td>\n",
       "      <td>0.145671</td>\n",
       "      <td>0.074715</td>\n",
       "      <td>0.038746</td>\n",
       "      <td>0.080651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8236</th>\n",
       "      <td>0.199708</td>\n",
       "      <td>0.300688</td>\n",
       "      <td>0.272043</td>\n",
       "      <td>0.403561</td>\n",
       "      <td>0.370847</td>\n",
       "      <td>0.316240</td>\n",
       "      <td>0.188411</td>\n",
       "      <td>0.329378</td>\n",
       "      <td>0.297209</td>\n",
       "      <td>0.238488</td>\n",
       "      <td>0.248535</td>\n",
       "      <td>0.230899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8243</th>\n",
       "      <td>0.067992</td>\n",
       "      <td>0.217199</td>\n",
       "      <td>0.191815</td>\n",
       "      <td>0.312226</td>\n",
       "      <td>0.222407</td>\n",
       "      <td>0.203155</td>\n",
       "      <td>0.111199</td>\n",
       "      <td>0.267454</td>\n",
       "      <td>0.243695</td>\n",
       "      <td>0.169684</td>\n",
       "      <td>0.136866</td>\n",
       "      <td>0.199211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8317</th>\n",
       "      <td>0.172035</td>\n",
       "      <td>0.220096</td>\n",
       "      <td>0.204707</td>\n",
       "      <td>0.256749</td>\n",
       "      <td>0.232320</td>\n",
       "      <td>0.229948</td>\n",
       "      <td>0.143242</td>\n",
       "      <td>0.241801</td>\n",
       "      <td>0.232677</td>\n",
       "      <td>0.121288</td>\n",
       "      <td>0.137328</td>\n",
       "      <td>0.160988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9052</th>\n",
       "      <td>0.189056</td>\n",
       "      <td>0.269484</td>\n",
       "      <td>0.400027</td>\n",
       "      <td>0.544218</td>\n",
       "      <td>0.491610</td>\n",
       "      <td>0.363750</td>\n",
       "      <td>0.135462</td>\n",
       "      <td>0.225814</td>\n",
       "      <td>0.395066</td>\n",
       "      <td>0.298317</td>\n",
       "      <td>0.307111</td>\n",
       "      <td>0.226268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9134</th>\n",
       "      <td>0.093692</td>\n",
       "      <td>0.200500</td>\n",
       "      <td>0.231806</td>\n",
       "      <td>0.312099</td>\n",
       "      <td>0.268831</td>\n",
       "      <td>0.178808</td>\n",
       "      <td>0.162163</td>\n",
       "      <td>0.294498</td>\n",
       "      <td>0.294040</td>\n",
       "      <td>0.212108</td>\n",
       "      <td>0.303130</td>\n",
       "      <td>0.294566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9484</th>\n",
       "      <td>0.568348</td>\n",
       "      <td>0.448149</td>\n",
       "      <td>0.551623</td>\n",
       "      <td>0.721005</td>\n",
       "      <td>0.676426</td>\n",
       "      <td>0.542733</td>\n",
       "      <td>0.525413</td>\n",
       "      <td>0.437206</td>\n",
       "      <td>0.643460</td>\n",
       "      <td>0.457206</td>\n",
       "      <td>0.492139</td>\n",
       "      <td>0.459968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9609</th>\n",
       "      <td>0.117508</td>\n",
       "      <td>0.206237</td>\n",
       "      <td>0.238633</td>\n",
       "      <td>0.347733</td>\n",
       "      <td>0.233225</td>\n",
       "      <td>0.161856</td>\n",
       "      <td>0.121775</td>\n",
       "      <td>0.240246</td>\n",
       "      <td>0.280799</td>\n",
       "      <td>0.195267</td>\n",
       "      <td>0.161979</td>\n",
       "      <td>0.163218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9647</th>\n",
       "      <td>0.377577</td>\n",
       "      <td>0.298944</td>\n",
       "      <td>0.276376</td>\n",
       "      <td>0.381785</td>\n",
       "      <td>0.384137</td>\n",
       "      <td>0.368209</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.911494</td>\n",
       "      <td>0.946515</td>\n",
       "      <td>0.698748</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9729</th>\n",
       "      <td>0.306245</td>\n",
       "      <td>0.560696</td>\n",
       "      <td>0.226274</td>\n",
       "      <td>0.458460</td>\n",
       "      <td>0.412396</td>\n",
       "      <td>0.395298</td>\n",
       "      <td>0.252849</td>\n",
       "      <td>0.521295</td>\n",
       "      <td>0.225937</td>\n",
       "      <td>0.284902</td>\n",
       "      <td>0.297172</td>\n",
       "      <td>0.285073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9912</th>\n",
       "      <td>0.078958</td>\n",
       "      <td>0.095393</td>\n",
       "      <td>0.096514</td>\n",
       "      <td>0.137328</td>\n",
       "      <td>0.149801</td>\n",
       "      <td>0.163715</td>\n",
       "      <td>0.065631</td>\n",
       "      <td>0.131362</td>\n",
       "      <td>0.112014</td>\n",
       "      <td>0.035487</td>\n",
       "      <td>0.061325</td>\n",
       "      <td>0.099684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9922</th>\n",
       "      <td>0.126133</td>\n",
       "      <td>0.220109</td>\n",
       "      <td>0.270342</td>\n",
       "      <td>0.410312</td>\n",
       "      <td>0.346492</td>\n",
       "      <td>0.252707</td>\n",
       "      <td>0.210120</td>\n",
       "      <td>0.297783</td>\n",
       "      <td>0.656228</td>\n",
       "      <td>0.549342</td>\n",
       "      <td>0.576069</td>\n",
       "      <td>0.520165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9932</th>\n",
       "      <td>0.039314</td>\n",
       "      <td>0.127777</td>\n",
       "      <td>0.175550</td>\n",
       "      <td>0.100293</td>\n",
       "      <td>0.136188</td>\n",
       "      <td>0.038777</td>\n",
       "      <td>0.076250</td>\n",
       "      <td>0.158422</td>\n",
       "      <td>0.194356</td>\n",
       "      <td>0.005245</td>\n",
       "      <td>0.062453</td>\n",
       "      <td>0.076385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9933</th>\n",
       "      <td>0.221638</td>\n",
       "      <td>0.223950</td>\n",
       "      <td>0.220813</td>\n",
       "      <td>0.282442</td>\n",
       "      <td>0.202153</td>\n",
       "      <td>0.174667</td>\n",
       "      <td>0.166210</td>\n",
       "      <td>0.263300</td>\n",
       "      <td>0.258165</td>\n",
       "      <td>0.161936</td>\n",
       "      <td>0.157895</td>\n",
       "      <td>0.207726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9971</th>\n",
       "      <td>0.183358</td>\n",
       "      <td>0.319774</td>\n",
       "      <td>0.335846</td>\n",
       "      <td>0.434003</td>\n",
       "      <td>0.383700</td>\n",
       "      <td>0.001631</td>\n",
       "      <td>0.077466</td>\n",
       "      <td>0.234405</td>\n",
       "      <td>0.270168</td>\n",
       "      <td>0.165000</td>\n",
       "      <td>0.157749</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9982</th>\n",
       "      <td>0.143904</td>\n",
       "      <td>0.230671</td>\n",
       "      <td>0.291574</td>\n",
       "      <td>0.294091</td>\n",
       "      <td>0.264141</td>\n",
       "      <td>0.187730</td>\n",
       "      <td>0.132651</td>\n",
       "      <td>0.240191</td>\n",
       "      <td>0.298131</td>\n",
       "      <td>0.134802</td>\n",
       "      <td>0.164150</td>\n",
       "      <td>0.160963</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>95 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        hvac_5    hvac_6    hvac_7    hvac_8    hvac_9   hvac_10  aggregate_5  \\\n",
       "26    0.268580  0.391562  0.354348  0.485952  0.423089  0.445286     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]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "Failure:Interrupted\n"
     ]
    },
    {
     "ename": "KeyError",
     "evalue": "'Interrupted'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-13-c44174c22da4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[0;31m# Ensure repeatably random problem data.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m         \u001b[0mA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mX_home\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m         \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnmf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0mpred_df\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mY\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-10-dca7d8f4b5ab>\u001b[0m in \u001b[0;36mnmf\u001b[0;34m(A, k, MAX_ITERS)\u001b[0m\n\u001b[1;32m     34\u001b[0m         \u001b[0mobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcvx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMinimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcvx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnorm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmask\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mY\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmask\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'nuc'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     35\u001b[0m         \u001b[0mprob\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcvx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconstraint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 36\u001b[0;31m         \u001b[0mprob\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcvx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSCS\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     37\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mprob\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatus\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mcvx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mOPTIMAL\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/nipunbatra/anaconda/lib/python2.7/site-packages/cvxpy-0.4.2-py2.7.egg/cvxpy/problems/problem.pyc\u001b[0m in \u001b[0;36msolve\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    171\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    172\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 173\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_solve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    174\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    175\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mclassmethod\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/nipunbatra/anaconda/lib/python2.7/site-packages/cvxpy-0.4.2-py2.7.egg/cvxpy/problems/problem.pyc\u001b[0m in \u001b[0;36m_solve\u001b[0;34m(self, solver, ignore_dcp, warm_start, verbose, parallel, **kwargs)\u001b[0m\n\u001b[1;32m    296\u001b[0m             results_dict = solver.solve(objective, constraints,\n\u001b[1;32m    297\u001b[0m                                         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cached_data\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwarm_start\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 298\u001b[0;31m                                         kwargs)\n\u001b[0m\u001b[1;32m    299\u001b[0m         \u001b[0;31m# Presolve determined problem was unbounded or infeasible.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    300\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/nipunbatra/anaconda/lib/python2.7/site-packages/cvxpy-0.4.2-py2.7.egg/cvxpy/problems/solvers/scs_intf.pyc\u001b[0m in \u001b[0;36msolve\u001b[0;34m(self, objective, constraints, cached_data, warm_start, verbose, solver_opts)\u001b[0m\n\u001b[1;32m    107\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    108\u001b[0m         \u001b[0mresults_dict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mscs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscs_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDIMS\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0msolver_opts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 109\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat_results\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresults_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcached_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    110\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    111\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mformat_results\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresults_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcached_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/nipunbatra/anaconda/lib/python2.7/site-packages/cvxpy-0.4.2-py2.7.egg/cvxpy/problems/solvers/scs_intf.pyc\u001b[0m in \u001b[0;36mformat_results\u001b[0;34m(self, results_dict, data, cached_data)\u001b[0m\n\u001b[1;32m    129\u001b[0m         \u001b[0mdims\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDIMS\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    130\u001b[0m         \u001b[0mnew_results\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 131\u001b[0;31m         \u001b[0mstatus\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSTATUS_MAP\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mresults_dict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"info\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"status\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    132\u001b[0m         \u001b[0mnew_results\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSTATUS\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstatus\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mnew_results\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSTATUS\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32min\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSOLUTION_PRESENT\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: 'Interrupted'"
     ]
    }
   ],
   "source": [
    "out = {}\n",
    "for lat in range(1,2):\n",
    "    out[lat]={}\n",
    "    print lat\n",
    "    for home in X_normalised.index[:]:\n",
    "        \n",
    "        X_home = X_normalised.copy()\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(A, lat, 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] = transform(pred_df.ix[home], appliance, col_max, col_min)[appliance_cols]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "error_lat = {}\n",
    "gt = X_matrix[appliance_cols]\n",
    "for lat in range(1,2):\n",
    "    \n",
    "    pr = pd.DataFrame(out[lat]).T\n",
    "    \n",
    "    error = (pr-gt).abs()\n",
    "    error_lat[lat] = error.div(gt).mul(100).median().mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 0.30102478,  0.37093592,  0.36574802, ...,  0.34690212,\n",
       "          0.36979753,  0.3241133 ],\n",
       "        [ 0.19106719,  0.23544135,  0.23214848, ...,  0.22018656,\n",
       "          0.23471879,  0.20572199],\n",
       "        [ 0.04250822,  0.05238049,  0.0516479 , ...,  0.04898664,\n",
       "          0.05221974,  0.04576859],\n",
       "        ..., \n",
       "        [ 0.16741394,  0.20629479,  0.20340956, ...,  0.19292847,\n",
       "          0.20566168,  0.18025454],\n",
       "        [ 0.17584396,  0.21668262,  0.21365211, ...,  0.20264325,\n",
       "          0.21601763,  0.18933114],\n",
       "        [ 0.1520278 ,  0.18733532,  0.18471525, ...,  0.17519743,\n",
       "          0.18676039,  0.16368829]])"
      ]
     },
     "execution_count": 369,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "results[appliance] = pd.Series(error_lat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    27.809656\n",
       "dtype: float64"
      ]
     },
     "execution_count": 379,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(error_lat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "      <th>0</th>\n",
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       "      <th>count</th>\n",
       "      <td>95.000000</td>\n",
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       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.660303</td>\n",
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       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.342348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.117898</td>\n",
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       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.423632</td>\n",
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       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.614642</td>\n",
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       "      <th>75%</th>\n",
       "      <td>0.827686</td>\n",
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       "    <tr>\n",
       "      <th>max</th>\n",
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      "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"
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     "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"
    },
    {
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enjoVddvIdTbCOnXdUasfRIh4depJZ+q2sV8A2v7eXnv8AgArVlBpnI7Z+7TW\n8Ustnfr0NH0v20Wvpyd8r1Il6gDl6lEiGJc8HaCLzuHDtL/CinpzM4m5GtvIVdSjOPXhYarSedOb\n7M+7/E7PP09/zfPbFHU9Dh0YqBT144+nx319oTY/NldeWTlQndlICpTPHa88HfBupK5rUfebkFfH\nq6TRhtlQqg/EU5T4BQjv1M2x1w8fppMhzfhl0aJ4oh6lTv3wYRJDW/XHkiXuFVUKXdTPOCN8Y6mU\nbnk6QNUoariAMOWMAJkSNbRu2qL+zDM005HXZ7j8Tjt20F+bqKtjPChTB7KJYF59tXLYiCCn7ifq\nDefUXUU9Tqbul+H5kWZDqZT+nY8Ab1G3OXUzflEdkIaG/IUjy/hlZqb6bsWlodQWvSgWL7bX8fsR\n16m/+CLt71NOcVtf5ephKl8UUUS9szO8qPtFL4Db76Scutn+EyZ+AWov6tPTpEnqogTYnbo67oOc\nup+o12X1i9cs6yZxRD2PTn18nE5Km9t0EXXTqdvGienpoX3hd/JnGb/osx4pXBygn6jHdepRRF1F\nL64NnipXDxu/AOVcPaxTD5upu4i6i1M/66zg+CVvon7gAAm7Lup+Tj2KqA8P07HqNYxAHDIXda9Z\n1k2ycOq2OvWkGkq9ohegvNwrU1+5MtipA3QyBDlBm6hPTACf/rT/64D4om42kgK1F/XpaXKS6v1U\n/BLmRHONXhSqrLGWoh7WqW/bRpNWexH0O42MkDief344p25m6kDtyxr37qXj4OWXyz1xkxb1oSH6\nXZqbk58mMxeinoZTtzWUAvmJX1xE3cupL1tG+0wdcGq4WrPeuafHTdRNQd63D/j85/0bsKWML+pm\nng64VVXo09iZhI1fVJuDEsjubjrOXN/j2DHg4YeBiy5y/0w9foki6qOjlM03OZ69YUV9epoqgFat\n8l4n6Hd68UW6eC1aFK6hNA+Z+t69tO2LFwO7dtGyNOKX+fO9hxGIQ6FE3bWk0dZQmoRTr5Woq5zd\nS9SbmykvVwe6PkKjjotTt2Xqamaln//c+3XDwxSbtLbGc+qmqNfaqevRiyJMY+kTT1B9e5hsXMUv\nYRtKARL1kRF3lw6EL2l84w06nmx114qg3+n552nYhQULqp26fudsayi1OfWo4+RHYe9eOnfOPLPc\nLpCGU294UQ9T/WKLX9QP0tZWHns8iCydekuL94ECVObqtugFILfR0+O/Hbb4RZWP+Ym6culqe/Mi\n6qrHrWvTQG77AAAekklEQVRds03Uw+Tq+/ZRHBaGBQvogvjyy9FF3dYW40VYp757d3l6SC+Cfqcd\nO0gUu7v9nbq6cIyP01+bqHd3x5+SLwxK1M86q5yr25y6mjpzaIhFvYJaNZSqH0QItx0pZbqdj4aG\nqg8SRVeX9/CtCj1Xt82QBACXXRY8f6gtfuntpZNt+3bv1yUl6rZMPU71y5w59Pu6Tqygxn3RCTNc\nwMGD5XlSw7B6NTVGhq1+UXOQhnXq/f3u7QSvvUamwQ91h+f1nqqRNEjUgUrhs2XqQUN7JN3QuHcv\nRZxnnlkWdZsJU1NnHjoUT9STroDJXNQXLqQv6Dfpr5Tk1KP2KDV/EJcIZmKC3JDuiJLsfORXztbT\nQxMd+GE6dVtU41KN4eXU3/Uuf1HXZx7Kk1MHyCi4ZuJeTt01fjl40H9URi9Wr6bvWYv4Zc4cOnfM\n3+iGG+xDIriIut9Y4YB//GJO4Kzn6rZM3U/UVZvIV74SPLzD8LBbJybX+AWgZS6ibl549Jmf6s6p\nNzXRSeWXg05M0EHs2jBkNpTaDqIgUbflZEnGL0F5atDJrjt1r/jFBa9M/aKLKB7wutjqjZVJNpTO\nnUu34n4nqIuou+bqceOXqE791FPpby1EHagua+ztBf7yL+1DIrjEL4D3BXhwkD5r+XI3p67n6rb4\nZe7c8uBnJmpyk+9/H3jnO/0vxrfcAmzaFPy9lKifdhoZp4kJe/wCBDv1OXMoatPv8KUs36mHmV7T\nlcxFHQjO1cNEL0C5oVRdHfWGGcBN1M1GUvW+tXDqLuhO3Vaj7oqXUz/5ZLpweJ0kaWXqTU20n73e\nb2aGjpWlS73fN66oL1lCv7NLg3qc+AWorajrufpzz9Ff22z2Lk4d8K6A2bGDLoxNTd5O3XY+SmkX\ndTWao82tq4vHT34CfOQjdIf54x/bt3fPnvL39mJigrZ38WKKIJcto2kO/Sa0OXjQv/3L1Jtjx2jf\nqKiwLkU9KFcPU/kClGMT5TKTdOpJZepRKh90knLqXpn6okU0JZpXY2lamTrgH8EcOECv8RuuNkxZ\no03UhXC/MBRF1M1epUrcbHckcZ26ytMB+q3MmZe8RF01ltqqbvxEvbOTRPLjHycnfv/99u3du5e+\nr99d4BtvUGO76hCnIhgvp67iF79KIVNvdDNTt6Ie5NTDVL4odAealFMPm6k/+STw7/9ufy6uUz/h\nBPpeaoLqJOMXlZeffbZ3rp6WUwf8Rd1FcOI69TDvEVXUTzmFJrPwEwMbSTn1Z5+lzkWmU5+cpO99\n0knB7+n1O6k8HSCxNS8oXqJuy9MVQaKuOPlk71E69+2jC4fZG1tHRS8KVQHj59T94heggUXd7wQK\nG78A1aIe1qnbRP244+gW0XXG+X/6J8r6bETpeKIjRHkMmDjxy5w55KL076Q79TRF3ZapA/4VMEmK\nupTk/E880f4eLm4/qqi3tNCgWa5DCyiSytSfew644opqp75vH+0Plztjr99Jd+oAHZt6BGMzWQMD\n9uhF0dnpJup+Qy/v3UsXUr37v20dXdSVU08yfjFFve6qX4DkM3WgUtT9Sqi8sMUvQrjn6hMTwA9+\n4N0rM2hIXBdUrh7HqauyLLWvJifpoOvuBt7yFhJ1W8lYnp26a/xy5AgdV7YoJ6jxHqDb+IGB6BfU\nKCTh1KenScwvv7zaqbvm6YB//KKcOlDdWOrVUGorZ9TXiSPqx47R97/44nJFiw2bqO/YERy/+Im6\n2cFKL2eua6eetKjr4puUUzff14+f/IRuPb06fcR16kA5V/eqU3dFF3VVotfURG69tdVeIZFVpp6k\nU/eKXlzfo7+ffkN9QLK0SSJT37mTfrtVq8pj3yjiivrhw3R+6J3e9MZSdVeoi6Aev/iJuq0Dkinq\nixfTZ5lVWyorf/Obwzn11avpItHf7+3UJybCOfXh4bKZqdvqF5eG0iSduss8peYEGQrXQb3uvJNa\n471EPW5DKVDp1OO4RT1XN8sFlVvXGR2lE1MdmC0twWWINrycut+4Inv2BIv6iSfSRSeoV2mQqAe5\n/ajRSxySiF+ee44mvxCiunzTtZEUsIu6cul6rKQ7dVW0oD+fZKY+a5ZdT/ReomGcenMzmafxcW9R\nBwqYqQshNgkh1gshrhJCXBWw7obS+iuEEB2l/y/3e43K1L16hoWtfgGSydRtP5SLU5+aoiz9qqv8\nnXrc+EVNlhEnfgEq95XuwAF7BYxaR52YqgwxbLmnX6Yex6k3N9NvHNSrNK5Tz1LUwwwTAFTGL0rU\nAarF1iOYME7ddvF9/vnKPB2odOpmJRrglqm7ijpgj2D02vOdO73bxUxRB+gi1dJivyMrpKgLITYD\n2CWlvEtKuQXAKiHEBp+XdAHYDGAngF2l1+72+4zWVjpYvcZ3iOPUpaS/+mQUaccvP/sZHRhnnFF+\nLx0pk4lfVqwo30q6zkhvQy9rNJ26rbHUNkpilAgmbKY+M0Mn68knB7+3TZS//OXKGmbbEAEKl0w9\nam/SOCQRvzz3HMUQAIlckk79hRfKx73CdOpmNp1kpg7YRX3fPoqEWlro3HzlFfvn2ET9rLOCR1Qt\nlKgD2CilvEt7fB+Aq33WlwA6AaySUnYbr/XEL1ePU9I4Okqv1Z1N1IZSwE3U77wT2FC67HV3V7v1\no0fJTYa9+zBZsYJOwjguHaiMX2xO3Sbq+jrqPcKIum3WI4VXVUVvL50ELhcwm6hv2UK1zKoe2s+p\nK1H3G1ckC6fe3Bx+7Beg0qk/+2zZqZ9+enSnbhP1V14p1+ArFizwF3XXTD0Jpw5UjumiMzZG22f+\npmee6T1OUxJOvabVL0KINSCR1ukHcLHfy6SUQ0Hu3GTRIjpJbMRpKLWVItlE/e//vrJ+1cupB2Xq\nMzPAXXdRZQFgHyEvCZcO0IG2YEF8UdfjF9Opr1pFv4t+QkUV9e3bgf/7P7pIq6n8bLe0Xk49jIs0\nK2D6+8k0nHUW8NWv0jI/UW9rIwH1u/gXMVM/epQuVmrqPd2pj49TTOLXW1fHdvHduZPmYNXRSxqD\nRN3rvHAtaQTsteq6qHvl6vv20Xc3hyN5+9uB97/fvl1RRT3L6pcukIjrDACAEMJy40wIIT6mZfAO\noy3YuxMr4sQvfgeRYmYG2LyZZrBReDWUBjn1Rx+lg1i5la6u6rLGJMoZFStXxi+p0+MXU7BnzaJb\ndT1X1wfzUriI+qc+Bfze79H2XnaZPXpR7xVX1E2n/thjND3bl78M3HgjfU8/UQeCI5isRD2OU9+x\ng4Rc3bmuWEEx1OgoCWFPj3s1j3nxnZwkYTR/o6D4JWr1i5Th4xfA26nboheAjqV/+Af7dkWJX/Tq\nl5aW8pyzSREk6h0gYdfpByAsyxX3AbjdyOB9G1eB9ETdxak/+ywdHM88U14WtaFUj14Ae/ySlFMH\n6KRM06kDFME8/HD5cVSn/vrrdOHcuxf4q78igbWRhFM3Rf2RR4ALLiCH+pGPAH/zN8GiHtRYmpWo\nDw+HF/V588ioPP10OXoBSNxXraLYJEz0ot5T/5327KF9ZsaK+rltdjwCyg2lYTN1dXEztSEofvFy\n6l6i7kfc+EUIt5FJwxDUhm4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iUUT9jjuK3+mIyR8qcy6iqNeK3Ik6QFes7dvrJ08HyqJe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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": 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472/03k9MNPzHOecGJ71eCdQCS7BOZakafxGR4stmCGiI935W0uN64Lw07++f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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": 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Q9u3LOg3AWzR6ekQEmpvjC09FdRqzZ+cnHU0iHCiNaDz9NHDrre7v/eEPwHMJr5RiiwaQ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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": 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], 'nuc'))\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": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'optimal'"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cvx.Minimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YUafLsiOnQvoFd/+eh/7ljwDjTbbZlLs/Q+h++LnsUUoXklNNB9z9XQ/1ImcJ\nIbPd3W/4nUHiN+eU5aV4e4kwstbTAGY2RW+fj4yIQRwgR0ZPMrD5TjNLTqNMAhcI/dBfTi17HOYP\nkO7uT8bTIlsJO7r18ansEIGdlsWBS6l5Z+PtJiDpD9+5M1AM9DaS1hPAW4Qjk/Vtlm3H47oSF4FV\n3r6SOlv+C3C7T/3VcV5Xn4+MDgWCVMrCyGPJ4N7Pufv3Wiye3dkl69hGOE2UTOsIpzRabtfDMIJZ\nk81ekjOv2xCYty53f9vMdhJ+gR+ls8rvFQW2127Q+1bBOUuPn4+MDp0ykrJld06HgdOEneS69BOx\ncnRlZvnZzDKrCDv//e7+ajxdkbezzNtunpOxLFOpeasJO7uyxguezJ5+cvfDcf1rc5ZPyp4Oq3U5\ny3VdHua/X4CHYrkuE07BdfX5yGhRIEgvJuJt+hdxssPYbGFM2wvx9MJJ4GA8YkjGu90Td0jJOvJ+\npSe/btfH101xZ9zb1anlFmw3Pp4XHvH8+VHCBWKJp5k/Pm1SlvQv67x5C5jZ2rjMgnP4hFNHeTvU\n9CmrZB3r4v10y6YJFv6NktM7rYwDs2a2Pa5zPJblOQhHMHT/+cgo6Xettqbhmwgtd84TWq7MEVrj\npFvtHInzTzO/5czLcdkrwDFiiyBCheb51Gu2Z7a3P77mHHda0xyP8zY02y6h8jhZ7zlgS2adx+Oy\nL6Tmb82UZUNO+TY0+bvMpP4mc+m/SeZvdzpn/q5YxmOxbLtSf9stTcqV3t4xQquj46nXJS2bzsW/\nx0zqPf9hThm6+nw0jc6kMZVFRATQKSMREYkUCCIiAigQREQkUiCIiAigQBARkUiBICIigAJBREQi\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": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "hvac_5     227.844843\n",
       "hvac_6     537.381419\n",
       "hvac_7     771.769991\n",
       "hvac_8     936.052200\n",
       "hvac_9     653.705150\n",
       "hvac_10    321.603356\n",
       "Name: 26, dtype: float64"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transform(pred_df.ix[26], 'hvac', col_max, col_min)[appliance_cols]"
   ]
  },
  {
   "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": []
  }
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