interaction_models.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [],
   "source": [
    "london_flows=pd.read_csv(\"data/london_flows.csv\")\n",
    "london_flows=london_flows[london_flows['station_origin']!=london_flows[\"station_destination\"]]\n",
    "london_flows=london_flows[london_flows['distance'] != 0]# drop intra station\n",
    "london_flows=london_flows[london_flows['station_origin'] != 'Battersea Park']\n",
    "london_flows=london_flows[london_flows['station_destination'] != 'Battersea Park']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [],
   "source": [
    "# change column name\n",
    "london_flows=london_flows.rename(columns={\"station_origin\":\"Orig\",\"station_destination\":'Dest','flows':'Total','distance':'Dist','population':'Oi_origpop','jobs':'Dj_destjob'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Orig</th>\n",
       "      <th>Dest</th>\n",
       "      <th>Total</th>\n",
       "      <th>Oi_origpop</th>\n",
       "      <th>Dj_destjob</th>\n",
       "      <th>Dist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>0</td>\n",
       "      <td>599</td>\n",
       "      <td>78549</td>\n",
       "      <td>8131.410852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Beckton</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>442</td>\n",
       "      <td>8510.047006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Blackwall</td>\n",
       "      <td>3</td>\n",
       "      <td>599</td>\n",
       "      <td>665</td>\n",
       "      <td>3775.359872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>58772</td>\n",
       "      <td>5086.404941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Canning Town</td>\n",
       "      <td>37</td>\n",
       "      <td>599</td>\n",
       "      <td>15428</td>\n",
       "      <td>2228.874185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Crossharbour</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>1208</td>\n",
       "      <td>6686.335036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Custom House</td>\n",
       "      <td>0</td>\n",
       "      <td>599</td>\n",
       "      <td>845</td>\n",
       "      <td>3824.789936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Cutty Sark</td>\n",
       "      <td>2</td>\n",
       "      <td>599</td>\n",
       "      <td>1748</td>\n",
       "      <td>8503.736582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Cyprus</td>\n",
       "      <td>7</td>\n",
       "      <td>599</td>\n",
       "      <td>850</td>\n",
       "      <td>6532.037185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Devons Road</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>611</td>\n",
       "      <td>3958.290432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>East India</td>\n",
       "      <td>2</td>\n",
       "      <td>599</td>\n",
       "      <td>1522</td>\n",
       "      <td>3384.060703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Island Gardens</td>\n",
       "      <td>2</td>\n",
       "      <td>599</td>\n",
       "      <td>691</td>\n",
       "      <td>7706.145393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>King George V</td>\n",
       "      <td>5</td>\n",
       "      <td>599</td>\n",
       "      <td>800</td>\n",
       "      <td>6805.940949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Langdon Park</td>\n",
       "      <td>8</td>\n",
       "      <td>599</td>\n",
       "      <td>1989</td>\n",
       "      <td>4810.624642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Lewisham</td>\n",
       "      <td>0</td>\n",
       "      <td>599</td>\n",
       "      <td>2400</td>\n",
       "      <td>11213.267832</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Orig               Dest  Total  Oi_origpop  Dj_destjob          Dist\n",
       "0   Abbey Road  Bank and Monument      0         599       78549   8131.410852\n",
       "1   Abbey Road            Beckton      1         599         442   8510.047006\n",
       "2   Abbey Road          Blackwall      3         599         665   3775.359872\n",
       "3   Abbey Road       Canary Wharf      1         599       58772   5086.404941\n",
       "4   Abbey Road       Canning Town     37         599       15428   2228.874185\n",
       "5   Abbey Road       Crossharbour      1         599        1208   6686.335036\n",
       "6   Abbey Road       Custom House      0         599         845   3824.789936\n",
       "7   Abbey Road         Cutty Sark      2         599        1748   8503.736582\n",
       "8   Abbey Road             Cyprus      7         599         850   6532.037185\n",
       "9   Abbey Road        Devons Road      1         599         611   3958.290432\n",
       "10  Abbey Road         East India      2         599        1522   3384.060703\n",
       "11  Abbey Road     Island Gardens      2         599         691   7706.145393\n",
       "12  Abbey Road      King George V      5         599         800   6805.940949\n",
       "13  Abbey Road       Langdon Park      8         599        1989   4810.624642\n",
       "14  Abbey Road           Lewisham      0         599        2400  11213.267832"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows.head(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a pivot table to monitor flows\n",
    "ldf_submat=pd.pivot_table(london_flows,values =\"Total\", index=\"Orig\", columns = \"Dest\",\n",
    "                            aggfunc=np.sum, margins=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
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       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
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       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32.0</td>\n",
       "      <td>599</td>\n",
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       "    <tr>\n",
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       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11.0</td>\n",
       "      <td>...</td>\n",
       "      <td>77.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3745</td>\n",
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       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>17.0</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2886</td>\n",
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       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
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       "      <td>24.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3172</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>59.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>345.0</td>\n",
       "      <td>750.0</td>\n",
       "      <td>2202.0</td>\n",
       "      <td>7782.0</td>\n",
       "      <td>7932.0</td>\n",
       "      <td>444.0</td>\n",
       "      <td>741.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>8103.0</td>\n",
       "      <td>...</td>\n",
       "      <td>6295.0</td>\n",
       "      <td>596.0</td>\n",
       "      <td>2146.0</td>\n",
       "      <td>1578.0</td>\n",
       "      <td>404.0</td>\n",
       "      <td>706.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>745.0</td>\n",
       "      <td>4428.0</td>\n",
       "      <td>1542283</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN      3.0   \n",
       "Aldgate                  NaN            NaN         0.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0      0.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         2.0      5.0   \n",
       "Woodgrange Park          NaN            0.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         1.0     26.0   \n",
       "Woolwich Arsenal        20.0            NaN         NaN      NaN   \n",
       "All                    345.0          750.0      2202.0   7782.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                17.0         NaN      35.0       0.0      NaN   \n",
       "Aldgate                    0.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       0.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  47.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             11.0         NaN       0.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN         7.0       NaN       NaN      NaN   \n",
       "All                     7932.0       444.0     741.0     256.0    173.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          11.0  ...       77.0             3.0         6.0   \n",
       "Aldgate             17.0  ...        0.0             NaN         4.0   \n",
       "Aldgate East        20.0  ...       24.0             0.0         0.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            22.0  ...        2.0             NaN         1.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       59.0  ...        0.0             NaN         0.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               8103.0  ...     6295.0           596.0      2146.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              0.0   \n",
       "Acton Town              9.0          NaN       0.0              NaN   \n",
       "Aldgate                 8.0          NaN       0.0              NaN   \n",
       "Aldgate East           12.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1578.0        404.0     706.0            242.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal      All  \n",
       "Orig                                                        \n",
       "Abbey Road                  NaN              32.0      599  \n",
       "Acton Central               NaN               NaN     1224  \n",
       "Acton Town                  0.0               NaN     3745  \n",
       "Aldgate                     0.0               NaN     2886  \n",
       "Aldgate East                1.0               NaN     3172  \n",
       "...                         ...               ...      ...  \n",
       "Woodford                    NaN               NaN     4868  \n",
       "Woodgrange Park             NaN               NaN      530  \n",
       "Woodside Park               NaN               NaN     3093  \n",
       "Woolwich Arsenal            NaN               NaN     7892  \n",
       "All                       745.0            4428.0  1542283  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldf_submat"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spatial Interaction model\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## classic multiplicate gravity model:\n",
    "\n",
    "\\begin{equation} \\tag{1}\n",
    "T_{ij} = k \\frac{O_i^\\alpha  D_j^\\gamma}{ d_{ij}^\\beta}\n",
    "\\end{equation}\n",
    "\n",
    "This gravity model can be written in the form more familiar from [Wilson's 1971 paper](http://journals.sagepub.com/doi/abs/10.1068/a030001) \n",
    "\n",
    "\\begin{equation} \\tag{2}\n",
    "T_{ij} = k O_i^\\alpha  D_j^\\gamma  d_{ij}^{-\\beta}\n",
    "\\end{equation}\n",
    "\n",
    "<b>This model just says that the flows between an origin and destination are proportional to the product of the mass (attractor) of the origin and destination and inversley proportional to the distance between them.\n",
    "    \n",
    "As origin and destination masses increase, flows increase, but as distance increases, flows decrease, and vice versa.</b>\n",
    "\n",
    "- Where $T_{ij}$ is the transition or flow, $T$, between origin $i$ (always the rows in a matrix) and destination $j$ (always the columns in a matrix). \n",
    "- $O$ is a vector (a 1 dimensional matrix - or, if you like, a single line of numbers) of origin attributes which relate to the emissiveness of all origins in the dataset, $i$ \n",
    "- $D$ is a vector of desination of attributes relating to the attractivenss of all destinations in the dataset, $j$ - in our sample dataset, we have a vector of destination populations (which I have called Dj1_destpop) and a vector of destination average salaries (which I have called Dj2_destsal) in 2001\n",
    "- $d$ is a matrix of costs relating to the flows between $i$ and $j$ \n",
    "- $k$, $\\alpha$, $\\gamma$ and $β$ are all the model parameters to be estimated\n",
    "\n",
    "$k$ is a constant of proportionality. Given that all flows estimated by the model will sum to any observed flow data used to calibrate the parameters:\n",
    "\n",
    "\\begin{equation} \\tag{3}\n",
    "k = \\frac{T}{\\sum_i \\sum_j O_i^\\alpha  D_j^\\gamma  d_{ij}^{-\\beta}}\n",
    "\\end{equation}\n",
    "\n",
    "and $T$ is the sum of our matrix of observed flows or:\n",
    "\n",
    "\\begin{equation} \\tag{4}\n",
    "T= \\sum_i \\sum_j T_{ij}\n",
    "\\end{equation}\n",
    "\n",
    "This is just the sum of all observed flows divided by the sum of all of the other elements in the model.\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating Model Parameters\n",
    "\n",
    "Try to produce some flow estimates by plugging some arbitrary or expected estimated values into our parameters. \n",
    "\n",
    "The parameters relate to the scaling effect / importance of the variables they are associated with.\n",
    "\n",
    " Most simply, where the effects of origin and destination attributes on flows scale in a linear fashion (i.e. for a 1 unit increase in, say, population at origin, we might expect a 1 unit increase in flows of people from that origin, or for a halving in average salary at destination, we might expect a halving of commuters), $\\alpha$ = 1 and $\\gamma$ = 1. \n",
    " \n",
    " In Newton’s original gravity equation, $\\beta$ = 2 where the influence of distance on flows follows a power law - i.e. for a 1 unit increase in distance, we have a $1^{-2}$ (1) unit decrease in flows, for a 2 unit increase in distance, we have $2^{-2}$ (0.25 or 1/4) of the flows, for a 3 unit increase, $3^{-2}$ (0.111) etc.\n",
    "\n",
    "Let’s see if these parameters are a fair first guess (we’ll use the whole dataset in order to get a less messy picture)…\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Start flow estimatin with initial parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [],
   "source": [
    "#set up some variables to hold our parameter values in:\n",
    "alpha = 1\n",
    "gamma = 1\n",
    "beta = 2\n",
    "k = 1\n",
    "T2 = sum(london_flows[\"Total\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [],
   "source": [
    "# apply parameters to variables\n",
    "Oi_alpha=london_flows['Oi_origpop']**alpha\n",
    "Dj_gamma = london_flows[\"Dj_destjob\"]**gamma\n",
    "dist_beta = london_flows[\"Dist\"]**-beta\n",
    "T1 = Oi_alpha*Dj_gamma*dist_beta\n",
    "k = T2/sum(T1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on equation 2\n",
    "\\begin{equation} \\tag{2}\n",
    "T_{ij} = k O_i^\\alpha  D_j^\\gamma  d_{ij}^{-\\beta}\n",
    "\\end{equation}\n",
    "\n",
    "get flow estimation simply by multiplying variables with parameter power"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [],
   "source": [
    "london_flows['unconstrainedEst1']=round(k*Oi_alpha*Dj_gamma*dist_beta,0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "# check for inf and nan values in column A\n",
    "mask = np.isinf(london_flows['unconstrainedEst1']) | np.isnan(london_flows['unconstrainedEst1'])\n",
    "\n",
    "# locate the rows with inf or nan values\n",
    "inf_nan_rows = london_flows[mask]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1538980"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# convert to int\n",
    "london_flows['unconstrainedEst1']=london_flows['unconstrainedEst1'].astype(int)\n",
    "#check estimation\n",
    "sum(london_flows['unconstrainedEst1'])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Turn the estimation into a matrix to look at the predictors flows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
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       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
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       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>149.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>24.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8082</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>381.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>396.0</td>\n",
       "      <td>14366.0</td>\n",
       "      <td>11155.0</td>\n",
       "      <td>186.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6674.0</td>\n",
       "      <td>...</td>\n",
       "      <td>460.0</td>\n",
       "      <td>71.0</td>\n",
       "      <td>529.0</td>\n",
       "      <td>582.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>65.0</td>\n",
       "      <td>137.0</td>\n",
       "      <td>1538980</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN      1.0   \n",
       "Aldgate                  NaN            NaN         0.0      NaN   \n",
       "Aldgate East             NaN            NaN         0.0    161.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         0.0      2.0   \n",
       "Woodgrange Park          NaN            0.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         0.0      1.0   \n",
       "Woolwich Arsenal         0.0            NaN         NaN      NaN   \n",
       "All                    381.0           29.0       396.0  14366.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                 1.0         NaN       2.0       0.0      NaN   \n",
       "Aldgate                  149.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       0.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                   3.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park              1.0         NaN       0.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN         0.0       NaN       NaN      NaN   \n",
       "All                    11155.0       186.0      37.0       0.0      3.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town           2.0  ...        1.0             0.0         0.0   \n",
       "Aldgate             25.0  ...        1.0             NaN         1.0   \n",
       "Aldgate East        24.0  ...        1.0             0.0         1.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford             2.0  ...        0.0             NaN         0.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park        2.0  ...        0.0             NaN         0.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               6674.0  ...      460.0            71.0       529.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              0.0   \n",
       "Acton Town              2.0          NaN       0.0              NaN   \n",
       "Aldgate                 0.0          NaN       0.0              NaN   \n",
       "Aldgate East            0.0          NaN       0.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                   582.0         57.0      52.0              4.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal      All  \n",
       "Orig                                                        \n",
       "Abbey Road                  NaN               0.0      562  \n",
       "Acton Central               NaN               NaN       54  \n",
       "Acton Town                  0.0               NaN      611  \n",
       "Aldgate                     0.0               NaN     9963  \n",
       "Aldgate East                0.0               NaN     8082  \n",
       "...                         ...               ...      ...  \n",
       "Woodford                    NaN               NaN      332  \n",
       "Woodgrange Park             NaN               NaN        8  \n",
       "Woodside Park               NaN               NaN      213  \n",
       "Woolwich Arsenal            NaN               NaN      280  \n",
       "All                        65.0             137.0  1538980  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldf_submat1=london_flows.pivot_table(values =\"unconstrainedEst1\", index=\"Orig\", columns = \"Dest\",\n",
    "                            aggfunc=np.sum, margins=True)\n",
    "ldf_submat1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evalutation of model\n",
    "Goodness of fit\n",
    "*coefficient of determination ($r^2$)\n",
    " $r^2$ is popular as it is quite intuitive and can be compared across models.\n",
    "*the Square Root of Mean Squared Error (RMSE).\n",
    "Less intuitive but can be used to comparing changes to the same model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats\n",
    "\n",
    "def CalcRSqaured(observed, estimated):\n",
    "    \"\"\"Calculate the r^2 from a series of observed and estimated target values\n",
    "    inputs:\n",
    "    Observed: Series of actual observed values\n",
    "    estimated: Series of predicted values\"\"\"\n",
    "    \n",
    "    r, p = scipy.stats.pearsonr(observed, estimated)\n",
    "    R2 = r **2\n",
    "    \n",
    "    return R2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "\n",
    "def CalcRMSE(observed, estimated):\n",
    "    \"\"\"Calculate Root Mean Square Error between a series of observed and estimated values\n",
    "    inputs:\n",
    "    Observed: Series of actual observed values\n",
    "    estimated: Series of predicted values\"\"\"\n",
    "    \n",
    "    res = (observed -estimated)**2\n",
    "    RMSE = round(sqrt(res.mean()), 3)\n",
    "    \n",
    "    return RMSE\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "485.566"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "CalcRMSE(london_flows[\"Total\"], london_flows[\"unconstrainedEst1\"])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMSE can be used to assessing whether changed to the model results in any improvements. The closer the value of RMSE to 0 the better the model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03463357885387822"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "CalcRSqaured(london_flows[\"Total\"], london_flows[\"unconstrainedEst1\"])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial model accounts for about 35% of the variation of flows in the system."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter calibration"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson regression\n",
    "( a Poisson or negative binomial regression model.)\n",
    "\n",
    "*Main theory*\n",
    "\n",
    "The sorts of flows that spatial interaction models deal with (such as migration or commuting flows) relate to non-negative integer counts (you can’t have negative people moving between places and you can’t - normally, if they are alive - have fractions of people moving either).\n",
    "As such, the continuous (normal) probability distributions which underpin standard regression models don’t hold. However, the discrete probability distributions such as the Poisson distribution and the negative binomial distribution (of which the Poisson distribution is a special case - wikipedia it) do hold and so we can use these associations to model our flows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "# distribution of flow\n",
    "plt.subplots(figsize=(10,10))\n",
    "\n",
    "plt.hist(london_flows[\"Total\"], histtype=\"stepfilled\" , bins = 50)\n",
    "plt.xlabel(\"London travel to work flows histogram\", fontsize = 15)\n",
    "plt.ylabel(\"Count\", fontsize= 15)\n",
    "plt.title(\"London travel to work flows\", fontsize = 20)\n",
    "plt.grid(True)\n",
    "#plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Respecify the poisson regression spatial interaction model\n",
    "\n",
    "Assume the flows follow a Poisson distribution\n",
    "Expected value $\\lambda$ verifies\n",
    "\\begin{equation} \\tag{6}\n",
    "\\lambda_{ij} = \\exp (K + \\alpha \\ln O_i + \\gamma \\ln D_j - \\beta \\ln d_{ij})\n",
    "\\end{equation}\n",
    "\n",
    "It means that $\\lambda_{ij}$, the estimate of $T_{ij}$ is *logarithmically linked* to a linear combination of the logarithm independent vairables in the model.\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run Poisson Regression Model using\n",
    "`glm` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "#take the variables and produce logarithms of them\n",
    "x_variables = [\"Oi_origpop\", \"Dj_destjob\", \"Dist\"]\n",
    "log_x_vars = []\n",
    "for x in x_variables:\n",
    "    london_flows[f\"log_{x}\"] = np.log(london_flows[x])\n",
    "    log_x_vars.append(f\"log_{x}\")\n",
    "\n",
    "#create the formula\n",
    "formula = 'Total ~ log_Oi_origpop + log_Dj_destjob + log_Dist'\n",
    "\n",
    "\n",
    "#run the regression\n",
    "uncosim = smf.glm(formula = formula, \n",
    "                  data=london_flows, \n",
    "                  family=sm.families.Poisson()).fit()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use `summmary()` function to check the model parameters\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                  Total   No. Observations:                61413\n",
      "Model:                            GLM   Df Residuals:                    61409\n",
      "Model Family:                 Poisson   Df Model:                            3\n",
      "Link Function:                    log   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:            -1.2785e+06\n",
      "Date:                Mon, 01 May 2023   Deviance:                   2.3847e+06\n",
      "Time:                        13:59:20   Pearson chi2:                 4.76e+06\n",
      "No. Iterations:                     6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept         -3.7473      0.014   -273.063      0.000      -3.774      -3.720\n",
      "log_Oi_origpop     0.7325      0.001   1048.172      0.000       0.731       0.734\n",
      "log_Dj_destjob     0.7608      0.001   1163.938      0.000       0.759       0.762\n",
      "log_Dist          -0.6228      0.001   -674.868      0.000      -0.625      -0.621\n",
      "==================================================================================\n"
     ]
    }
   ],
   "source": [
    "#extract the summary of the constrained model\n",
    "print(uncosim.summary())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: $\\beta=0.6228$ since it has a negative mark\n",
    " \n",
    "Now assign the calibrated parameters back to the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [],
   "source": [
    "#first assign the parameter values from the model to the appropriate variables\n",
    "K = uncosim.params[0]\n",
    "alpha = uncosim.params[1]\n",
    "gamma = uncosim.params[2]\n",
    "beta = -uncosim.params[3]\n",
    "\n",
    "#now plug everything back into the Equation 6 model ... \n",
    "#be careful with the negative signing of the parameter beta\n",
    "london_flows[\"unconstrainedEst2\"] = np.exp(K \n",
    "                                       + alpha*london_flows[\"log_Oi_origpop\"] \n",
    "                                       + gamma*london_flows[\"log_Dj_destjob\"] \n",
    "                                       - beta*london_flows[\"log_Dist\"])\n",
    "\n",
    "#or we can just extract the results from the actual poisson regression and apply them to the data\n",
    "predictions = uncosim.get_prediction()\n",
    "predictions_summary_frame = predictions.summary_frame()\n",
    "london_flows[\"fitted\"] = predictions_summary_frame[\"mean\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([49.61660108,  0.93718508,  2.12143467, ...,  5.34868361,\n",
       "       14.1152109 , 12.38811083])"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "uncosim.mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1542350"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#round the numbers so that we don't get a half of a person\n",
    "london_flows[\"unconstrainedEst2\"] = round(london_flows[\"unconstrainedEst2\"], 0)\n",
    "#convert to integers\n",
    "london_flows[\"unconstrainedEst2\"] = london_flows[\"unconstrainedEst2\"].astype(int)\n",
    "#check that the sum of these estimates make sense\n",
    "sum(london_flows[\"unconstrainedEst2\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>21.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>...</td>\n",
       "      <td>18.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3862</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>81.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>47.0</td>\n",
       "      <td>...</td>\n",
       "      <td>14.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>85.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>48.0</td>\n",
       "      <td>...</td>\n",
       "      <td>14.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6470</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",
       "      <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>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25.0</td>\n",
       "      <td>...</td>\n",
       "      <td>14.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>21.0</td>\n",
       "      <td>...</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>222.0</td>\n",
       "      <td>244.0</td>\n",
       "      <td>2490.0</td>\n",
       "      <td>9785.0</td>\n",
       "      <td>10329.0</td>\n",
       "      <td>260.0</td>\n",
       "      <td>725.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>10403.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4512.0</td>\n",
       "      <td>664.0</td>\n",
       "      <td>2517.0</td>\n",
       "      <td>1922.0</td>\n",
       "      <td>122.0</td>\n",
       "      <td>803.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>779.0</td>\n",
       "      <td>721.0</td>\n",
       "      <td>1542350</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN     21.0   \n",
       "Aldgate                  NaN            NaN         7.0      NaN   \n",
       "Aldgate East             NaN            NaN         7.0     85.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         7.0     26.0   \n",
       "Woodgrange Park          NaN            1.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         5.0     18.0   \n",
       "Woolwich Arsenal         5.0            NaN         NaN      NaN   \n",
       "All                    222.0          244.0      2490.0   9785.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                21.0         NaN       7.0       1.0      NaN   \n",
       "Aldgate                   81.0         NaN       NaN       1.0      NaN   \n",
       "Aldgate East               NaN         NaN       3.0       1.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  28.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             18.0         NaN       2.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN         6.0       NaN       NaN      NaN   \n",
       "All                    10329.0       260.0     725.0     187.0     39.0   \n",
       "\n",
       "Dest                Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                       ...                                          \n",
       "Abbey Road            NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central         NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town           22.0  ...       18.0             3.0         6.0   \n",
       "Aldgate              47.0  ...       14.0             NaN         8.0   \n",
       "Aldgate East         48.0  ...       14.0             3.0         8.0   \n",
       "...                   ...  ...        ...             ...         ...   \n",
       "Woodford             25.0  ...       14.0             NaN         8.0   \n",
       "Woodgrange Park       NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park        21.0  ...       11.0             NaN         6.0   \n",
       "Woolwich Arsenal      NaN  ...        NaN             NaN         NaN   \n",
       "All               10403.0  ...     4512.0           664.0      2517.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              0.0   \n",
       "Acton Town             11.0          NaN       2.0              NaN   \n",
       "Aldgate                 6.0          NaN       3.0              NaN   \n",
       "Aldgate East            7.0          NaN       3.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1922.0        122.0     803.0             42.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal      All  \n",
       "Orig                                                        \n",
       "Abbey Road                  NaN               5.0      392  \n",
       "Acton Central               NaN               NaN      333  \n",
       "Acton Town                  3.0               NaN     3862  \n",
       "Aldgate                     3.0               NaN     6107  \n",
       "Aldgate East                3.0               NaN     6470  \n",
       "...                         ...               ...      ...  \n",
       "Woodford                    NaN               NaN     3707  \n",
       "Woodgrange Park             NaN               NaN       62  \n",
       "Woodside Park               NaN               NaN     2648  \n",
       "Woolwich Arsenal            NaN               NaN     1291  \n",
       "All                       779.0             721.0  1542350  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldf_submat2=london_flows.pivot_table(values =\"unconstrainedEst2\", index=\"Orig\", columns = \"Dest\",\n",
    "                            aggfunc=np.sum, margins=True)\n",
    "ldf_submat2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32.0</td>\n",
       "      <td>599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11.0</td>\n",
       "      <td>...</td>\n",
       "      <td>77.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>...</td>\n",
       "      <td>24.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3172</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",
       "      <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>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>59.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>345.0</td>\n",
       "      <td>750.0</td>\n",
       "      <td>2202.0</td>\n",
       "      <td>7782.0</td>\n",
       "      <td>7932.0</td>\n",
       "      <td>444.0</td>\n",
       "      <td>741.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>8103.0</td>\n",
       "      <td>...</td>\n",
       "      <td>6295.0</td>\n",
       "      <td>596.0</td>\n",
       "      <td>2146.0</td>\n",
       "      <td>1578.0</td>\n",
       "      <td>404.0</td>\n",
       "      <td>706.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>745.0</td>\n",
       "      <td>4428.0</td>\n",
       "      <td>1542283</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN      3.0   \n",
       "Aldgate                  NaN            NaN         0.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0      0.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         2.0      5.0   \n",
       "Woodgrange Park          NaN            0.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         1.0     26.0   \n",
       "Woolwich Arsenal        20.0            NaN         NaN      NaN   \n",
       "All                    345.0          750.0      2202.0   7782.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                17.0         NaN      35.0       0.0      NaN   \n",
       "Aldgate                    0.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       0.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  47.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             11.0         NaN       0.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN         7.0       NaN       NaN      NaN   \n",
       "All                     7932.0       444.0     741.0     256.0    173.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          11.0  ...       77.0             3.0         6.0   \n",
       "Aldgate             17.0  ...        0.0             NaN         4.0   \n",
       "Aldgate East        20.0  ...       24.0             0.0         0.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            22.0  ...        2.0             NaN         1.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       59.0  ...        0.0             NaN         0.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               8103.0  ...     6295.0           596.0      2146.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              0.0   \n",
       "Acton Town              9.0          NaN       0.0              NaN   \n",
       "Aldgate                 8.0          NaN       0.0              NaN   \n",
       "Aldgate East           12.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1578.0        404.0     706.0            242.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal      All  \n",
       "Orig                                                        \n",
       "Abbey Road                  NaN              32.0      599  \n",
       "Acton Central               NaN               NaN     1224  \n",
       "Acton Town                  0.0               NaN     3745  \n",
       "Aldgate                     0.0               NaN     2886  \n",
       "Aldgate East                1.0               NaN     3172  \n",
       "...                         ...               ...      ...  \n",
       "Woodford                    NaN               NaN     4868  \n",
       "Woodgrange Park             NaN               NaN      530  \n",
       "Woodside Park               NaN               NaN     3093  \n",
       "Woolwich Arsenal            NaN               NaN     7892  \n",
       "All                       745.0            4428.0  1542283  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare to the real data\n",
    "ldf_submat"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check goodness of fit to see if the model has improved\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "108.335"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRMSE(london_flows[\"Total\"], london_flows[\"unconstrainedEst2\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.321184453964865"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "CalcRSqaured(london_flows[\"Total\"], london_flows[\"unconstrainedEst2\"])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RMSE improved from 485.566 to 108.335 and $r^2$ improved from 0.346 to0.321"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Production (origin)-constrained model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation} \\tag{7}\n",
    "T_{ij} = A_i O_i D_j^\\gamma d_{ij}^{-\\beta}\n",
    "\\end{equation}\n",
    "where\n",
    "\n",
    "\\begin{equation}  \\tag{8}\n",
    "O_i = \\sum_j T_{ij}\n",
    "\\end{equation}\n",
    "and\n",
    "\\begin{equation}  \\tag{9}\n",
    "A_i = \\frac{1}{\\sum_j D_j^\\gamma d_{ij}^{-\\beta}}\n",
    "\\end{equation}\n",
    " \n",
    " In the production-constrained model, $O_i$ does not have a parameter as it is a known constraint. $A_i$ is known as a <i>balancing factor</i> and is a vector of values which relate to each origin, $i$, which do the equivalent job to $k$ in the unconstrained/total constrained model but ensure that flow estimates from each origin sum to the known totals, $O_i$ rather than just the overall total."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We set about re-specifying the Production Constrained model as a Poisson regression model.\n",
    "\n",
    " We need to take logs of the right-hand side of the equation and assume that these are logarithmically linked to the Poisson distributed mean ($\\lambda_{ij}$) of the $T_{ij}$ variable. As such, Equation (7) becomes:\n",
    " \n",
    " \\begin{equation}  \\tag{10}\n",
    "\\lambda_{ij} = \\exp (\\alpha_i + \\gamma \\ln D_j - \\beta \\ln d_{ij})\n",
    "\\end{equation}\n",
    "\n",
    "where $\\alpha_i$ is the equivalent of the vector of balancing factors $A_i$, but in regression /log-linear modelling terminology can also be described as either <b>dummy variables</b> or <b>fixed effects</b>. In practical terms, what this means is that in our regression model, $\\alpha_i$ is modelled as a [categorical predictor](https://en.wikipedia.org/wiki/Categorical_variable) and therefore in the Poisson regression model, we don't use the numeric values of $O_i$, we can use a categorical identifier for the origin. In terms of the example table above, for Barking and Dagenham we wouldn't use 5675 as we would if we were fitting Equation (1), we would just used 'Barking and Dagenham'.\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model parameter calibration "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                  Total   No. Observations:                61413\n",
      "Model:                            GLM   Df Residuals:                    61013\n",
      "Model Family:                 Poisson   Df Model:                          399\n",
      "Link Function:                    log   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:            -1.0169e+06\n",
      "Date:                Mon, 01 May 2023   Deviance:                   1.8615e+06\n",
      "Time:                        13:59:52   Pearson chi2:                 2.78e+06\n",
      "No. Iterations:                     8                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================================\n",
      "                                        coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------------------------\n",
      "Orig[Abbey Road]                      3.2505      0.042     76.946      0.000       3.168       3.333\n",
      "Orig[Acton Central]                   5.0173      0.031    162.472      0.000       4.957       5.078\n",
      "Orig[Acton Town]                      4.5633      0.020    224.202      0.000       4.523       4.603\n",
      "Orig[Aldgate]                         3.3241      0.022    153.553      0.000       3.282       3.367\n",
      "Orig[Aldgate East]                    3.4580      0.021    164.953      0.000       3.417       3.499\n",
      "Orig[All Saints]                      3.3809      0.038     88.257      0.000       3.306       3.456\n",
      "Orig[Alperton]                        4.1763      0.028    150.090      0.000       4.122       4.231\n",
      "Orig[Amersham]                        4.6063      0.032    143.938      0.000       4.544       4.669\n",
      "Orig[Anerley]                         5.1612      0.041    125.449      0.000       5.081       5.242\n",
      "Orig[Angel]                           3.8368      0.019    200.477      0.000       3.799       3.874\n",
      "Orig[Archway]                         4.7031      0.018    262.859      0.000       4.668       4.738\n",
      "Orig[Arnos Grove]                     4.5650      0.022    207.369      0.000       4.522       4.608\n",
      "Orig[Arsenal]                         3.5569      0.024    145.315      0.000       3.509       3.605\n",
      "Orig[Baker Street]                    4.3779      0.016    272.017      0.000       4.346       4.409\n",
      "Orig[Balham]                          5.4264      0.016    342.836      0.000       5.395       5.457\n",
      "Orig[Bank and Monument]               5.4514      0.012    445.908      0.000       5.427       5.475\n",
      "Orig[Barbican]                        2.4094      0.030     79.130      0.000       2.350       2.469\n",
      "Orig[Barking]                         5.4781      0.017    329.043      0.000       5.445       5.511\n",
      "Orig[Barkingside]                     4.0637      0.031    133.053      0.000       4.004       4.124\n",
      "Orig[Barons Court]                    4.2171      0.020    216.083      0.000       4.179       4.255\n",
      "Orig[Bayswater]                       3.2075      0.028    115.599      0.000       3.153       3.262\n",
      "Orig[Beckton]                         4.8935      0.031    155.368      0.000       4.832       4.955\n",
      "Orig[Beckton Park]                    3.2399      0.060     54.424      0.000       3.123       3.357\n",
      "Orig[Becontree]                       4.4600      0.024    183.711      0.000       4.412       4.508\n",
      "Orig[Belsize Park]                    3.9032      0.022    173.890      0.000       3.859       3.947\n",
      "Orig[Bermondsey]                      4.2334      0.018    233.323      0.000       4.198       4.269\n",
      "Orig[Bethnal Green]                   4.5542      0.017    271.058      0.000       4.521       4.587\n",
      "Orig[Blackfriars]                     4.1492      0.016    252.343      0.000       4.117       4.181\n",
      "Orig[Blackhorse Road]                 5.3731      0.016    328.982      0.000       5.341       5.405\n",
      "Orig[Blackwall]                       3.6096      0.034    105.752      0.000       3.543       3.676\n",
      "Orig[Bond Street]                     2.8967      0.025    117.280      0.000       2.848       2.945\n",
      "Orig[Borough]                         2.5897      0.029     88.016      0.000       2.532       2.647\n",
      "Orig[Boston Manor]                    3.7072      0.032    117.123      0.000       3.645       3.769\n",
      "Orig[Bounds Green]                    4.8466      0.019    249.133      0.000       4.808       4.885\n",
      "Orig[Bow Church]                      4.5138      0.027    167.393      0.000       4.461       4.567\n",
      "Orig[Bow Road]                        4.2112      0.020    213.967      0.000       4.173       4.250\n",
      "Orig[Brent Cross]                     3.7783      0.029    131.875      0.000       3.722       3.834\n",
      "Orig[Brentwood]                       7.0930      0.025    283.952      0.000       7.044       7.142\n",
      "Orig[Brixton]                         6.0884      0.014    446.893      0.000       6.062       6.115\n",
      "Orig[Brockley]                        5.7718      0.024    243.600      0.000       5.725       5.818\n",
      "Orig[Bromley-by-Bow]                  3.8372      0.023    166.451      0.000       3.792       3.882\n",
      "Orig[Brondesbury]                     5.1543      0.025    205.717      0.000       5.105       5.203\n",
      "Orig[Brondesbury Park]                4.1189      0.040    103.791      0.000       4.041       4.197\n",
      "Orig[Bruce Grove]                     4.9399      0.034    144.518      0.000       4.873       5.007\n",
      "Orig[Buckhurst Hill]                  4.2600      0.028    152.264      0.000       4.205       4.315\n",
      "Orig[Burnt Oak]                       4.7367      0.022    213.956      0.000       4.693       4.780\n",
      "Orig[Bush Hill Park]                  5.7031      0.029    193.783      0.000       5.645       5.761\n",
      "Orig[Bushey]                          4.1824      0.066     63.400      0.000       4.053       4.312\n",
      "Orig[Caledonian Road]                 3.6920      0.022    167.472      0.000       3.649       3.735\n",
      "Orig[Caledonian Road & Barnsbury]     3.4463      0.044     77.843      0.000       3.360       3.533\n",
      "Orig[Cambridge Heath]                 3.3448      0.056     59.363      0.000       3.234       3.455\n",
      "Orig[Camden Road]                     4.5212      0.031    146.068      0.000       4.461       4.582\n",
      "Orig[Camden Town]                     3.7450      0.021    180.507      0.000       3.704       3.786\n",
      "Orig[Canada Water]                    5.9310      0.013    453.555      0.000       5.905       5.957\n",
      "Orig[Canary Wharf]                    5.3826      0.014    382.889      0.000       5.355       5.410\n",
      "Orig[Canning Town]                    5.8929      0.014    433.423      0.000       5.866       5.920\n",
      "Orig[Cannon Street]                   3.2989      0.019    171.691      0.000       3.261       3.337\n",
      "Orig[Canonbury]                       4.8840      0.023    211.250      0.000       4.839       4.929\n",
      "Orig[Canons Park]                     4.6020      0.024    188.614      0.000       4.554       4.650\n",
      "Orig[Carpenders Park]                 5.8768      0.030    195.349      0.000       5.818       5.936\n",
      "Orig[Chadwell Heath]                  7.0122      0.020    350.980      0.000       6.973       7.051\n",
      "Orig[Chalfont & Latimer]              4.4226      0.035    125.311      0.000       4.353       4.492\n",
      "Orig[Chalk Farm]                      3.6081      0.024    153.440      0.000       3.562       3.654\n",
      "Orig[Chancery Lane]                   2.3540      0.032     74.710      0.000       2.292       2.416\n",
      "Orig[Charing Cross]                   3.9131      0.016    238.531      0.000       3.881       3.945\n",
      "Orig[Chesham]                         4.5093      0.035    127.041      0.000       4.440       4.579\n",
      "Orig[Cheshunt]                        4.2752      0.077     55.169      0.000       4.123       4.427\n",
      "Orig[Chigwell]                        3.2399      0.048     67.717      0.000       3.146       3.334\n",
      "Orig[Chingford]                       6.1056      0.025    239.586      0.000       6.056       6.156\n",
      "Orig[Chiswick Park]                   3.4758      0.030    114.303      0.000       3.416       3.535\n",
      "Orig[Chorleywood]                     4.3280      0.036    120.505      0.000       4.258       4.398\n",
      "Orig[Clapham Common]                  4.5150      0.019    243.312      0.000       4.479       4.551\n",
      "Orig[Clapham High Street]             5.6802      0.028    201.272      0.000       5.625       5.736\n",
      "Orig[Clapham Junction]                6.8316      0.017    403.398      0.000       6.798       6.865\n",
      "Orig[Clapham North]                   3.8971      0.022    176.130      0.000       3.854       3.940\n",
      "Orig[Clapham South]                   4.9353      0.017    287.611      0.000       4.902       4.969\n",
      "Orig[Clapton]                         5.1186      0.028    179.939      0.000       5.063       5.174\n",
      "Orig[Cockfosters]                     3.7890      0.034    111.009      0.000       3.722       3.856\n",
      "Orig[Colindale]                       5.2181      0.019    281.572      0.000       5.182       5.254\n",
      "Orig[Colliers Wood]                   5.0816      0.018    278.933      0.000       5.046       5.117\n",
      "Orig[Covent Garden]                   1.2227      0.050     24.577      0.000       1.125       1.320\n",
      "Orig[Crossharbour]                    4.3361      0.026    164.283      0.000       4.284       4.388\n",
      "Orig[Crouch Hill]                     4.0859      0.052     78.657      0.000       3.984       4.188\n",
      "Orig[Croxley]                         4.2774      0.034    126.658      0.000       4.211       4.344\n",
      "Orig[Crystal Palace]                  6.3061      0.026    245.027      0.000       6.256       6.357\n",
      "Orig[Custom House]                    3.8338      0.037    102.540      0.000       3.760       3.907\n",
      "Orig[Cutty Sark]                      4.9468      0.024    202.283      0.000       4.899       4.995\n",
      "Orig[Cyprus]                          3.8319      0.046     82.919      0.000       3.741       3.922\n",
      "Orig[Dagenham East]                   4.4272      0.026    169.343      0.000       4.376       4.478\n",
      "Orig[Dagenham Heathway]               4.8835      0.021    227.994      0.000       4.841       4.925\n",
      "Orig[Dalston Junction]                5.6646      0.020    289.901      0.000       5.626       5.703\n",
      "Orig[Dalston Kingsland]               5.3150      0.022    243.883      0.000       5.272       5.358\n",
      "Orig[Debden]                          4.4303      0.028    158.610      0.000       4.376       4.485\n",
      "Orig[Denmark Hill]                    5.6427      0.026    216.839      0.000       5.592       5.694\n",
      "Orig[Deptford Bridge]                 5.2986      0.023    229.598      0.000       5.253       5.344\n",
      "Orig[Devons Road]                     4.2504      0.029    146.256      0.000       4.193       4.307\n",
      "Orig[Dollis Hill]                     4.1873      0.023    179.787      0.000       4.142       4.233\n",
      "Orig[Ealing Broadway]                 5.9319      0.015    390.827      0.000       5.902       5.962\n",
      "Orig[Ealing Common]                   4.0075      0.025    157.550      0.000       3.958       4.057\n",
      "Orig[Earl's Court]                    4.7579      0.016    301.934      0.000       4.727       4.789\n",
      "Orig[East Acton]                      4.0310      0.024    168.778      0.000       3.984       4.078\n",
      "Orig[East Finchley]                   5.0351      0.018    280.349      0.000       5.000       5.070\n",
      "Orig[East Ham]                        5.3224      0.017    319.654      0.000       5.290       5.355\n",
      "Orig[East India]                      4.2534      0.026    162.543      0.000       4.202       4.305\n",
      "Orig[East Putney]                     4.8447      0.018    266.972      0.000       4.809       4.880\n",
      "Orig[Eastcote]                        4.7755      0.024    201.911      0.000       4.729       4.822\n",
      "Orig[Edgware]                         4.9250      0.021    230.575      0.000       4.883       4.967\n",
      "Orig[Edgware Road]                    3.5276      0.022    161.136      0.000       3.485       3.571\n",
      "Orig[Edmonton Green]                  5.8359      0.025    233.802      0.000       5.787       5.885\n",
      "Orig[Elephant & Castle]               4.6169      0.015    301.537      0.000       4.587       4.647\n",
      "Orig[Elm Park]                        4.8801      0.023    211.592      0.000       4.835       4.925\n",
      "Orig[Elverson Road]                   4.6196      0.032    146.342      0.000       4.558       4.681\n",
      "Orig[Embankment]                      3.4815      0.019    183.087      0.000       3.444       3.519\n",
      "Orig[Emerson Park]                    6.4012      0.056    115.144      0.000       6.292       6.510\n",
      "Orig[Enfield Town]                    6.0142      0.027    225.983      0.000       5.962       6.066\n",
      "Orig[Epping]                          5.1645      0.023    226.300      0.000       5.120       5.209\n",
      "Orig[Euston]                          5.1141      0.013    384.015      0.000       5.088       5.140\n",
      "Orig[Euston Square]                   4.0242      0.018    221.764      0.000       3.989       4.060\n",
      "Orig[Fairlop]                         3.8649      0.034    112.976      0.000       3.798       3.932\n",
      "Orig[Farringdon]                      3.9370      0.018    219.279      0.000       3.902       3.972\n",
      "Orig[Finchley Central]                5.2672      0.018    296.754      0.000       5.232       5.302\n",
      "Orig[Finchley Road]                   4.4219      0.019    236.857      0.000       4.385       4.458\n",
      "Orig[Finchley Road & Frognal]         4.5509      0.032    143.904      0.000       4.489       4.613\n",
      "Orig[Finsbury Park]                   6.0491      0.013    450.963      0.000       6.023       6.075\n",
      "Orig[Forest Gate]                     5.7517      0.023    246.222      0.000       5.706       5.797\n",
      "Orig[Forest Hill]                     6.1013      0.023    260.413      0.000       6.055       6.147\n",
      "Orig[Fulham Broadway]                 4.0273      0.021    191.953      0.000       3.986       4.068\n",
      "Orig[Gallions Reach]                  4.1719      0.041    100.884      0.000       4.091       4.253\n",
      "Orig[Gants Hill]                      5.2089      0.019    278.150      0.000       5.172       5.246\n",
      "Orig[Gidea Park]                      7.0950      0.021    338.697      0.000       7.054       7.136\n",
      "Orig[Gloucester Road]                 4.1217      0.018    224.263      0.000       4.086       4.158\n",
      "Orig[Golders Green]                   4.8034      0.019    253.704      0.000       4.766       4.840\n",
      "Orig[Goldhawk Road]                   3.3610      0.030    113.330      0.000       3.303       3.419\n",
      "Orig[Goodge Street]                   1.2026      0.053     22.519      0.000       1.098       1.307\n",
      "Orig[Goodmayes]                       6.6800      0.021    311.496      0.000       6.638       6.722\n",
      "Orig[Gospel Oak]                      4.3418      0.032    133.833      0.000       4.278       4.405\n",
      "Orig[Grange Hill]                     3.5695      0.041     86.682      0.000       3.489       3.650\n",
      "Orig[Great Portland Street]           2.6018      0.032     81.994      0.000       2.540       2.664\n",
      "Orig[Green Park]                      2.9029      0.025    118.146      0.000       2.855       2.951\n",
      "Orig[Greenford]                       4.6460      0.023    201.886      0.000       4.601       4.691\n",
      "Orig[Greenwich]                       4.5998      0.029    157.304      0.000       4.543       4.657\n",
      "Orig[Gunnersbury]                     4.0043      0.024    165.296      0.000       3.957       4.052\n",
      "Orig[Hackney Central]                 5.5538      0.021    268.766      0.000       5.513       5.594\n",
      "Orig[Hackney Downs]                   4.8990      0.036    135.247      0.000       4.828       4.970\n",
      "Orig[Hackney Wick]                    4.4134      0.028    155.374      0.000       4.358       4.469\n",
      "Orig[Haggerston]                      4.9651      0.025    200.651      0.000       4.917       5.014\n",
      "Orig[Hainault]                        4.9621      0.022    224.767      0.000       4.919       5.005\n",
      "Orig[Hammersmith]                     5.3868      0.015    361.137      0.000       5.358       5.416\n",
      "Orig[Hampstead]                       3.6910      0.026    143.041      0.000       3.640       3.742\n",
      "Orig[Hampstead Heath]                 4.2251      0.035    120.709      0.000       4.156       4.294\n",
      "Orig[Hanger Lane]                     4.1945      0.026    163.754      0.000       4.144       4.245\n",
      "Orig[Harlesden]                       3.6275      0.029    127.161      0.000       3.572       3.683\n",
      "Orig[Harold Wood]                     7.1727      0.022    323.707      0.000       7.129       7.216\n",
      "Orig[Harringay Green Lanes]           4.5906      0.046     99.951      0.000       4.501       4.681\n",
      "Orig[Harrow & Wealdstone]             4.2615      0.027    156.963      0.000       4.208       4.315\n",
      "Orig[Harrow-on-the-Hill]              5.4444      0.018    305.894      0.000       5.409       5.479\n",
      "Orig[Hatch End]                       5.4926      0.036    150.621      0.000       5.421       5.564\n",
      "Orig[Hatton Cross]                    4.1848      0.030    139.221      0.000       4.126       4.244\n",
      "Orig[Headstone Lane]                  4.7890      0.048    100.339      0.000       4.695       4.883\n",
      "Orig[Heathrow Terminal 4]             3.7040      0.037     98.939      0.000       3.631       3.777\n",
      "Orig[Heathrow Terminal 5]             3.9501      0.035    112.256      0.000       3.881       4.019\n",
      "Orig[Heathrow Terminals 2 & 3]        4.6778      0.025    187.265      0.000       4.629       4.727\n",
      "Orig[Hendon Central]                  4.8067      0.020    240.108      0.000       4.767       4.846\n",
      "Orig[Heron Quays]                     3.7343      0.026    145.444      0.000       3.684       3.785\n",
      "Orig[High Barnet]                     4.9382      0.022    227.423      0.000       4.896       4.981\n",
      "Orig[High Street Kensington]          3.4193      0.024    140.211      0.000       3.371       3.467\n",
      "Orig[Highams Park]                    6.1397      0.022    276.703      0.000       6.096       6.183\n",
      "Orig[Highbury & Islington]            5.7845      0.013    435.271      0.000       5.758       5.811\n",
      "Orig[Highgate]                        4.6619      0.019    243.983      0.000       4.624       4.699\n",
      "Orig[Hillingdon]                      4.3397      0.030    143.410      0.000       4.280       4.399\n",
      "Orig[Holborn]                         2.6430      0.027     98.468      0.000       2.590       2.696\n",
      "Orig[Holland Park]                    3.2004      0.028    114.478      0.000       3.146       3.255\n",
      "Orig[Holloway Road]                   3.8276      0.022    177.765      0.000       3.785       3.870\n",
      "Orig[Homerton]                        5.3998      0.020    263.723      0.000       5.360       5.440\n",
      "Orig[Honor Oak Park]                  5.6630      0.027    212.996      0.000       5.611       5.715\n",
      "Orig[Hornchurch]                      4.5201      0.027    164.658      0.000       4.466       4.574\n",
      "Orig[Hounslow Central]                4.4807      0.025    181.118      0.000       4.432       4.529\n",
      "Orig[Hounslow East]                   4.4546      0.025    178.948      0.000       4.406       4.503\n",
      "Orig[Hounslow West]                   4.5013      0.025    177.110      0.000       4.451       4.551\n",
      "Orig[Hoxton]                          4.2549      0.033    129.231      0.000       4.190       4.319\n",
      "Orig[Hyde Park Corner]                0.9684      0.063     15.342      0.000       0.845       1.092\n",
      "Orig[Ickenham]                        3.8251      0.039     97.974      0.000       3.749       3.902\n",
      "Orig[Ilford]                          7.0791      0.018    389.319      0.000       7.043       7.115\n",
      "Orig[Imperial Wharf]                  4.4992      0.036    125.364      0.000       4.429       4.570\n",
      "Orig[Island Gardens]                  4.4114      0.029    153.022      0.000       4.355       4.468\n",
      "Orig[Kennington]                      3.7628      0.020    186.201      0.000       3.723       3.802\n",
      "Orig[Kensal Green]                    3.7768      0.026    144.239      0.000       3.726       3.828\n",
      "Orig[Kensal Rise]                     5.1087      0.025    200.788      0.000       5.059       5.159\n",
      "Orig[Kensington]                      2.0413      0.050     41.232      0.000       1.944       2.138\n",
      "Orig[Kentish Town]                    3.6333      0.023    154.818      0.000       3.587       3.679\n",
      "Orig[Kentish Town West]               3.9128      0.039     99.976      0.000       3.836       3.989\n",
      "Orig[Kenton]                          4.0411      0.033    121.136      0.000       3.976       4.107\n",
      "Orig[Kew Gardens]                     4.0929      0.024    167.557      0.000       4.045       4.141\n",
      "Orig[Kilburn]                         4.5874      0.019    242.033      0.000       4.550       4.625\n",
      "Orig[Kilburn High Road]               4.1420      0.055     75.327      0.000       4.034       4.250\n",
      "Orig[Kilburn Park]                    3.6307      0.026    140.170      0.000       3.580       3.681\n",
      "Orig[King George V]                   4.4734      0.034    130.886      0.000       4.406       4.540\n",
      "Orig[King's Cross St. Pancras]        5.6172      0.013    446.665      0.000       5.593       5.642\n",
      "Orig[Kingsbury]                       4.5973      0.023    200.468      0.000       4.552       4.642\n",
      "Orig[Knightsbridge]                   2.5503      0.032     79.991      0.000       2.488       2.613\n",
      "Orig[Ladbroke Grove]                  3.7836      0.024    159.763      0.000       3.737       3.830\n",
      "Orig[Lambeth North]                   2.4198      0.032     75.738      0.000       2.357       2.482\n",
      "Orig[Lancaster Gate]                  3.8682      0.020    189.727      0.000       3.828       3.908\n",
      "Orig[Langdon Park]                    4.2187      0.028    148.916      0.000       4.163       4.274\n",
      "Orig[Latimer Road]                    2.8415      0.036     78.799      0.000       2.771       2.912\n",
      "Orig[Leicester Square]                1.9982      0.034     59.470      0.000       1.932       2.064\n",
      "Orig[Lewisham]                        6.6655      0.016    409.188      0.000       6.634       6.697\n",
      "Orig[Leyton]                          5.1581      0.017    309.778      0.000       5.126       5.191\n",
      "Orig[Leyton Midland Road]             5.5454      0.036    153.423      0.000       5.475       5.616\n",
      "Orig[Leytonstone]                     5.1785      0.017    298.572      0.000       5.144       5.212\n",
      "Orig[Leytonstone High Road]           5.3539      0.042    128.692      0.000       5.272       5.435\n",
      "Orig[Limehouse]                       5.4604      0.018    310.240      0.000       5.426       5.495\n",
      "Orig[Liverpool Street]                5.5910      0.012    457.939      0.000       5.567       5.615\n",
      "Orig[London Bridge]                   5.6957      0.012    461.787      0.000       5.672       5.720\n",
      "Orig[London City Airport]             5.1062      0.025    203.814      0.000       5.057       5.155\n",
      "Orig[London Fields]                   4.8417      0.032    149.649      0.000       4.778       4.905\n",
      "Orig[Loughton]                        4.8288      0.023    209.259      0.000       4.784       4.874\n",
      "Orig[Maida Vale]                      3.6251      0.025    147.418      0.000       3.577       3.673\n",
      "Orig[Manor House]                     4.6584      0.018    258.188      0.000       4.623       4.694\n",
      "Orig[Manor Park]                      5.7111      0.027    215.463      0.000       5.659       5.763\n",
      "Orig[Mansion House]                   1.4690      0.045     32.408      0.000       1.380       1.558\n",
      "Orig[Marble Arch]                     2.9551      0.026    113.499      0.000       2.904       3.006\n",
      "Orig[Maryland]                        4.1673      0.035    117.687      0.000       4.098       4.237\n",
      "Orig[Marylebone]                      4.2213      0.017    248.716      0.000       4.188       4.255\n",
      "Orig[Mile End]                        4.7130      0.017    283.280      0.000       4.680       4.746\n",
      "Orig[Mill Hill East]                  3.8667      0.031    126.669      0.000       3.807       3.927\n",
      "Orig[Moor Park]                       3.7786      0.041     91.249      0.000       3.697       3.860\n",
      "Orig[Moorgate]                        3.5234      0.018    190.777      0.000       3.487       3.560\n",
      "Orig[Morden]                          5.6225      0.017    334.117      0.000       5.590       5.656\n",
      "Orig[Mornington Crescent]             2.0685      0.040     52.153      0.000       1.991       2.146\n",
      "Orig[Mudchute]                        4.2282      0.029    144.458      0.000       4.171       4.286\n",
      "Orig[Neasden]                         4.1478      0.024    172.376      0.000       4.101       4.195\n",
      "Orig[New Cross]                       5.3356      0.029    185.645      0.000       5.279       5.392\n",
      "Orig[New Cross Gate]                  5.3319      0.027    199.208      0.000       5.279       5.384\n",
      "Orig[Newbury Park]                    5.1059      0.020    255.114      0.000       5.067       5.145\n",
      "Orig[North Acton]                     4.3849      0.022    201.444      0.000       4.342       4.428\n",
      "Orig[North Ealing]                    2.9572      0.046     64.058      0.000       2.867       3.048\n",
      "Orig[North Greenwich]                 5.3416      0.015    349.303      0.000       5.312       5.372\n",
      "Orig[North Harrow]                    4.4695      0.026    170.723      0.000       4.418       4.521\n",
      "Orig[North Wembley]                   3.6739      0.033    111.991      0.000       3.610       3.738\n",
      "Orig[Northfields]                     4.5387      0.022    204.888      0.000       4.495       4.582\n",
      "Orig[Northolt]                        5.0234      0.021    238.831      0.000       4.982       5.065\n",
      "Orig[Northwick Park]                  4.3347      0.025    172.697      0.000       4.285       4.384\n",
      "Orig[Northwood]                       4.7021      0.026    182.710      0.000       4.652       4.752\n",
      "Orig[Northwood Hills]                 4.3236      0.029    147.889      0.000       4.266       4.381\n",
      "Orig[Norwood Junction]                5.2320      0.040    129.892      0.000       5.153       5.311\n",
      "Orig[Notting Hill Gate]               4.2283      0.018    231.682      0.000       4.193       4.264\n",
      "Orig[Oakwood]                         4.2732      0.027    158.472      0.000       4.220       4.326\n",
      "Orig[Old Street]                      4.0142      0.018    227.480      0.000       3.980       4.049\n",
      "Orig[Osterley]                        4.0184      0.029    136.810      0.000       3.961       4.076\n",
      "Orig[Oval]                            3.9318      0.020    194.102      0.000       3.892       3.972\n",
      "Orig[Oxford Circus]                   3.1635      0.022    144.866      0.000       3.121       3.206\n",
      "Orig[Paddington]                      5.7734      0.013    437.389      0.000       5.748       5.799\n",
      "Orig[Park Royal]                      3.0356      0.044     68.856      0.000       2.949       3.122\n",
      "Orig[Parsons Green]                   4.3925      0.019    229.064      0.000       4.355       4.430\n",
      "Orig[Peckham Rye]                     5.7362      0.023    245.670      0.000       5.690       5.782\n",
      "Orig[Penge West]                      4.6344      0.054     86.048      0.000       4.529       4.740\n",
      "Orig[Perivale]                        4.1058      0.028    147.583      0.000       4.051       4.160\n",
      "Orig[Piccadilly Circus]               2.0928      0.033     63.680      0.000       2.028       2.157\n",
      "Orig[Pimlico]                         3.9141      0.020    199.358      0.000       3.876       3.953\n",
      "Orig[Pinner]                          4.9112      0.023    216.912      0.000       4.867       4.956\n",
      "Orig[Plaistow]                        4.3072      0.020    210.825      0.000       4.267       4.347\n",
      "Orig[Pontoon Dock]                    4.9229      0.025    196.723      0.000       4.874       4.972\n",
      "Orig[Poplar]                          4.1194      0.023    176.265      0.000       4.074       4.165\n",
      "Orig[Preston Road]                    4.3717      0.024    181.768      0.000       4.325       4.419\n",
      "Orig[Prince Regent]                   4.0980      0.035    118.558      0.000       4.030       4.166\n",
      "Orig[Pudding Mill Lane]               3.0159      0.049     61.101      0.000       2.919       3.113\n",
      "Orig[Putney Bridge]                   4.1110      0.022    187.378      0.000       4.068       4.154\n",
      "Orig[Queen's Park]                    4.6147      0.018    253.095      0.000       4.579       4.650\n",
      "Orig[Queens Road Peckham]             5.4829      0.025    215.822      0.000       5.433       5.533\n",
      "Orig[Queensbury]                      4.7283      0.022    210.446      0.000       4.684       4.772\n",
      "Orig[Queensway]                       3.6686      0.022    164.081      0.000       3.625       3.712\n",
      "Orig[Ravenscourt Park]                3.4140      0.028    122.214      0.000       3.359       3.469\n",
      "Orig[Rayners Lane]                    4.9551      0.021    233.511      0.000       4.913       4.997\n",
      "Orig[Rectory Road]                    4.6642      0.034    135.579      0.000       4.597       4.732\n",
      "Orig[Redbridge]                       4.2329      0.025    167.067      0.000       4.183       4.283\n",
      "Orig[Regent's Park]                   1.3624      0.053     25.659      0.000       1.258       1.466\n",
      "Orig[Richmond]                        5.0637      0.019    270.555      0.000       5.027       5.100\n",
      "Orig[Rickmansworth]                   4.4091      0.031    141.581      0.000       4.348       4.470\n",
      "Orig[Roding Valley]                   3.1813      0.051     62.163      0.000       3.081       3.282\n",
      "Orig[Romford]                         7.4010      0.019    380.809      0.000       7.363       7.439\n",
      "Orig[Rotherhithe]                     4.3862      0.027    162.521      0.000       4.333       4.439\n",
      "Orig[Royal Albert]                    3.9123      0.041     95.717      0.000       3.832       3.992\n",
      "Orig[Royal Oak]                       3.1474      0.029    108.353      0.000       3.091       3.204\n",
      "Orig[Royal Victoria]                  4.6648      0.025    189.316      0.000       4.616       4.713\n",
      "Orig[Ruislip]                         4.2504      0.031    139.320      0.000       4.191       4.310\n",
      "Orig[Ruislip Gardens]                 4.0542      0.035    116.845      0.000       3.986       4.122\n",
      "Orig[Ruislip Manor]                   4.2721      0.030    144.116      0.000       4.214       4.330\n",
      "Orig[Russell Square]                  2.6244      0.028     93.704      0.000       2.569       2.679\n",
      "Orig[Seven Kings]                     6.6629      0.021    317.201      0.000       6.622       6.704\n",
      "Orig[Seven Sisters]                   6.0264      0.014    427.081      0.000       5.999       6.054\n",
      "Orig[Shadwell]                        5.2879      0.016    322.353      0.000       5.256       5.320\n",
      "Orig[Shenfield]                       5.0659      0.065     78.154      0.000       4.939       5.193\n",
      "Orig[Shepherd's Bush]                 5.1288      0.015    337.488      0.000       5.099       5.159\n",
      "Orig[Shepherd's Bush Market]          3.6332      0.026    137.918      0.000       3.582       3.685\n",
      "Orig[Shoreditch High Street]          4.1337      0.035    119.474      0.000       4.066       4.202\n",
      "Orig[Silver Street]                   5.6019      0.027    203.959      0.000       5.548       5.656\n",
      "Orig[Sloane Square]                   4.0787      0.018    224.329      0.000       4.043       4.114\n",
      "Orig[Snaresbrook]                     4.0430      0.027    151.062      0.000       3.990       4.095\n",
      "Orig[South Acton]                     4.4199      0.041    107.741      0.000       4.339       4.500\n",
      "Orig[South Ealing]                    4.2029      0.025    170.097      0.000       4.154       4.251\n",
      "Orig[South Hampstead]                 4.0605      0.064     62.972      0.000       3.934       4.187\n",
      "Orig[South Harrow]                    4.2260      0.029    147.342      0.000       4.170       4.282\n",
      "Orig[South Kensington]                4.1608      0.018    229.622      0.000       4.125       4.196\n",
      "Orig[South Kenton]                    3.7960      0.033    115.008      0.000       3.731       3.861\n",
      "Orig[South Quay]                      4.1478      0.027    155.737      0.000       4.096       4.200\n",
      "Orig[South Ruislip]                   4.2549      0.030    143.255      0.000       4.197       4.313\n",
      "Orig[South Tottenham]                 4.5276      0.050     90.213      0.000       4.429       4.626\n",
      "Orig[South Wimbledon]                 4.8196      0.020    235.355      0.000       4.779       4.860\n",
      "Orig[South Woodford]                  4.9073      0.020    245.714      0.000       4.868       4.946\n",
      "Orig[Southbury]                       4.9559      0.044    111.463      0.000       4.869       5.043\n",
      "Orig[Southfields]                     4.9299      0.018    266.719      0.000       4.894       4.966\n",
      "Orig[Southgate]                       4.8485      0.021    232.987      0.000       4.808       4.889\n",
      "Orig[Southwark]                       3.8254      0.018    211.320      0.000       3.790       3.861\n",
      "Orig[St James Street]                 4.9434      0.033    149.932      0.000       4.879       5.008\n",
      "Orig[St. James's Park]                2.8634      0.026    110.213      0.000       2.813       2.914\n",
      "Orig[St. John's Wood]                 3.9202      0.021    185.898      0.000       3.879       3.962\n",
      "Orig[St. Paul's]                      2.0808      0.036     58.585      0.000       2.011       2.150\n",
      "Orig[Stamford Brook]                  3.6653      0.026    140.187      0.000       3.614       3.717\n",
      "Orig[Stamford Hill]                   4.2372      0.046     91.140      0.000       4.146       4.328\n",
      "Orig[Stanmore]                        4.7910      0.023    205.281      0.000       4.745       4.837\n",
      "Orig[Star Lane]                       3.0049      0.049     61.325      0.000       2.909       3.101\n",
      "Orig[Stepney Green]                   3.6503      0.022    163.219      0.000       3.607       3.694\n",
      "Orig[Stockwell]                       5.0865      0.015    336.065      0.000       5.057       5.116\n",
      "Orig[Stoke Newington]                 4.8656      0.032    150.391      0.000       4.802       4.929\n",
      "Orig[Stonebridge Park]                3.7271      0.029    129.712      0.000       3.671       3.783\n",
      "Orig[Stratford]                       6.9149      0.012    555.238      0.000       6.890       6.939\n",
      "Orig[Stratford High Street]           2.7158      0.052     51.883      0.000       2.613       2.818\n",
      "Orig[Stratford International]         4.9633      0.024    209.922      0.000       4.917       5.010\n",
      "Orig[Sudbury Hill]                    4.0632      0.030    134.705      0.000       4.004       4.122\n",
      "Orig[Sudbury Town]                    4.1677      0.029    144.606      0.000       4.111       4.224\n",
      "Orig[Surrey Quays]                    5.3120      0.020    266.412      0.000       5.273       5.351\n",
      "Orig[Swiss Cottage]                   4.0918      0.020    199.614      0.000       4.052       4.132\n",
      "Orig[Sydenham]                        5.9224      0.026    226.133      0.000       5.871       5.974\n",
      "Orig[Temple]                          1.1977      0.055     21.910      0.000       1.091       1.305\n",
      "Orig[Theobalds Grove]                 5.2464      0.046    115.300      0.000       5.157       5.336\n",
      "Orig[Theydon Bois]                    3.7828      0.041     93.108      0.000       3.703       3.862\n",
      "Orig[Tooting Bec]                     5.0997      0.017    296.853      0.000       5.066       5.133\n",
      "Orig[Tooting Broadway]                5.5424      0.016    346.678      0.000       5.511       5.574\n",
      "Orig[Tottenham Court Road]            2.6629      0.026    102.043      0.000       2.612       2.714\n",
      "Orig[Tottenham Hale]                  5.3598      0.016    332.368      0.000       5.328       5.391\n",
      "Orig[Totteridge & Whetstone]          4.4970      0.024    184.214      0.000       4.449       4.545\n",
      "Orig[Tower Gateway]                   3.9722      0.036    110.033      0.000       3.901       4.043\n",
      "Orig[Tower Hill]                      4.3510      0.015    281.469      0.000       4.321       4.381\n",
      "Orig[Tufnell Park]                    3.8688      0.022    172.524      0.000       3.825       3.913\n",
      "Orig[Turkey Street]                   5.4835      0.037    146.309      0.000       5.410       5.557\n",
      "Orig[Turnham Green]                   4.3810      0.020    214.932      0.000       4.341       4.421\n",
      "Orig[Turnpike Lane]                   5.0609      0.017    293.275      0.000       5.027       5.095\n",
      "Orig[Upminster]                       3.7190      0.039     94.570      0.000       3.642       3.796\n",
      "Orig[Upminster Bridge]                3.8680      0.038    101.535      0.000       3.793       3.943\n",
      "Orig[Upney]                           4.0825      0.027    151.086      0.000       4.030       4.135\n",
      "Orig[Upper Holloway]                  3.8811      0.053     73.071      0.000       3.777       3.985\n",
      "Orig[Upton Park]                      4.9368      0.018    278.116      0.000       4.902       4.972\n",
      "Orig[Uxbridge]                        5.0258      0.023    217.403      0.000       4.981       5.071\n",
      "Orig[Vauxhall]                        5.4789      0.014    391.029      0.000       5.451       5.506\n",
      "Orig[Victoria]                        5.9610      0.012    485.458      0.000       5.937       5.985\n",
      "Orig[Walthamstow Central]             6.1643      0.014    426.335      0.000       6.136       6.193\n",
      "Orig[Walthamstow Queens Road]         5.8409      0.033    174.408      0.000       5.775       5.907\n",
      "Orig[Wandsworth Road]                 4.6341      0.042    110.817      0.000       4.552       4.716\n",
      "Orig[Wanstead]                        4.1227      0.026    160.630      0.000       4.072       4.173\n",
      "Orig[Wanstead Park]                   5.6655      0.038    149.272      0.000       5.591       5.740\n",
      "Orig[Wapping]                         4.3586      0.030    144.690      0.000       4.300       4.418\n",
      "Orig[Warren Street]                   2.8454      0.025    112.236      0.000       2.796       2.895\n",
      "Orig[Warwick Avenue]                  3.6174      0.024    153.839      0.000       3.571       3.663\n",
      "Orig[Waterloo]                        6.4159      0.012    550.700      0.000       6.393       6.439\n",
      "Orig[Watford]                         4.5940      0.030    153.885      0.000       4.536       4.653\n",
      "Orig[Watford High Street]             4.9465      0.048    103.409      0.000       4.853       5.040\n",
      "Orig[Watford Junction]                5.1324      0.047    109.651      0.000       5.041       5.224\n",
      "Orig[Wembley Central]                 4.2204      0.024    172.372      0.000       4.172       4.268\n",
      "Orig[Wembley Park]                    5.3698      0.017    311.914      0.000       5.336       5.404\n",
      "Orig[West Acton]                      3.5896      0.032    113.276      0.000       3.528       3.652\n",
      "Orig[West Brompton]                   3.9990      0.020    201.856      0.000       3.960       4.038\n",
      "Orig[West Croydon]                    6.2104      0.030    206.449      0.000       6.151       6.269\n",
      "Orig[West Finchley]                   4.0019      0.028    141.379      0.000       3.946       4.057\n",
      "Orig[West Ham]                        4.9864      0.016    316.184      0.000       4.956       5.017\n",
      "Orig[West Hampstead]                  5.1881      0.015    339.459      0.000       5.158       5.218\n",
      "Orig[West Harrow]                     3.7603      0.034    111.484      0.000       3.694       3.826\n",
      "Orig[West India Quay]                 1.1845      0.079     14.959      0.000       1.029       1.340\n",
      "Orig[West Kensington]                 3.7518      0.022    167.628      0.000       3.708       3.796\n",
      "Orig[West Ruislip]                    4.1920      0.033    126.659      0.000       4.127       4.257\n",
      "Orig[West Silvertown]                 4.0022      0.035    113.703      0.000       3.933       4.071\n",
      "Orig[Westbourne Park]                 3.7701      0.023    160.476      0.000       3.724       3.816\n",
      "Orig[Westferry]                       4.3127      0.024    181.151      0.000       4.266       4.359\n",
      "Orig[Westminster]                     2.6045      0.028     93.354      0.000       2.550       2.659\n",
      "Orig[White City]                      3.9076      0.023    166.549      0.000       3.862       3.954\n",
      "Orig[White Hart Lane]                 4.9897      0.033    150.075      0.000       4.925       5.055\n",
      "Orig[Whitechapel]                     4.9327      0.015    340.170      0.000       4.904       4.961\n",
      "Orig[Willesden Green]                 4.8735      0.018    271.341      0.000       4.838       4.909\n",
      "Orig[Willesden Junction]              4.7270      0.018    258.586      0.000       4.691       4.763\n",
      "Orig[Wimbledon]                       5.4450      0.017    315.133      0.000       5.411       5.479\n",
      "Orig[Wimbledon Park]                  3.9560      0.027    144.168      0.000       3.902       4.010\n",
      "Orig[Wood Green]                      5.1384      0.017    296.298      0.000       5.104       5.172\n",
      "Orig[Wood Lane]                       3.1550      0.033     96.994      0.000       3.091       3.219\n",
      "Orig[Wood Street]                     5.2424      0.030    177.454      0.000       5.184       5.300\n",
      "Orig[Woodford]                        5.1610      0.019    269.965      0.000       5.124       5.199\n",
      "Orig[Woodgrange Park]                 5.2550      0.045    117.035      0.000       5.167       5.343\n",
      "Orig[Woodside Park]                   4.6990      0.022    213.973      0.000       4.656       4.742\n",
      "Orig[Woolwich Arsenal]                6.9060      0.017    417.032      0.000       6.874       6.938\n",
      "log_Dj_destjob                        0.7686      0.001   1229.524      0.000       0.767       0.770\n",
      "log_Dist                             -0.8782      0.001   -767.082      0.000      -0.880      -0.876\n",
      "=====================================================================================================\n"
     ]
    }
   ],
   "source": [
    "#create the formula (the \"-1\" indicates no intercept in the regression model).\n",
    "formula = 'Total ~ Orig + log_Dj_destjob + log_Dist-1'\n",
    "#run a production constrained sim\n",
    "prodSim = smf.glm(formula = formula, data=london_flows, family=sm.families.Poisson()).fit()\n",
    "#let's have a look at it's summary\n",
    "print(prodSim.summary())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\gamma$=0.7686\n",
    "\n",
    "$\\beta$=0.8782"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model estimates"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create $O_i$ and $D_j$ columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create some Oi and Dj columns in the dataframe and store row and column totals in them:\n",
    "#to create O_i, take london_flows ...then... group by orig ...then... summarise by calculating the sum of Total\n",
    "O_i = pd.DataFrame(london_flows.groupby([\"Orig\"])[\"Total\"].agg(np.sum))\n",
    "O_i.rename(columns={\"Total\":\"O_i\"}, inplace = True)\n",
    "london_flows = london_flows.merge(O_i, on = \"Orig\", how = \"left\" )\n",
    "\n",
    "D_j = pd.DataFrame(london_flows.groupby([\"Dest\"])[\"Total\"].agg(np.sum))\n",
    "D_j.rename(columns={\"Total\":\"D_j\"}, inplace = True)\n",
    "london_flows = london_flows.merge(D_j, on = \"Dest\", how = \"left\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\skyla\\miniconda3\\envs\\urbsim\\lib\\site-packages\\ipykernel_launcher.py:8: FutureWarning: The default value of regex will change from True to False in a future version.\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Orig</th>\n",
       "      <th>Dest</th>\n",
       "      <th>Total</th>\n",
       "      <th>Oi_origpop</th>\n",
       "      <th>Dj_destjob</th>\n",
       "      <th>Dist</th>\n",
       "      <th>unconstrainedEst1</th>\n",
       "      <th>log_Oi_origpop</th>\n",
       "      <th>log_Dj_destjob</th>\n",
       "      <th>log_Dist</th>\n",
       "      <th>unconstrainedEst2</th>\n",
       "      <th>fitted</th>\n",
       "      <th>O_i</th>\n",
       "      <th>D_j</th>\n",
       "      <th>alpha_i</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>0</td>\n",
       "      <td>599</td>\n",
       "      <td>78549</td>\n",
       "      <td>8131.410852</td>\n",
       "      <td>10</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>11.271478</td>\n",
       "      <td>9.003490</td>\n",
       "      <td>50</td>\n",
       "      <td>49.616601</td>\n",
       "      <td>599</td>\n",
       "      <td>78549</td>\n",
       "      <td>3.250549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Beckton</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>442</td>\n",
       "      <td>8510.047006</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.091310</td>\n",
       "      <td>9.049003</td>\n",
       "      <td>1</td>\n",
       "      <td>0.937185</td>\n",
       "      <td>599</td>\n",
       "      <td>442</td>\n",
       "      <td>3.250549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Blackwall</td>\n",
       "      <td>3</td>\n",
       "      <td>599</td>\n",
       "      <td>665</td>\n",
       "      <td>3775.359872</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.499787</td>\n",
       "      <td>8.236251</td>\n",
       "      <td>2</td>\n",
       "      <td>2.121435</td>\n",
       "      <td>599</td>\n",
       "      <td>665</td>\n",
       "      <td>3.250549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>58772</td>\n",
       "      <td>5086.404941</td>\n",
       "      <td>18</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>10.981421</td>\n",
       "      <td>8.534327</td>\n",
       "      <td>53</td>\n",
       "      <td>53.296799</td>\n",
       "      <td>599</td>\n",
       "      <td>58772</td>\n",
       "      <td>3.250549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Canning Town</td>\n",
       "      <td>37</td>\n",
       "      <td>599</td>\n",
       "      <td>15428</td>\n",
       "      <td>2228.874185</td>\n",
       "      <td>25</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>9.643939</td>\n",
       "      <td>7.709252</td>\n",
       "      <td>32</td>\n",
       "      <td>32.209683</td>\n",
       "      <td>599</td>\n",
       "      <td>15428</td>\n",
       "      <td>3.250549</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Orig               Dest  Total  Oi_origpop  Dj_destjob         Dist  \\\n",
       "0  Abbey Road  Bank and Monument      0         599       78549  8131.410852   \n",
       "1  Abbey Road            Beckton      1         599         442  8510.047006   \n",
       "2  Abbey Road          Blackwall      3         599         665  3775.359872   \n",
       "3  Abbey Road       Canary Wharf      1         599       58772  5086.404941   \n",
       "4  Abbey Road       Canning Town     37         599       15428  2228.874185   \n",
       "\n",
       "   unconstrainedEst1  log_Oi_origpop  log_Dj_destjob  log_Dist  \\\n",
       "0                 10        6.395262       11.271478  9.003490   \n",
       "1                  0        6.395262        6.091310  9.049003   \n",
       "2                  0        6.395262        6.499787  8.236251   \n",
       "3                 18        6.395262       10.981421  8.534327   \n",
       "4                 25        6.395262        9.643939  7.709252   \n",
       "\n",
       "   unconstrainedEst2     fitted  O_i    D_j   alpha_i  \n",
       "0                 50  49.616601  599  78549  3.250549  \n",
       "1                  1   0.937185  599    442  3.250549  \n",
       "2                  2   2.121435  599    665  3.250549  \n",
       "3                 53  53.296799  599  58772  3.250549  \n",
       "4                 32  32.209683  599  15428  3.250549  "
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get coefficient in prodsim\n",
    "#We can do this by pulling out the parameter values\n",
    "coefs = pd.DataFrame(prodSim.params)\n",
    "coefs.reset_index(inplace=True)\n",
    "coefs.rename(columns = {0:\"alpha_i\", \"index\":\"coef\"}, inplace = True)\n",
    "to_repl = [\"(Orig)\", \"\\[\", \"\\]\"]\n",
    "for x in to_repl:\n",
    "    coefs[\"coef\"] = coefs[\"coef\"].str.replace(x, \"\")\n",
    "#then once you have done this you can join them back into the dataframes\n",
    "london_flows = london_flows.merge(coefs, left_on=\"Orig\", right_on=\"coef\", how = \"left\")\n",
    "london_flows.drop(columns = [\"coef\"], inplace = True)\n",
    "#check this has worked\n",
    "london_flows.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [],
   "source": [
    "# save parameter values into some variables\n",
    "alpha_i=prodSim.params[0:-2]\n",
    "gamma = prodSim.params[-2]\n",
    "beta = -prodSim.params[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.768612478678105"
      ]
     },
     "execution_count": 321,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8781569676332593"
      ]
     },
     "execution_count": 322,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now generate estimates:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>6.395262</td>\n",
       "      <td>11.271478</td>\n",
       "      <td>9.003490</td>\n",
       "      <td>50</td>\n",
       "      <td>49.616601</td>\n",
       "      <td>599</td>\n",
       "      <td>78549</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>55.007531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Beckton</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>442</td>\n",
       "      <td>8510.047006</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.091310</td>\n",
       "      <td>9.049003</td>\n",
       "      <td>1</td>\n",
       "      <td>0.937185</td>\n",
       "      <td>599</td>\n",
       "      <td>442</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>0.986059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Blackwall</td>\n",
       "      <td>3</td>\n",
       "      <td>599</td>\n",
       "      <td>665</td>\n",
       "      <td>3775.359872</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.499787</td>\n",
       "      <td>8.236251</td>\n",
       "      <td>2</td>\n",
       "      <td>2.121435</td>\n",
       "      <td>599</td>\n",
       "      <td>665</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>2.755627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>58772</td>\n",
       "      <td>5086.404941</td>\n",
       "      <td>18</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>10.981421</td>\n",
       "      <td>8.534327</td>\n",
       "      <td>53</td>\n",
       "      <td>53.296799</td>\n",
       "      <td>599</td>\n",
       "      <td>58772</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>66.455165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Canning Town</td>\n",
       "      <td>37</td>\n",
       "      <td>599</td>\n",
       "      <td>15428</td>\n",
       "      <td>2228.874185</td>\n",
       "      <td>25</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>9.643939</td>\n",
       "      <td>7.709252</td>\n",
       "      <td>32</td>\n",
       "      <td>32.209683</td>\n",
       "      <td>599</td>\n",
       "      <td>15428</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>49.061156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Crossharbour</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>1208</td>\n",
       "      <td>6686.335036</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>7.096721</td>\n",
       "      <td>8.807821</td>\n",
       "      <td>2</td>\n",
       "      <td>2.340156</td>\n",
       "      <td>599</td>\n",
       "      <td>1208</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>2.639337</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Custom House</td>\n",
       "      <td>0</td>\n",
       "      <td>599</td>\n",
       "      <td>845</td>\n",
       "      <td>3824.789936</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.739337</td>\n",
       "      <td>8.249259</td>\n",
       "      <td>3</td>\n",
       "      <td>2.524972</td>\n",
       "      <td>599</td>\n",
       "      <td>845</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>3.275082</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Cutty Sark</td>\n",
       "      <td>2</td>\n",
       "      <td>599</td>\n",
       "      <td>1748</td>\n",
       "      <td>8503.736582</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>7.466228</td>\n",
       "      <td>9.048261</td>\n",
       "      <td>3</td>\n",
       "      <td>2.668634</td>\n",
       "      <td>599</td>\n",
       "      <td>1748</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>2.838827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Cyprus</td>\n",
       "      <td>7</td>\n",
       "      <td>599</td>\n",
       "      <td>850</td>\n",
       "      <td>6532.037185</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.745236</td>\n",
       "      <td>8.784474</td>\n",
       "      <td>2</td>\n",
       "      <td>1.817323</td>\n",
       "      <td>599</td>\n",
       "      <td>850</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>2.056230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Devons Road</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>611</td>\n",
       "      <td>3958.290432</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.415097</td>\n",
       "      <td>8.283568</td>\n",
       "      <td>2</td>\n",
       "      <td>1.931300</td>\n",
       "      <td>599</td>\n",
       "      <td>611</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>2.476880</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Orig               Dest  Total  Oi_origpop  Dj_destjob         Dist  \\\n",
       "0  Abbey Road  Bank and Monument      0         599       78549  8131.410852   \n",
       "1  Abbey Road            Beckton      1         599         442  8510.047006   \n",
       "2  Abbey Road          Blackwall      3         599         665  3775.359872   \n",
       "3  Abbey Road       Canary Wharf      1         599       58772  5086.404941   \n",
       "4  Abbey Road       Canning Town     37         599       15428  2228.874185   \n",
       "5  Abbey Road       Crossharbour      1         599        1208  6686.335036   \n",
       "6  Abbey Road       Custom House      0         599         845  3824.789936   \n",
       "7  Abbey Road         Cutty Sark      2         599        1748  8503.736582   \n",
       "8  Abbey Road             Cyprus      7         599         850  6532.037185   \n",
       "9  Abbey Road        Devons Road      1         599         611  3958.290432   \n",
       "\n",
       "   unconstrainedEst1  log_Oi_origpop  log_Dj_destjob  log_Dist  \\\n",
       "0                 10        6.395262       11.271478  9.003490   \n",
       "1                  0        6.395262        6.091310  9.049003   \n",
       "2                  0        6.395262        6.499787  8.236251   \n",
       "3                 18        6.395262       10.981421  8.534327   \n",
       "4                 25        6.395262        9.643939  7.709252   \n",
       "5                  0        6.395262        7.096721  8.807821   \n",
       "6                  0        6.395262        6.739337  8.249259   \n",
       "7                  0        6.395262        7.466228  9.048261   \n",
       "8                  0        6.395262        6.745236  8.784474   \n",
       "9                  0        6.395262        6.415097  8.283568   \n",
       "\n",
       "   unconstrainedEst2     fitted  O_i    D_j   alpha_i  prodsimest1  \n",
       "0                 50  49.616601  599  78549  3.250549    55.007531  \n",
       "1                  1   0.937185  599    442  3.250549     0.986059  \n",
       "2                  2   2.121435  599    665  3.250549     2.755627  \n",
       "3                 53  53.296799  599  58772  3.250549    66.455165  \n",
       "4                 32  32.209683  599  15428  3.250549    49.061156  \n",
       "5                  2   2.340156  599   1208  3.250549     2.639337  \n",
       "6                  3   2.524972  599    845  3.250549     3.275082  \n",
       "7                  3   2.668634  599   1748  3.250549     2.838827  \n",
       "8                  2   1.817323  599    850  3.250549     2.056230  \n",
       "9                  2   1.931300  599    611  3.250549     2.476880  "
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows[\"prodsimest1\"] = np.exp(london_flows[\"alpha_i\"]+gamma*london_flows[\"log_Dj_destjob\"] \n",
    "                                 - beta*london_flows[\"log_Dist\"])\n",
    "#or you could do it the easy way like we did last week with the fitted column (See previous practical)\n",
    "london_flows.head(10)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Assessing the model output\n",
    "\n",
    "Flow matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
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       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>599.0</td>\n",
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       "      <th>Acton Central</th>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1223.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
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       "      <td>16.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
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       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3749.0</td>\n",
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       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>47.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>21.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2882.0</td>\n",
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       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>23.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>3167.0</td>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32.0</td>\n",
       "      <td>...</td>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4866.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>532.0</td>\n",
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       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>20.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25.0</td>\n",
       "      <td>...</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3092.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>29.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>33.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7890.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>445.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>2156.0</td>\n",
       "      <td>8753.0</td>\n",
       "      <td>9308.0</td>\n",
       "      <td>504.0</td>\n",
       "      <td>582.0</td>\n",
       "      <td>108.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>9202.0</td>\n",
       "      <td>...</td>\n",
       "      <td>3426.0</td>\n",
       "      <td>523.0</td>\n",
       "      <td>2161.0</td>\n",
       "      <td>1647.0</td>\n",
       "      <td>341.0</td>\n",
       "      <td>654.0</td>\n",
       "      <td>156.0</td>\n",
       "      <td>603.0</td>\n",
       "      <td>1009.0</td>\n",
       "      <td>1541812.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN     18.0   \n",
       "Aldgate                  NaN            NaN         2.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0     52.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         7.0     35.0   \n",
       "Woodgrange Park          NaN            4.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         5.0     20.0   \n",
       "Woolwich Arsenal        29.0            NaN         NaN      NaN   \n",
       "All                    445.0          391.0      2156.0   8753.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                18.0         NaN       9.0       1.0      NaN   \n",
       "Aldgate                   47.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       1.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  39.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             20.0         NaN       2.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN        33.0       NaN       NaN      NaN   \n",
       "All                     9308.0       504.0     582.0     108.0    140.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          20.0  ...       16.0             3.0         5.0   \n",
       "Aldgate             21.0  ...        4.0             NaN         3.0   \n",
       "Aldgate East        23.0  ...        5.0             1.0         3.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            32.0  ...       15.0             NaN        10.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       25.0  ...       11.0             NaN         6.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               9202.0  ...     3426.0           523.0      2161.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              1.0   \n",
       "Acton Town             13.0          NaN       2.0              NaN   \n",
       "Aldgate                 2.0          NaN       1.0              NaN   \n",
       "Aldgate East            2.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1647.0        341.0     654.0            156.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                  NaN               5.0      599.0  \n",
       "Acton Central               NaN               NaN     1223.0  \n",
       "Acton Town                  2.0               NaN     3749.0  \n",
       "Aldgate                     1.0               NaN     2882.0  \n",
       "Aldgate East                1.0               NaN     3167.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                    NaN               NaN     4866.0  \n",
       "Woodgrange Park             NaN               NaN      532.0  \n",
       "Woodside Park               NaN               NaN     3092.0  \n",
       "Woolwich Arsenal            NaN               NaN     7890.0  \n",
       "All                       603.0            1009.0  1541812.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#first round the estimates\n",
    "london_flows[\"prodsimest1\"] = round(london_flows[\"prodsimest1\"],0)\n",
    "#now we can create a pivot tabel to turn the paired list into a matrix, and compute the margins as well\n",
    "ldf_submat_prodc = london_flows.pivot_table(values =\"prodsimest1\", index=\"Orig\", columns = \"Dest\",\n",
    "                            aggfunc=np.sum, margins=True)\n",
    "ldf_submat_prodc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32.0</td>\n",
       "      <td>599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11.0</td>\n",
       "      <td>...</td>\n",
       "      <td>77.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>...</td>\n",
       "      <td>24.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3172</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",
       "      <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>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>47.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>...</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>59.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>345.0</td>\n",
       "      <td>750.0</td>\n",
       "      <td>2202.0</td>\n",
       "      <td>7782.0</td>\n",
       "      <td>7932.0</td>\n",
       "      <td>444.0</td>\n",
       "      <td>741.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>8103.0</td>\n",
       "      <td>...</td>\n",
       "      <td>6295.0</td>\n",
       "      <td>596.0</td>\n",
       "      <td>2146.0</td>\n",
       "      <td>1578.0</td>\n",
       "      <td>404.0</td>\n",
       "      <td>706.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>745.0</td>\n",
       "      <td>4428.0</td>\n",
       "      <td>1542283</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN      3.0   \n",
       "Aldgate                  NaN            NaN         0.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0      0.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         2.0      5.0   \n",
       "Woodgrange Park          NaN            0.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         1.0     26.0   \n",
       "Woolwich Arsenal        20.0            NaN         NaN      NaN   \n",
       "All                    345.0          750.0      2202.0   7782.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                17.0         NaN      35.0       0.0      NaN   \n",
       "Aldgate                    0.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       0.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  47.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             11.0         NaN       0.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN         7.0       NaN       NaN      NaN   \n",
       "All                     7932.0       444.0     741.0     256.0    173.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          11.0  ...       77.0             3.0         6.0   \n",
       "Aldgate             17.0  ...        0.0             NaN         4.0   \n",
       "Aldgate East        20.0  ...       24.0             0.0         0.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            22.0  ...        2.0             NaN         1.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       59.0  ...        0.0             NaN         0.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               8103.0  ...     6295.0           596.0      2146.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              0.0   \n",
       "Acton Town              9.0          NaN       0.0              NaN   \n",
       "Aldgate                 8.0          NaN       0.0              NaN   \n",
       "Aldgate East           12.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1578.0        404.0     706.0            242.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal      All  \n",
       "Orig                                                        \n",
       "Abbey Road                  NaN              32.0      599  \n",
       "Acton Central               NaN               NaN     1224  \n",
       "Acton Town                  0.0               NaN     3745  \n",
       "Aldgate                     0.0               NaN     2886  \n",
       "Aldgate East                1.0               NaN     3172  \n",
       "...                         ...               ...      ...  \n",
       "Woodford                    NaN               NaN     4868  \n",
       "Woodgrange Park             NaN               NaN      530  \n",
       "Woodside Park               NaN               NaN     3093  \n",
       "Woolwich Arsenal            NaN               NaN     7892  \n",
       "All                       745.0            4428.0  1542283  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldf_submat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3883286233312407"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRSqaured(london_flows[\"Total\"], london_flows[\"prodsimest1\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "102.888"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRMSE(london_flows[\"Total\"], london_flows[\"prodsimest1\"])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Attraction (destination)-constrained model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Description \n",
    "Equation \n",
    "Parameters"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Attraction-Constrained Model\n",
    "\n",
    "The attraction constrained model is virtually the same as the PRoduction constrained model:\n",
    "\n",
    "\\begin{equation}  \\tag{5}\n",
    "T_{ij} = D_j B_j O_i^\\alpha d_{ij}^{-\\beta}\n",
    "\\end{equation}\n",
    "\n",
    "Where\n",
    "\n",
    "\\begin{equation}  \\tag{6}\n",
    "D_j = \\sum_i T_{ij}\n",
    "\\end{equation}\n",
    "\n",
    "and \n",
    "\n",
    "\\begin{equation}  \\tag{7}\n",
    "B_j = \\frac{1}{\\sum_i O_i^\\alpha d_{ij}^{-\\beta}}\n",
    "\\end{equation}\n",
    "\n",
    "I won't dwell on the attraction constrained model, except to say that it can be run in Python as you would expect:\n",
    "\n",
    "\\begin{equation}  \\tag{8}\n",
    "\\lambda_{ij} = \\exp (\\alpha \\ln O_i + \\gamma_j - \\beta \\ln d_{ij})\n",
    "\\end{equation}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                  Total   No. Observations:                61413\n",
      "Model:                            GLM   Df Residuals:                    61013\n",
      "Model Family:                 Poisson   Df Model:                          399\n",
      "Link Function:                    log   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:            -1.1646e+06\n",
      "Date:                Mon, 01 May 2023   Deviance:                   2.1570e+06\n",
      "Time:                        14:00:23   Pearson chi2:                 3.65e+06\n",
      "No. Iterations:                     8                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================================\n",
      "                                        coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------------------------\n",
      "Dest[Abbey Road]                      1.1082      0.055     20.188      0.000       1.001       1.216\n",
      "Dest[Acton Central]                   2.4206      0.038     63.170      0.000       2.346       2.496\n",
      "Dest[Acton Town]                      1.9909      0.024     81.706      0.000       1.943       2.039\n",
      "Dest[Aldgate]                         2.8296      0.016    177.243      0.000       2.798       2.861\n",
      "Dest[Aldgate East]                    2.8103      0.016    176.566      0.000       2.779       2.841\n",
      "Dest[All Saints]                      1.4035      0.049     28.850      0.000       1.308       1.499\n",
      "Dest[Alperton]                        1.3069      0.039     33.780      0.000       1.231       1.383\n",
      "Dest[Amersham]                        0.8320      0.064     13.035      0.000       0.707       0.957\n",
      "Dest[Anerley]                         1.6349      0.077     21.261      0.000       1.484       1.786\n",
      "Dest[Angel]                           2.8439      0.016    178.956      0.000       2.813       2.875\n",
      "Dest[Archway]                         1.8646      0.024     76.525      0.000       1.817       1.912\n",
      "Dest[Arnos Grove]                     1.0927      0.039     28.379      0.000       1.017       1.168\n",
      "Dest[Arsenal]                        -0.1970      0.058     -3.426      0.001      -0.310      -0.084\n",
      "Dest[Baker Street]                    3.4450      0.014    247.282      0.000       3.418       3.472\n",
      "Dest[Balham]                          2.4819      0.020    123.981      0.000       2.443       2.521\n",
      "Dest[Bank and Monument]               4.9251      0.012    423.824      0.000       4.902       4.948\n",
      "Dest[Barbican]                        2.8954      0.015    188.556      0.000       2.865       2.925\n",
      "Dest[Barking]                         3.1848      0.017    187.863      0.000       3.152       3.218\n",
      "Dest[Barkingside]                     0.3160      0.063      5.017      0.000       0.193       0.439\n",
      "Dest[Barons Court]                    2.0512      0.022     94.551      0.000       2.009       2.094\n",
      "Dest[Bayswater]                       0.6309      0.042     15.054      0.000       0.549       0.713\n",
      "Dest[Beckton]                         2.0168      0.049     41.197      0.000       1.921       2.113\n",
      "Dest[Beckton Park]                    0.3872      0.107      3.612      0.000       0.177       0.597\n",
      "Dest[Becontree]                       0.7168      0.048     14.813      0.000       0.622       0.812\n",
      "Dest[Belsize Park]                    1.9166      0.024     79.596      0.000       1.869       1.964\n",
      "Dest[Bermondsey]                      2.0017      0.021     94.625      0.000       1.960       2.043\n",
      "Dest[Bethnal Green]                   2.3766      0.019    127.503      0.000       2.340       2.413\n",
      "Dest[Blackfriars]                     3.0920      0.015    208.702      0.000       3.063       3.121\n",
      "Dest[Blackhorse Road]                 2.2856      0.022    104.448      0.000       2.243       2.329\n",
      "Dest[Blackwall]                       1.7435      0.040     43.372      0.000       1.665       1.822\n",
      "Dest[Bond Street]                     3.7380      0.013    283.274      0.000       3.712       3.764\n",
      "Dest[Borough]                         1.8769      0.021     90.228      0.000       1.836       1.918\n",
      "Dest[Boston Manor]                    1.3510      0.036     37.970      0.000       1.281       1.421\n",
      "Dest[Bounds Green]                    1.0427      0.038     27.583      0.000       0.969       1.117\n",
      "Dest[Bow Church]                      2.2969      0.035     66.259      0.000       2.229       2.365\n",
      "Dest[Bow Road]                        1.1409      0.031     36.591      0.000       1.080       1.202\n",
      "Dest[Brent Cross]                     0.6520      0.049     13.404      0.000       0.557       0.747\n",
      "Dest[Brentwood]                       3.6135      0.039     93.335      0.000       3.538       3.689\n",
      "Dest[Brixton]                         2.6438      0.018    144.688      0.000       2.608       2.680\n",
      "Dest[Brockley]                        2.0650      0.048     43.426      0.000       1.972       2.158\n",
      "Dest[Bromley-by-Bow]                  1.4769      0.027     53.741      0.000       1.423       1.531\n",
      "Dest[Brondesbury]                     2.1651      0.039     55.396      0.000       2.089       2.242\n",
      "Dest[Brondesbury Park]                2.3951      0.035     67.950      0.000       2.326       2.464\n",
      "Dest[Bruce Grove]                     1.9002      0.055     34.798      0.000       1.793       2.007\n",
      "Dest[Buckhurst Hill]                  0.2117      0.067      3.143      0.002       0.080       0.344\n",
      "Dest[Burnt Oak]                       1.1388      0.041     27.699      0.000       1.058       1.219\n",
      "Dest[Bush Hill Park]                  1.4593      0.076     19.130      0.000       1.310       1.609\n",
      "Dest[Bushey]                          2.6590      0.048     55.000      0.000       2.564       2.754\n",
      "Dest[Caledonian Road]                 1.4558      0.026     55.570      0.000       1.404       1.507\n",
      "Dest[Caledonian Road & Barnsbury]     2.7516      0.027    102.369      0.000       2.699       2.804\n",
      "Dest[Cambridge Heath]                 2.0462      0.048     42.635      0.000       1.952       2.140\n",
      "Dest[Camden Road]                     3.6418      0.020    183.597      0.000       3.603       3.681\n",
      "Dest[Camden Town]                     2.6733      0.017    157.514      0.000       2.640       2.707\n",
      "Dest[Canada Water]                    3.8140      0.013    284.666      0.000       3.788       3.840\n",
      "Dest[Canary Wharf]                    4.8987      0.012    403.455      0.000       4.875       4.922\n",
      "Dest[Canning Town]                    3.6395      0.014    258.595      0.000       3.612       3.667\n",
      "Dest[Cannon Street]                   2.1797      0.018    119.069      0.000       2.144       2.216\n",
      "Dest[Canonbury]                       2.0296      0.036     56.195      0.000       1.959       2.100\n",
      "Dest[Canons Park]                     1.0066      0.045     22.220      0.000       0.918       1.095\n",
      "Dest[Carpenders Park]                 2.2926      0.056     41.264      0.000       2.184       2.401\n",
      "Dest[Chadwell Heath]                  2.7795      0.044     63.541      0.000       2.694       2.865\n",
      "Dest[Chalfont & Latimer]              1.7746      0.044     39.980      0.000       1.688       1.862\n",
      "Dest[Chalk Farm]                      1.3004      0.030     43.684      0.000       1.242       1.359\n",
      "Dest[Chancery Lane]                   3.4351      0.014    247.670      0.000       3.408       3.462\n",
      "Dest[Charing Cross]                   2.5738      0.016    157.746      0.000       2.542       2.606\n",
      "Dest[Chesham]                         1.0052      0.065     15.356      0.000       0.877       1.134\n",
      "Dest[Cheshunt]                        1.6848      0.094     17.999      0.000       1.501       1.868\n",
      "Dest[Chigwell]                        0.1287      0.083      1.548      0.122      -0.034       0.292\n",
      "Dest[Chingford]                       1.7531      0.066     26.531      0.000       1.624       1.883\n",
      "Dest[Chiswick Park]                   1.6674      0.028     59.047      0.000       1.612       1.723\n",
      "Dest[Chorleywood]                     2.0006      0.040     50.207      0.000       1.923       2.079\n",
      "Dest[Clapham Common]                  1.6956      0.025     67.561      0.000       1.646       1.745\n",
      "Dest[Clapham High Street]             3.3826      0.030    112.687      0.000       3.324       3.441\n",
      "Dest[Clapham Junction]                4.3665      0.018    237.038      0.000       4.330       4.403\n",
      "Dest[Clapham North]                   1.1783      0.031     38.417      0.000       1.118       1.238\n",
      "Dest[Clapham South]                   1.4981      0.028     53.028      0.000       1.443       1.553\n",
      "Dest[Clapton]                         1.9346      0.050     38.854      0.000       1.837       2.032\n",
      "Dest[Cockfosters]                     0.3781      0.063      6.002      0.000       0.255       0.502\n",
      "Dest[Colindale]                       2.1936      0.025     87.491      0.000       2.144       2.243\n",
      "Dest[Colliers Wood]                   1.1693      0.036     32.442      0.000       1.099       1.240\n",
      "Dest[Covent Garden]                   2.1248      0.019    112.810      0.000       2.088       2.162\n",
      "Dest[Crossharbour]                    2.4936      0.031     81.216      0.000       2.433       2.554\n",
      "Dest[Crouch Hill]                     2.2245      0.051     43.570      0.000       2.124       2.325\n",
      "Dest[Croxley]                         1.0935      0.056     19.637      0.000       0.984       1.203\n",
      "Dest[Crystal Palace]                  2.7304      0.046     59.030      0.000       2.640       2.821\n",
      "Dest[Custom House]                    2.1610      0.036     59.904      0.000       2.090       2.232\n",
      "Dest[Cutty Sark]                      3.0548      0.026    116.192      0.000       3.003       3.106\n",
      "Dest[Cyprus]                          2.4980      0.036     69.188      0.000       2.427       2.569\n",
      "Dest[Dagenham East]                   1.1945      0.041     29.037      0.000       1.114       1.275\n",
      "Dest[Dagenham Heathway]               1.5952      0.032     49.159      0.000       1.532       1.659\n",
      "Dest[Dalston Junction]                2.7121      0.030     90.326      0.000       2.653       2.771\n",
      "Dest[Dalston Kingsland]               2.9624      0.025    120.023      0.000       2.914       3.011\n",
      "Dest[Debden]                          1.6178      0.036     44.687      0.000       1.547       1.689\n",
      "Dest[Denmark Hill]                    3.8163      0.023    168.749      0.000       3.772       3.861\n",
      "Dest[Deptford Bridge]                 2.4348      0.036     67.224      0.000       2.364       2.506\n",
      "Dest[Devons Road]                     1.8127      0.042     43.262      0.000       1.731       1.895\n",
      "Dest[Dollis Hill]                     1.0899      0.036     29.986      0.000       1.019       1.161\n",
      "Dest[Ealing Broadway]                 2.8662      0.019    153.222      0.000       2.830       2.903\n",
      "Dest[Ealing Common]                   1.2435      0.035     35.422      0.000       1.175       1.312\n",
      "Dest[Earl's Court]                    2.7425      0.017    163.676      0.000       2.710       2.775\n",
      "Dest[East Acton]                      1.6183      0.028     57.030      0.000       1.563       1.674\n",
      "Dest[East Finchley]                   1.5090      0.031     49.183      0.000       1.449       1.569\n",
      "Dest[East Ham]                        1.9195      0.025     76.628      0.000       1.870       1.969\n",
      "Dest[East India]                      2.5628      0.028     92.349      0.000       2.508       2.617\n",
      "Dest[East Putney]                     1.8286      0.026     70.533      0.000       1.778       1.879\n",
      "Dest[Eastcote]                        0.6559      0.054     12.187      0.000       0.550       0.761\n",
      "Dest[Edgware]                         1.3598      0.038     35.743      0.000       1.285       1.434\n",
      "Dest[Edgware Road]                    2.6989      0.017    163.190      0.000       2.666       2.731\n",
      "Dest[Edmonton Green]                  2.6115      0.038     69.524      0.000       2.538       2.685\n",
      "Dest[Elephant & Castle]               2.5753      0.017    153.011      0.000       2.542       2.608\n",
      "Dest[Elm Park]                        0.4548      0.062      7.310      0.000       0.333       0.577\n",
      "Dest[Elverson Road]                   1.1709      0.067     17.371      0.000       1.039       1.303\n",
      "Dest[Embankment]                      2.9103      0.015    195.961      0.000       2.881       2.939\n",
      "Dest[Emerson Park]                    2.3051      0.155     14.906      0.000       2.002       2.608\n",
      "Dest[Enfield Town]                    2.8887      0.038     75.187      0.000       2.813       2.964\n",
      "Dest[Epping]                          1.2141      0.047     26.070      0.000       1.123       1.305\n",
      "Dest[Euston]                          3.5539      0.014    260.691      0.000       3.527       3.581\n",
      "Dest[Euston Square]                   2.9953      0.016    188.781      0.000       2.964       3.026\n",
      "Dest[Fairlop]                         0.0630      0.075      0.839      0.402      -0.084       0.210\n",
      "Dest[Farringdon]                      3.9654      0.013    306.632      0.000       3.940       3.991\n",
      "Dest[Finchley Central]                2.0421      0.026     79.120      0.000       1.991       2.093\n",
      "Dest[Finchley Road]                   2.2329      0.021    108.110      0.000       2.192       2.273\n",
      "Dest[Finchley Road & Frognal]         2.8182      0.028    101.111      0.000       2.764       2.873\n",
      "Dest[Finsbury Park]                   2.8583      0.017    170.182      0.000       2.825       2.891\n",
      "Dest[Forest Gate]                     2.7912      0.037     75.865      0.000       2.719       2.863\n",
      "Dest[Forest Hill]                     2.4941      0.042     59.251      0.000       2.412       2.577\n",
      "Dest[Fulham Broadway]                 2.3914      0.019    124.088      0.000       2.354       2.429\n",
      "Dest[Gallions Reach]                  2.1927      0.044     49.972      0.000       2.107       2.279\n",
      "Dest[Gants Hill]                      0.8999      0.043     21.143      0.000       0.817       0.983\n",
      "Dest[Gidea Park]                      2.3355      0.059     39.593      0.000       2.220       2.451\n",
      "Dest[Gloucester Road]                 2.4713      0.018    137.723      0.000       2.436       2.506\n",
      "Dest[Golders Green]                   1.9326      0.026     74.254      0.000       1.882       1.984\n",
      "Dest[Goldhawk Road]                   0.2339      0.053      4.391      0.000       0.129       0.338\n",
      "Dest[Goodge Street]                   2.6082      0.017    155.501      0.000       2.575       2.641\n",
      "Dest[Goodmayes]                       2.8563      0.040     71.625      0.000       2.778       2.934\n",
      "Dest[Gospel Oak]                      3.0781      0.025    123.303      0.000       3.029       3.127\n",
      "Dest[Grange Hill]                    -0.5912      0.115     -5.125      0.000      -0.817      -0.365\n",
      "Dest[Great Portland Street]           2.7588      0.016    167.214      0.000       2.726       2.791\n",
      "Dest[Green Park]                      3.9501      0.013    309.376      0.000       3.925       3.975\n",
      "Dest[Greenford]                       1.6711      0.032     52.468      0.000       1.609       1.734\n",
      "Dest[Greenwich]                       2.7008      0.031     87.151      0.000       2.640       2.761\n",
      "Dest[Gunnersbury]                     2.7179      0.019    145.461      0.000       2.681       2.755\n",
      "Dest[Hackney Central]                 3.2606      0.023    140.577      0.000       3.215       3.306\n",
      "Dest[Hackney Downs]                   2.8373      0.036     78.133      0.000       2.766       2.908\n",
      "Dest[Hackney Wick]                    2.4148      0.030     79.558      0.000       2.355       2.474\n",
      "Dest[Haggerston]                      2.5506      0.031     81.914      0.000       2.490       2.612\n",
      "Dest[Hainault]                        0.5833      0.054     10.720      0.000       0.477       0.690\n",
      "Dest[Hammersmith]                     3.8884      0.014    283.256      0.000       3.861       3.915\n",
      "Dest[Hampstead]                       1.8887      0.025     74.870      0.000       1.839       1.938\n",
      "Dest[Hampstead Heath]                 3.3866      0.022    153.444      0.000       3.343       3.430\n",
      "Dest[Hanger Lane]                     1.8669      0.029     65.323      0.000       1.811       1.923\n",
      "Dest[Harlesden]                       1.8021      0.027     66.261      0.000       1.749       1.855\n",
      "Dest[Harold Wood]                     3.0364      0.045     67.434      0.000       2.948       3.125\n",
      "Dest[Harringay Green Lanes]           2.5388      0.044     57.181      0.000       2.452       2.626\n",
      "Dest[Harrow & Wealdstone]             1.9365      0.030     64.526      0.000       1.878       1.995\n",
      "Dest[Harrow-on-the-Hill]              2.5087      0.022    114.798      0.000       2.466       2.551\n",
      "Dest[Hatch End]                       1.0340      0.104      9.907      0.000       0.829       1.239\n",
      "Dest[Hatton Cross]                    1.9033      0.031     60.954      0.000       1.842       1.965\n",
      "Dest[Headstone Lane]                  2.2171      0.058     38.215      0.000       2.103       2.331\n",
      "Dest[Heathrow Terminal 4]             1.3835      0.040     34.587      0.000       1.305       1.462\n",
      "Dest[Heathrow Terminal 5]             1.7624      0.034     51.187      0.000       1.695       1.830\n",
      "Dest[Heathrow Terminals 2 & 3]        2.5393      0.024    106.085      0.000       2.492       2.586\n",
      "Dest[Hendon Central]                  2.0260      0.026     77.791      0.000       1.975       2.077\n",
      "Dest[Heron Quays]                     3.9117      0.017    236.065      0.000       3.879       3.944\n",
      "Dest[High Barnet]                     1.5776      0.035     45.478      0.000       1.510       1.646\n",
      "Dest[High Street Kensington]          2.5422      0.018    143.336      0.000       2.507       2.577\n",
      "Dest[Highams Park]                    2.0006      0.052     38.473      0.000       1.899       2.103\n",
      "Dest[Highbury & Islington]            4.0209      0.013    307.870      0.000       3.995       4.047\n",
      "Dest[Highgate]                        1.0493      0.036     29.005      0.000       0.978       1.120\n",
      "Dest[Hillingdon]                      0.7442      0.057     12.958      0.000       0.632       0.857\n",
      "Dest[Holborn]                         3.7649      0.013    288.348      0.000       3.739       3.791\n",
      "Dest[Holland Park]                    1.6933      0.025     68.159      0.000       1.645       1.742\n",
      "Dest[Holloway Road]                   1.4050      0.027     52.295      0.000       1.352       1.458\n",
      "Dest[Homerton]                        2.9070      0.025    115.647      0.000       2.858       2.956\n",
      "Dest[Honor Oak Park]                  1.8779      0.055     33.953      0.000       1.769       1.986\n",
      "Dest[Hornchurch]                      1.0927      0.049     22.434      0.000       0.997       1.188\n",
      "Dest[Hounslow Central]                1.1809      0.040     29.885      0.000       1.103       1.258\n",
      "Dest[Hounslow East]                   1.3233      0.037     36.226      0.000       1.252       1.395\n",
      "Dest[Hounslow West]                   0.7077      0.051     13.759      0.000       0.607       0.809\n",
      "Dest[Hoxton]                          3.1437      0.024    130.098      0.000       3.096       3.191\n",
      "Dest[Hyde Park Corner]                1.6351      0.023     70.156      0.000       1.589       1.681\n",
      "Dest[Ickenham]                        0.7437      0.061     12.229      0.000       0.624       0.863\n",
      "Dest[Ilford]                          3.7701      0.027    139.349      0.000       3.717       3.823\n",
      "Dest[Imperial Wharf]                  3.2982      0.025    132.145      0.000       3.249       3.347\n",
      "Dest[Island Gardens]                  2.0726      0.040     52.390      0.000       1.995       2.150\n",
      "Dest[Kennington]                      0.9280      0.031     29.495      0.000       0.866       0.990\n",
      "Dest[Kensal Green]                    0.5433      0.048     11.435      0.000       0.450       0.636\n",
      "Dest[Kensal Rise]                     2.7091      0.029     92.578      0.000       2.652       2.766\n",
      "Dest[Kensington]                      2.1545      0.024     89.608      0.000       2.107       2.202\n",
      "Dest[Kentish Town]                    2.1746      0.021    105.142      0.000       2.134       2.215\n",
      "Dest[Kentish Town West]               2.4931      0.032     78.231      0.000       2.431       2.556\n",
      "Dest[Kenton]                          1.6986      0.038     44.594      0.000       1.624       1.773\n",
      "Dest[Kew Gardens]                     1.0152      0.037     27.080      0.000       0.942       1.089\n",
      "Dest[Kilburn]                         1.7929      0.025     70.364      0.000       1.743       1.843\n",
      "Dest[Kilburn High Road]               2.0001      0.062     32.124      0.000       1.878       2.122\n",
      "Dest[Kilburn Park]                    0.9882      0.037     26.889      0.000       0.916       1.060\n",
      "Dest[King George V]                   2.4949      0.037     67.189      0.000       2.422       2.568\n",
      "Dest[King's Cross St. Pancras]        4.2139      0.012    337.275      0.000       4.189       4.238\n",
      "Dest[Kingsbury]                       1.5046      0.034     44.755      0.000       1.439       1.570\n",
      "Dest[Knightsbridge]                   2.7070      0.017    162.799      0.000       2.674       2.740\n",
      "Dest[Ladbroke Grove]                  1.7727      0.025     72.099      0.000       1.724       1.821\n",
      "Dest[Lambeth North]                   0.9292      0.030     31.269      0.000       0.871       0.987\n",
      "Dest[Lancaster Gate]                  1.5445      0.026     59.170      0.000       1.493       1.596\n",
      "Dest[Langdon Park]                    2.9510      0.025    118.563      0.000       2.902       3.000\n",
      "Dest[Latimer Road]                    1.2023      0.032     37.340      0.000       1.139       1.265\n",
      "Dest[Leicester Square]                2.8000      0.015    182.043      0.000       2.770       2.830\n",
      "Dest[Lewisham]                        3.6505      0.023    156.668      0.000       3.605       3.696\n",
      "Dest[Leyton]                          1.5044      0.029     52.195      0.000       1.448       1.561\n",
      "Dest[Leyton Midland Road]             2.4700      0.049     50.658      0.000       2.374       2.566\n",
      "Dest[Leytonstone]                     1.8373      0.026     70.250      0.000       1.786       1.889\n",
      "Dest[Leytonstone High Road]           2.4094      0.058     41.886      0.000       2.297       2.522\n",
      "Dest[Limehouse]                       3.3877      0.021    158.161      0.000       3.346       3.430\n",
      "Dest[Liverpool Street]                4.7469      0.012    399.558      0.000       4.724       4.770\n",
      "Dest[London Bridge]                   4.0728      0.013    323.281      0.000       4.048       4.098\n",
      "Dest[London City Airport]             3.2533      0.025    128.460      0.000       3.204       3.303\n",
      "Dest[London Fields]                   2.4709      0.037     66.157      0.000       2.398       2.544\n",
      "Dest[Loughton]                        1.2625      0.041     30.809      0.000       1.182       1.343\n",
      "Dest[Maida Vale]                      1.0005      0.034     29.030      0.000       0.933       1.068\n",
      "Dest[Manor House]                     1.2792      0.030     42.664      0.000       1.220       1.338\n",
      "Dest[Manor Park]                      2.2762      0.049     46.242      0.000       2.180       2.373\n",
      "Dest[Mansion House]                   2.7503      0.016    173.505      0.000       2.719       2.781\n",
      "Dest[Marble Arch]                     2.5898      0.017    151.649      0.000       2.556       2.623\n",
      "Dest[Maryland]                        1.6105      0.055     29.517      0.000       1.504       1.717\n",
      "Dest[Marylebone]                      2.2231      0.019    116.652      0.000       2.186       2.260\n",
      "Dest[Mile End]                        2.2143      0.020    110.791      0.000       2.175       2.253\n",
      "Dest[Mill Hill East]                  1.2311      0.040     30.616      0.000       1.152       1.310\n",
      "Dest[Moor Park]                       1.6102      0.044     36.243      0.000       1.523       1.697\n",
      "Dest[Moorgate]                        3.8050      0.013    297.593      0.000       3.780       3.830\n",
      "Dest[Morden]                          1.7964      0.029     62.001      0.000       1.740       1.853\n",
      "Dest[Mornington Crescent]             1.8976      0.022     87.537      0.000       1.855       1.940\n",
      "Dest[Mudchute]                        1.1922      0.059     20.365      0.000       1.077       1.307\n",
      "Dest[Neasden]                         0.9962      0.039     25.655      0.000       0.920       1.072\n",
      "Dest[New Cross]                       3.0247      0.033     91.153      0.000       2.960       3.090\n",
      "Dest[New Cross Gate]                  2.9941      0.029    101.571      0.000       2.936       3.052\n",
      "Dest[Newbury Park]                    0.9309      0.044     21.142      0.000       0.845       1.017\n",
      "Dest[North Acton]                     2.4029      0.021    112.334      0.000       2.361       2.445\n",
      "Dest[North Ealing]                    0.6899      0.056     12.287      0.000       0.580       0.800\n",
      "Dest[North Greenwich]                 2.8938      0.017    167.491      0.000       2.860       2.928\n",
      "Dest[North Harrow]                    0.0513      0.074      0.697      0.486      -0.093       0.195\n",
      "Dest[North Wembley]                   0.6307      0.054     11.739      0.000       0.525       0.736\n",
      "Dest[Northfields]                     1.2560      0.036     34.828      0.000       1.185       1.327\n",
      "Dest[Northolt]                        1.1850      0.041     29.080      0.000       1.105       1.265\n",
      "Dest[Northwick Park]                  1.9564      0.027     72.436      0.000       1.903       2.009\n",
      "Dest[Northwood]                       1.8061      0.034     53.560      0.000       1.740       1.872\n",
      "Dest[Northwood Hills]                 1.0937      0.047     23.308      0.000       1.002       1.186\n",
      "Dest[Norwood Junction]                2.5077      0.051     49.198      0.000       2.408       2.608\n",
      "Dest[Notting Hill Gate]               2.5544      0.018    144.616      0.000       2.520       2.589\n",
      "Dest[Oakwood]                         0.7514      0.050     14.983      0.000       0.653       0.850\n",
      "Dest[Old Street]                      3.4966      0.014    252.810      0.000       3.469       3.524\n",
      "Dest[Osterley]                        0.9127      0.045     20.074      0.000       0.824       1.002\n",
      "Dest[Oval]                            1.7835      0.023     77.889      0.000       1.739       1.828\n",
      "Dest[Oxford Circus]                   4.4480      0.012    366.011      0.000       4.424       4.472\n",
      "Dest[Paddington]                      3.8562      0.013    287.718      0.000       3.830       3.882\n",
      "Dest[Park Royal]                      1.9892      0.028     70.818      0.000       1.934       2.044\n",
      "Dest[Parsons Green]                   2.0272      0.022     90.316      0.000       1.983       2.071\n",
      "Dest[Peckham Rye]                     2.8927      0.033     88.849      0.000       2.829       2.957\n",
      "Dest[Penge West]                      1.3809      0.082     16.756      0.000       1.219       1.542\n",
      "Dest[Perivale]                        0.9173      0.045     20.368      0.000       0.829       1.006\n",
      "Dest[Piccadilly Circus]               3.2420      0.014    230.743      0.000       3.214       3.270\n",
      "Dest[Pimlico]                         2.5208      0.018    143.334      0.000       2.486       2.555\n",
      "Dest[Pinner]                          0.4789      0.060      8.008      0.000       0.362       0.596\n",
      "Dest[Plaistow]                        1.1229      0.033     34.013      0.000       1.058       1.188\n",
      "Dest[Pontoon Dock]                    2.5867      0.032     81.255      0.000       2.524       2.649\n",
      "Dest[Poplar]                          2.3244      0.030     78.486      0.000       2.266       2.382\n",
      "Dest[Preston Road]                    0.5411      0.051     10.657      0.000       0.442       0.641\n",
      "Dest[Prince Regent]                   2.1549      0.038     56.644      0.000       2.080       2.229\n",
      "Dest[Pudding Mill Lane]               1.4091      0.049     28.528      0.000       1.312       1.506\n",
      "Dest[Putney Bridge]                   2.0122      0.023     86.762      0.000       1.967       2.058\n",
      "Dest[Queen's Park]                    1.8303      0.024     74.868      0.000       1.782       1.878\n",
      "Dest[Queens Road Peckham]             2.5166      0.038     65.809      0.000       2.442       2.592\n",
      "Dest[Queensbury]                      0.7300      0.049     14.818      0.000       0.633       0.827\n",
      "Dest[Queensway]                       1.5937      0.026     61.909      0.000       1.543       1.644\n",
      "Dest[Ravenscourt Park]                1.7136      0.026     66.616      0.000       1.663       1.764\n",
      "Dest[Rayners Lane]                    0.6782      0.050     13.579      0.000       0.580       0.776\n",
      "Dest[Rectory Road]                    1.2489      0.069     18.223      0.000       1.115       1.383\n",
      "Dest[Redbridge]                      -0.1633      0.072     -2.266      0.023      -0.305      -0.022\n",
      "Dest[Regent's Park]                   2.0320      0.021     98.515      0.000       1.992       2.072\n",
      "Dest[Richmond]                        2.9847      0.018    163.882      0.000       2.949       3.020\n",
      "Dest[Rickmansworth]                   1.9283      0.035     55.049      0.000       1.860       1.997\n",
      "Dest[Roding Valley]                  -0.3566      0.110     -3.248      0.001      -0.572      -0.141\n",
      "Dest[Romford]                         4.2786      0.024    176.160      0.000       4.231       4.326\n",
      "Dest[Rotherhithe]                     1.1579      0.057     20.407      0.000       1.047       1.269\n",
      "Dest[Royal Albert]                    2.1869      0.040     54.908      0.000       2.109       2.265\n",
      "Dest[Royal Oak]                       0.8474      0.036     23.494      0.000       0.777       0.918\n",
      "Dest[Royal Victoria]                  2.0044      0.038     53.050      0.000       1.930       2.078\n",
      "Dest[Ruislip]                         0.5028      0.064      7.911      0.000       0.378       0.627\n",
      "Dest[Ruislip Gardens]                 0.2549      0.078      3.252      0.001       0.101       0.408\n",
      "Dest[Ruislip Manor]                   0.8953      0.051     17.562      0.000       0.795       0.995\n",
      "Dest[Russell Square]                  2.3272      0.018    130.122      0.000       2.292       2.362\n",
      "Dest[Seven Kings]                     2.6462      0.044     60.452      0.000       2.560       2.732\n",
      "Dest[Seven Sisters]                   3.3744      0.015    219.724      0.000       3.344       3.404\n",
      "Dest[Shadwell]                        3.7512      0.016    235.837      0.000       3.720       3.782\n",
      "Dest[Shenfield]                       3.8923      0.035    111.227      0.000       3.824       3.961\n",
      "Dest[Shepherd's Bush]                 3.2269      0.015    210.621      0.000       3.197       3.257\n",
      "Dest[Shepherd's Bush Market]          0.3102      0.050      6.158      0.000       0.211       0.409\n",
      "Dest[Shoreditch High Street]          4.3770      0.016    273.623      0.000       4.346       4.408\n",
      "Dest[Silver Street]                   2.9128      0.034     84.760      0.000       2.845       2.980\n",
      "Dest[Sloane Square]                   2.8864      0.016    182.148      0.000       2.855       2.917\n",
      "Dest[Snaresbrook]                     0.7476      0.046     16.327      0.000       0.658       0.837\n",
      "Dest[South Acton]                     2.7870      0.034     81.910      0.000       2.720       2.854\n",
      "Dest[South Ealing]                    0.9750      0.040     24.115      0.000       0.896       1.054\n",
      "Dest[South Hampstead]                 1.9269      0.066     29.188      0.000       1.797       2.056\n",
      "Dest[South Harrow]                    0.7578      0.052     14.496      0.000       0.655       0.860\n",
      "Dest[South Kensington]                3.5391      0.014    253.406      0.000       3.512       3.566\n",
      "Dest[South Kenton]                    0.5637      0.063      8.939      0.000       0.440       0.687\n",
      "Dest[South Quay]                      3.7518      0.018    206.184      0.000       3.716       3.787\n",
      "Dest[South Ruislip]                   0.6121      0.060     10.182      0.000       0.494       0.730\n",
      "Dest[South Tottenham]                 2.6919      0.044     61.042      0.000       2.605       2.778\n",
      "Dest[South Wimbledon]                 1.7418      0.030     58.734      0.000       1.684       1.800\n",
      "Dest[South Woodford]                  1.1129      0.038     29.215      0.000       1.038       1.188\n",
      "Dest[Southbury]                       2.7069      0.045     60.515      0.000       2.619       2.795\n",
      "Dest[Southfields]                     1.5927      0.030     53.615      0.000       1.534       1.651\n",
      "Dest[Southgate]                       1.2871      0.036     35.795      0.000       1.217       1.358\n",
      "Dest[Southwark]                       2.9603      0.015    198.802      0.000       2.931       2.989\n",
      "Dest[St James Street]                 1.1146      0.075     14.945      0.000       0.968       1.261\n",
      "Dest[St. James's Park]                3.2578      0.014    229.772      0.000       3.230       3.286\n",
      "Dest[St. John's Wood]                 2.3191      0.020    118.249      0.000       2.281       2.358\n",
      "Dest[St. Paul's]                      3.2768      0.014    231.176      0.000       3.249       3.305\n",
      "Dest[Stamford Brook]                  0.9453      0.038     25.167      0.000       0.872       1.019\n",
      "Dest[Stamford Hill]                   1.7769      0.054     32.627      0.000       1.670       1.884\n",
      "Dest[Stanmore]                        1.6294      0.034     47.623      0.000       1.562       1.696\n",
      "Dest[Star Lane]                       2.2247      0.033     68.159      0.000       2.161       2.289\n",
      "Dest[Stepney Green]                   1.4906      0.026     57.825      0.000       1.440       1.541\n",
      "Dest[Stockwell]                       1.3600      0.027     49.729      0.000       1.306       1.414\n",
      "Dest[Stoke Newington]                 2.0646      0.047     43.857      0.000       1.972       2.157\n",
      "Dest[Stonebridge Park]                1.0640      0.039     27.339      0.000       0.988       1.140\n",
      "Dest[Stratford]                       4.8431      0.012    395.548      0.000       4.819       4.867\n",
      "Dest[Stratford High Street]           1.8399      0.037     49.513      0.000       1.767       1.913\n",
      "Dest[Stratford International]         2.7958      0.028    100.755      0.000       2.741       2.850\n",
      "Dest[Sudbury Hill]                    0.3709      0.061      6.050      0.000       0.251       0.491\n",
      "Dest[Sudbury Town]                    0.2147      0.069      3.120      0.002       0.080       0.350\n",
      "Dest[Surrey Quays]                    2.2971      0.033     69.072      0.000       2.232       2.362\n",
      "Dest[Swiss Cottage]                   1.9531      0.023     85.735      0.000       1.908       1.998\n",
      "Dest[Sydenham]                        2.3864      0.045     52.456      0.000       2.297       2.476\n",
      "Dest[Temple]                          2.6064      0.017    157.542      0.000       2.574       2.639\n",
      "Dest[Theobalds Grove]                 1.9820      0.075     26.387      0.000       1.835       2.129\n",
      "Dest[Theydon Bois]                   -0.1296      0.102     -1.274      0.203      -0.329       0.070\n",
      "Dest[Tooting Bec]                     1.3855      0.031     45.040      0.000       1.325       1.446\n",
      "Dest[Tooting Broadway]                2.7097      0.019    142.162      0.000       2.672       2.747\n",
      "Dest[Tottenham Court Road]            3.6022      0.013    270.452      0.000       3.576       3.628\n",
      "Dest[Tottenham Hale]                  2.3393      0.021    110.438      0.000       2.298       2.381\n",
      "Dest[Totteridge & Whetstone]          0.3530      0.060      5.856      0.000       0.235       0.471\n",
      "Dest[Tower Gateway]                   3.7514      0.021    182.104      0.000       3.711       3.792\n",
      "Dest[Tower Hill]                      2.8084      0.016    178.662      0.000       2.778       2.839\n",
      "Dest[Tufnell Park]                    0.4715      0.044     10.731      0.000       0.385       0.558\n",
      "Dest[Turkey Street]                   2.7388      0.048     56.757      0.000       2.644       2.833\n",
      "Dest[Turnham Green]                   1.5409      0.028     54.595      0.000       1.486       1.596\n",
      "Dest[Turnpike Lane]                   1.1420      0.034     33.698      0.000       1.076       1.208\n",
      "Dest[Upminster]                       1.9616      0.032     60.816      0.000       1.898       2.025\n",
      "Dest[Upminster Bridge]                1.5876      0.044     36.269      0.000       1.502       1.673\n",
      "Dest[Upney]                           0.7781      0.047     16.559      0.000       0.686       0.870\n",
      "Dest[Upper Holloway]                  2.7247      0.035     77.220      0.000       2.656       2.794\n",
      "Dest[Upton Park]                      1.6234      0.027     59.317      0.000       1.570       1.677\n",
      "Dest[Uxbridge]                        3.1428      0.020    159.285      0.000       3.104       3.182\n",
      "Dest[Vauxhall]                        3.6661      0.014    263.158      0.000       3.639       3.693\n",
      "Dest[Victoria]                        4.2530      0.013    338.732      0.000       4.228       4.278\n",
      "Dest[Walthamstow Central]             2.8946      0.018    158.902      0.000       2.859       2.930\n",
      "Dest[Walthamstow Queens Road]         3.8443      0.030    127.540      0.000       3.785       3.903\n",
      "Dest[Wandsworth Road]                 2.5007      0.046     54.153      0.000       2.410       2.591\n",
      "Dest[Wanstead]                        0.5599      0.050     11.131      0.000       0.461       0.659\n",
      "Dest[Wanstead Park]                   2.6696      0.050     53.053      0.000       2.571       2.768\n",
      "Dest[Wapping]                         2.4423      0.032     75.461      0.000       2.379       2.506\n",
      "Dest[Warren Street]                   3.5217      0.014    260.176      0.000       3.495       3.548\n",
      "Dest[Warwick Avenue]                  1.1356      0.031     36.208      0.000       1.074       1.197\n",
      "Dest[Waterloo]                        3.8573      0.013    298.100      0.000       3.832       3.883\n",
      "Dest[Watford]                         2.0570      0.035     59.333      0.000       1.989       2.125\n",
      "Dest[Watford High Street]             3.2417      0.038     86.246      0.000       3.168       3.315\n",
      "Dest[Watford Junction]                3.9300      0.030    132.638      0.000       3.872       3.988\n",
      "Dest[Wembley Central]                 1.6605      0.030     55.407      0.000       1.602       1.719\n",
      "Dest[Wembley Park]                    3.0472      0.018    170.892      0.000       3.012       3.082\n",
      "Dest[West Acton]                      0.7768      0.047     16.588      0.000       0.685       0.869\n",
      "Dest[West Brompton]                   2.6011      0.017    149.963      0.000       2.567       2.635\n",
      "Dest[West Croydon]                    4.2534      0.025    169.547      0.000       4.204       4.303\n",
      "Dest[West Finchley]                  -0.7793      0.106     -7.385      0.000      -0.986      -0.572\n",
      "Dest[West Ham]                        2.5744      0.018    145.224      0.000       2.540       2.609\n",
      "Dest[West Hampstead]                  2.7331      0.017    156.856      0.000       2.699       2.767\n",
      "Dest[West Harrow]                    -0.3863      0.091     -4.230      0.000      -0.565      -0.207\n",
      "Dest[West India Quay]                 1.0675      0.051     20.918      0.000       0.967       1.168\n",
      "Dest[West Kensington]                 1.2481      0.030     42.205      0.000       1.190       1.306\n",
      "Dest[West Ruislip]                    0.4385      0.073      6.015      0.000       0.296       0.581\n",
      "Dest[West Silvertown]                 2.2974      0.035     65.220      0.000       2.228       2.366\n",
      "Dest[Westbourne Park]                 1.3082      0.030     44.174      0.000       1.250       1.366\n",
      "Dest[Westferry]                       2.3682      0.030     78.419      0.000       2.309       2.427\n",
      "Dest[Westminster]                     3.3590      0.014    244.277      0.000       3.332       3.386\n",
      "Dest[White City]                      2.9033      0.017    166.187      0.000       2.869       2.938\n",
      "Dest[White Hart Lane]                 2.3542      0.041     57.276      0.000       2.274       2.435\n",
      "Dest[Whitechapel]                     3.5916      0.014    263.552      0.000       3.565       3.618\n",
      "Dest[Willesden Green]                 0.9772      0.037     26.654      0.000       0.905       1.049\n",
      "Dest[Willesden Junction]              2.5409      0.019    130.802      0.000       2.503       2.579\n",
      "Dest[Wimbledon]                       3.2474      0.018    185.527      0.000       3.213       3.282\n",
      "Dest[Wimbledon Park]                  1.0127      0.043     23.732      0.000       0.929       1.096\n",
      "Dest[Wood Green]                      1.9333      0.025     78.440      0.000       1.885       1.982\n",
      "Dest[Wood Lane]                       1.6601      0.028     59.886      0.000       1.606       1.714\n",
      "Dest[Wood Street]                     1.9876      0.051     38.946      0.000       1.888       2.088\n",
      "Dest[Woodford]                        1.1172      0.040     28.251      0.000       1.040       1.195\n",
      "Dest[Woodgrange Park]                 2.1595      0.065     33.086      0.000       2.032       2.287\n",
      "Dest[Woodside Park]                   1.2423      0.039     32.182      0.000       1.167       1.318\n",
      "Dest[Woolwich Arsenal]                4.4584      0.019    234.342      0.000       4.421       4.496\n",
      "log_Oi_origpop                        0.7451      0.001   1086.239      0.000       0.744       0.746\n",
      "log_Dist                             -0.6352      0.001   -643.767      0.000      -0.637      -0.633\n",
      "=====================================================================================================\n"
     ]
    }
   ],
   "source": [
    "#create the formula (the \"-1\" indicates no intercept in the regression model).\n",
    "attr_form = 'Total ~ Dest + log_Oi_origpop + log_Dist-1'\n",
    "#run a destination constrained sim\n",
    "attrSim = smf.glm(formula = attr_form, data=london_flows, family=sm.families.Poisson()).fit()\n",
    "#let's have a look at it's summary\n",
    "print(attrSim.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>31.0</td>\n",
       "      <td>591.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>586.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.0</td>\n",
       "      <td>...</td>\n",
       "      <td>26.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3546.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>62.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>36.0</td>\n",
       "      <td>...</td>\n",
       "      <td>19.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5702.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>37.0</td>\n",
       "      <td>...</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6029.0</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",
       "      <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>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>19.0</td>\n",
       "      <td>...</td>\n",
       "      <td>19.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3431.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>163.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>16.0</td>\n",
       "      <td>...</td>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2404.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2179.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>345.0</td>\n",
       "      <td>747.0</td>\n",
       "      <td>2196.0</td>\n",
       "      <td>7788.0</td>\n",
       "      <td>7932.0</td>\n",
       "      <td>442.0</td>\n",
       "      <td>740.0</td>\n",
       "      <td>261.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>8099.0</td>\n",
       "      <td>...</td>\n",
       "      <td>6295.0</td>\n",
       "      <td>597.0</td>\n",
       "      <td>2150.0</td>\n",
       "      <td>1578.0</td>\n",
       "      <td>404.0</td>\n",
       "      <td>707.0</td>\n",
       "      <td>243.0</td>\n",
       "      <td>741.0</td>\n",
       "      <td>4429.0</td>\n",
       "      <td>1542262.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN     16.0   \n",
       "Aldgate                  NaN            NaN         6.0      NaN   \n",
       "Aldgate East             NaN            NaN         6.0     68.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         6.0     20.0   \n",
       "Woodgrange Park          NaN            2.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         5.0     14.0   \n",
       "Woolwich Arsenal         7.0            NaN         NaN      NaN   \n",
       "All                    345.0          747.0      2196.0   7788.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                16.0         NaN       8.0       1.0      NaN   \n",
       "Aldgate                   62.0         NaN       NaN       1.0      NaN   \n",
       "Aldgate East               NaN         NaN       3.0       1.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  21.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             13.0         NaN       2.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN         9.0       NaN       NaN      NaN   \n",
       "All                     7932.0       442.0     740.0     261.0    173.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          17.0  ...       26.0             3.0         5.0   \n",
       "Aldgate             36.0  ...       19.0             NaN         6.0   \n",
       "Aldgate East        37.0  ...       20.0             2.0         7.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            19.0  ...       19.0             NaN         7.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       16.0  ...       15.0             NaN         5.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               8099.0  ...     6295.0           597.0      2150.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              3.0   \n",
       "Acton Town              9.0          NaN       2.0              NaN   \n",
       "Aldgate                 5.0          NaN       2.0              NaN   \n",
       "Aldgate East            5.0          NaN       3.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1578.0        404.0     707.0            243.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                  NaN              31.0      591.0  \n",
       "Acton Central               NaN               NaN      586.0  \n",
       "Acton Town                  2.0               NaN     3546.0  \n",
       "Aldgate                     3.0               NaN     5702.0  \n",
       "Aldgate East                3.0               NaN     6029.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                    NaN               NaN     3431.0  \n",
       "Woodgrange Park             NaN               NaN      163.0  \n",
       "Woodside Park               NaN               NaN     2404.0  \n",
       "Woolwich Arsenal            NaN               NaN     2179.0  \n",
       "All                       741.0            4429.0  1542262.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#get the predictions\n",
    "predictions = attrSim.get_prediction(london_flows[[\"Dest\", \"log_Oi_origpop\", \"log_Dist\"]])\n",
    "predictions_summary_frame = predictions.summary_frame()\n",
    "london_flows[\"attrsimFitted\"] = round(predictions_summary_frame[\"mean\"],0)\n",
    "#now we can create pivot table to turn paired list into matrix (and compute the margins as well)\n",
    "ldf_submat_attrcon = london_flows.pivot_table(values =\"attrsimFitted\", index=\"Orig\", columns = \"Dest\",\n",
    "                                    aggfunc=np.sum, margins=True)\n",
    "ldf_submat_attrcon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [],
   "source": [
    "# follow the prodecure of production constrained model \n",
    "# save parameter values into some variables\n",
    "alpha_i=attrSim.params[0:-2]\n",
    "gamma = attrSim.params[-2]\n",
    "beta = -attrSim.params[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "106.015"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRMSE(london_flows['Total'],london_flows[\"attrsimFitted\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.34991505573480136"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRSqaured(london_flows['Total'],london_flows[\"attrsimFitted\"])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make estimation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Doubly constrained model"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the doubly constrained model:\n",
    "\n",
    "- We might be interested in understanding the changing patterns of commuting or migration over time. Data from the Census allows us to know an accurate snap-shot of migrating and commuting patterns every 10 years. In these full data matrices, we know both the numbers of commuters/migrants leaving origins and arriving at destinations as well as the interactions between them. If we constrain our model estimates to this known information at origin and destination, we can examine various things, including:\n",
    "    - The ways that the patterns of commuting/migration differ from the model predictions - where we might get more migrant/commuter flows than we would expect\n",
    "    - How the model parameters vary over time - for example how does distance / cost of travel affect flows over time? Are people prepared to travel further or less far than before?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Which we can now introduce.\n",
    "\n",
    "Let us begin with the formula:\n",
    "\n",
    "\\begin{equation} \\tag{9}\n",
    "T_{ij} = A_i B_j O_i D_j d_{ij}^{-\\beta}\n",
    "\\end{equation}\n",
    "\n",
    "Where\n",
    "\n",
    "\\begin{equation} \\tag{10}\n",
    "O_i = \\sum_j T_{ij}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation} \\tag{11}\n",
    "D_j = \\sum_i T_{ij} \n",
    "\\end{equation}\n",
    "\n",
    "and\n",
    "\n",
    "\\begin{equation} \\tag{12}\n",
    "A_i = \\frac{1}{\\sum_j B_j D_j d_{ij}^{-\\beta}}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation} \\tag{13}\n",
    "B_j = \\frac{1}{\\sum_i A_i O_i d_{ij}^{-\\beta}}\n",
    "\\end{equation}\n",
    "\n",
    "Now, the astute will have noticed that the calculation of $A_i$ relies on knowing $B_j$ and the calculation of $B_j$ relies on knowing $A_i$. A conundrum!! If I don’t know $A_i$ how can I calcuate $B_j$ and then in turn $A_i$ and then $B_j$ ad infinitum???!!\n",
    "\n",
    "Well, I wrestled with that for a while until I came across [this paper by Martyn Senior](http://journals.sagepub.com/doi/abs/10.1177/030913257900300218) where he sketches out a very useful algorithm for iteratively arriving at values for $A_i$ and $B_j$ by setting each to equal to 1 initially and then continuing to calculate each in turn until the difference between each value is small enough not to matter.\n",
    "\n",
    "We will return to this later, but for now, we will once again used the awesome power of Python to deal with all this difficulty for us!\n",
    "\n",
    "We can run the doubly constrained model in exactly the same way as we ran the singly constrained models:\n",
    "\n",
    "\\begin{equation} \\tag{14}\n",
    "\\lambda_{ij} = \\exp (\\alpha_i + \\gamma_j -\\beta \\ln d_{ij})\n",
    "\\end{equation}\n",
    "\n",
    "now in python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Orig</th>\n",
       "      <th>Dest</th>\n",
       "      <th>Total</th>\n",
       "      <th>Oi_origpop</th>\n",
       "      <th>Dj_destjob</th>\n",
       "      <th>Dist</th>\n",
       "      <th>unconstrainedEst1</th>\n",
       "      <th>log_Oi_origpop</th>\n",
       "      <th>log_Dj_destjob</th>\n",
       "      <th>log_Dist</th>\n",
       "      <th>unconstrainedEst2</th>\n",
       "      <th>fitted</th>\n",
       "      <th>O_i</th>\n",
       "      <th>D_j</th>\n",
       "      <th>alpha_i</th>\n",
       "      <th>prodsimest1</th>\n",
       "      <th>attrsimFitted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>0</td>\n",
       "      <td>599</td>\n",
       "      <td>78549</td>\n",
       "      <td>8131.410852</td>\n",
       "      <td>10</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>11.271478</td>\n",
       "      <td>9.003490</td>\n",
       "      <td>50</td>\n",
       "      <td>49.616601</td>\n",
       "      <td>599</td>\n",
       "      <td>78549</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>55.0</td>\n",
       "      <td>53.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Beckton</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>442</td>\n",
       "      <td>8510.047006</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.091310</td>\n",
       "      <td>9.049003</td>\n",
       "      <td>1</td>\n",
       "      <td>0.937185</td>\n",
       "      <td>599</td>\n",
       "      <td>442</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Blackwall</td>\n",
       "      <td>3</td>\n",
       "      <td>599</td>\n",
       "      <td>665</td>\n",
       "      <td>3775.359872</td>\n",
       "      <td>0</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>6.499787</td>\n",
       "      <td>8.236251</td>\n",
       "      <td>2</td>\n",
       "      <td>2.121435</td>\n",
       "      <td>599</td>\n",
       "      <td>665</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>1</td>\n",
       "      <td>599</td>\n",
       "      <td>58772</td>\n",
       "      <td>5086.404941</td>\n",
       "      <td>18</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>10.981421</td>\n",
       "      <td>8.534327</td>\n",
       "      <td>53</td>\n",
       "      <td>53.296799</td>\n",
       "      <td>599</td>\n",
       "      <td>58772</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>66.0</td>\n",
       "      <td>70.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Abbey Road</td>\n",
       "      <td>Canning Town</td>\n",
       "      <td>37</td>\n",
       "      <td>599</td>\n",
       "      <td>15428</td>\n",
       "      <td>2228.874185</td>\n",
       "      <td>25</td>\n",
       "      <td>6.395262</td>\n",
       "      <td>9.643939</td>\n",
       "      <td>7.709252</td>\n",
       "      <td>32</td>\n",
       "      <td>32.209683</td>\n",
       "      <td>599</td>\n",
       "      <td>15428</td>\n",
       "      <td>3.250549</td>\n",
       "      <td>49.0</td>\n",
       "      <td>33.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Orig               Dest  Total  Oi_origpop  Dj_destjob         Dist  \\\n",
       "0  Abbey Road  Bank and Monument      0         599       78549  8131.410852   \n",
       "1  Abbey Road            Beckton      1         599         442  8510.047006   \n",
       "2  Abbey Road          Blackwall      3         599         665  3775.359872   \n",
       "3  Abbey Road       Canary Wharf      1         599       58772  5086.404941   \n",
       "4  Abbey Road       Canning Town     37         599       15428  2228.874185   \n",
       "\n",
       "   unconstrainedEst1  log_Oi_origpop  log_Dj_destjob  log_Dist  \\\n",
       "0                 10        6.395262       11.271478  9.003490   \n",
       "1                  0        6.395262        6.091310  9.049003   \n",
       "2                  0        6.395262        6.499787  8.236251   \n",
       "3                 18        6.395262       10.981421  8.534327   \n",
       "4                 25        6.395262        9.643939  7.709252   \n",
       "\n",
       "   unconstrainedEst2     fitted  O_i    D_j   alpha_i  prodsimest1  \\\n",
       "0                 50  49.616601  599  78549  3.250549         55.0   \n",
       "1                  1   0.937185  599    442  3.250549          1.0   \n",
       "2                  2   2.121435  599    665  3.250549          3.0   \n",
       "3                 53  53.296799  599  58772  3.250549         66.0   \n",
       "4                 32  32.209683  599  15428  3.250549         49.0   \n",
       "\n",
       "   attrsimFitted  \n",
       "0           53.0  \n",
       "1            3.0  \n",
       "2            4.0  \n",
       "3           70.0  \n",
       "4           33.0  "
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                  Total   No. Observations:                61413\n",
      "Model:                            GLM   Df Residuals:                    60617\n",
      "Model Family:                 Poisson   Df Model:                          795\n",
      "Link Function:                    log   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:            -9.7074e+05\n",
      "Date:                Mon, 01 May 2023   Deviance:                   1.7693e+06\n",
      "Time:                        15:00:18   Pearson chi2:                 2.47e+06\n",
      "No. Iterations:                     8                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=======================================================================================================\n",
      "                                          coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------\n",
      "Dest[Abbey Road]                        7.7407      0.068    113.624      0.000       7.607       7.874\n",
      "Dest[Acton Central]                     9.3149      0.056    166.710      0.000       9.205       9.424\n",
      "Dest[Acton Town]                        9.3644      0.047    198.490      0.000       9.272       9.457\n",
      "Dest[Aldgate]                          10.1768      0.044    233.904      0.000      10.091      10.262\n",
      "Dest[Aldgate East]                     10.1538      0.043    233.519      0.000      10.069      10.239\n",
      "Dest[All Saints]                        8.1657      0.063    128.940      0.000       8.042       8.290\n",
      "Dest[Alperton]                          8.7481      0.056    156.412      0.000       8.638       8.858\n",
      "Dest[Amersham]                          8.5157      0.076    112.733      0.000       8.368       8.664\n",
      "Dest[Anerley]                           7.7917      0.087     89.341      0.000       7.621       7.963\n",
      "Dest[Angel]                            10.2056      0.043    234.713      0.000      10.120      10.291\n",
      "Dest[Archway]                           9.2953      0.047    196.840      0.000       9.203       9.388\n",
      "Dest[Arnos Grove]                       8.5423      0.056    153.095      0.000       8.433       8.652\n",
      "Dest[Arsenal]                           7.0747      0.070    100.697      0.000       6.937       7.212\n",
      "Dest[Baker Street]                     10.7941      0.043    252.154      0.000      10.710      10.878\n",
      "Dest[Balham]                            9.8393      0.045    218.323      0.000       9.751       9.928\n",
      "Dest[Bank and Monument]                12.1944      0.042    289.697      0.000      12.112      12.277\n",
      "Dest[Barbican]                         10.2420      0.043    236.580      0.000      10.157      10.327\n",
      "Dest[Barking]                          10.4204      0.044    237.787      0.000      10.334      10.506\n",
      "Dest[Barkingside]                       7.6979      0.075    102.963      0.000       7.551       7.844\n",
      "Dest[Barons Court]                      9.3979      0.046    204.822      0.000       9.308       9.488\n",
      "Dest[Bayswater]                         8.0400      0.058    138.003      0.000       7.926       8.154\n",
      "Dest[Beckton]                           8.9551      0.063    141.119      0.000       8.831       9.079\n",
      "Dest[Beckton Park]                      7.1675      0.115     62.532      0.000       6.943       7.392\n",
      "Dest[Becontree]                         8.1398      0.063    129.202      0.000       8.016       8.263\n",
      "Dest[Belsize Park]                      9.3472      0.047    198.523      0.000       9.255       9.440\n",
      "Dest[Bermondsey]                        9.3458      0.046    204.826      0.000       9.256       9.435\n",
      "Dest[Bethnal Green]                     9.6059      0.045    215.670      0.000       9.519       9.693\n",
      "Dest[Blackfriars]                      10.4557      0.043    242.526      0.000      10.371      10.540\n",
      "Dest[Blackhorse Road]                   9.4647      0.046    206.043      0.000       9.375       9.555\n",
      "Dest[Blackwall]                         8.4846      0.057    148.924      0.000       8.373       8.596\n",
      "Dest[Bond Street]                      11.0996      0.043    260.619      0.000      11.016      11.183\n",
      "Dest[Borough]                           9.1746      0.045    201.742      0.000       9.086       9.264\n",
      "Dest[Boston Manor]                      8.7798      0.054    163.118      0.000       8.674       8.885\n",
      "Dest[Bounds Green]                      8.4682      0.055    153.088      0.000       8.360       8.577\n",
      "Dest[Bow Church]                        9.0428      0.053    169.720      0.000       8.938       9.147\n",
      "Dest[Bow Road]                          8.4614      0.051    165.843      0.000       8.361       8.561\n",
      "Dest[Brent Cross]                       8.1057      0.063    128.194      0.000       7.982       8.230\n",
      "Dest[Brentwood]                         8.8093      0.056    156.509      0.000       8.699       8.920\n",
      "Dest[Brixton]                          10.0643      0.044    226.725      0.000       9.977      10.151\n",
      "Dest[Brockley]                          8.3210      0.063    132.726      0.000       8.198       8.444\n",
      "Dest[Bromley-by-Bow]                    8.7824      0.049    179.850      0.000       8.687       8.878\n",
      "Dest[Brondesbury]                       8.7723      0.056    155.525      0.000       8.662       8.883\n",
      "Dest[Brondesbury Park]                  9.0775      0.054    168.581      0.000       8.972       9.183\n",
      "Dest[Bruce Grove]                       8.1855      0.068    120.223      0.000       8.052       8.319\n",
      "Dest[Buckhurst Hill]                    7.6461      0.079     97.402      0.000       7.492       7.800\n",
      "Dest[Burnt Oak]                         8.6074      0.058    149.396      0.000       8.494       8.720\n",
      "Dest[Bush Hill Park]                    7.6789      0.087     88.678      0.000       7.509       7.849\n",
      "Dest[Bushey]                            9.2858      0.064    145.561      0.000       9.161       9.411\n",
      "Dest[Caledonian Road]                   8.8058      0.048    182.745      0.000       8.711       8.900\n",
      "Dest[Caledonian Road & Barnsbury]       9.3630      0.049    192.424      0.000       9.268       9.458\n",
      "Dest[Cambridge Heath]                   8.5325      0.063    135.434      0.000       8.409       8.656\n",
      "Dest[Camden Road]                      10.2129      0.045    225.869      0.000      10.124      10.302\n",
      "Dest[Camden Town]                      10.0510      0.044    229.018      0.000       9.965      10.137\n",
      "Dest[Canada Water]                     10.8897      0.043    255.397      0.000      10.806      10.973\n",
      "Dest[Canary Wharf]                     12.1008      0.042    287.040      0.000      12.018      12.183\n",
      "Dest[Canning Town]                     10.8283      0.043    253.891      0.000      10.745      10.912\n",
      "Dest[Cannon Street]                     9.4690      0.044    213.253      0.000       9.382       9.556\n",
      "Dest[Canonbury]                         8.5516      0.054    157.438      0.000       8.445       8.658\n",
      "Dest[Canons Park]                       8.4701      0.061    139.608      0.000       8.351       8.589\n",
      "Dest[Carpenders Park]                   9.1192      0.069    131.808      0.000       8.984       9.255\n",
      "Dest[Chadwell Heath]                    7.7277      0.060    129.184      0.000       7.610       7.845\n",
      "Dest[Chalfont & Latimer]                9.3882      0.060    156.469      0.000       9.271       9.506\n",
      "Dest[Chalk Farm]                        8.7071      0.050    173.327      0.000       8.609       8.806\n",
      "Dest[Chancery Lane]                    10.8010      0.043    252.361      0.000      10.717      10.885\n",
      "Dest[Charing Cross]                     9.8984      0.044    226.780      0.000       9.813       9.984\n",
      "Dest[Chesham]                           8.6965      0.077    113.051      0.000       8.546       8.847\n",
      "Dest[Cheshunt]                          7.9942      0.103     77.942      0.000       7.793       8.195\n",
      "Dest[Chigwell]                          7.5496      0.092     81.734      0.000       7.369       7.731\n",
      "Dest[Chingford]                         8.4020      0.078    108.310      0.000       8.250       8.554\n",
      "Dest[Chiswick Park]                     9.0365      0.049    183.317      0.000       8.940       9.133\n",
      "Dest[Chorleywood]                       9.5788      0.057    168.879      0.000       9.468       9.690\n",
      "Dest[Clapham Common]                    9.0412      0.048    190.067      0.000       8.948       9.134\n",
      "Dest[Clapham High Street]               9.7569      0.051    192.056      0.000       9.657       9.856\n",
      "Dest[Clapham Junction]                 11.0923      0.045    248.191      0.000      11.005      11.180\n",
      "Dest[Clapham North]                     8.5025      0.051    167.622      0.000       8.403       8.602\n",
      "Dest[Clapham South]                     8.8501      0.049    179.551      0.000       8.753       8.947\n",
      "Dest[Clapton]                           8.5749      0.064    133.531      0.000       8.449       8.701\n",
      "Dest[Cockfosters]                       7.9285      0.075    105.928      0.000       7.782       8.075\n",
      "Dest[Colindale]                         9.6894      0.048    203.766      0.000       9.596       9.783\n",
      "Dest[Colliers Wood]                     8.5231      0.054    157.565      0.000       8.417       8.629\n",
      "Dest[Covent Garden]                     9.4837      0.045    212.336      0.000       9.396       9.571\n",
      "Dest[Crossharbour]                      9.2392      0.051    181.832      0.000       9.140       9.339\n",
      "Dest[Crouch Hill]                       8.8347      0.065    135.085      0.000       8.706       8.963\n",
      "Dest[Croxley]                           8.6108      0.069    125.214      0.000       8.476       8.746\n",
      "Dest[Crystal Palace]                    9.1422      0.062    147.673      0.000       9.021       9.264\n",
      "Dest[Custom House]                      8.8922      0.054    164.326      0.000       8.786       8.998\n",
      "Dest[Cutty Sark]                        9.7691      0.048    202.241      0.000       9.674       9.864\n",
      "Dest[Cyprus]                            9.3200      0.054    171.950      0.000       9.214       9.426\n",
      "Dest[Dagenham East]                     8.6239      0.058    149.703      0.000       8.511       8.737\n",
      "Dest[Dagenham Heathway]                 9.0400      0.052    174.593      0.000       8.939       9.141\n",
      "Dest[Dalston Junction]                  9.3372      0.051    184.719      0.000       9.238       9.436\n",
      "Dest[Dalston Kingsland]                 9.6843      0.047    204.197      0.000       9.591       9.777\n",
      "Dest[Debden]                            9.1276      0.054    168.372      0.000       9.021       9.234\n",
      "Dest[Denmark Hill]                     10.1989      0.047    218.492      0.000      10.107      10.290\n",
      "Dest[Deptford Bridge]                   9.0028      0.054    165.354      0.000       8.896       9.110\n",
      "Dest[Devons Road]                       8.5796      0.058    147.558      0.000       8.466       8.694\n",
      "Dest[Dollis Hill]                       8.4710      0.054    155.899      0.000       8.365       8.578\n",
      "Dest[Ealing Broadway]                  10.3179      0.045    231.627      0.000      10.231      10.405\n",
      "Dest[Ealing Common]                     8.6003      0.053    160.760      0.000       8.495       8.705\n",
      "Dest[Earl's Court]                     10.0944      0.044    230.514      0.000      10.009      10.180\n",
      "Dest[East Acton]                        9.0449      0.049    183.121      0.000       8.948       9.142\n",
      "Dest[East Finchley]                     8.9753      0.051    176.851      0.000       8.876       9.075\n",
      "Dest[East Ham]                          9.2898      0.048    195.572      0.000       9.197       9.383\n",
      "Dest[East India]                        9.3126      0.049    190.220      0.000       9.217       9.409\n",
      "Dest[East Putney]                       9.2722      0.048    193.018      0.000       9.178       9.366\n",
      "Dest[Eastcote]                          8.0381      0.067    119.526      0.000       7.906       8.170\n",
      "Dest[Edgware]                           8.8979      0.055    160.331      0.000       8.789       9.007\n",
      "Dest[Edgware Road]                     10.0230      0.044    229.366      0.000       9.937      10.109\n",
      "Dest[Edmonton Green]                    8.8759      0.055    160.076      0.000       8.767       8.985\n",
      "Dest[Elephant & Castle]                 9.9084      0.044    226.099      0.000       9.823       9.994\n",
      "Dest[Elm Park]                          7.9462      0.074    107.150      0.000       7.801       8.092\n",
      "Dest[Elverson Road]                     7.3829      0.079     93.725      0.000       7.229       7.537\n",
      "Dest[Embankment]                       10.2016      0.043    236.678      0.000      10.117      10.286\n",
      "Dest[Emerson Park]                      6.5646      0.161     40.887      0.000       6.250       6.879\n",
      "Dest[Enfield Town]                      9.2567      0.056    164.914      0.000       9.147       9.367\n",
      "Dest[Epping]                            8.8542      0.062    143.604      0.000       8.733       8.975\n",
      "Dest[Euston]                           10.8771      0.043    254.639      0.000      10.793      10.961\n",
      "Dest[Euston Square]                    10.3494      0.043    238.097      0.000      10.264      10.435\n",
      "Dest[Fairlop]                           7.4289      0.085     87.146      0.000       7.262       7.596\n",
      "Dest[Farringdon]                       11.3264      0.042    266.534      0.000      11.243      11.410\n",
      "Dest[Finchley Central]                  9.5209      0.048    198.563      0.000       9.427       9.615\n",
      "Dest[Finchley Road]                     9.5967      0.045    211.402      0.000       9.508       9.686\n",
      "Dest[Finchley Road & Frognal]           9.4419      0.049    191.685      0.000       9.345       9.538\n",
      "Dest[Finsbury Park]                    10.2044      0.044    233.145      0.000      10.119      10.290\n",
      "Dest[Forest Gate]                       8.3562      0.055    152.421      0.000       8.249       8.464\n",
      "Dest[Forest Hill]                       8.6304      0.059    146.854      0.000       8.515       8.746\n",
      "Dest[Fulham Broadway]                   9.7670      0.045    217.996      0.000       9.679       9.855\n",
      "Dest[Gallions Reach]                    9.0340      0.060    151.104      0.000       8.917       9.151\n",
      "Dest[Gants Hill]                        8.3276      0.059    141.983      0.000       8.213       8.443\n",
      "Dest[Gidea Park]                        7.1011      0.072     98.917      0.000       6.960       7.242\n",
      "Dest[Gloucester Road]                   9.8258      0.044    221.983      0.000       9.739       9.913\n",
      "Dest[Golders Green]                     9.4217      0.048    195.891      0.000       9.327       9.516\n",
      "Dest[Goldhawk Road]                     7.6038      0.067    113.717      0.000       7.473       7.735\n",
      "Dest[Goodge Street]                     9.9759      0.044    227.625      0.000       9.890      10.062\n",
      "Dest[Goodmayes]                         7.6995      0.057    134.873      0.000       7.588       7.811\n",
      "Dest[Gospel Oak]                        9.6901      0.048    203.152      0.000       9.597       9.784\n",
      "Dest[Grange Hill]                       6.7852      0.122     55.528      0.000       6.546       7.025\n",
      "Dest[Great Portland Street]            10.1041      0.044    231.199      0.000      10.018      10.190\n",
      "Dest[Green Park]                       11.2897      0.042    265.958      0.000      11.207      11.373\n",
      "Dest[Greenford]                         9.1819      0.051    178.476      0.000       9.081       9.283\n",
      "Dest[Greenwich]                         9.3164      0.051    182.294      0.000       9.216       9.417\n",
      "Dest[Gunnersbury]                       9.9713      0.045    223.692      0.000       9.884      10.059\n",
      "Dest[Hackney Central]                   9.8639      0.047    211.084      0.000       9.772       9.956\n",
      "Dest[Hackney Downs]                     9.0888      0.055    166.254      0.000       8.982       9.196\n",
      "Dest[Hackney Wick]                      8.9651      0.051    177.316      0.000       8.866       9.064\n",
      "Dest[Haggerston]                        9.0797      0.051    177.251      0.000       8.979       9.180\n",
      "Dest[Hainault]                          8.0430      0.068    118.739      0.000       7.910       8.176\n",
      "Dest[Hammersmith]                      11.2739      0.043    263.897      0.000      11.190      11.358\n",
      "Dest[Hampstead]                         9.3349      0.048    195.806      0.000       9.241       9.428\n",
      "Dest[Hampstead Heath]                   9.9726      0.046    215.594      0.000       9.882      10.063\n",
      "Dest[Hanger Lane]                       9.3652      0.050    189.175      0.000       9.268       9.462\n",
      "Dest[Harlesden]                         9.0784      0.049    186.206      0.000       8.983       9.174\n",
      "Dest[Harold Wood]                       7.9740      0.061    131.115      0.000       7.855       8.093\n",
      "Dest[Harringay Green Lanes]             9.0381      0.060    149.852      0.000       8.920       9.156\n",
      "Dest[Harrow & Wealdstone]               9.3005      0.050    184.532      0.000       9.202       9.399\n",
      "Dest[Harrow-on-the-Hill]                9.8918      0.046    215.575      0.000       9.802       9.982\n",
      "Dest[Hatch End]                         7.7421      0.112     68.927      0.000       7.522       7.962\n",
      "Dest[Hatton Cross]                      9.4599      0.051    185.277      0.000       9.360       9.560\n",
      "Dest[Headstone Lane]                    9.0813      0.071    127.943      0.000       8.942       9.220\n",
      "Dest[Heathrow Terminal 4]               8.9510      0.057    157.437      0.000       8.840       9.062\n",
      "Dest[Heathrow Terminal 5]               9.3868      0.053    176.788      0.000       9.283       9.491\n",
      "Dest[Heathrow Terminals 2 & 3]         10.1229      0.047    215.504      0.000      10.031      10.215\n",
      "Dest[Hendon Central]                    9.5052      0.048    197.700      0.000       9.411       9.599\n",
      "Dest[Heron Quays]                      10.6049      0.044    242.108      0.000      10.519      10.691\n",
      "Dest[High Barnet]                       9.1605      0.053    171.955      0.000       9.056       9.265\n",
      "Dest[High Street Kensington]            9.9057      0.044    224.207      0.000       9.819       9.992\n",
      "Dest[Highams Park]                      8.5013      0.066    128.830      0.000       8.372       8.631\n",
      "Dest[Highbury & Islington]             11.1441      0.043    262.075      0.000      11.061      11.227\n",
      "Dest[Highgate]                          8.4938      0.054    156.556      0.000       8.388       8.600\n",
      "Dest[Hillingdon]                        8.1933      0.070    116.737      0.000       8.056       8.331\n",
      "Dest[Holborn]                          11.1229      0.043    261.421      0.000      11.039      11.206\n",
      "Dest[Holland Park]                      9.0562      0.047    190.802      0.000       8.963       9.149\n",
      "Dest[Holloway Road]                     8.7322      0.049    179.913      0.000       8.637       8.827\n",
      "Dest[Homerton]                          9.5043      0.048    199.353      0.000       9.411       9.598\n",
      "Dest[Honor Oak Park]                    8.0283      0.069    116.647      0.000       7.893       8.163\n",
      "Dest[Hornchurch]                        8.6000      0.063    135.971      0.000       8.476       8.724\n",
      "Dest[Hounslow Central]                  8.6327      0.056    152.807      0.000       8.522       8.743\n",
      "Dest[Hounslow East]                     8.7719      0.054    161.106      0.000       8.665       8.879\n",
      "Dest[Hounslow West]                     8.2279      0.065    125.806      0.000       8.100       8.356\n",
      "Dest[Hoxton]                            9.7034      0.047    205.160      0.000       9.611       9.796\n",
      "Dest[Hyde Park Corner]                  9.0086      0.047    192.835      0.000       8.917       9.100\n",
      "Dest[Ickenham]                          8.1289      0.073    111.403      0.000       7.986       8.272\n",
      "Dest[Ilford]                            9.0227      0.049    184.413      0.000       8.927       9.119\n",
      "Dest[Imperial Wharf]                    9.9443      0.048    208.489      0.000       9.851      10.038\n",
      "Dest[Island Gardens]                    8.7730      0.057    154.974      0.000       8.662       8.884\n",
      "Dest[Kennington]                        8.2660      0.051    161.291      0.000       8.166       8.366\n",
      "Dest[Kensal Green]                      7.8853      0.062    126.364      0.000       7.763       8.008\n",
      "Dest[Kensal Rise]                       9.4053      0.050    187.799      0.000       9.307       9.503\n",
      "Dest[Kensington]                        9.3029      0.047    197.541      0.000       9.211       9.395\n",
      "Dest[Kentish Town]                      9.5705      0.045    210.622      0.000       9.481       9.660\n",
      "Dest[Kentish Town West]                 9.0907      0.052    176.026      0.000       8.989       9.192\n",
      "Dest[Kenton]                            9.0182      0.056    162.202      0.000       8.909       9.127\n",
      "Dest[Kew Gardens]                       8.3405      0.055    151.203      0.000       8.232       8.449\n",
      "Dest[Kilburn]                           9.1626      0.048    191.799      0.000       9.069       9.256\n",
      "Dest[Kilburn High Road]                 8.8126      0.075    118.004      0.000       8.666       8.959\n",
      "Dest[Kilburn Park]                      8.4238      0.055    154.136      0.000       8.317       8.531\n",
      "Dest[King George V]                     9.1057      0.055    166.035      0.000       8.998       9.213\n",
      "Dest[King's Cross St. Pancras]         11.5616      0.042    272.893      0.000      11.479      11.645\n",
      "Dest[Kingsbury]                         8.9362      0.053    170.114      0.000       8.833       9.039\n",
      "Dest[Knightsbridge]                    10.0872      0.044    230.479      0.000      10.001      10.173\n",
      "Dest[Ladbroke Grove]                    9.1718      0.047    193.741      0.000       9.079       9.265\n",
      "Dest[Lambeth North]                     8.1948      0.050    163.337      0.000       8.096       8.293\n",
      "Dest[Lancaster Gate]                    8.9334      0.048    185.493      0.000       8.839       9.028\n",
      "Dest[Langdon Park]                      9.7395      0.047    205.340      0.000       9.647       9.832\n",
      "Dest[Latimer Road]                      8.5999      0.052    166.346      0.000       8.499       8.701\n",
      "Dest[Leicester Square]                 10.1449      0.043    234.184      0.000      10.060      10.230\n",
      "Dest[Lewisham]                         10.5471      0.047    225.075      0.000      10.455      10.639\n",
      "Dest[Leyton]                            8.8109      0.050    177.760      0.000       8.714       8.908\n",
      "Dest[Leyton Midland Road]               8.7230      0.064    136.429      0.000       8.598       8.848\n",
      "Dest[Leytonstone]                       9.1805      0.048    190.966      0.000       9.086       9.275\n",
      "Dest[Leytonstone High Road]             8.4207      0.071    118.768      0.000       8.282       8.560\n",
      "Dest[Limehouse]                        10.2421      0.046    223.905      0.000      10.152      10.332\n",
      "Dest[Liverpool Street]                 11.8532      0.042    280.764      0.000      11.770      11.936\n",
      "Dest[London Bridge]                    11.4039      0.042    269.027      0.000      11.321      11.487\n",
      "Dest[London City Airport]               9.9703      0.048    209.316      0.000       9.877      10.064\n",
      "Dest[London Fields]                     8.9357      0.055    161.817      0.000       8.827       9.044\n",
      "Dest[Loughton]                          8.7504      0.058    152.154      0.000       8.638       8.863\n",
      "Dest[Maida Vale]                        8.4119      0.053    158.286      0.000       8.308       8.516\n",
      "Dest[Manor House]                       8.5955      0.050    170.915      0.000       8.497       8.694\n",
      "Dest[Manor Park]                        7.5785      0.064    118.655      0.000       7.453       7.704\n",
      "Dest[Mansion House]                    10.0754      0.043    231.783      0.000       9.990      10.161\n",
      "Dest[Marble Arch]                       9.9688      0.044    226.856      0.000       9.883      10.055\n",
      "Dest[Maryland]                          7.3512      0.068    108.168      0.000       7.218       7.484\n",
      "Dest[Marylebone]                        9.5728      0.045    214.010      0.000       9.485       9.660\n",
      "Dest[Mile End]                          9.5286      0.045    211.423      0.000       9.440       9.617\n",
      "Dest[Mill Hill East]                    8.7137      0.057    152.902      0.000       8.602       8.825\n",
      "Dest[Moor Park]                         9.0522      0.060    150.867      0.000       8.935       9.170\n",
      "Dest[Moorgate]                         11.0987      0.042    261.573      0.000      11.016      11.182\n",
      "Dest[Morden]                            9.2755      0.050    186.583      0.000       9.178       9.373\n",
      "Dest[Mornington Crescent]               9.2532      0.046    201.565      0.000       9.163       9.343\n",
      "Dest[Mudchute]                          7.9008      0.071    110.890      0.000       7.761       8.040\n",
      "Dest[Neasden]                           8.3887      0.056    149.730      0.000       8.279       8.499\n",
      "Dest[New Cross]                         9.6559      0.053    183.669      0.000       9.553       9.759\n",
      "Dest[New Cross Gate]                    9.3137      0.050    184.974      0.000       9.215       9.412\n",
      "Dest[Newbury Park]                      8.3769      0.060    140.272      0.000       8.260       8.494\n",
      "Dest[North Acton]                       9.8312      0.046    214.975      0.000       9.742       9.921\n",
      "Dest[North Ealing]                      8.1395      0.069    117.640      0.000       8.004       8.275\n",
      "Dest[North Greenwich]                  10.2631      0.044    233.627      0.000      10.177      10.349\n",
      "Dest[North Harrow]                      7.4304      0.084     88.575      0.000       7.266       7.595\n",
      "Dest[North Wembley]                     7.9858      0.067    118.734      0.000       7.854       8.118\n",
      "Dest[Northfields]                       8.6651      0.054    160.030      0.000       8.559       8.771\n",
      "Dest[Northolt]                          8.7313      0.057    152.139      0.000       8.619       8.844\n",
      "Dest[Northwick Park]                    9.3030      0.049    191.680      0.000       9.208       9.398\n",
      "Dest[Northwood]                         9.2917      0.053    176.694      0.000       9.189       9.395\n",
      "Dest[Northwood Hills]                   8.5266      0.062    137.807      0.000       8.405       8.648\n",
      "Dest[Norwood Junction]                  8.7268      0.066    133.066      0.000       8.598       8.855\n",
      "Dest[Notting Hill Gate]                 9.9187      0.044    224.644      0.000       9.832      10.005\n",
      "Dest[Oakwood]                           8.2711      0.064    128.442      0.000       8.145       8.397\n",
      "Dest[Old Street]                       10.8587      0.043    253.854      0.000      10.775      10.943\n",
      "Dest[Osterley]                          8.3714      0.061    137.662      0.000       8.252       8.491\n",
      "Dest[Oval]                              9.1287      0.046    196.422      0.000       9.038       9.220\n",
      "Dest[Oxford Circus]                    11.8001      0.042    279.093      0.000      11.717      11.883\n",
      "Dest[Paddington]                       11.2441      0.043    263.674      0.000      11.160      11.328\n",
      "Dest[Park Royal]                        9.3842      0.049    190.770      0.000       9.288       9.481\n",
      "Dest[Parsons Green]                     9.4296      0.046    203.846      0.000       9.339       9.520\n",
      "Dest[Peckham Rye]                       9.2654      0.052    177.293      0.000       9.163       9.368\n",
      "Dest[Penge West]                        7.2630      0.092     78.752      0.000       7.082       7.444\n",
      "Dest[Perivale]                          8.4244      0.061    139.233      0.000       8.306       8.543\n",
      "Dest[Piccadilly Circus]                10.5880      0.043    247.012      0.000      10.504      10.672\n",
      "Dest[Pimlico]                           9.8404      0.044    223.173      0.000       9.754       9.927\n",
      "Dest[Pinner]                            7.9202      0.072    109.798      0.000       7.779       8.062\n",
      "Dest[Plaistow]                          8.4097      0.052    161.357      0.000       8.308       8.512\n",
      "Dest[Pontoon Dock]                      9.3179      0.051    181.392      0.000       9.217       9.419\n",
      "Dest[Poplar]                            9.0590      0.050    180.785      0.000       8.961       9.157\n",
      "Dest[Preston Road]                      7.9098      0.065    121.974      0.000       7.783       8.037\n",
      "Dest[Prince Regent]                     8.9252      0.055    160.984      0.000       8.817       9.034\n",
      "Dest[Pudding Mill Lane]                 8.0571      0.064    126.339      0.000       7.932       8.182\n",
      "Dest[Putney Bridge]                     9.4216      0.047    202.117      0.000       9.330       9.513\n",
      "Dest[Queen's Park]                      9.1464      0.047    193.412      0.000       9.054       9.239\n",
      "Dest[Queens Road Peckham]               8.9521      0.056    159.975      0.000       8.842       9.062\n",
      "Dest[Queensbury]                        8.1737      0.064    128.340      0.000       8.049       8.298\n",
      "Dest[Queensway]                         8.9782      0.048    187.207      0.000       8.884       9.072\n",
      "Dest[Ravenscourt Park]                  9.0629      0.048    189.181      0.000       8.969       9.157\n",
      "Dest[Rayners Lane]                      8.0569      0.064    125.504      0.000       7.931       8.183\n",
      "Dest[Rectory Road]                      7.7036      0.080     96.630      0.000       7.547       7.860\n",
      "Dest[Redbridge]                         7.2072      0.083     87.265      0.000       7.045       7.369\n",
      "Dest[Regent's Park]                     9.3973      0.045    206.841      0.000       9.308       9.486\n",
      "Dest[Richmond]                         10.3595      0.044    233.357      0.000      10.272      10.446\n",
      "Dest[Rickmansworth]                     9.4826      0.053    177.416      0.000       9.378       9.587\n",
      "Dest[Roding Valley]                     6.9739      0.117     59.637      0.000       6.745       7.203\n",
      "Dest[Romford]                           9.1466      0.048    191.487      0.000       9.053       9.240\n",
      "Dest[Rotherhithe]                       7.4780      0.070    107.092      0.000       7.341       7.615\n",
      "Dest[Royal Albert]                      8.9904      0.057    158.580      0.000       8.879       9.102\n",
      "Dest[Royal Oak]                         8.1985      0.054    151.310      0.000       8.092       8.305\n",
      "Dest[Royal Victoria]                    8.7393      0.055    157.840      0.000       8.631       8.848\n",
      "Dest[Ruislip]                           7.8457      0.075    104.224      0.000       7.698       7.993\n",
      "Dest[Ruislip Gardens]                   7.7801      0.088     88.236      0.000       7.607       7.953\n",
      "Dest[Ruislip Manor]                     8.2224      0.065    126.498      0.000       8.095       8.350\n",
      "Dest[Russell Square]                    9.6716      0.044    218.553      0.000       9.585       9.758\n",
      "Dest[Seven Kings]                       7.5634      0.060    126.366      0.000       7.446       7.681\n",
      "Dest[Seven Sisters]                    10.5261      0.043    243.562      0.000      10.441      10.611\n",
      "Dest[Shadwell]                         10.4161      0.044    239.330      0.000      10.331      10.501\n",
      "Dest[Shenfield]                         8.9879      0.054    166.718      0.000       8.882       9.094\n",
      "Dest[Shepherd's Bush]                  10.4819      0.043    242.147      0.000      10.397      10.567\n",
      "Dest[Shepherd's Bush Market]            7.6954      0.065    119.118      0.000       7.569       7.822\n",
      "Dest[Shoreditch High Street]           10.9660      0.044    251.029      0.000      10.880      11.052\n",
      "Dest[Silver Street]                     9.1656      0.053    171.744      0.000       9.061       9.270\n",
      "Dest[Sloane Square]                    10.2325      0.043    235.477      0.000      10.147      10.318\n",
      "Dest[Snaresbrook]                       8.0898      0.061    132.603      0.000       7.970       8.209\n",
      "Dest[South Acton]                       9.6252      0.053    181.364      0.000       9.521       9.729\n",
      "Dest[South Ealing]                      8.3588      0.057    146.282      0.000       8.247       8.471\n",
      "Dest[South Hampstead]                   8.8908      0.078    114.152      0.000       8.738       9.043\n",
      "Dest[South Harrow]                      8.1810      0.066    123.886      0.000       8.052       8.310\n",
      "Dest[South Kensington]                 10.9022      0.043    254.644      0.000      10.818      10.986\n",
      "Dest[South Kenton]                      7.9494      0.075    106.068      0.000       7.803       8.096\n",
      "Dest[South Quay]                       10.5191      0.044    237.107      0.000      10.432      10.606\n",
      "Dest[South Ruislip]                     8.1505      0.072    112.528      0.000       8.009       8.292\n",
      "Dest[South Tottenham]                   9.2642      0.060    153.947      0.000       9.146       9.382\n",
      "Dest[South Wimbledon]                   9.0902      0.050    181.618      0.000       8.992       9.188\n",
      "Dest[South Woodford]                    8.5002      0.055    153.208      0.000       8.391       8.609\n",
      "Dest[Southbury]                         9.1864      0.061    151.505      0.000       9.068       9.305\n",
      "Dest[Southfields]                       9.0676      0.050    180.719      0.000       8.969       9.166\n",
      "Dest[Southgate]                         8.7863      0.054    162.446      0.000       8.680       8.892\n",
      "Dest[Southwark]                        10.2246      0.043    237.306      0.000      10.140      10.309\n",
      "Dest[St James Street]                   7.4935      0.085     88.318      0.000       7.327       7.660\n",
      "Dest[St. James's Park]                 10.5603      0.043    246.366      0.000      10.476      10.644\n",
      "Dest[St. John's Wood]                   9.7110      0.045    215.972      0.000       9.623       9.799\n",
      "Dest[St. Paul's]                       10.6262      0.043    247.758      0.000      10.542      10.710\n",
      "Dest[Stamford Brook]                    8.3166      0.055    150.736      0.000       8.208       8.425\n",
      "Dest[Stamford Hill]                     8.1983      0.068    120.689      0.000       8.065       8.331\n",
      "Dest[Stanmore]                          9.1403      0.053    172.688      0.000       9.037       9.244\n",
      "Dest[Star Lane]                         8.9130      0.052    172.626      0.000       8.812       9.014\n",
      "Dest[Stepney Green]                     8.8272      0.048    184.132      0.000       8.733       8.921\n",
      "Dest[Stockwell]                         8.6856      0.049    177.980      0.000       8.590       8.781\n",
      "Dest[Stoke Newington]                   8.4187      0.062    135.315      0.000       8.297       8.541\n",
      "Dest[Stonebridge Park]                  8.3826      0.056    149.287      0.000       8.273       8.493\n",
      "Dest[Stratford]                        11.6810      0.042    277.366      0.000      11.598      11.764\n",
      "Dest[Stratford High Street]             8.2815      0.054    152.362      0.000       8.175       8.388\n",
      "Dest[Stratford International]           9.5151      0.049    195.335      0.000       9.420       9.611\n",
      "Dest[Sudbury Hill]                      7.8074      0.073    106.364      0.000       7.664       7.951\n",
      "Dest[Sudbury Town]                      7.6838      0.080     96.300      0.000       7.527       7.840\n",
      "Dest[Surrey Quays]                      8.6560      0.053    164.760      0.000       8.553       8.759\n",
      "Dest[Swiss Cottage]                     9.3322      0.046    201.064      0.000       9.241       9.423\n",
      "Dest[Sydenham]                          8.4406      0.061    137.671      0.000       8.320       8.561\n",
      "Dest[Temple]                            9.9550      0.044    227.634      0.000       9.869      10.041\n",
      "Dest[Theobalds Grove]                   8.3717      0.086     97.580      0.000       8.204       8.540\n",
      "Dest[Theydon Bois]                      7.3979      0.109     67.565      0.000       7.183       7.613\n",
      "Dest[Tooting Bec]                       8.7042      0.051    171.578      0.000       8.605       8.804\n",
      "Dest[Tooting Broadway]                 10.0715      0.045    225.627      0.000       9.984      10.159\n",
      "Dest[Tottenham Court Road]             10.9600      0.043    257.078      0.000      10.876      11.044\n",
      "Dest[Tottenham Hale]                    9.6450      0.046    211.734      0.000       9.556       9.734\n",
      "Dest[Totteridge & Whetstone]            7.8605      0.073    108.324      0.000       7.718       8.003\n",
      "Dest[Tower Gateway]                    10.6434      0.045    234.015      0.000      10.554      10.733\n",
      "Dest[Tower Hill]                       10.1496      0.043    233.772      0.000      10.064      10.235\n",
      "Dest[Tufnell Park]                      7.8874      0.060    132.069      0.000       7.770       8.004\n",
      "Dest[Turkey Street]                     9.1665      0.063    144.603      0.000       9.042       9.291\n",
      "Dest[Turnham Green]                     8.9181      0.049    180.891      0.000       8.821       9.015\n",
      "Dest[Turnpike Lane]                     8.5172      0.053    161.565      0.000       8.414       8.620\n",
      "Dest[Upminster]                         9.0504      0.052    172.766      0.000       8.948       9.153\n",
      "Dest[Upminster Bridge]                  9.0788      0.060    152.492      0.000       8.962       9.196\n",
      "Dest[Upney]                             8.1506      0.062    131.643      0.000       8.029       8.272\n",
      "Dest[Upper Holloway]                    9.2946      0.054    172.553      0.000       9.189       9.400\n",
      "Dest[Upton Park]                        8.9537      0.049    183.655      0.000       8.858       9.049\n",
      "Dest[Uxbridge]                         10.6866      0.045    237.727      0.000      10.598      10.775\n",
      "Dest[Vauxhall]                         11.0281      0.043    257.774      0.000      10.944      11.112\n",
      "Dest[Victoria]                         11.6119      0.042    273.957      0.000      11.529      11.695\n",
      "Dest[Walthamstow Central]              10.1067      0.044    228.071      0.000      10.020      10.194\n",
      "Dest[Walthamstow Queens Road]          10.2577      0.051    200.140      0.000      10.157      10.358\n",
      "Dest[Wandsworth Road]                   8.6255      0.062    139.181      0.000       8.504       8.747\n",
      "Dest[Wanstead]                          7.9158      0.064    122.789      0.000       7.789       8.042\n",
      "Dest[Wanstead Park]                     8.8805      0.065    136.245      0.000       8.753       9.008\n",
      "Dest[Wapping]                           8.8411      0.052    169.887      0.000       8.739       8.943\n",
      "Dest[Warren Street]                    10.8597      0.043    254.429      0.000      10.776      10.943\n",
      "Dest[Warwick Avenue]                    8.5065      0.051    166.218      0.000       8.406       8.607\n",
      "Dest[Waterloo]                         11.2222      0.043    263.947      0.000      11.139      11.305\n",
      "Dest[Watford]                           9.6303      0.053    180.953      0.000       9.526       9.735\n",
      "Dest[Watford High Street]               9.9609      0.056    177.331      0.000       9.851      10.071\n",
      "Dest[Watford Junction]                 10.6629      0.051    209.326      0.000      10.563      10.763\n",
      "Dest[Wembley Central]                   9.0075      0.050    178.850      0.000       8.909       9.106\n",
      "Dest[Wembley Park]                     10.4588      0.044    236.890      0.000      10.372      10.545\n",
      "Dest[West Acton]                        8.1932      0.062    132.513      0.000       8.072       8.314\n",
      "Dest[West Brompton]                     9.7896      0.044    222.348      0.000       9.703       9.876\n",
      "Dest[West Croydon]                     10.6705      0.048    221.791      0.000      10.576      10.765\n",
      "Dest[West Finchley]                     6.6352      0.113     58.734      0.000       6.414       6.857\n",
      "Dest[West Ham]                          9.7295      0.044    222.758      0.000       9.644       9.815\n",
      "Dest[West Hampstead]                    9.8862      0.044    224.445      0.000       9.800       9.973\n",
      "Dest[West Harrow]                       6.8885      0.100     69.006      0.000       6.693       7.084\n",
      "Dest[West India Quay]                   7.7585      0.065    119.019      0.000       7.631       7.886\n",
      "Dest[West Kensington]                   8.6051      0.050    171.755      0.000       8.507       8.703\n",
      "Dest[West Ruislip]                      8.0931      0.083     97.094      0.000       7.930       8.256\n",
      "Dest[West Silvertown]                   9.0087      0.054    168.359      0.000       8.904       9.114\n",
      "Dest[Westbourne Park]                   8.7024      0.050    173.578      0.000       8.604       8.801\n",
      "Dest[Westferry]                         9.1319      0.050    180.959      0.000       9.033       9.231\n",
      "Dest[Westminster]                      10.6534      0.043    249.324      0.000      10.570      10.737\n",
      "Dest[White City]                       10.3094      0.044    234.029      0.000      10.223      10.396\n",
      "Dest[White Hart Lane]                   8.5858      0.058    148.375      0.000       8.472       8.699\n",
      "Dest[Whitechapel]                      10.7288      0.043    251.184      0.000      10.645      10.812\n",
      "Dest[Willesden Green]                   8.3740      0.055    153.468      0.000       8.267       8.481\n",
      "Dest[Willesden Junction]                9.7160      0.045    216.360      0.000       9.628       9.804\n",
      "Dest[Wimbledon]                        10.7770      0.044    244.491      0.000      10.691      10.863\n",
      "Dest[Wimbledon Park]                    8.4544      0.059    143.882      0.000       8.339       8.570\n",
      "Dest[Wood Green]                        9.3119      0.047    196.843      0.000       9.219       9.405\n",
      "Dest[Wood Lane]                         9.0417      0.049    184.413      0.000       8.946       9.138\n",
      "Dest[Wood Street]                       8.2855      0.065    127.144      0.000       8.158       8.413\n",
      "Dest[Woodford]                          8.5368      0.056    151.109      0.000       8.426       8.648\n",
      "Dest[Woodgrange Park]                   8.3353      0.077    107.773      0.000       8.184       8.487\n",
      "Dest[Woodside Park]                     8.7161      0.056    156.025      0.000       8.607       8.826\n",
      "Dest[Woolwich Arsenal]                 11.5667      0.045    259.447      0.000      11.479      11.654\n",
      "Orig[T.Acton Central]                   1.6537      0.050     32.953      0.000       1.555       1.752\n",
      "Orig[T.Acton Town]                      1.4186      0.044     32.133      0.000       1.332       1.505\n",
      "Orig[T.Aldgate]                         0.1860      0.045      4.132      0.000       0.098       0.274\n",
      "Orig[T.Aldgate East]                    0.3274      0.045      7.333      0.000       0.240       0.415\n",
      "Orig[T.All Saints]                     -0.0749      0.055     -1.361      0.174      -0.183       0.033\n",
      "Orig[T.Alperton]                        1.0326      0.048     21.535      0.000       0.939       1.127\n",
      "Orig[T.Amersham]                        1.4704      0.050     29.235      0.000       1.372       1.569\n",
      "Orig[T.Anerley]                         1.7327      0.057     30.199      0.000       1.620       1.845\n",
      "Orig[T.Angel]                           0.6948      0.044     15.867      0.000       0.609       0.781\n",
      "Orig[T.Archway]                         1.5856      0.043     36.784      0.000       1.501       1.670\n",
      "Orig[T.Arnos Grove]                     1.4625      0.045     32.614      0.000       1.375       1.550\n",
      "Orig[T.Arsenal]                         0.4333      0.046      9.359      0.000       0.343       0.524\n",
      "Orig[T.Baker Street]                    1.2401      0.043     29.115      0.000       1.157       1.324\n",
      "Orig[T.Balham]                          2.3182      0.042     54.863      0.000       2.235       2.401\n",
      "Orig[T.Bank and Monument]               2.3056      0.041     55.715      0.000       2.224       2.387\n",
      "Orig[T.Barbican]                       -0.7520      0.050    -15.080      0.000      -0.850      -0.654\n",
      "Orig[T.Barking]                         2.3347      0.042     54.969      0.000       2.251       2.418\n",
      "Orig[T.Barkingside]                     0.9644      0.050     19.474      0.000       0.867       1.061\n",
      "Orig[T.Barons Court]                    1.0648      0.044     24.253      0.000       0.979       1.151\n",
      "Orig[T.Bayswater]                       0.0731      0.048      1.518      0.129      -0.021       0.167\n",
      "Orig[T.Beckton]                         1.4588      0.050     29.004      0.000       1.360       1.557\n",
      "Orig[T.Beckton Park]                   -0.2218      0.071     -3.106      0.002      -0.362      -0.082\n",
      "Orig[T.Becontree]                       1.3477      0.046     29.327      0.000       1.258       1.438\n",
      "Orig[T.Belsize Park]                    0.7816      0.045     17.283      0.000       0.693       0.870\n",
      "Orig[T.Bermondsey]                      1.1004      0.043     25.412      0.000       1.016       1.185\n",
      "Orig[T.Bethnal Green]                   1.4202      0.043     33.232      0.000       1.336       1.504\n",
      "Orig[T.Blackfriars]                     1.0182      0.043     23.824      0.000       0.934       1.102\n",
      "Orig[T.Blackhorse Road]                 2.1958      0.042     51.736      0.000       2.113       2.279\n",
      "Orig[T.Blackwall]                       0.1779      0.052      3.406      0.001       0.076       0.280\n",
      "Orig[T.Bond Street]                    -0.2649      0.047     -5.686      0.000      -0.356      -0.174\n",
      "Orig[T.Borough]                        -0.5603      0.049    -11.383      0.000      -0.657      -0.464\n",
      "Orig[T.Boston Manor]                    0.5766      0.050     11.464      0.000       0.478       0.675\n",
      "Orig[T.Bounds Green]                    1.7418      0.044     39.884      0.000       1.656       1.827\n",
      "Orig[T.Bow Church]                      1.1285      0.048     23.653      0.000       1.035       1.222\n",
      "Orig[T.Bow Road]                        1.1098      0.044     25.271      0.000       1.024       1.196\n",
      "Orig[T.Brent Cross]                     0.6557      0.048     13.522      0.000       0.561       0.751\n",
      "Orig[T.Brentwood]                       4.0802      0.047     87.458      0.000       3.989       4.172\n",
      "Orig[T.Brixton]                         2.9717      0.042     71.580      0.000       2.890       3.053\n",
      "Orig[T.Brockley]                        2.3918      0.046     51.778      0.000       2.301       2.482\n",
      "Orig[T.Bromley-by-Bow]                  0.7335      0.045     16.123      0.000       0.644       0.823\n",
      "Orig[T.Brondesbury]                     1.7944      0.047     38.225      0.000       1.702       1.886\n",
      "Orig[T.Brondesbury Park]                0.7621      0.056     13.594      0.000       0.652       0.872\n",
      "Orig[T.Bruce Grove]                     1.6775      0.052     32.027      0.000       1.575       1.780\n",
      "Orig[T.Buckhurst Hill]                  1.1557      0.048     24.088      0.000       1.062       1.250\n",
      "Orig[T.Burnt Oak]                       1.6174      0.045     36.033      0.000       1.529       1.705\n",
      "Orig[T.Bush Hill Park]                  2.3761      0.049     48.164      0.000       2.279       2.473\n",
      "Orig[T.Bushey]                          0.4629      0.077      5.974      0.000       0.311       0.615\n",
      "Orig[T.Caledonian Road]                 0.5647      0.045     12.527      0.000       0.476       0.653\n",
      "Orig[T.Caledonian Road & Barnsbury]     0.1843      0.059      3.102      0.002       0.068       0.301\n",
      "Orig[T.Cambridge Heath]                 0.1788      0.069      2.597      0.009       0.044       0.314\n",
      "Orig[T.Camden Road]                     1.1682      0.050     23.275      0.000       1.070       1.267\n",
      "Orig[T.Camden Town]                     0.6157      0.045     13.835      0.000       0.528       0.703\n",
      "Orig[T.Canada Water]                    2.7498      0.041     66.374      0.000       2.669       2.831\n",
      "Orig[T.Canary Wharf]                    2.1221      0.042     50.779      0.000       2.040       2.204\n",
      "Orig[T.Canning Town]                    2.6710      0.042     64.348      0.000       2.590       2.752\n",
      "Orig[T.Cannon Street]                   0.1154      0.044      2.622      0.009       0.029       0.202\n",
      "Orig[T.Canonbury]                       1.5841      0.046     34.537      0.000       1.494       1.674\n",
      "Orig[T.Canons Park]                     1.4761      0.046     32.087      0.000       1.386       1.566\n",
      "Orig[T.Carpenders Park]                 2.2767      0.050     45.543      0.000       2.179       2.375\n",
      "Orig[T.Chadwell Heath]                  4.0494      0.044     91.618      0.000       3.963       4.136\n",
      "Orig[T.Chalfont & Latimer]              1.2726      0.052     24.253      0.000       1.170       1.375\n",
      "Orig[T.Chalk Farm]                      0.4811      0.046     10.502      0.000       0.391       0.571\n",
      "Orig[T.Chancery Lane]                  -0.7902      0.051    -15.646      0.000      -0.889      -0.691\n",
      "Orig[T.Charing Cross]                   0.7871      0.043     18.380      0.000       0.703       0.871\n",
      "Orig[T.Chesham]                         1.3800      0.053     26.257      0.000       1.277       1.483\n",
      "Orig[T.Cheshunt]                        0.9150      0.087     10.497      0.000       0.744       1.086\n",
      "Orig[T.Chigwell]                        0.1346      0.062      2.181      0.029       0.014       0.255\n",
      "Orig[T.Chingford]                       2.8871      0.047     61.792      0.000       2.795       2.979\n",
      "Orig[T.Chiswick Park]                   0.3316      0.050      6.684      0.000       0.234       0.429\n",
      "Orig[T.Chorleywood]                     1.1675      0.053     22.064      0.000       1.064       1.271\n",
      "Orig[T.Clapham Common]                  1.4020      0.043     32.298      0.000       1.317       1.487\n",
      "Orig[T.Clapham High Street]             2.1683      0.049     44.319      0.000       2.072       2.264\n",
      "Orig[T.Clapham Junction]                3.4865      0.043     81.265      0.000       3.402       3.571\n",
      "Orig[T.Clapham North]                   0.7820      0.045     17.348      0.000       0.694       0.870\n",
      "Orig[T.Clapham South]                   1.8231      0.043     42.598      0.000       1.739       1.907\n",
      "Orig[T.Clapton]                         1.9056      0.049     39.264      0.000       1.811       2.001\n",
      "Orig[T.Cockfosters]                     0.6879      0.052     13.278      0.000       0.586       0.789\n",
      "Orig[T.Colindale]                       2.1099      0.043     48.808      0.000       2.025       2.195\n",
      "Orig[T.Colliers Wood]                   1.9654      0.043     45.539      0.000       1.881       2.050\n",
      "Orig[T.Covent Garden]                  -1.9129      0.064    -30.101      0.000      -2.037      -1.788\n",
      "Orig[T.Crossharbour]                    0.8297      0.048     17.449      0.000       0.736       0.923\n",
      "Orig[T.Crouch Hill]                     0.6845      0.065     10.471      0.000       0.556       0.813\n",
      "Orig[T.Croxley]                         1.1043      0.052     21.436      0.000       1.003       1.205\n",
      "Orig[T.Crystal Palace]                  2.9580      0.047     62.653      0.000       2.866       3.051\n",
      "Orig[T.Custom House]                    0.4143      0.054      7.625      0.000       0.308       0.521\n",
      "Orig[T.Cutty Sark]                      1.4608      0.046     31.477      0.000       1.370       1.552\n",
      "Orig[T.Cyprus]                          0.3936      0.061      6.485      0.000       0.275       0.513\n",
      "Orig[T.Dagenham East]                   1.3116      0.047     27.942      0.000       1.220       1.404\n",
      "Orig[T.Dagenham Heathway]               1.7749      0.044     39.890      0.000       1.688       1.862\n",
      "Orig[T.Dalston Junction]                2.3540      0.044     53.346      0.000       2.268       2.441\n",
      "Orig[T.Dalston Kingsland]               2.0292      0.045     44.994      0.000       1.941       2.118\n",
      "Orig[T.Debden]                          1.3342      0.048     27.847      0.000       1.240       1.428\n",
      "Orig[T.Denmark Hill]                    2.2318      0.047     47.081      0.000       2.139       2.325\n",
      "Orig[T.Deptford Bridge]                 1.7973      0.046     39.303      0.000       1.708       1.887\n",
      "Orig[T.Devons Road]                     0.8388      0.049     17.129      0.000       0.743       0.935\n",
      "Orig[T.Dollis Hill]                     1.0643      0.046     23.362      0.000       0.975       1.154\n",
      "Orig[T.Ealing Broadway]                 2.7969      0.042     66.659      0.000       2.715       2.879\n",
      "Orig[T.Ealing Common]                   0.8536      0.047     18.275      0.000       0.762       0.945\n",
      "Orig[T.Earl's Court]                    1.6265      0.042     38.345      0.000       1.543       1.710\n",
      "Orig[T.East Acton]                      0.8906      0.046     19.407      0.000       0.801       0.981\n",
      "Orig[T.East Finchley]                   1.9229      0.043     44.669      0.000       1.839       2.007\n",
      "Orig[T.East Ham]                        2.2119      0.043     52.036      0.000       2.129       2.295\n",
      "Orig[T.East India]                      0.8334      0.047     17.595      0.000       0.741       0.926\n",
      "Orig[T.East Putney]                     1.7163      0.043     39.741      0.000       1.632       1.801\n",
      "Orig[T.Eastcote]                        1.6269      0.046     35.664      0.000       1.537       1.716\n",
      "Orig[T.Edgware]                         1.8188      0.044     40.901      0.000       1.732       1.906\n",
      "Orig[T.Edgware Road]                    0.3790      0.045      8.407      0.000       0.291       0.467\n",
      "Orig[T.Edmonton Green]                  2.4802      0.047     53.033      0.000       2.389       2.572\n",
      "Orig[T.Elephant & Castle]               1.4913      0.042     35.281      0.000       1.408       1.574\n",
      "Orig[T.Elm Park]                        1.7635      0.045     38.952      0.000       1.675       1.852\n",
      "Orig[T.Elverson Road]                   1.0089      0.051     19.849      0.000       0.909       1.108\n",
      "Orig[T.Embankment]                      0.3526      0.044      8.036      0.000       0.267       0.439\n",
      "Orig[T.Emerson Park]                    3.2328      0.071     45.429      0.000       3.093       3.372\n",
      "Orig[T.Enfield Town]                    2.7359      0.047     57.624      0.000       2.643       2.829\n",
      "Orig[T.Epping]                          2.0742      0.045     46.027      0.000       1.986       2.162\n",
      "Orig[T.Euston]                          1.9599      0.042     47.037      0.000       1.878       2.042\n",
      "Orig[T.Euston Square]                   0.8786      0.043     20.247      0.000       0.794       0.964\n",
      "Orig[T.Fairlop]                         0.7685      0.052     14.820      0.000       0.667       0.870\n",
      "Orig[T.Farringdon]                      0.8064      0.043     18.612      0.000       0.722       0.891\n",
      "Orig[T.Finchley Central]                2.1585      0.043     50.290      0.000       2.074       2.243\n",
      "Orig[T.Finchley Road]                   1.3016      0.043     29.925      0.000       1.216       1.387\n",
      "Orig[T.Finchley Road & Frognal]         1.2087      0.051     23.813      0.000       1.109       1.308\n",
      "Orig[T.Finsbury Park]                   2.9347      0.041     70.747      0.000       2.853       3.016\n",
      "Orig[T.Forest Gate]                     2.7269      0.046     59.519      0.000       2.637       2.817\n",
      "Orig[T.Forest Hill]                     2.7307      0.046     59.288      0.000       2.640       2.821\n",
      "Orig[T.Fulham Broadway]                 0.9005      0.045     20.211      0.000       0.813       0.988\n",
      "Orig[T.Gallions Reach]                  0.7219      0.057     12.645      0.000       0.610       0.834\n",
      "Orig[T.Gants Hill]                      2.1120      0.043     48.799      0.000       2.027       2.197\n",
      "Orig[T.Gidea Park]                      4.0985      0.045     91.411      0.000       4.011       4.186\n",
      "Orig[T.Gloucester Road]                 0.9811      0.043     22.570      0.000       0.896       1.066\n",
      "Orig[T.Golders Green]                   1.6881      0.043     38.827      0.000       1.603       1.773\n",
      "Orig[T.Goldhawk Road]                   0.1982      0.049      4.027      0.000       0.102       0.295\n",
      "Orig[T.Goodge Street]                  -1.9406      0.066    -29.215      0.000      -2.071      -1.810\n",
      "Orig[T.Goodmayes]                       3.7140      0.045     82.625      0.000       3.626       3.802\n",
      "Orig[T.Gospel Oak]                      0.9749      0.051     19.066      0.000       0.875       1.075\n",
      "Orig[T.Grange Hill]                     0.4682      0.057      8.259      0.000       0.357       0.579\n",
      "Orig[T.Great Portland Street]          -0.5486      0.051    -10.843      0.000      -0.648      -0.449\n",
      "Orig[T.Green Park]                     -0.2419      0.047     -5.200      0.000      -0.333      -0.151\n",
      "Orig[T.Greenford]                       1.5300      0.045     33.770      0.000       1.441       1.619\n",
      "Orig[T.Greenwich]                       1.1089      0.049     22.564      0.000       1.013       1.205\n",
      "Orig[T.Gunnersbury]                     0.8141      0.046     17.671      0.000       0.724       0.904\n",
      "Orig[T.Hackney Central]                 2.2622      0.045     50.775      0.000       2.175       2.349\n",
      "Orig[T.Hackney Downs]                   1.6357      0.054     30.376      0.000       1.530       1.741\n",
      "Orig[T.Hackney Wick]                    1.1915      0.049     24.537      0.000       1.096       1.287\n",
      "Orig[T.Haggerston]                      1.6130      0.047     34.523      0.000       1.521       1.705\n",
      "Orig[T.Hainault]                        1.8667      0.045     41.686      0.000       1.779       1.954\n",
      "Orig[T.Hammersmith]                     2.2721      0.042     54.071      0.000       2.190       2.354\n",
      "Orig[T.Hampstead]                       0.5733      0.047     12.212      0.000       0.481       0.665\n",
      "Orig[T.Hampstead Heath]                 0.8635      0.053     16.361      0.000       0.760       0.967\n",
      "Orig[T.Hanger Lane]                     1.0756      0.047     23.018      0.000       0.984       1.167\n",
      "Orig[T.Harlesden]                       0.4498      0.048      9.282      0.000       0.355       0.545\n",
      "Orig[T.Harold Wood]                     4.1763      0.045     92.439      0.000       4.088       4.265\n",
      "Orig[T.Harringay Green Lanes]           1.1040      0.061     18.180      0.000       0.985       1.223\n",
      "Orig[T.Harrow & Wealdstone]             1.0702      0.048     22.513      0.000       0.977       1.163\n",
      "Orig[T.Harrow-on-the-Hill]              2.3054      0.043     53.718      0.000       2.221       2.390\n",
      "Orig[T.Hatch End]                       1.9856      0.054     36.806      0.000       1.880       2.091\n",
      "Orig[T.Hatton Cross]                    1.0480      0.049     21.294      0.000       0.952       1.144\n",
      "Orig[T.Headstone Lane]                  1.2986      0.062     20.903      0.000       1.177       1.420\n",
      "Orig[T.Heathrow Terminal 4]             0.5564      0.054     10.299      0.000       0.451       0.662\n",
      "Orig[T.Heathrow Terminal 5]             0.8265      0.052     15.754      0.000       0.724       0.929\n",
      "Orig[T.Heathrow Terminals 2 & 3]        1.5446      0.046     33.383      0.000       1.454       1.635\n",
      "Orig[T.Hendon Central]                  1.6919      0.044     38.523      0.000       1.606       1.778\n",
      "Orig[T.Heron Quays]                     0.2474      0.047      5.227      0.000       0.155       0.340\n",
      "Orig[T.High Barnet]                     1.8393      0.045     41.231      0.000       1.752       1.927\n",
      "Orig[T.High Street Kensington]          0.2863      0.046      6.183      0.000       0.196       0.377\n",
      "Orig[T.Highams Park]                    2.8801      0.045     63.897      0.000       2.792       2.968\n",
      "Orig[T.Highbury & Islington]            2.6051      0.041     62.773      0.000       2.524       2.686\n",
      "Orig[T.Highgate]                        1.5472      0.044     35.502      0.000       1.462       1.633\n",
      "Orig[T.Hillingdon]                      1.1593      0.049     23.495      0.000       1.063       1.256\n",
      "Orig[T.Holborn]                        -0.4947      0.048    -10.358      0.000      -0.588      -0.401\n",
      "Orig[T.Holland Park]                    0.0620      0.048      1.285      0.199      -0.033       0.157\n",
      "Orig[T.Holloway Road]                   0.7045      0.045     15.720      0.000       0.617       0.792\n",
      "Orig[T.Homerton]                        2.1341      0.044     48.070      0.000       2.047       2.221\n",
      "Orig[T.Honor Oak Park]                  2.2780      0.048     47.734      0.000       2.184       2.371\n",
      "Orig[T.Hornchurch]                      1.4016      0.048     29.410      0.000       1.308       1.495\n",
      "Orig[T.Hounslow Central]                1.3437      0.046     29.071      0.000       1.253       1.434\n",
      "Orig[T.Hounslow East]                   1.3223      0.046     28.552      0.000       1.232       1.413\n",
      "Orig[T.Hounslow West]                   1.3681      0.047     29.390      0.000       1.277       1.459\n",
      "Orig[T.Hoxton]                          0.8902      0.052     17.274      0.000       0.789       0.991\n",
      "Orig[T.Hyde Park Corner]               -2.1774      0.074    -29.252      0.000      -2.323      -2.032\n",
      "Orig[T.Ickenham]                        0.6438      0.055     11.671      0.000       0.536       0.752\n",
      "Orig[T.Ilford]                          4.0990      0.043     94.622      0.000       4.014       4.184\n",
      "Orig[T.Imperial Wharf]                  1.1154      0.053     20.899      0.000       1.011       1.220\n",
      "Orig[T.Island Gardens]                  0.9143      0.049     18.706      0.000       0.819       1.010\n",
      "Orig[T.Kennington]                      0.6446      0.044     14.565      0.000       0.558       0.731\n",
      "Orig[T.Kensal Green]                    0.6216      0.047     13.185      0.000       0.529       0.714\n",
      "Orig[T.Kensal Rise]                     1.7649      0.047     37.566      0.000       1.673       1.857\n",
      "Orig[T.Kensington]                     -1.1388      0.063    -18.016      0.000      -1.263      -1.015\n",
      "Orig[T.Kentish Town]                    0.5097      0.046     11.137      0.000       0.420       0.599\n",
      "Orig[T.Kentish Town West]               0.5307      0.056      9.535      0.000       0.422       0.640\n",
      "Orig[T.Kenton]                          0.8247      0.051     16.055      0.000       0.724       0.925\n",
      "Orig[T.Kew Gardens]                     0.9171      0.046     19.877      0.000       0.827       1.007\n",
      "Orig[T.Kilburn]                         1.4678      0.044     33.698      0.000       1.382       1.553\n",
      "Orig[T.Kilburn High Road]               0.7910      0.068     11.625      0.000       0.658       0.924\n",
      "Orig[T.Kilburn Park]                    0.5102      0.047     10.849      0.000       0.418       0.602\n",
      "Orig[T.King George V]                   0.8882      0.052     17.038      0.000       0.786       0.990\n",
      "Orig[T.King's Cross St. Pancras]        2.4875      0.041     60.066      0.000       2.406       2.569\n",
      "Orig[T.Kingsbury]                       1.4708      0.045     32.483      0.000       1.382       1.560\n",
      "Orig[T.Knightsbridge]                  -0.5866      0.051    -11.573      0.000      -0.686      -0.487\n",
      "Orig[T.Ladbroke Grove]                  0.6549      0.046     14.283      0.000       0.565       0.745\n",
      "Orig[T.Lambeth North]                  -0.7085      0.051    -13.955      0.000      -0.808      -0.609\n",
      "Orig[T.Lancaster Gate]                  0.7318      0.044     16.511      0.000       0.645       0.819\n",
      "Orig[T.Langdon Park]                    0.7978      0.049     16.432      0.000       0.703       0.893\n",
      "Orig[T.Latimer Road]                   -0.2955      0.053     -5.542      0.000      -0.400      -0.191\n",
      "Orig[T.Leicester Square]               -1.1353      0.052    -21.867      0.000      -1.237      -1.034\n",
      "Orig[T.Lewisham]                        3.2716      0.043     76.907      0.000       3.188       3.355\n",
      "Orig[T.Leyton]                          2.0550      0.043     48.308      0.000       1.972       2.138\n",
      "Orig[T.Leyton Midland Road]             1.8772      0.054     34.597      0.000       1.771       1.984\n",
      "Orig[T.Leytonstone]                     2.0772      0.043     48.560      0.000       1.993       2.161\n",
      "Orig[T.Leytonstone High Road]           1.7170      0.058     29.602      0.000       1.603       1.831\n",
      "Orig[T.Limehouse]                       2.0278      0.043     46.963      0.000       1.943       2.112\n",
      "Orig[T.Liverpool Street]                2.4412      0.041     59.014      0.000       2.360       2.522\n",
      "Orig[T.London Bridge]                   2.5622      0.041     61.965      0.000       2.481       2.643\n",
      "Orig[T.London City Airport]             1.6072      0.047     34.473      0.000       1.516       1.699\n",
      "Orig[T.London Fields]                   1.6294      0.051     31.855      0.000       1.529       1.730\n",
      "Orig[T.Loughton]                        1.7264      0.045     38.130      0.000       1.638       1.815\n",
      "Orig[T.Maida Vale]                      0.5022      0.046     10.836      0.000       0.411       0.593\n",
      "Orig[T.Manor House]                     1.5427      0.043     35.732      0.000       1.458       1.627\n",
      "Orig[T.Manor Park]                      2.6933      0.047     56.704      0.000       2.600       2.786\n",
      "Orig[T.Mansion House]                  -1.6861      0.060    -28.034      0.000      -1.804      -1.568\n",
      "Orig[T.Marble Arch]                    -0.1974      0.047     -4.176      0.000      -0.290      -0.105\n",
      "Orig[T.Maryland]                        1.1096      0.053     20.886      0.000       1.005       1.214\n",
      "Orig[T.Marylebone]                      1.0786      0.043     25.121      0.000       0.994       1.163\n",
      "Orig[T.Mile End]                        1.6078      0.043     37.702      0.000       1.524       1.691\n",
      "Orig[T.Mill Hill East]                  0.7581      0.050     15.295      0.000       0.661       0.855\n",
      "Orig[T.Moor Park]                       0.5987      0.057     10.535      0.000       0.487       0.710\n",
      "Orig[T.Moorgate]                        0.3620      0.044      8.292      0.000       0.276       0.448\n",
      "Orig[T.Morden]                          2.5202      0.043     59.274      0.000       2.437       2.603\n",
      "Orig[T.Mornington Crescent]            -1.0731      0.056    -19.189      0.000      -1.183      -0.963\n",
      "Orig[T.Mudchute]                        0.7266      0.049     14.771      0.000       0.630       0.823\n",
      "Orig[T.Neasden]                         1.0224      0.046     22.253      0.000       0.932       1.112\n",
      "Orig[T.New Cross]                       2.0002      0.049     40.910      0.000       1.904       2.096\n",
      "Orig[T.New Cross Gate]                  2.0043      0.048     41.930      0.000       1.911       2.098\n",
      "Orig[T.Newbury Park]                    2.0112      0.044     45.891      0.000       1.925       2.097\n",
      "Orig[T.North Acton]                     1.2534      0.045     27.980      0.000       1.166       1.341\n",
      "Orig[T.North Ealing]                   -0.2019      0.061     -3.336      0.001      -0.321      -0.083\n",
      "Orig[T.North Greenwich]                 2.1981      0.042     52.250      0.000       2.116       2.281\n",
      "Orig[T.North Harrow]                    1.3265      0.047     28.233      0.000       1.234       1.419\n",
      "Orig[T.North Wembley]                   0.5009      0.051      9.817      0.000       0.401       0.601\n",
      "Orig[T.Northfields]                     1.4075      0.045     31.301      0.000       1.319       1.496\n",
      "Orig[T.Northolt]                        1.9085      0.044     43.074      0.000       1.822       1.995\n",
      "Orig[T.Northwick Park]                  1.1891      0.046     25.605      0.000       1.098       1.280\n",
      "Orig[T.Northwood]                       1.5549      0.047     33.307      0.000       1.463       1.646\n",
      "Orig[T.Northwood Hills]                 1.1738      0.049     24.095      0.000       1.078       1.269\n",
      "Orig[T.Norwood Junction]                1.7376      0.057     30.654      0.000       1.627       1.849\n",
      "Orig[T.Notting Hill Gate]               1.0961      0.043     25.262      0.000       1.011       1.181\n",
      "Orig[T.Oakwood]                         1.1686      0.047     24.646      0.000       1.076       1.261\n",
      "Orig[T.Old Street]                      0.8774      0.043     20.313      0.000       0.793       0.962\n",
      "Orig[T.Osterley]                        0.8840      0.049     18.091      0.000       0.788       0.980\n",
      "Orig[T.Oval]                            0.8163      0.044     18.458      0.000       0.730       0.903\n",
      "Orig[T.Oxford Circus]                   0.0270      0.045      0.599      0.549      -0.061       0.116\n",
      "Orig[T.Paddington]                      2.6547      0.042     63.953      0.000       2.573       2.736\n",
      "Orig[T.Park Royal]                     -0.1185      0.059     -2.011      0.044      -0.234      -0.003\n",
      "Orig[T.Parsons Green]                   1.2640      0.044     28.918      0.000       1.178       1.350\n",
      "Orig[T.Peckham Rye]                     2.3070      0.046     50.055      0.000       2.217       2.397\n",
      "Orig[T.Penge West]                      1.2406      0.067     18.505      0.000       1.109       1.372\n",
      "Orig[T.Perivale]                        0.9800      0.048     20.439      0.000       0.886       1.074\n",
      "Orig[T.Piccadilly Circus]              -1.0476      0.051    -20.371      0.000      -1.148      -0.947\n",
      "Orig[T.Pimlico]                         0.7623      0.044     17.329      0.000       0.676       0.849\n",
      "Orig[T.Pinner]                          1.7713      0.045     39.290      0.000       1.683       1.860\n",
      "Orig[T.Plaistow]                        1.2013      0.044     27.182      0.000       1.115       1.288\n",
      "Orig[T.Pontoon Dock]                    1.4486      0.047     31.060      0.000       1.357       1.540\n",
      "Orig[T.Poplar]                          0.6538      0.046     14.204      0.000       0.564       0.744\n",
      "Orig[T.Preston Road]                    1.2226      0.046     26.634      0.000       1.133       1.313\n",
      "Orig[T.Prince Regent]                   0.6736      0.052     12.852      0.000       0.571       0.776\n",
      "Orig[T.Pudding Mill Lane]              -0.2973      0.063     -4.708      0.000      -0.421      -0.174\n",
      "Orig[T.Putney Bridge]                   0.9834      0.045     21.879      0.000       0.895       1.071\n",
      "Orig[T.Queen's Park]                    1.4528      0.043     33.578      0.000       1.368       1.538\n",
      "Orig[T.Queens Road Peckham]             2.1081      0.047     44.734      0.000       2.016       2.200\n",
      "Orig[T.Queensbury]                      1.6007      0.045     35.542      0.000       1.512       1.689\n",
      "Orig[T.Queensway]                       0.5319      0.045     11.752      0.000       0.443       0.621\n",
      "Orig[T.Ravenscourt Park]                0.2502      0.048      5.188      0.000       0.156       0.345\n",
      "Orig[T.Rayners Lane]                    1.8065      0.044     40.662      0.000       1.719       1.894\n",
      "Orig[T.Rectory Road]                    1.4515      0.052     27.698      0.000       1.349       1.554\n",
      "Orig[T.Redbridge]                       1.1347      0.047     24.376      0.000       1.043       1.226\n",
      "Orig[T.Regent's Park]                  -1.7932      0.066    -27.110      0.000      -1.923      -1.664\n",
      "Orig[T.Richmond]                        1.9025      0.043     43.911      0.000       1.818       1.987\n",
      "Orig[T.Rickmansworth]                   1.2581      0.050     25.251      0.000       1.160       1.356\n",
      "Orig[T.Roding Valley]                   0.0670      0.064      1.042      0.298      -0.059       0.193\n",
      "Orig[T.Romford]                         4.4073      0.044    100.379      0.000       4.321       4.493\n",
      "Orig[T.Rotherhithe]                     1.1325      0.048     23.468      0.000       1.038       1.227\n",
      "Orig[T.Royal Albert]                    0.4738      0.057      8.354      0.000       0.363       0.585\n",
      "Orig[T.Royal Oak]                      -0.0036      0.049     -0.073      0.941      -0.099       0.092\n",
      "Orig[T.Royal Victoria]                  1.2625      0.046     27.157      0.000       1.171       1.354\n",
      "Orig[T.Ruislip]                         1.0845      0.050     21.900      0.000       0.987       1.182\n",
      "Orig[T.Ruislip Gardens]                 0.9292      0.052     17.809      0.000       0.827       1.031\n",
      "Orig[T.Ruislip Manor]                   1.1119      0.049     22.693      0.000       1.016       1.208\n",
      "Orig[T.Russell Square]                 -0.5275      0.048    -10.898      0.000      -0.622      -0.433\n",
      "Orig[T.Seven Kings]                     3.6887      0.045     82.447      0.000       3.601       3.776\n",
      "Orig[T.Seven Sisters]                   2.8947      0.042     69.499      0.000       2.813       2.976\n",
      "Orig[T.Shadwell]                        1.8893      0.043     44.211      0.000       1.806       1.973\n",
      "Orig[T.Shenfield]                       2.0552      0.076     27.102      0.000       1.907       2.204\n",
      "Orig[T.Shepherd's Bush]                 1.9546      0.042     46.383      0.000       1.872       2.037\n",
      "Orig[T.Shepherd's Bush Market]          0.4808      0.047     10.164      0.000       0.388       0.574\n",
      "Orig[T.Shoreditch High Street]          0.8915      0.053     16.955      0.000       0.788       0.995\n",
      "Orig[T.Silver Street]                   2.3022      0.048     47.785      0.000       2.208       2.397\n",
      "Orig[T.Sloane Square]                   0.9309      0.043     21.461      0.000       0.846       1.016\n",
      "Orig[T.Snaresbrook]                     0.9423      0.047     19.898      0.000       0.850       1.035\n",
      "Orig[T.South Acton]                     1.0562      0.057     18.512      0.000       0.944       1.168\n",
      "Orig[T.South Ealing]                    1.0652      0.046     23.011      0.000       0.974       1.156\n",
      "Orig[T.South Hampstead]                 0.7299      0.076      9.606      0.000       0.581       0.879\n",
      "Orig[T.South Harrow]                    1.0887      0.048     22.488      0.000       0.994       1.184\n",
      "Orig[T.South Kensington]                1.0306      0.043     23.776      0.000       0.946       1.116\n",
      "Orig[T.South Kenton]                    0.6037      0.051     11.803      0.000       0.503       0.704\n",
      "Orig[T.South Quay]                      0.6739      0.048     14.126      0.000       0.580       0.767\n",
      "Orig[T.South Ruislip]                   1.1397      0.049     23.260      0.000       1.044       1.236\n",
      "Orig[T.South Tottenham]                 1.1046      0.064     17.254      0.000       0.979       1.230\n",
      "Orig[T.South Wimbledon]                 1.7098      0.044     38.747      0.000       1.623       1.796\n",
      "Orig[T.South Woodford]                  1.8066      0.044     41.194      0.000       1.721       1.893\n",
      "Orig[T.Southbury]                       1.6869      0.059     28.369      0.000       1.570       1.803\n",
      "Orig[T.Southfields]                     1.7983      0.043     41.544      0.000       1.713       1.883\n",
      "Orig[T.Southgate]                       1.7499      0.044     39.561      0.000       1.663       1.837\n",
      "Orig[T.Southwark]                       0.6832      0.043     15.739      0.000       0.598       0.768\n",
      "Orig[T.St James Street]                 1.7345      0.052     33.678      0.000       1.634       1.835\n",
      "Orig[T.St. James's Park]               -0.2818      0.047     -5.964      0.000      -0.374      -0.189\n",
      "Orig[T.St. John's Wood]                 0.7942      0.045     17.807      0.000       0.707       0.882\n",
      "Orig[T.St. Paul's]                     -1.0771      0.053    -20.290      0.000      -1.181      -0.973\n",
      "Orig[T.Stamford Brook]                  0.5168      0.047     10.955      0.000       0.424       0.609\n",
      "Orig[T.Stamford Hill]                   1.0275      0.061     16.801      0.000       0.908       1.147\n",
      "Orig[T.Stanmore]                        1.6765      0.045     36.906      0.000       1.587       1.765\n",
      "Orig[T.Star Lane]                      -0.3313      0.063     -5.268      0.000      -0.455      -0.208\n",
      "Orig[T.Stepney Green]                   0.5390      0.045     11.918      0.000       0.450       0.628\n",
      "Orig[T.Stockwell]                       1.9607      0.042     46.552      0.000       1.878       2.043\n",
      "Orig[T.Stoke Newington]                 1.6295      0.051     31.913      0.000       1.529       1.730\n",
      "Orig[T.Stonebridge Park]                0.5538      0.049     11.407      0.000       0.459       0.649\n",
      "Orig[T.Stratford]                       3.6991      0.041     89.871      0.000       3.618       3.780\n",
      "Orig[T.Stratford High Street]          -0.4826      0.066     -7.348      0.000      -0.611      -0.354\n",
      "Orig[T.Stratford International]         1.6721      0.046     36.409      0.000       1.582       1.762\n",
      "Orig[T.Sudbury Hill]                    0.9217      0.049     18.689      0.000       0.825       1.018\n",
      "Orig[T.Sudbury Town]                    1.0314      0.049     21.259      0.000       0.936       1.126\n",
      "Orig[T.Surrey Quays]                    2.0367      0.045     45.693      0.000       1.949       2.124\n",
      "Orig[T.Swiss Cottage]                   0.9689      0.044     21.864      0.000       0.882       1.056\n",
      "Orig[T.Sydenham]                        2.5180      0.048     52.873      0.000       2.425       2.611\n",
      "Orig[T.Temple]                         -1.9301      0.067    -28.630      0.000      -2.062      -1.798\n",
      "Orig[T.Theobalds Grove]                 1.9118      0.060     31.609      0.000       1.793       2.030\n",
      "Orig[T.Theydon Bois]                    0.6817      0.056     12.122      0.000       0.571       0.792\n",
      "Orig[T.Tooting Bec]                     1.9793      0.043     46.265      0.000       1.895       2.063\n",
      "Orig[T.Tooting Broadway]                2.4358      0.042     57.623      0.000       2.353       2.519\n",
      "Orig[T.Tottenham Court Road]           -0.4794      0.047    -10.121      0.000      -0.572      -0.387\n",
      "Orig[T.Tottenham Hale]                  2.2453      0.042     53.008      0.000       2.162       2.328\n",
      "Orig[T.Totteridge & Whetstone]          1.3872      0.046     30.140      0.000       1.297       1.477\n",
      "Orig[T.Tower Gateway]                   0.5789      0.053     10.847      0.000       0.474       0.683\n",
      "Orig[T.Tower Hill]                      1.2058      0.042     28.446      0.000       1.123       1.289\n",
      "Orig[T.Tufnell Park]                    0.7472      0.045     16.523      0.000       0.659       0.836\n",
      "Orig[T.Turkey Street]                   2.1766      0.054     39.956      0.000       2.070       2.283\n",
      "Orig[T.Turnham Green]                   1.2370      0.044     27.974      0.000       1.150       1.324\n",
      "Orig[T.Turnpike Lane]                   1.9507      0.043     45.588      0.000       1.867       2.035\n",
      "Orig[T.Upminster]                       0.6050      0.055     10.934      0.000       0.497       0.713\n",
      "Orig[T.Upminster Bridge]                0.7480      0.054     13.730      0.000       0.641       0.855\n",
      "Orig[T.Upney]                           0.9643      0.047     20.302      0.000       0.871       1.057\n",
      "Orig[T.Upper Holloway]                  0.4722      0.066      7.127      0.000       0.342       0.602\n",
      "Orig[T.Upton Park]                      1.8282      0.043     42.537      0.000       1.744       1.912\n",
      "Orig[T.Uxbridge]                        1.9144      0.045     42.301      0.000       1.826       2.003\n",
      "Orig[T.Vauxhall]                        2.3565      0.042     56.461      0.000       2.275       2.438\n",
      "Orig[T.Victoria]                        2.8352      0.041     68.632      0.000       2.754       2.916\n",
      "Orig[T.Walthamstow Central]             3.0439      0.042     72.983      0.000       2.962       3.126\n",
      "Orig[T.Walthamstow Queens Road]         2.3987      0.052     45.811      0.000       2.296       2.501\n",
      "Orig[T.Wandsworth Road]                 1.0263      0.058     17.693      0.000       0.913       1.140\n",
      "Orig[T.Wanstead]                        1.0259      0.047     21.948      0.000       0.934       1.118\n",
      "Orig[T.Wanstead Park]                   2.1033      0.055     37.999      0.000       1.995       2.212\n",
      "Orig[T.Wapping]                         1.0747      0.050     21.516      0.000       0.977       1.173\n",
      "Orig[T.Warren Street]                  -0.3049      0.047     -6.497      0.000      -0.397      -0.213\n",
      "Orig[T.Warwick Avenue]                  0.4759      0.046     10.387      0.000       0.386       0.566\n",
      "Orig[T.Waterloo]                        3.3025      0.041     80.229      0.000       3.222       3.383\n",
      "Orig[T.Watford]                         1.4600      0.049     29.791      0.000       1.364       1.556\n",
      "Orig[T.Watford High Street]             1.1329      0.063     17.933      0.000       1.009       1.257\n",
      "Orig[T.Watford Junction]                1.5039      0.062     24.245      0.000       1.382       1.625\n",
      "Orig[T.Wembley Central]                 1.0469      0.046     22.694      0.000       0.957       1.137\n",
      "Orig[T.Wembley Park]                    2.2496      0.043     52.670      0.000       2.166       2.333\n",
      "Orig[T.West Acton]                      0.4521      0.050      8.978      0.000       0.353       0.551\n",
      "Orig[T.West Brompton]                   0.8139      0.044     18.470      0.000       0.728       0.900\n",
      "Orig[T.West Croydon]                    2.9102      0.050     58.632      0.000       2.813       3.007\n",
      "Orig[T.West Finchley]                   0.8875      0.048     18.393      0.000       0.793       0.982\n",
      "Orig[T.West Ham]                        1.8148      0.042     42.917      0.000       1.732       1.898\n",
      "Orig[T.West Hampstead]                  1.9969      0.042     47.361      0.000       1.914       2.080\n",
      "Orig[T.West Harrow]                     0.5995      0.052     11.615      0.000       0.498       0.701\n",
      "Orig[T.West India Quay]                -2.3001      0.089    -25.953      0.000      -2.474      -2.126\n",
      "Orig[T.West Kensington]                 0.6124      0.045     13.528      0.000       0.524       0.701\n",
      "Orig[T.West Ruislip]                    1.0828      0.051     21.199      0.000       0.983       1.183\n",
      "Orig[T.West Silvertown]                 0.5577      0.053     10.560      0.000       0.454       0.661\n",
      "Orig[T.Westbourne Park]                 0.6346      0.046     13.866      0.000       0.545       0.724\n",
      "Orig[T.Westferry]                       0.8404      0.046     18.206      0.000       0.750       0.931\n",
      "Orig[T.Westminster]                    -0.5319      0.048    -10.999      0.000      -0.627      -0.437\n",
      "Orig[T.White City]                      0.7784      0.046     17.028      0.000       0.689       0.868\n",
      "Orig[T.White Hart Lane]                 1.6550      0.052     32.026      0.000       1.554       1.756\n",
      "Orig[T.Whitechapel]                     1.7522      0.042     41.762      0.000       1.670       1.834\n",
      "Orig[T.Willesden Green]                 1.7551      0.043     40.721      0.000       1.671       1.840\n",
      "Orig[T.Willesden Junction]              1.5299      0.043     35.363      0.000       1.445       1.615\n",
      "Orig[T.Wimbledon]                       2.3354      0.043     54.676      0.000       2.252       2.419\n",
      "Orig[T.Wimbledon Park]                  0.8045      0.048     16.836      0.000       0.711       0.898\n",
      "Orig[T.Wood Green]                      2.0298      0.043     47.426      0.000       1.946       2.114\n",
      "Orig[T.Wood Lane]                       0.0123      0.051      0.241      0.810      -0.088       0.112\n",
      "Orig[T.Wood Street]                     1.9917      0.049     40.444      0.000       1.895       2.088\n",
      "Orig[T.Woodford]                        2.0625      0.043     47.470      0.000       1.977       2.148\n",
      "Orig[T.Woodgrange Park]                 1.6669      0.060     27.654      0.000       1.549       1.785\n",
      "Orig[T.Woodside Park]                   1.5896      0.045     35.485      0.000       1.502       1.677\n",
      "Orig[T.Woolwich Arsenal]                3.5490      0.042     83.526      0.000       3.466       3.632\n",
      "log_Dist                               -0.9097      0.001   -776.770      0.000      -0.912      -0.907\n",
      "=======================================================================================================\n"
     ]
    }
   ],
   "source": [
    "#create the formula (the \"-1\" indicates no intercept in the regression model).\n",
    "dbl_form = 'Total ~ Dest + Orig + log_Dist-1'\n",
    "#run a doubly constrained sim\n",
    "doubSim_pow = smf.glm(formula = dbl_form, data=london_flows, family=sm.families.Poisson()).fit()\n",
    "#let's have a look at it's summary\n",
    "print(doubSim_pow.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>26.0</td>\n",
       "      <td>600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1224.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>11.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.0</td>\n",
       "      <td>...</td>\n",
       "      <td>30.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3747.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>42.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>19.0</td>\n",
       "      <td>...</td>\n",
       "      <td>7.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2873.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>21.0</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3172.0</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",
       "      <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>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>29.0</td>\n",
       "      <td>...</td>\n",
       "      <td>29.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4862.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>530.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>...</td>\n",
       "      <td>21.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3093.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>28.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7893.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>346.0</td>\n",
       "      <td>751.0</td>\n",
       "      <td>2198.0</td>\n",
       "      <td>7788.0</td>\n",
       "      <td>7934.0</td>\n",
       "      <td>446.0</td>\n",
       "      <td>741.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>174.0</td>\n",
       "      <td>8108.0</td>\n",
       "      <td>...</td>\n",
       "      <td>6278.0</td>\n",
       "      <td>599.0</td>\n",
       "      <td>2141.0</td>\n",
       "      <td>1576.0</td>\n",
       "      <td>402.0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>240.0</td>\n",
       "      <td>740.0</td>\n",
       "      <td>4427.0</td>\n",
       "      <td>1541959.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN     15.0   \n",
       "Aldgate                  NaN            NaN         2.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0     49.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         7.0     31.0   \n",
       "Woodgrange Park          NaN            6.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         5.0     18.0   \n",
       "Woolwich Arsenal        20.0            NaN         NaN      NaN   \n",
       "All                    346.0          751.0      2198.0   7788.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                15.0         NaN      11.0       1.0      NaN   \n",
       "Aldgate                   42.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       1.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  33.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             17.0         NaN       3.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN        28.0       NaN       NaN      NaN   \n",
       "All                     7934.0       446.0     741.0     256.0    174.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          17.0  ...       30.0             3.0         5.0   \n",
       "Aldgate             19.0  ...        7.0             NaN         2.0   \n",
       "Aldgate East        21.0  ...        8.0             1.0         3.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            29.0  ...       29.0             NaN        10.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       22.0  ...       21.0             NaN         6.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               8108.0  ...     6278.0           599.0      2141.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              2.0   \n",
       "Acton Town             12.0          NaN       2.0              NaN   \n",
       "Aldgate                 2.0          NaN       1.0              NaN   \n",
       "Aldgate East            2.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1576.0        402.0     700.0            240.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                  NaN              26.0      600.0  \n",
       "Acton Central               NaN               NaN     1224.0  \n",
       "Acton Town                  2.0               NaN     3747.0  \n",
       "Aldgate                     1.0               NaN     2873.0  \n",
       "Aldgate East                1.0               NaN     3172.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                    NaN               NaN     4862.0  \n",
       "Woodgrange Park             NaN               NaN      530.0  \n",
       "Woodside Park               NaN               NaN     3093.0  \n",
       "Woolwich Arsenal            NaN               NaN     7893.0  \n",
       "All                       740.0            4427.0  1541959.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#get the estimates\n",
    "london_flows[\"doubsimfitted\"] = np.round(doubSim_pow.mu)\n",
    "#here's the matrix\n",
    "ldf_submat_dbc = london_flows.pivot_table(values =\"doubsimfitted\", index=\"Orig\", columns = \"Dest\",\n",
    "                                    aggfunc=np.sum, margins=True)\n",
    "ldf_submat_dbc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101.331"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# evaluate the goodness of fit\n",
    "CalcRMSE(london_flows['Total'],london_flows[\"doubsimfitted\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.40772748658809344"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRSqaured(london_flows['Total'],london_flows[\"doubsimfitted\"])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calibration"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Tweaking our model\n",
    "\n",
    "### 4.1.1 Distance Decay\n",
    "\n",
    "Now, all of the way through these practicals, we have assumed that the distance decay parameter follows a negative power law. Well, it doesn't need to.\n",
    "\n",
    "In [Wilson's original paper](http://journals.sagepub.com/doi/abs/10.1068/a030001) he generalised the distance decay parameter to:\n",
    "\n",
    "\\begin{equation} \\tag{15}\n",
    "f(d_{ij})\n",
    "\\end{equation}\n",
    "\n",
    "Where $f$ represents some function of distance describing the rate at which the flow interactions change as distance increase. Lots of people have written about this, including [Talyor](https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1538-4632.1971.tb00364.x) and more recently Robin Lovelace in a transport context, [here](https://www.slideshare.net/ITSLeeds/estimating-distance-decay-for-the-national-propensity-to-cycle-tool).\n",
    "\n",
    "For the inverse power law that we have been using one pussible function of distance, the other common one that is used is the negative exponential function:\n",
    "\n",
    "\\begin{equation} \\tag{16}\n",
    "\\exp (-\\beta d_{ij})\n",
    "\\end{equation}\n",
    "\n",
    "We can get a feel for how different distance decay parameters work by plotting some sample data (try different parameters):"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The inverse power function has a far more rapid distance decay effect than the negative exponential function.\n",
    "\n",
    "* If the observed interacion drop off rapidly with distance-> inverse power law. e.g the trips to local convenience store by walking.\n",
    "\n",
    "* If the effect of distance is less severe, eg migration across London as commuication-> negative exponential function "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poission regression model:\n",
    "\n",
    "$-\\beta d_{ij}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                  Total   No. Observations:                61413\n",
      "Model:                            GLM   Df Residuals:                    60617\n",
      "Model Family:                 Poisson   Df Model:                          795\n",
      "Link Function:                    log   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:            -8.5105e+05\n",
      "Date:                Mon, 01 May 2023   Deviance:                   1.5299e+06\n",
      "Time:                        15:01:38   Pearson chi2:                 2.02e+06\n",
      "No. Iterations:                     8                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=======================================================================================================\n",
      "                                          coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------------------\n",
      "Orig[Abbey Road]                        1.3542      0.068     20.016      0.000       1.222       1.487\n",
      "Orig[Acton Central]                     2.9653      0.061     48.421      0.000       2.845       3.085\n",
      "Orig[Acton Town]                        2.7807      0.056     49.309      0.000       2.670       2.891\n",
      "Orig[Aldgate]                           1.5372      0.057     26.941      0.000       1.425       1.649\n",
      "Orig[Aldgate East]                      1.6255      0.057     28.627      0.000       1.514       1.737\n",
      "Orig[All Saints]                        1.2836      0.065     19.669      0.000       1.156       1.411\n",
      "Orig[Alperton]                          2.7154      0.059     45.685      0.000       2.599       2.832\n",
      "Orig[Amersham]                          5.2244      0.063     83.194      0.000       5.101       5.348\n",
      "Orig[Anerley]                           3.1015      0.067     46.034      0.000       2.969       3.234\n",
      "Orig[Angel]                             1.8928      0.056     33.738      0.000       1.783       2.003\n",
      "Orig[Archway]                           2.7644      0.056     49.749      0.000       2.655       2.873\n",
      "Orig[Arnos Grove]                       3.0621      0.057     53.777      0.000       2.950       3.174\n",
      "Orig[Arsenal]                           1.5985      0.058     27.522      0.000       1.485       1.712\n",
      "Orig[Baker Street]                      2.4710      0.055     44.785      0.000       2.363       2.579\n",
      "Orig[Balham]                            3.5944      0.055     65.459      0.000       3.487       3.702\n",
      "Orig[Bank and Monument]                 3.7090      0.054     68.410      0.000       3.603       3.815\n",
      "Orig[Barbican]                          0.6391      0.061     10.483      0.000       0.520       0.759\n",
      "Orig[Barking]                           3.9250      0.055     71.249      0.000       3.817       4.033\n",
      "Orig[Barkingside]                       3.0304      0.061     49.908      0.000       2.911       3.149\n",
      "Orig[Barons Court]                      2.3045      0.056     41.012      0.000       2.194       2.415\n",
      "Orig[Bayswater]                         1.2314      0.060     20.677      0.000       1.115       1.348\n",
      "Orig[Beckton]                           2.6670      0.061     43.608      0.000       2.547       2.787\n",
      "Orig[Beckton Park]                      1.0048      0.080     12.636      0.000       0.849       1.161\n",
      "Orig[Becontree]                         3.1608      0.058     54.652      0.000       3.047       3.274\n",
      "Orig[Belsize Park]                      1.9210      0.057     33.570      0.000       1.809       2.033\n",
      "Orig[Bermondsey]                        2.2650      0.056     40.648      0.000       2.156       2.374\n",
      "Orig[Bethnal Green]                     2.5668      0.055     46.430      0.000       2.458       2.675\n",
      "Orig[Blackfriars]                       2.2962      0.055     41.533      0.000       2.188       2.405\n",
      "Orig[Blackhorse Road]                   3.6490      0.055     66.274      0.000       3.541       3.757\n",
      "Orig[Blackwall]                         1.5482      0.063     24.659      0.000       1.425       1.671\n",
      "Orig[Bond Street]                       1.0906      0.058     18.703      0.000       0.976       1.205\n",
      "Orig[Borough]                           0.7535      0.060     12.468      0.000       0.635       0.872\n",
      "Orig[Boston Manor]                      2.1531      0.061     35.100      0.000       2.033       2.273\n",
      "Orig[Bounds Green]                      3.2367      0.056     57.781      0.000       3.127       3.346\n",
      "Orig[Bow Church]                        2.2984      0.059     38.802      0.000       2.182       2.414\n",
      "Orig[Bow Road]                          2.2862      0.056     40.677      0.000       2.176       2.396\n",
      "Orig[Brent Cross]                       2.0412      0.060     34.105      0.000       1.924       2.159\n",
      "Orig[Brentwood]                         6.3788      0.059    107.851      0.000       6.263       6.495\n",
      "Orig[Brixton]                           4.1352      0.054     76.096      0.000       4.029       4.242\n",
      "Orig[Brockley]                          3.6113      0.058     62.275      0.000       3.498       3.725\n",
      "Orig[Bromley-by-Bow]                    1.9345      0.057     33.673      0.000       1.822       2.047\n",
      "Orig[Brondesbury]                       3.0982      0.059     52.893      0.000       2.983       3.213\n",
      "Orig[Brondesbury Park]                  2.0231      0.066     30.599      0.000       1.893       2.153\n",
      "Orig[Bruce Grove]                       3.0435      0.063     48.273      0.000       2.920       3.167\n",
      "Orig[Buckhurst Hill]                    3.1196      0.059     52.458      0.000       3.003       3.236\n",
      "Orig[Burnt Oak]                         3.3623      0.057     58.985      0.000       3.251       3.474\n",
      "Orig[Bush Hill Park]                    3.9526      0.061     65.181      0.000       3.834       4.071\n",
      "Orig[Bushey]                            1.9339      0.086     22.381      0.000       1.765       2.103\n",
      "Orig[Caledonian Road]                   1.7039      0.057     29.833      0.000       1.592       1.816\n",
      "Orig[Caledonian Road & Barnsbury]       1.5652      0.069     22.686      0.000       1.430       1.700\n",
      "Orig[Cambridge Heath]                   1.4215      0.077     18.404      0.000       1.270       1.573\n",
      "Orig[Camden Road]                       2.4234      0.061     39.580      0.000       2.303       2.543\n",
      "Orig[Camden Town]                       1.7894      0.057     31.583      0.000       1.678       1.900\n",
      "Orig[Canada Water]                      3.9190      0.054     72.204      0.000       3.813       4.025\n",
      "Orig[Canary Wharf]                      3.4454      0.054     63.228      0.000       3.339       3.552\n",
      "Orig[Canning Town]                      3.9219      0.054     72.284      0.000       3.816       4.028\n",
      "Orig[Cannon Street]                     1.7254      0.056     30.659      0.000       1.615       1.836\n",
      "Orig[Canonbury]                         2.9255      0.058     50.673      0.000       2.812       3.039\n",
      "Orig[Canons Park]                       3.5298      0.058     60.939      0.000       3.416       3.643\n",
      "Orig[Carpenders Park]                   3.6756      0.063     58.694      0.000       3.553       3.798\n",
      "Orig[Chadwell Heath]                    5.4688      0.056     96.838      0.000       5.358       5.579\n",
      "Orig[Chalfont & Latimer]                4.6007      0.064     71.372      0.000       4.474       4.727\n",
      "Orig[Chalk Farm]                        1.6252      0.058     28.171      0.000       1.512       1.738\n",
      "Orig[Chancery Lane]                     0.5057      0.061      8.225      0.000       0.385       0.626\n",
      "Orig[Charing Cross]                     2.1786      0.055     39.361      0.000       2.070       2.287\n",
      "Orig[Chesham]                           5.4438      0.065     84.090      0.000       5.317       5.571\n",
      "Orig[Cheshunt]                          2.8148      0.095     29.785      0.000       2.630       3.000\n",
      "Orig[Chigwell]                          2.1365      0.071     30.089      0.000       1.997       2.276\n",
      "Orig[Chingford]                         4.6302      0.059     79.092      0.000       4.515       4.745\n",
      "Orig[Chiswick Park]                     1.6308      0.061     26.839      0.000       1.512       1.750\n",
      "Orig[Chorleywood]                       4.2468      0.064     66.103      0.000       4.121       4.373\n",
      "Orig[Clapham Common]                    2.5643      0.056     45.953      0.000       2.455       2.674\n",
      "Orig[Clapham High Street]               3.3050      0.060     54.947      0.000       3.187       3.423\n",
      "Orig[Clapham Junction]                  4.9089      0.055     88.495      0.000       4.800       5.018\n",
      "Orig[Clapham North]                     1.9246      0.057     33.700      0.000       1.813       2.036\n",
      "Orig[Clapham South]                     3.0358      0.055     54.869      0.000       2.927       3.144\n",
      "Orig[Clapton]                           3.1250      0.060     52.193      0.000       3.008       3.242\n",
      "Orig[Cockfosters]                       2.7442      0.063     43.831      0.000       2.622       2.867\n",
      "Orig[Colindale]                         3.7773      0.056     67.828      0.000       3.668       3.886\n",
      "Orig[Colliers Wood]                     3.4752      0.056     62.483      0.000       3.366       3.584\n",
      "Orig[Covent Garden]                    -0.5410      0.073     -7.454      0.000      -0.683      -0.399\n",
      "Orig[Crossharbour]                      2.1982      0.059     37.277      0.000       2.083       2.314\n",
      "Orig[Crouch Hill]                       1.9039      0.074     25.670      0.000       1.759       2.049\n",
      "Orig[Croxley]                           3.8755      0.063     61.629      0.000       3.752       3.999\n",
      "Orig[Crystal Palace]                    4.3853      0.059     74.385      0.000       4.270       4.501\n",
      "Orig[Custom House]                      1.5814      0.065     24.455      0.000       1.455       1.708\n",
      "Orig[Cutty Sark]                        2.6359      0.058     45.404      0.000       2.522       2.750\n",
      "Orig[Cyprus]                            1.5689      0.070     22.436      0.000       1.432       1.706\n",
      "Orig[Dagenham East]                     3.3525      0.059     57.160      0.000       3.238       3.467\n",
      "Orig[Dagenham Heathway]                 3.7277      0.057     65.754      0.000       3.617       3.839\n",
      "Orig[Dalston Junction]                  3.6045      0.056     63.964      0.000       3.494       3.715\n",
      "Orig[Dalston Kingsland]                 3.2658      0.057     57.167      0.000       3.154       3.378\n",
      "Orig[Debden]                            3.6870      0.059     61.988      0.000       3.570       3.804\n",
      "Orig[Denmark Hill]                      3.4149      0.059     57.907      0.000       3.299       3.530\n",
      "Orig[Deptford Bridge]                   2.9915      0.058     51.962      0.000       2.879       3.104\n",
      "Orig[Devons Road]                       2.0292      0.060     33.769      0.000       1.911       2.147\n",
      "Orig[Dollis Hill]                       2.4302      0.057     42.268      0.000       2.318       2.543\n",
      "Orig[Ealing Broadway]                   4.2816      0.055     78.275      0.000       4.174       4.389\n",
      "Orig[Ealing Common]                     2.2742      0.058     38.928      0.000       2.160       2.389\n",
      "Orig[Earl's Court]                      2.8240      0.055     51.310      0.000       2.716       2.932\n",
      "Orig[East Acton]                        2.1717      0.058     37.598      0.000       2.058       2.285\n",
      "Orig[East Finchley]                     3.2828      0.056     59.120      0.000       3.174       3.392\n",
      "Orig[East Ham]                          3.6306      0.055     65.880      0.000       3.523       3.739\n",
      "Orig[East India]                        2.1152      0.059     35.964      0.000       2.000       2.230\n",
      "Orig[East Putney]                       2.9888      0.056     53.721      0.000       2.880       3.098\n",
      "Orig[Eastcote]                          3.6587      0.058     63.460      0.000       3.546       3.772\n",
      "Orig[Edgware]                           3.7098      0.057     65.450      0.000       3.599       3.821\n",
      "Orig[Edgware Road]                      1.5996      0.057     28.009      0.000       1.488       1.712\n",
      "Orig[Edmonton Green]                    3.9488      0.059     67.472      0.000       3.834       4.064\n",
      "Orig[Elephant & Castle]                 2.6887      0.055     48.954      0.000       2.581       2.796\n",
      "Orig[Elm Park]                          3.9762      0.057     69.298      0.000       3.864       4.089\n",
      "Orig[Elverson Road]                     2.3601      0.062     38.366      0.000       2.240       2.481\n",
      "Orig[Embankment]                        1.7195      0.056     30.615      0.000       1.609       1.830\n",
      "Orig[Emerson Park]                      4.6797      0.080     58.514      0.000       4.523       4.836\n",
      "Orig[Enfield Town]                      4.4057      0.059     74.442      0.000       4.290       4.522\n",
      "Orig[Epping]                            5.1125      0.057     89.229      0.000       5.000       5.225\n",
      "Orig[Euston]                            3.2643      0.054     59.940      0.000       3.158       3.371\n",
      "Orig[Euston Square]                     2.1057      0.056     37.743      0.000       1.996       2.215\n",
      "Orig[Fairlop]                           2.9308      0.063     46.779      0.000       2.808       3.054\n",
      "Orig[Farringdon]                        2.0669      0.056     37.079      0.000       1.958       2.176\n",
      "Orig[Finchley Central]                  3.7014      0.055     66.765      0.000       3.593       3.810\n",
      "Orig[Finchley Road]                     2.4989      0.056     44.726      0.000       2.389       2.608\n",
      "Orig[Finchley Road & Frognal]           2.5339      0.062     41.078      0.000       2.413       2.655\n",
      "Orig[Finsbury Park]                     4.0992      0.054     75.466      0.000       3.993       4.206\n",
      "Orig[Forest Gate]                       4.0364      0.058     69.878      0.000       3.923       4.150\n",
      "Orig[Forest Hill]                       4.0401      0.058     69.735      0.000       3.927       4.154\n",
      "Orig[Fulham Broadway]                   2.0896      0.057     36.855      0.000       1.978       2.201\n",
      "Orig[Gallions Reach]                    1.9375      0.067     29.002      0.000       1.807       2.068\n",
      "Orig[Gants Hill]                        3.8968      0.056     69.937      0.000       3.788       4.006\n",
      "Orig[Gidea Park]                        5.9259      0.057    103.885      0.000       5.814       6.038\n",
      "Orig[Gloucester Road]                   2.1837      0.056     39.098      0.000       2.074       2.293\n",
      "Orig[Golders Green]                     2.9850      0.056     53.438      0.000       2.876       3.095\n",
      "Orig[Goldhawk Road]                     1.4727      0.060     24.364      0.000       1.354       1.591\n",
      "Orig[Goodge Street]                    -0.6093      0.075     -8.112      0.000      -0.756      -0.462\n",
      "Orig[Goodmayes]                         5.0880      0.057     89.231      0.000       4.976       5.200\n",
      "Orig[Gospel Oak]                        2.2557      0.062     36.390      0.000       2.134       2.377\n",
      "Orig[Grange Hill]                       2.6263      0.067     39.366      0.000       2.496       2.757\n",
      "Orig[Great Portland Street]             0.6736      0.062     10.942      0.000       0.553       0.794\n",
      "Orig[Green Park]                        1.0861      0.058     18.644      0.000       0.972       1.200\n",
      "Orig[Greenford]                         3.3447      0.057     58.336      0.000       3.232       3.457\n",
      "Orig[Greenwich]                         2.3075      0.060     38.253      0.000       2.189       2.426\n",
      "Orig[Gunnersbury]                       2.1708      0.058     37.490      0.000       2.057       2.284\n",
      "Orig[Hackney Central]                   3.5291      0.057     62.246      0.000       3.418       3.640\n",
      "Orig[Hackney Downs]                     2.8108      0.064     43.814      0.000       2.685       2.937\n",
      "Orig[Hackney Wick]                      2.5405      0.060     42.390      0.000       2.423       2.658\n",
      "Orig[Haggerston]                        2.9143      0.058     49.920      0.000       2.800       3.029\n",
      "Orig[Hainault]                          4.1546      0.057     72.965      0.000       4.043       4.266\n",
      "Orig[Hammersmith]                       3.4775      0.055     63.537      0.000       3.370       3.585\n",
      "Orig[Hampstead]                         1.7389      0.059     29.678      0.000       1.624       1.854\n",
      "Orig[Hampstead Heath]                   2.1473      0.063     33.893      0.000       2.023       2.272\n",
      "Orig[Hanger Lane]                       2.5720      0.058     44.011      0.000       2.457       2.686\n",
      "Orig[Harlesden]                         1.7537      0.060     29.313      0.000       1.636       1.871\n",
      "Orig[Harold Wood]                       6.0839      0.058    105.798      0.000       5.971       6.197\n",
      "Orig[Harringay Green Lanes]             2.3891      0.070     34.055      0.000       2.252       2.527\n",
      "Orig[Harrow & Wealdstone]               2.9853      0.059     50.423      0.000       2.869       3.101\n",
      "Orig[Harrow-on-the-Hill]                4.1755      0.055     75.264      0.000       4.067       4.284\n",
      "Orig[Hatch End]                         3.2710      0.065     50.040      0.000       3.143       3.399\n",
      "Orig[Hatton Cross]                      3.1384      0.061     51.676      0.000       3.019       3.257\n",
      "Orig[Headstone Lane]                    2.5974      0.072     36.084      0.000       2.456       2.738\n",
      "Orig[Heathrow Terminal 4]               2.6393      0.065     40.671      0.000       2.512       2.766\n",
      "Orig[Heathrow Terminal 5]               3.2658      0.064     51.322      0.000       3.141       3.391\n",
      "Orig[Heathrow Terminals 2 & 3]          3.8740      0.059     66.217      0.000       3.759       3.989\n",
      "Orig[Hendon Central]                    3.1822      0.056     56.610      0.000       3.072       3.292\n",
      "Orig[Heron Quays]                       2.1770      0.059     36.972      0.000       2.062       2.292\n",
      "Orig[High Barnet]                       3.9690      0.057     69.881      0.000       3.858       4.080\n",
      "Orig[High Street Kensington]            1.4611      0.058     25.156      0.000       1.347       1.575\n",
      "Orig[Highams Park]                      4.4218      0.057     77.330      0.000       4.310       4.534\n",
      "Orig[Highbury & Islington]              3.7376      0.054     68.795      0.000       3.631       3.844\n",
      "Orig[Highgate]                          2.7938      0.056     49.945      0.000       2.684       2.903\n",
      "Orig[Hillingdon]                        3.3745      0.061     55.382      0.000       3.255       3.494\n",
      "Orig[Holborn]                           0.8385      0.059     14.151      0.000       0.722       0.955\n",
      "Orig[Holland Park]                      1.2499      0.060     20.952      0.000       1.133       1.367\n",
      "Orig[Holloway Road]                     1.8468      0.057     32.455      0.000       1.735       1.958\n",
      "Orig[Homerton]                          3.4168      0.057     60.391      0.000       3.306       3.528\n",
      "Orig[Honor Oak Park]                    3.5437      0.059     59.823      0.000       3.428       3.660\n",
      "Orig[Hornchurch]                        3.7447      0.059     63.126      0.000       3.628       3.861\n",
      "Orig[Hounslow Central]                  3.2116      0.058     55.271      0.000       3.098       3.325\n",
      "Orig[Hounslow East]                     3.1766      0.058     54.612      0.000       3.063       3.291\n",
      "Orig[Hounslow West]                     3.3079      0.058     56.616      0.000       3.193       3.422\n",
      "Orig[Hoxton]                            2.2341      0.062     35.864      0.000       2.112       2.356\n",
      "Orig[Hyde Park Corner]                 -0.9148      0.082    -11.117      0.000      -1.076      -0.754\n",
      "Orig[Ickenham]                          2.7750      0.066     42.266      0.000       2.646       2.904\n",
      "Orig[Ilford]                            5.2928      0.056     94.873      0.000       5.183       5.402\n",
      "Orig[Imperial Wharf]                    2.4114      0.064     37.723      0.000       2.286       2.537\n",
      "Orig[Island Gardens]                    2.1411      0.060     35.655      0.000       2.023       2.259\n",
      "Orig[Kennington]                        1.8023      0.056     31.917      0.000       1.692       1.913\n",
      "Orig[Kensal Green]                      1.8337      0.059     31.208      0.000       1.719       1.949\n",
      "Orig[Kensal Rise]                       3.0129      0.059     51.384      0.000       2.898       3.128\n",
      "Orig[Kensington]                        0.0483      0.072      0.668      0.504      -0.093       0.190\n",
      "Orig[Kentish Town]                      1.6510      0.058     28.636      0.000       1.538       1.764\n",
      "Orig[Kentish Town West]                 1.8281      0.066     27.797      0.000       1.699       1.957\n",
      "Orig[Kenton]                            2.5072      0.062     40.245      0.000       2.385       2.629\n",
      "Orig[Kew Gardens]                       2.3547      0.058     40.623      0.000       2.241       2.468\n",
      "Orig[Kilburn]                           2.7140      0.056     48.532      0.000       2.604       2.824\n",
      "Orig[Kilburn High Road]                 1.9684      0.076     25.773      0.000       1.819       2.118\n",
      "Orig[Kilburn Park]                      1.6908      0.059     28.824      0.000       1.576       1.806\n",
      "Orig[King George V]                     2.0890      0.063     33.327      0.000       1.966       2.212\n",
      "Orig[King's Cross St. Pancras]          3.7431      0.054     68.977      0.000       3.637       3.849\n",
      "Orig[Kingsbury]                         3.2779      0.057     57.194      0.000       3.166       3.390\n",
      "Orig[Knightsbridge]                     0.6011      0.062      9.753      0.000       0.480       0.722\n",
      "Orig[Ladbroke Grove]                    1.8407      0.058     31.886      0.000       1.728       1.954\n",
      "Orig[Lambeth North]                     0.5551      0.062      8.997      0.000       0.434       0.676\n",
      "Orig[Lancaster Gate]                    1.8803      0.057     33.267      0.000       1.769       1.991\n",
      "Orig[Langdon Park]                      2.0199      0.060     33.719      0.000       1.902       2.137\n",
      "Orig[Latimer Road]                      0.9257      0.064     14.506      0.000       0.801       1.051\n",
      "Orig[Leicester Square]                  0.2912      0.063      4.649      0.000       0.168       0.414\n",
      "Orig[Lewisham]                          4.3971      0.055     79.914      0.000       4.289       4.505\n",
      "Orig[Leyton]                            3.4033      0.055     61.721      0.000       3.295       3.511\n",
      "Orig[Leyton Midland Road]               3.2715      0.065     50.633      0.000       3.145       3.398\n",
      "Orig[Leytonstone]                       3.5112      0.055     63.472      0.000       3.403       3.620\n",
      "Orig[Leytonstone High Road]             3.0182      0.068     44.513      0.000       2.885       3.151\n",
      "Orig[Limehouse]                         3.2629      0.056     58.751      0.000       3.154       3.372\n",
      "Orig[Liverpool Street]                  3.8666      0.054     71.301      0.000       3.760       3.973\n",
      "Orig[London Bridge]                     3.8878      0.054     71.704      0.000       3.782       3.994\n",
      "Orig[London City Airport]               2.7322      0.058     46.949      0.000       2.618       2.846\n",
      "Orig[London Fields]                     2.8159      0.062     45.453      0.000       2.694       2.937\n",
      "Orig[Loughton]                          3.8839      0.057     67.740      0.000       3.772       3.996\n",
      "Orig[Maida Vale]                        1.6624      0.058     28.605      0.000       1.548       1.776\n",
      "Orig[Manor House]                       2.7461      0.056     49.373      0.000       2.637       2.855\n",
      "Orig[Manor Park]                        3.9129      0.059     66.235      0.000       3.797       4.029\n",
      "Orig[Mansion House]                    -0.2403      0.070     -3.452      0.001      -0.377      -0.104\n",
      "Orig[Marble Arch]                       1.0537      0.059     17.906      0.000       0.938       1.169\n",
      "Orig[Maryland]                          2.8414      0.064     44.597      0.000       2.716       2.966\n",
      "Orig[Marylebone]                        2.3208      0.055     41.864      0.000       2.212       2.429\n",
      "Orig[Mile End]                          2.7743      0.055     50.244      0.000       2.666       2.883\n",
      "Orig[Mill Hill East]                    2.3895      0.061     39.343      0.000       2.270       2.508\n",
      "Orig[Moor Park]                         3.1157      0.067     46.434      0.000       2.984       3.247\n",
      "Orig[Moorgate]                          1.8869      0.056     33.697      0.000       1.777       1.997\n",
      "Orig[Morden]                            4.2452      0.055     77.000      0.000       4.137       4.353\n",
      "Orig[Mornington Crescent]               0.1584      0.066      2.400      0.016       0.029       0.288\n",
      "Orig[Mudchute]                          2.0356      0.060     33.709      0.000       1.917       2.154\n",
      "Orig[Neasden]                           2.4436      0.058     42.272      0.000       2.330       2.557\n",
      "Orig[New Cross]                         3.1911      0.060     53.030      0.000       3.073       3.309\n",
      "Orig[New Cross Gate]                    3.2059      0.059     54.071      0.000       3.090       3.322\n",
      "Orig[Newbury Park]                      4.0176      0.056     71.539      0.000       3.907       4.128\n",
      "Orig[North Acton]                       2.5900      0.057     45.521      0.000       2.479       2.702\n",
      "Orig[North Ealing]                      1.2731      0.070     18.197      0.000       1.136       1.410\n",
      "Orig[North Greenwich]                   3.4898      0.055     63.711      0.000       3.382       3.597\n",
      "Orig[North Harrow]                      3.3348      0.059     56.799      0.000       3.220       3.450\n",
      "Orig[North Wembley]                     2.0892      0.062     33.724      0.000       1.968       2.211\n",
      "Orig[Northfields]                       2.9522      0.057     51.753      0.000       2.840       3.064\n",
      "Orig[Northolt]                          3.8831      0.057     68.636      0.000       3.772       3.994\n",
      "Orig[Northwick Park]                    2.9847      0.058     51.250      0.000       2.871       3.099\n",
      "Orig[Northwood]                         4.0053      0.059     68.371      0.000       3.890       4.120\n",
      "Orig[Northwood Hills]                   3.4791      0.060     57.817      0.000       3.361       3.597\n",
      "Orig[Norwood Junction]                  3.2181      0.067     48.033      0.000       3.087       3.349\n",
      "Orig[Notting Hill Gate]                 2.2640      0.056     40.581      0.000       2.155       2.373\n",
      "Orig[Oakwood]                           3.1043      0.059     52.603      0.000       2.989       3.220\n",
      "Orig[Old Street]                        2.1564      0.056     38.758      0.000       2.047       2.265\n",
      "Orig[Osterley]                          2.6344      0.060     43.759      0.000       2.516       2.752\n",
      "Orig[Oval]                              1.9364      0.056     34.307      0.000       1.826       2.047\n",
      "Orig[Oxford Circus]                     1.3806      0.057     24.148      0.000       1.269       1.493\n",
      "Orig[Paddington]                        3.8050      0.054     70.021      0.000       3.698       3.911\n",
      "Orig[Park Royal]                        1.4274      0.069     20.810      0.000       1.293       1.562\n",
      "Orig[Parsons Green]                     2.4712      0.056     44.100      0.000       2.361       2.581\n",
      "Orig[Peckham Rye]                       3.5464      0.058     61.282      0.000       3.433       3.660\n",
      "Orig[Penge West]                        2.5539      0.076     33.709      0.000       2.405       2.702\n",
      "Orig[Perivale]                          2.6328      0.059     44.298      0.000       2.516       2.749\n",
      "Orig[Piccadilly Circus]                 0.3507      0.062      5.634      0.000       0.229       0.473\n",
      "Orig[Pimlico]                           1.9654      0.056     34.934      0.000       1.855       2.076\n",
      "Orig[Pinner]                            3.9025      0.057     68.198      0.000       3.790       4.015\n",
      "Orig[Plaistow]                          2.4928      0.056     44.175      0.000       2.382       2.603\n",
      "Orig[Pontoon Dock]                      2.5794      0.058     44.318      0.000       2.465       2.693\n",
      "Orig[Poplar]                            2.2987      0.058     39.806      0.000       2.186       2.412\n",
      "Orig[Preston Road]                      2.9004      0.058     50.181      0.000       2.787       3.014\n",
      "Orig[Prince Regent]                     1.8206      0.063     28.942      0.000       1.697       1.944\n",
      "Orig[Pudding Mill Lane]                 0.9810      0.072     13.608      0.000       0.840       1.122\n",
      "Orig[Putney Bridge]                     2.2141      0.057     38.836      0.000       2.102       2.326\n",
      "Orig[Queen's Park]                      2.6335      0.056     47.287      0.000       2.524       2.743\n",
      "Orig[Queens Road Peckham]               3.3077      0.059     56.324      0.000       3.193       3.423\n",
      "Orig[Queensbury]                        3.5068      0.057     61.379      0.000       3.395       3.619\n",
      "Orig[Queensway]                         1.6904      0.057     29.522      0.000       1.578       1.803\n",
      "Orig[Ravenscourt Park]                  1.5399      0.060     25.828      0.000       1.423       1.657\n",
      "Orig[Rayners Lane]                      3.7209      0.057     65.649      0.000       3.610       3.832\n",
      "Orig[Rectory Road]                      2.6359      0.063     41.837      0.000       2.512       2.759\n",
      "Orig[Redbridge]                         2.7658      0.058     47.451      0.000       2.652       2.880\n",
      "Orig[Regent's Park]                    -0.5133      0.075     -6.856      0.000      -0.660      -0.367\n",
      "Orig[Richmond]                          3.5541      0.056     63.741      0.000       3.445       3.663\n",
      "Orig[Rickmansworth]                     4.1469      0.061     67.589      0.000       4.027       4.267\n",
      "Orig[Roding Valley]                     1.8306      0.073     24.973      0.000       1.687       1.974\n",
      "Orig[Romford]                           6.0160      0.056    106.693      0.000       5.906       6.127\n",
      "Orig[Rotherhithe]                       2.8068      0.060     47.071      0.000       2.690       2.924\n",
      "Orig[Royal Albert]                      1.5972      0.067     24.004      0.000       1.467       1.728\n",
      "Orig[Royal Oak]                         1.1883      0.060     19.750      0.000       1.070       1.306\n",
      "Orig[Royal Victoria]                    2.4632      0.058     42.283      0.000       2.349       2.577\n",
      "Orig[Ruislip]                           3.1890      0.061     52.404      0.000       3.070       3.308\n",
      "Orig[Ruislip Gardens]                   3.1115      0.063     49.374      0.000       2.988       3.235\n",
      "Orig[Ruislip Manor]                     3.1923      0.060     52.858      0.000       3.074       3.311\n",
      "Orig[Russell Square]                    0.7751      0.060     12.968      0.000       0.658       0.892\n",
      "Orig[Seven Kings]                       5.0174      0.057     88.256      0.000       4.906       5.129\n",
      "Orig[Seven Sisters]                     4.1971      0.054     77.086      0.000       4.090       4.304\n",
      "Orig[Shadwell]                          3.1557      0.055     57.155      0.000       3.047       3.264\n",
      "Orig[Shenfield]                         4.6036      0.085     54.449      0.000       4.438       4.769\n",
      "Orig[Shepherd's Bush]                   3.1251      0.055     57.002      0.000       3.018       3.233\n",
      "Orig[Shepherd's Bush Market]            1.7351      0.059     29.466      0.000       1.620       1.850\n",
      "Orig[Shoreditch High Street]            2.1797      0.063     34.489      0.000       2.056       2.304\n",
      "Orig[Silver Street]                     3.7012      0.060     62.071      0.000       3.584       3.818\n",
      "Orig[Sloane Square]                     2.1207      0.056     38.019      0.000       2.011       2.230\n",
      "Orig[Snaresbrook]                       2.4673      0.059     41.863      0.000       2.352       2.583\n",
      "Orig[South Acton]                       2.4392      0.067     36.414      0.000       2.308       2.571\n",
      "Orig[South Ealing]                      2.5768      0.058     44.360      0.000       2.463       2.691\n",
      "Orig[South Hampstead]                   1.9045      0.084     22.805      0.000       1.741       2.068\n",
      "Orig[South Harrow]                      3.0354      0.060     50.719      0.000       2.918       3.153\n",
      "Orig[South Kensington]                  2.1960      0.056     39.386      0.000       2.087       2.305\n",
      "Orig[South Kenton]                      2.2140      0.062     35.672      0.000       2.092       2.336\n",
      "Orig[South Quay]                        2.1416      0.059     36.238      0.000       2.026       2.257\n",
      "Orig[South Ruislip]                     3.2932      0.060     54.551      0.000       3.175       3.411\n",
      "Orig[South Tottenham]                   2.3733      0.073     32.479      0.000       2.230       2.517\n",
      "Orig[South Wimbledon]                   3.2778      0.056     58.140      0.000       3.167       3.388\n",
      "Orig[South Woodford]                    3.4568      0.056     61.549      0.000       3.347       3.567\n",
      "Orig[Southbury]                         3.2222      0.069     46.547      0.000       3.086       3.358\n",
      "Orig[Southfields]                       3.1504      0.056     56.543      0.000       3.041       3.260\n",
      "Orig[Southgate]                         3.5338      0.056     62.576      0.000       3.423       3.644\n",
      "Orig[Southwark]                         1.9623      0.056     35.165      0.000       1.853       2.072\n",
      "Orig[St James Street]                   3.0520      0.062     48.999      0.000       2.930       3.174\n",
      "Orig[St. James's Park]                  1.0058      0.059     17.094      0.000       0.891       1.121\n",
      "Orig[St. John's Wood]                   1.9374      0.057     34.149      0.000       1.826       2.049\n",
      "Orig[St. Paul's]                        0.2502      0.064      3.932      0.000       0.125       0.375\n",
      "Orig[Stamford Brook]                    1.7918      0.059     30.479      0.000       1.677       1.907\n",
      "Orig[Stamford Hill]                     2.3735      0.070     33.676      0.000       2.235       2.512\n",
      "Orig[Stanmore]                          3.9032      0.057     67.923      0.000       3.791       4.016\n",
      "Orig[Star Lane]                         0.9325      0.072     12.977      0.000       0.792       1.073\n",
      "Orig[Stepney Green]                     1.7044      0.057     29.782      0.000       1.592       1.817\n",
      "Orig[Stockwell]                         3.1027      0.055     56.614      0.000       2.995       3.210\n",
      "Orig[Stoke Newington]                   2.8207      0.062     45.553      0.000       2.699       2.942\n",
      "Orig[Stonebridge Park]                  1.9383      0.060     32.357      0.000       1.821       2.056\n",
      "Orig[Stratford]                         4.9266      0.054     91.283      0.000       4.821       5.032\n",
      "Orig[Stratford High Street]             1.3457      0.074     18.149      0.000       1.200       1.491\n",
      "Orig[Stratford International]           2.9415      0.058     51.106      0.000       2.829       3.054\n",
      "Orig[Sudbury Hill]                      2.8118      0.061     46.423      0.000       2.693       2.931\n",
      "Orig[Sudbury Town]                      2.8300      0.060     47.241      0.000       2.713       2.947\n",
      "Orig[Surrey Quays]                      3.5605      0.057     62.784      0.000       3.449       3.672\n",
      "Orig[Swiss Cottage]                     2.1516      0.057     38.074      0.000       2.041       2.262\n",
      "Orig[Sydenham]                          3.8919      0.059     65.718      0.000       3.776       4.008\n",
      "Orig[Temple]                           -0.6681      0.076     -8.792      0.000      -0.817      -0.519\n",
      "Orig[Theobalds Grove]                   3.7108      0.070     52.648      0.000       3.573       3.849\n",
      "Orig[Theydon Bois]                      3.2200      0.067     48.361      0.000       3.090       3.351\n",
      "Orig[Tooting Bec]                       3.3408      0.055     60.392      0.000       3.232       3.449\n",
      "Orig[Tooting Broadway]                  3.8662      0.055     70.386      0.000       3.759       3.974\n",
      "Orig[Tottenham Court Road]              0.9015      0.059     15.296      0.000       0.786       1.017\n",
      "Orig[Tottenham Hale]                    3.6386      0.055     66.164      0.000       3.531       3.746\n",
      "Orig[Totteridge & Whetstone]            3.2039      0.058     55.326      0.000       3.090       3.317\n",
      "Orig[Tower Gateway]                     1.6893      0.064     26.485      0.000       1.564       1.814\n",
      "Orig[Tower Hill]                        2.5695      0.055     46.704      0.000       2.462       2.677\n",
      "Orig[Tufnell Park]                      1.9035      0.057     33.263      0.000       1.791       2.016\n",
      "Orig[Turkey Street]                     3.8695      0.065     59.384      0.000       3.742       3.997\n",
      "Orig[Turnham Green]                     2.5197      0.056     44.641      0.000       2.409       2.630\n",
      "Orig[Turnpike Lane]                     3.2802      0.055     59.289      0.000       3.172       3.389\n",
      "Orig[Upminster]                         3.1948      0.066     48.602      0.000       3.066       3.324\n",
      "Orig[Upminster Bridge]                  3.1725      0.065     48.840      0.000       3.045       3.300\n",
      "Orig[Upney]                             2.6278      0.059     44.497      0.000       2.512       2.744\n",
      "Orig[Upper Holloway]                    1.6844      0.075     22.470      0.000       1.537       1.831\n",
      "Orig[Upton Park]                        3.1705      0.055     57.151      0.000       3.062       3.279\n",
      "Orig[Uxbridge]                          4.8043      0.057     83.626      0.000       4.692       4.917\n",
      "Orig[Vauxhall]                          3.5044      0.055     64.286      0.000       3.398       3.611\n",
      "Orig[Victoria]                          4.0666      0.054     75.046      0.000       3.960       4.173\n",
      "Orig[Walthamstow Central]               4.5158      0.054     82.868      0.000       4.409       4.623\n",
      "Orig[Walthamstow Queens Road]           3.6814      0.063     58.371      0.000       3.558       3.805\n",
      "Orig[Wandsworth Road]                   2.3289      0.068     34.436      0.000       2.196       2.461\n",
      "Orig[Wanstead]                          2.5518      0.058     43.664      0.000       2.437       2.666\n",
      "Orig[Wanstead Park]                     3.3925      0.066     51.716      0.000       3.264       3.521\n",
      "Orig[Wapping]                           2.5615      0.061     41.971      0.000       2.442       2.681\n",
      "Orig[Warren Street]                     1.0228      0.059     17.458      0.000       0.908       1.138\n",
      "Orig[Warwick Avenue]                    1.6619      0.058     28.804      0.000       1.549       1.775\n",
      "Orig[Waterloo]                          4.5743      0.054     84.590      0.000       4.468       4.680\n",
      "Orig[Watford]                           4.5758      0.061     75.382      0.000       4.457       4.695\n",
      "Orig[Watford High Street]               2.7018      0.074     36.510      0.000       2.557       2.847\n",
      "Orig[Watford Junction]                  3.2456      0.073     44.281      0.000       3.102       3.389\n",
      "Orig[Wembley Central]                   2.5476      0.058     43.948      0.000       2.434       2.661\n",
      "Orig[Wembley Park]                      3.8432      0.055     69.517      0.000       3.735       3.952\n",
      "Orig[West Acton]                        1.8700      0.061     30.469      0.000       1.750       1.990\n",
      "Orig[West Brompton]                     2.0170      0.056     35.815      0.000       1.907       2.127\n",
      "Orig[West Croydon]                      4.7221      0.061     77.337      0.000       4.602       4.842\n",
      "Orig[West Finchley]                     2.4930      0.060     41.779      0.000       2.376       2.610\n",
      "Orig[West Ham]                          3.0766      0.055     56.110      0.000       2.969       3.184\n",
      "Orig[West Hampstead]                    3.2157      0.055     58.639      0.000       3.108       3.323\n",
      "Orig[West Harrow]                       2.4804      0.062     39.710      0.000       2.358       2.603\n",
      "Orig[West India Quay]                  -0.3412      0.095     -3.580      0.000      -0.528      -0.154\n",
      "Orig[West Kensington]                   1.8183      0.057     31.755      0.000       1.706       1.931\n",
      "Orig[West Ruislip]                      3.5342      0.062     56.890      0.000       3.412       3.656\n",
      "Orig[West Silvertown]                   1.6937      0.063     26.776      0.000       1.570       1.818\n",
      "Orig[Westbourne Park]                   1.8067      0.058     31.334      0.000       1.694       1.920\n",
      "Orig[Westferry]                         2.3001      0.058     39.747      0.000       2.187       2.414\n",
      "Orig[Westminster]                       0.7824      0.060     13.099      0.000       0.665       0.900\n",
      "Orig[White City]                        1.9797      0.058     34.359      0.000       1.867       2.093\n",
      "Orig[White Hart Lane]                   3.0375      0.062     48.623      0.000       2.915       3.160\n",
      "Orig[Whitechapel]                       2.9651      0.055     54.222      0.000       2.858       3.072\n",
      "Orig[Willesden Green]                   3.0498      0.056     54.883      0.000       2.941       3.159\n",
      "Orig[Willesden Junction]                2.7811      0.056     49.935      0.000       2.672       2.890\n",
      "Orig[Wimbledon]                         3.9811      0.055     72.018      0.000       3.873       4.089\n",
      "Orig[Wimbledon Park]                    2.2385      0.059     37.755      0.000       2.122       2.355\n",
      "Orig[Wood Green]                        3.4266      0.055     61.925      0.000       3.318       3.535\n",
      "Orig[Wood Lane]                         1.2371      0.062     19.990      0.000       1.116       1.358\n",
      "Orig[Wood Street]                       3.3910      0.060     56.067      0.000       3.272       3.510\n",
      "Orig[Woodford]                          3.8569      0.056     69.051      0.000       3.747       3.966\n",
      "Orig[Woodgrange Park]                   3.0630      0.070     43.865      0.000       2.926       3.200\n",
      "Orig[Woodside Park]                     3.2928      0.057     57.852      0.000       3.181       3.404\n",
      "Orig[Woolwich Arsenal]                  4.7429      0.055     86.342      0.000       4.635       4.851\n",
      "Dest[T.Acton Central]                   1.4861      0.065     22.761      0.000       1.358       1.614\n",
      "Dest[T.Acton Town]                      1.4408      0.058     24.827      0.000       1.327       1.555\n",
      "Dest[T.Aldgate]                         2.2224      0.055     40.322      0.000       2.114       2.330\n",
      "Dest[T.Aldgate East]                    2.1538      0.055     39.096      0.000       2.046       2.262\n",
      "Dest[T.All Saints]                      0.1630      0.072      2.271      0.023       0.022       0.304\n",
      "Dest[T.Alperton]                        0.7994      0.065     12.236      0.000       0.671       0.927\n",
      "Dest[T.Amersham]                        0.3548      0.085      4.197      0.000       0.189       0.520\n",
      "Dest[T.Anerley]                        -0.3098      0.094     -3.304      0.001      -0.494      -0.126\n",
      "Dest[T.Angel]                           2.1537      0.055     39.107      0.000       2.046       2.262\n",
      "Dest[T.Archway]                         1.3558      0.058     23.365      0.000       1.242       1.470\n",
      "Dest[T.Arnos Grove]                     0.8382      0.065     12.855      0.000       0.710       0.966\n",
      "Dest[T.Arsenal]                        -0.8615      0.078    -11.044      0.000      -1.014      -0.709\n",
      "Dest[T.Baker Street]                    2.7536      0.055     50.469      0.000       2.647       2.861\n",
      "Dest[T.Balham]                          2.0140      0.056     35.747      0.000       1.904       2.124\n",
      "Dest[T.Bank and Monument]               4.2429      0.054     78.522      0.000       4.137       4.349\n",
      "Dest[T.Barbican]                        2.2332      0.055     40.646      0.000       2.125       2.341\n",
      "Dest[T.Barking]                         2.5784      0.055     46.625      0.000       2.470       2.687\n",
      "Dest[T.Barkingside]                    -0.2032      0.082     -2.474      0.013      -0.364      -0.042\n",
      "Dest[T.Barons Court]                    1.4811      0.057     25.982      0.000       1.369       1.593\n",
      "Dest[T.Bayswater]                       0.0129      0.067      0.191      0.848      -0.119       0.145\n",
      "Dest[T.Beckton]                         0.9444      0.072     13.139      0.000       0.804       1.085\n",
      "Dest[T.Beckton Park]                   -0.8727      0.119     -7.306      0.000      -1.107      -0.639\n",
      "Dest[T.Becontree]                       0.3102      0.071      4.339      0.000       0.170       0.450\n",
      "Dest[T.Belsize Park]                    1.3375      0.058     23.095      0.000       1.224       1.451\n",
      "Dest[T.Bermondsey]                      1.3767      0.057     24.245      0.000       1.265       1.488\n",
      "Dest[T.Bethnal Green]                   1.5236      0.056     27.258      0.000       1.414       1.633\n",
      "Dest[T.Blackfriars]                     2.4340      0.055     44.426      0.000       2.327       2.541\n",
      "Dest[T.Blackhorse Road]                 1.6627      0.057     29.133      0.000       1.551       1.775\n",
      "Dest[T.Blackwall]                       0.5277      0.066      7.951      0.000       0.398       0.658\n",
      "Dest[T.Bond Street]                     3.0399      0.054     55.896      0.000       2.933       3.146\n",
      "Dest[T.Borough]                         1.2546      0.057     22.121      0.000       1.143       1.366\n",
      "Dest[T.Boston Manor]                    0.9862      0.064     15.518      0.000       0.862       1.111\n",
      "Dest[T.Bounds Green]                    0.7189      0.065     11.094      0.000       0.592       0.846\n",
      "Dest[T.Bow Church]                      1.0355      0.063     16.411      0.000       0.912       1.159\n",
      "Dest[T.Bow Road]                        0.4388      0.061      7.169      0.000       0.319       0.559\n",
      "Dest[T.Brent Cross]                     0.3350      0.072      4.674      0.000       0.195       0.475\n",
      "Dest[T.Brentwood]                       0.2893      0.066      4.358      0.000       0.159       0.419\n",
      "Dest[T.Brixton]                         2.1462      0.056     38.500      0.000       2.037       2.255\n",
      "Dest[T.Brockley]                        0.2414      0.071      3.386      0.001       0.102       0.381\n",
      "Dest[T.Bromley-by-Bow]                  0.7789      0.059     13.115      0.000       0.663       0.895\n",
      "Dest[T.Brondesbury]                     0.9759      0.066     14.833      0.000       0.847       1.105\n",
      "Dest[T.Brondesbury Park]                1.2472      0.064     19.615      0.000       1.123       1.372\n",
      "Dest[T.Bruce Grove]                     0.0988      0.076      1.296      0.195      -0.051       0.248\n",
      "Dest[T.Buckhurst Hill]                 -0.3877      0.086     -4.534      0.000      -0.555      -0.220\n",
      "Dest[T.Burnt Oak]                       1.1222      0.067     16.793      0.000       0.991       1.253\n",
      "Dest[T.Bush Hill Park]                 -0.2958      0.093     -3.176      0.001      -0.478      -0.113\n",
      "Dest[T.Bushey]                          1.4753      0.074     20.043      0.000       1.331       1.620\n",
      "Dest[T.Caledonian Road]                 0.7737      0.059     13.145      0.000       0.658       0.889\n",
      "Dest[T.Caledonian Road & Barnsbury]     1.4732      0.059     24.838      0.000       1.357       1.589\n",
      "Dest[T.Cambridge Heath]                 0.4700      0.072      6.572      0.000       0.330       0.610\n",
      "Dest[T.Camden Road]                     2.2519      0.056     39.910      0.000       2.141       2.362\n",
      "Dest[T.Camden Town]                     2.0106      0.055     36.302      0.000       1.902       2.119\n",
      "Dest[T.Canada Water]                    2.9231      0.054     53.721      0.000       2.816       3.030\n",
      "Dest[T.Canary Wharf]                    4.1485      0.054     76.756      0.000       4.043       4.254\n",
      "Dest[T.Canning Town]                    2.8563      0.054     52.427      0.000       2.749       2.963\n",
      "Dest[T.Cannon Street]                   1.5889      0.056     28.437      0.000       1.479       1.698\n",
      "Dest[T.Canonbury]                       0.6710      0.064     10.480      0.000       0.546       0.797\n",
      "Dest[T.Canons Park]                     0.7156      0.069     10.297      0.000       0.579       0.852\n",
      "Dest[T.Carpenders Park]                 1.3282      0.078     17.022      0.000       1.175       1.481\n",
      "Dest[T.Chadwell Heath]                 -0.5963      0.069     -8.647      0.000      -0.731      -0.461\n",
      "Dest[T.Chalfont & Latimer]              0.5774      0.071      8.134      0.000       0.438       0.717\n",
      "Dest[T.Chalk Farm]                      0.6695      0.061     11.063      0.000       0.551       0.788\n",
      "Dest[T.Chancery Lane]                   2.7360      0.055     50.167      0.000       2.629       2.843\n",
      "Dest[T.Charing Cross]                   1.9116      0.055     34.601      0.000       1.803       2.020\n",
      "Dest[T.Chesham]                         0.6880      0.086      8.029      0.000       0.520       0.856\n",
      "Dest[T.Cheshunt]                       -0.0713      0.109     -0.657      0.511      -0.284       0.141\n",
      "Dest[T.Chigwell]                       -0.6580      0.098     -6.686      0.000      -0.851      -0.465\n",
      "Dest[T.Chingford]                       0.4266      0.085      5.032      0.000       0.260       0.593\n",
      "Dest[T.Chiswick Park]                   1.0926      0.060     18.281      0.000       0.975       1.210\n",
      "Dest[T.Chorleywood]                     0.8702      0.067     12.906      0.000       0.738       1.002\n",
      "Dest[T.Clapham Common]                  1.1198      0.058     19.187      0.000       1.005       1.234\n",
      "Dest[T.Clapham High Street]             1.7127      0.061     28.073      0.000       1.593       1.832\n",
      "Dest[T.Clapham Junction]                3.3767      0.056     60.289      0.000       3.267       3.486\n",
      "Dest[T.Clapham North]                   0.5717      0.061      9.376      0.000       0.452       0.691\n",
      "Dest[T.Clapham South]                   0.9629      0.060     16.110      0.000       0.846       1.080\n",
      "Dest[T.Clapton]                         0.4134      0.073      5.696      0.000       0.271       0.556\n",
      "Dest[T.Cockfosters]                     0.4707      0.082      5.733      0.000       0.310       0.632\n",
      "Dest[T.Colindale]                       2.1821      0.058     37.419      0.000       2.068       2.296\n",
      "Dest[T.Colliers Wood]                   0.8288      0.064     12.989      0.000       0.704       0.954\n",
      "Dest[T.Covent Garden]                   1.4448      0.056     25.787      0.000       1.335       1.555\n",
      "Dest[T.Crossharbour]                    1.2452      0.061     20.384      0.000       1.125       1.365\n",
      "Dest[T.Crouch Hill]                     0.7854      0.074     10.668      0.000       0.641       0.930\n",
      "Dest[T.Croxley]                         0.2556      0.077      3.311      0.001       0.104       0.407\n",
      "Dest[T.Crystal Palace]                  1.1596      0.071     16.408      0.000       1.021       1.298\n",
      "Dest[T.Custom House]                    0.9025      0.064     14.121      0.000       0.777       1.028\n",
      "Dest[T.Cutty Sark]                      1.8028      0.059     30.558      0.000       1.687       1.918\n",
      "Dest[T.Cyprus]                          1.2956      0.064     20.283      0.000       1.170       1.421\n",
      "Dest[T.Dagenham East]                   0.8500      0.067     12.712      0.000       0.719       0.981\n",
      "Dest[T.Dagenham Heathway]               1.3179      0.062     21.305      0.000       1.197       1.439\n",
      "Dest[T.Dalston Junction]                1.4050      0.061     23.108      0.000       1.286       1.524\n",
      "Dest[T.Dalston Kingsland]               1.7274      0.058     29.654      0.000       1.613       1.842\n",
      "Dest[T.Debden]                          1.1824      0.064     18.459      0.000       1.057       1.308\n",
      "Dest[T.Denmark Hill]                    2.1856      0.058     37.920      0.000       2.073       2.299\n",
      "Dest[T.Deptford Bridge]                 1.1993      0.064     18.723      0.000       1.074       1.325\n",
      "Dest[T.Devons Road]                     0.5462      0.067      8.108      0.000       0.414       0.678\n",
      "Dest[T.Dollis Hill]                     0.5072      0.064      7.927      0.000       0.382       0.633\n",
      "Dest[T.Ealing Broadway]                 2.5097      0.056     44.924      0.000       2.400       2.619\n",
      "Dest[T.Ealing Common]                   0.6771      0.063     10.696      0.000       0.553       0.801\n",
      "Dest[T.Earl's Court]                    2.1183      0.055     38.281      0.000       2.010       2.227\n",
      "Dest[T.East Acton]                      1.1583      0.060     19.367      0.000       1.041       1.276\n",
      "Dest[T.East Finchley]                   1.1914      0.061     19.556      0.000       1.072       1.311\n",
      "Dest[T.East Ham]                        1.3885      0.058     23.834      0.000       1.274       1.503\n",
      "Dest[T.East India]                      1.3233      0.060     22.185      0.000       1.206       1.440\n",
      "Dest[T.East Putney]                     1.4547      0.059     24.783      0.000       1.340       1.570\n",
      "Dest[T.Eastcote]                       -0.0667      0.075     -0.885      0.376      -0.214       0.081\n",
      "Dest[T.Edgware]                         1.5379      0.065     23.674      0.000       1.411       1.665\n",
      "Dest[T.Edgware Road]                    2.0502      0.055     37.087      0.000       1.942       2.159\n",
      "Dest[T.Edmonton Green]                  0.8226      0.065     12.625      0.000       0.695       0.950\n",
      "Dest[T.Elephant & Castle]               1.9222      0.055     34.719      0.000       1.814       2.031\n",
      "Dest[T.Elm Park]                        0.2128      0.082      2.607      0.009       0.053       0.373\n",
      "Dest[T.Elverson Road]                  -0.0239      0.086     -0.279      0.780      -0.192       0.144\n",
      "Dest[T.Embankment]                      2.2758      0.055     41.498      0.000       2.168       2.383\n",
      "Dest[T.Emerson Park]                   -1.8880      0.164    -11.498      0.000      -2.210      -1.566\n",
      "Dest[T.Enfield Town]                    1.2912      0.066     19.642      0.000       1.162       1.420\n",
      "Dest[T.Epping]                          1.5505      0.071     21.971      0.000       1.412       1.689\n",
      "Dest[T.Euston]                          2.8360      0.054     52.044      0.000       2.729       2.943\n",
      "Dest[T.Euston Square]                   2.3100      0.055     41.942      0.000       2.202       2.418\n",
      "Dest[T.Fairlop]                        -0.5153      0.092     -5.613      0.000      -0.695      -0.335\n",
      "Dest[T.Farringdon]                      3.2764      0.054     60.341      0.000       3.170       3.383\n",
      "Dest[T.Finchley Central]                1.8644      0.059     31.800      0.000       1.750       1.979\n",
      "Dest[T.Finchley Road]                   1.6366      0.057     28.914      0.000       1.526       1.748\n",
      "Dest[T.Finchley Road & Frognal]         1.6057      0.060     26.851      0.000       1.489       1.723\n",
      "Dest[T.Finsbury Park]                   2.2087      0.055     39.942      0.000       2.100       2.317\n",
      "Dest[T.Forest Gate]                     0.2027      0.065      3.139      0.002       0.076       0.329\n",
      "Dest[T.Forest Hill]                     0.6122      0.068      9.010      0.000       0.479       0.745\n",
      "Dest[T.Fulham Broadway]                 1.8394      0.056     32.776      0.000       1.729       1.949\n",
      "Dest[T.Gallions Reach]                  1.0262      0.069     14.969      0.000       0.892       1.161\n",
      "Dest[T.Gants Hill]                      0.4667      0.068      6.897      0.000       0.334       0.599\n",
      "Dest[T.Gidea Park]                     -1.3059      0.080    -16.385      0.000      -1.462      -1.150\n",
      "Dest[T.Gloucester Road]                 1.8324      0.056     32.893      0.000       1.723       1.942\n",
      "Dest[T.Golders Green]                   1.5867      0.059     27.023      0.000       1.472       1.702\n",
      "Dest[T.Goldhawk Road]                  -0.3004      0.075     -4.009      0.000      -0.447      -0.153\n",
      "Dest[T.Goodge Street]                   1.9200      0.055     34.683      0.000       1.812       2.029\n",
      "Dest[T.Goodmayes]                      -0.4152      0.067     -6.237      0.000      -0.546      -0.285\n",
      "Dest[T.Gospel Oak]                      1.7375      0.058     29.730      0.000       1.623       1.852\n",
      "Dest[T.Grange Hill]                    -1.3587      0.127    -10.712      0.000      -1.607      -1.110\n",
      "Dest[T.Great Portland Street]           2.0637      0.055     37.342      0.000       1.955       2.172\n",
      "Dest[T.Green Park]                      3.2628      0.054     60.101      0.000       3.156       3.369\n",
      "Dest[T.Greenford]                       1.5993      0.062     25.970      0.000       1.479       1.720\n",
      "Dest[T.Greenwich]                       1.4543      0.061     23.746      0.000       1.334       1.574\n",
      "Dest[T.Gunnersbury]                     2.1953      0.056     39.282      0.000       2.086       2.305\n",
      "Dest[T.Hackney Central]                 1.9812      0.058     34.348      0.000       1.868       2.094\n",
      "Dest[T.Hackney Downs]                   0.9793      0.064     15.231      0.000       0.853       1.105\n",
      "Dest[T.Hackney Wick]                    1.1516      0.061     18.918      0.000       1.032       1.271\n",
      "Dest[T.Haggerston]                      1.1669      0.061     19.016      0.000       1.047       1.287\n",
      "Dest[T.Hainault]                        0.2818      0.076      3.721      0.000       0.133       0.430\n",
      "Dest[T.Hammersmith]                     3.3327      0.054     61.191      0.000       3.226       3.439\n",
      "Dest[T.Hampstead]                       1.3772      0.058     23.589      0.000       1.263       1.492\n",
      "Dest[T.Hampstead Heath]                 2.0819      0.057     36.352      0.000       1.970       2.194\n",
      "Dest[T.Hanger Lane]                     1.6257      0.060     27.144      0.000       1.508       1.743\n",
      "Dest[T.Harlesden]                       1.2340      0.059     20.815      0.000       1.118       1.350\n",
      "Dest[T.Harold Wood]                    -0.6021      0.070     -8.593      0.000      -0.739      -0.465\n",
      "Dest[T.Harringay Green Lanes]           0.9664      0.069     13.969      0.000       0.831       1.102\n",
      "Dest[T.Harrow & Wealdstone]             1.8770      0.061     30.835      0.000       1.758       1.996\n",
      "Dest[T.Harrow-on-the-Hill]              1.8298      0.057     32.068      0.000       1.718       1.942\n",
      "Dest[T.Hatch End]                      -0.1403      0.118     -1.192      0.233      -0.371       0.090\n",
      "Dest[T.Hatton Cross]                    1.9248      0.061     31.328      0.000       1.804       2.045\n",
      "Dest[T.Headstone Lane]                  1.1188      0.079     14.130      0.000       0.964       1.274\n",
      "Dest[T.Heathrow Terminal 4]             1.3971      0.067     21.009      0.000       1.267       1.527\n",
      "Dest[T.Heathrow Terminal 5]             2.2177      0.063     35.023      0.000       2.094       2.342\n",
      "Dest[T.Heathrow Terminals 2 & 3]        2.8434      0.058     48.865      0.000       2.729       2.957\n",
      "Dest[T.Hendon Central]                  1.8420      0.059     31.367      0.000       1.727       1.957\n",
      "Dest[T.Heron Quays]                     2.7999      0.055     50.531      0.000       2.691       2.909\n",
      "Dest[T.High Barnet]                     1.9182      0.063     30.427      0.000       1.795       2.042\n",
      "Dest[T.High Street Kensington]          1.9238      0.056     34.580      0.000       1.815       2.033\n",
      "Dest[T.Highams Park]                    0.4160      0.074      5.598      0.000       0.270       0.562\n",
      "Dest[T.Highbury & Islington]            3.1044      0.054     57.160      0.000       2.998       3.211\n",
      "Dest[T.Highgate]                        0.6211      0.064      9.723      0.000       0.496       0.746\n",
      "Dest[T.Hillingdon]                      0.1210      0.078      1.548      0.122      -0.032       0.274\n",
      "Dest[T.Holborn]                         3.0679      0.054     56.444      0.000       2.961       3.174\n",
      "Dest[T.Holland Park]                    1.1049      0.058     18.961      0.000       0.991       1.219\n",
      "Dest[T.Holloway Road]                   0.7397      0.059     12.504      0.000       0.624       0.856\n",
      "Dest[T.Homerton]                        1.6329      0.058     27.943      0.000       1.518       1.747\n",
      "Dest[T.Honor Oak Park]                  0.0029      0.077      0.038      0.970      -0.148       0.153\n",
      "Dest[T.Hornchurch]                      0.8451      0.072     11.746      0.000       0.704       0.986\n",
      "Dest[T.Hounslow Central]                1.0556      0.066     16.020      0.000       0.926       1.185\n",
      "Dest[T.Hounslow East]                   1.1704      0.064     18.250      0.000       1.045       1.296\n",
      "Dest[T.Hounslow West]                   0.6433      0.074      8.730      0.000       0.499       0.788\n",
      "Dest[T.Hoxton]                          1.7302      0.058     29.765      0.000       1.616       1.844\n",
      "Dest[T.Hyde Park Corner]                0.9510      0.058     16.492      0.000       0.838       1.064\n",
      "Dest[T.Ickenham]                       -0.0712      0.081     -0.883      0.377      -0.229       0.087\n",
      "Dest[T.Ilford]                          0.7403      0.060     12.408      0.000       0.623       0.857\n",
      "Dest[T.Imperial Wharf]                  2.0448      0.059     34.924      0.000       1.930       2.160\n",
      "Dest[T.Island Gardens]                  0.8008      0.066     12.137      0.000       0.671       0.930\n",
      "Dest[T.Kennington]                      0.2659      0.061      4.330      0.000       0.146       0.386\n",
      "Dest[T.Kensal Green]                   -0.0294      0.071     -0.414      0.679      -0.168       0.110\n",
      "Dest[T.Kensal Rise]                     1.5658      0.060     25.920      0.000       1.447       1.684\n",
      "Dest[T.Kensington]                      1.3629      0.058     23.519      0.000       1.249       1.477\n",
      "Dest[T.Kentish Town]                    1.5662      0.057     27.668      0.000       1.455       1.677\n",
      "Dest[T.Kentish Town West]               1.1360      0.062     18.410      0.000       1.015       1.257\n",
      "Dest[T.Kenton]                          1.3492      0.065     20.701      0.000       1.221       1.477\n",
      "Dest[T.Kew Gardens]                     0.6127      0.065      9.479      0.000       0.486       0.739\n",
      "Dest[T.Kilburn]                         1.2113      0.059     20.701      0.000       1.097       1.326\n",
      "Dest[T.Kilburn High Road]               0.8731      0.082     10.666      0.000       0.713       1.034\n",
      "Dest[T.Kilburn Park]                    0.5212      0.064      8.113      0.000       0.395       0.647\n",
      "Dest[T.King George V]                   1.1106      0.064     17.225      0.000       0.984       1.237\n",
      "Dest[T.King's Cross St. Pancras]        3.5070      0.054     64.683      0.000       3.401       3.613\n",
      "Dest[T.Kingsbury]                       1.0539      0.062     16.870      0.000       0.931       1.176\n",
      "Dest[T.Knightsbridge]                   2.0280      0.055     36.681      0.000       1.920       2.136\n",
      "Dest[T.Ladbroke Grove]                  1.2326      0.058     21.200      0.000       1.119       1.347\n",
      "Dest[T.Lambeth North]                   0.3243      0.061      5.355      0.000       0.206       0.443\n",
      "Dest[T.Lancaster Gate]                  0.8819      0.059     14.994      0.000       0.767       0.997\n",
      "Dest[T.Langdon Park]                    1.6870      0.058     28.916      0.000       1.573       1.801\n",
      "Dest[T.Latimer Road]                    0.6813      0.062     11.033      0.000       0.560       0.802\n",
      "Dest[T.Leicester Square]                2.1355      0.055     38.841      0.000       2.028       2.243\n",
      "Dest[T.Lewisham]                        2.6194      0.058     45.398      0.000       2.506       2.733\n",
      "Dest[T.Leyton]                          0.8251      0.060     13.754      0.000       0.708       0.943\n",
      "Dest[T.Leyton Midland Road]             0.7225      0.072      9.992      0.000       0.581       0.864\n",
      "Dest[T.Leytonstone]                     1.1728      0.059     19.962      0.000       1.058       1.288\n",
      "Dest[T.Leytonstone High Road]           0.3822      0.079      4.865      0.000       0.228       0.536\n",
      "Dest[T.Limehouse]                       2.1722      0.057     38.143      0.000       2.061       2.284\n",
      "Dest[T.Liverpool Street]                3.8977      0.054     72.052      0.000       3.792       4.004\n",
      "Dest[T.London Bridge]                   3.4352      0.054     63.325      0.000       3.329       3.541\n",
      "Dest[T.London City Airport]             1.8992      0.058     32.479      0.000       1.785       2.014\n",
      "Dest[T.London Fields]                   0.8186      0.065     12.646      0.000       0.692       0.945\n",
      "Dest[T.Loughton]                        0.8059      0.067     12.069      0.000       0.675       0.937\n",
      "Dest[T.Maida Vale]                      0.4666      0.063      7.410      0.000       0.343       0.590\n",
      "Dest[T.Manor House]                     0.6659      0.061     10.988      0.000       0.547       0.785\n",
      "Dest[T.Manor Park]                     -0.5832      0.072     -8.055      0.000      -0.725      -0.441\n",
      "Dest[T.Mansion House]                   2.1433      0.055     38.892      0.000       2.035       2.251\n",
      "Dest[T.Marble Arch]                     1.8969      0.055     34.220      0.000       1.788       2.006\n",
      "Dest[T.Maryland]                       -0.5782      0.076     -7.596      0.000      -0.727      -0.429\n",
      "Dest[T.Marylebone]                      1.5549      0.056     27.724      0.000       1.445       1.665\n",
      "Dest[T.Mile End]                        1.5059      0.056     26.730      0.000       1.395       1.616\n",
      "Dest[T.Mill Hill East]                  1.0588      0.066     15.986      0.000       0.929       1.189\n",
      "Dest[T.Moor Park]                       0.4434      0.069      6.392      0.000       0.307       0.579\n",
      "Dest[T.Moorgate]                        3.1893      0.054     58.723      0.000       3.083       3.296\n",
      "Dest[T.Morden]                          1.7532      0.060     29.191      0.000       1.636       1.871\n",
      "Dest[T.Mornington Crescent]             1.2210      0.057     21.412      0.000       1.109       1.333\n",
      "Dest[T.Mudchute]                       -0.0661      0.079     -0.839      0.402      -0.221       0.088\n",
      "Dest[T.Neasden]                         0.4115      0.065      6.290      0.000       0.283       0.540\n",
      "Dest[T.New Cross]                       1.5734      0.063     25.171      0.000       1.451       1.696\n",
      "Dest[T.New Cross Gate]                  1.2581      0.061     20.719      0.000       1.139       1.377\n",
      "Dest[T.Newbury Park]                    0.5719      0.069      8.333      0.000       0.437       0.706\n",
      "Dest[T.North Acton]                     1.9726      0.057     34.712      0.000       1.861       2.084\n",
      "Dest[T.North Ealing]                    0.1130      0.077      1.468      0.142      -0.038       0.264\n",
      "Dest[T.North Greenwich]                 2.3487      0.055     42.409      0.000       2.240       2.457\n",
      "Dest[T.North Harrow]                   -0.7640      0.091     -8.438      0.000      -0.941      -0.587\n",
      "Dest[T.North Wembley]                   0.3235      0.075      4.298      0.000       0.176       0.471\n",
      "Dest[T.Northfields]                     0.8871      0.064     13.898      0.000       0.762       1.012\n",
      "Dest[T.Northolt]                        1.2486      0.067     18.727      0.000       1.118       1.379\n",
      "Dest[T.Northwick Park]                  1.2467      0.059     21.054      0.000       1.131       1.363\n",
      "Dest[T.Northwood]                       1.0859      0.063     17.288      0.000       0.963       1.209\n",
      "Dest[T.Northwood Hills]                 0.2791      0.071      3.946      0.000       0.140       0.418\n",
      "Dest[T.Norwood Junction]                0.5935      0.074      7.996      0.000       0.448       0.739\n",
      "Dest[T.Notting Hill Gate]               1.9279      0.056     34.666      0.000       1.819       2.037\n",
      "Dest[T.Oakwood]                         0.7605      0.073     10.460      0.000       0.618       0.903\n",
      "Dest[T.Old Street]                      2.8275      0.055     51.863      0.000       2.721       2.934\n",
      "Dest[T.Osterley]                        0.6492      0.070      9.328      0.000       0.513       0.786\n",
      "Dest[T.Oval]                            1.1321      0.057     19.698      0.000       1.019       1.245\n",
      "Dest[T.Oxford Circus]                   3.7461      0.054     69.178      0.000       3.640       3.852\n",
      "Dest[T.Paddington]                      3.2195      0.054     59.176      0.000       3.113       3.326\n",
      "Dest[T.Park Royal]                      1.4290      0.060     23.947      0.000       1.312       1.546\n",
      "Dest[T.Parsons Green]                   1.5146      0.057     26.445      0.000       1.402       1.627\n",
      "Dest[T.Peckham Rye]                     1.2727      0.062     20.451      0.000       1.151       1.395\n",
      "Dest[T.Penge West]                     -0.7286      0.098     -7.410      0.000      -0.921      -0.536\n",
      "Dest[T.Perivale]                        0.7154      0.069     10.324      0.000       0.580       0.851\n",
      "Dest[T.Piccadilly Circus]               2.5710      0.055     47.072      0.000       2.464       2.678\n",
      "Dest[T.Pimlico]                         1.8786      0.056     33.799      0.000       1.770       1.988\n",
      "Dest[T.Pinner]                         -0.2504      0.080     -3.140      0.002      -0.407      -0.094\n",
      "Dest[T.Plaistow]                        0.4551      0.062      7.324      0.000       0.333       0.577\n",
      "Dest[T.Pontoon Dock]                    1.2381      0.062     20.105      0.000       1.117       1.359\n",
      "Dest[T.Poplar]                          1.1729      0.061     19.361      0.000       1.054       1.292\n",
      "Dest[T.Preston Road]                   -0.1525      0.073     -2.084      0.037      -0.296      -0.009\n",
      "Dest[T.Prince Regent]                   0.8830      0.065     13.581      0.000       0.756       1.010\n",
      "Dest[T.Pudding Mill Lane]               0.2384      0.072      3.299      0.001       0.097       0.380\n",
      "Dest[T.Putney Bridge]                   1.5669      0.058     27.222      0.000       1.454       1.680\n",
      "Dest[T.Queen's Park]                    1.2231      0.058     21.057      0.000       1.109       1.337\n",
      "Dest[T.Queens Road Peckham]             0.9279      0.065     14.191      0.000       0.800       1.056\n",
      "Dest[T.Queensbury]                      0.3505      0.072      4.860      0.000       0.209       0.492\n",
      "Dest[T.Queensway]                       0.9836      0.059     16.766      0.000       0.869       1.099\n",
      "Dest[T.Ravenscourt Park]                1.1579      0.059     19.743      0.000       1.043       1.273\n",
      "Dest[T.Rayners Lane]                   -0.0686      0.073     -0.945      0.345      -0.211       0.074\n",
      "Dest[T.Rectory Road]                   -0.3567      0.087     -4.120      0.000      -0.526      -0.187\n",
      "Dest[T.Redbridge]                      -0.7817      0.089     -8.760      0.000      -0.957      -0.607\n",
      "Dest[T.Regent's Park]                   1.3463      0.057     23.772      0.000       1.235       1.457\n",
      "Dest[T.Richmond]                        2.8653      0.056     51.453      0.000       2.756       2.974\n",
      "Dest[T.Rickmansworth]                   1.1381      0.064     17.777      0.000       1.013       1.264\n",
      "Dest[T.Roding Valley]                  -1.2550      0.122    -10.307      0.000      -1.494      -1.016\n",
      "Dest[T.Romford]                         0.6716      0.059     11.411      0.000       0.556       0.787\n",
      "Dest[T.Rotherhithe]                    -0.2106      0.078     -2.708      0.007      -0.363      -0.058\n",
      "Dest[T.Royal Albert]                    0.9259      0.066     14.016      0.000       0.796       1.055\n",
      "Dest[T.Royal Oak]                       0.2374      0.064      3.717      0.000       0.112       0.363\n",
      "Dest[T.Royal Victoria]                  0.7562      0.065     11.653      0.000       0.629       0.883\n",
      "Dest[T.Ruislip]                        -0.3056      0.083     -3.698      0.000      -0.468      -0.144\n",
      "Dest[T.Ruislip Gardens]                 0.1205      0.095      1.273      0.203      -0.065       0.306\n",
      "Dest[T.Ruislip Manor]                   0.1049      0.073      1.429      0.153      -0.039       0.249\n",
      "Dest[T.Russell Square]                  1.6375      0.056     29.395      0.000       1.528       1.747\n",
      "Dest[T.Seven Kings]                    -0.5643      0.069     -8.186      0.000      -0.699      -0.429\n",
      "Dest[T.Seven Sisters]                   2.5646      0.055     46.717      0.000       2.457       2.672\n",
      "Dest[T.Shadwell]                        2.3779      0.055     43.100      0.000       2.270       2.486\n",
      "Dest[T.Shenfield]                       0.3658      0.065      5.644      0.000       0.239       0.493\n",
      "Dest[T.Shepherd's Bush]                 2.4935      0.055     45.427      0.000       2.386       2.601\n",
      "Dest[T.Shepherd's Bush Market]         -0.2254      0.073     -3.091      0.002      -0.368      -0.082\n",
      "Dest[T.Shoreditch High Street]          2.9204      0.055     52.856      0.000       2.812       3.029\n",
      "Dest[T.Silver Street]                   1.1012      0.063     17.374      0.000       0.977       1.225\n",
      "Dest[T.Sloane Square]                   2.2205      0.055     40.328      0.000       2.113       2.328\n",
      "Dest[T.Snaresbrook]                     0.0417      0.070      0.598      0.550      -0.095       0.178\n",
      "Dest[T.South Acton]                     1.8445      0.063     29.311      0.000       1.721       1.968\n",
      "Dest[T.South Ealing]                    0.5721      0.066      8.617      0.000       0.442       0.702\n",
      "Dest[T.South Hampstead]                 0.8952      0.085     10.565      0.000       0.729       1.061\n",
      "Dest[T.South Harrow]                    0.1713      0.074      2.307      0.021       0.026       0.317\n",
      "Dest[T.South Kensington]                2.8797      0.055     52.791      0.000       2.773       2.987\n",
      "Dest[T.South Kenton]                    0.1971      0.082      2.396      0.017       0.036       0.358\n",
      "Dest[T.South Quay]                      2.5275      0.056     45.245      0.000       2.418       2.637\n",
      "Dest[T.South Ruislip]                   0.5782      0.080      7.215      0.000       0.421       0.735\n",
      "Dest[T.South Tottenham]                 1.2668      0.069     18.314      0.000       1.131       1.402\n",
      "Dest[T.South Wimbledon]                 1.4068      0.060     23.282      0.000       1.288       1.525\n",
      "Dest[T.South Woodford]                  0.5228      0.065      8.049      0.000       0.395       0.650\n",
      "Dest[T.Southbury]                       1.0387      0.070     14.871      0.000       0.902       1.176\n",
      "Dest[T.Southfields]                     1.3276      0.060     21.963      0.000       1.209       1.446\n",
      "Dest[T.Southgate]                       1.2354      0.064     19.385      0.000       1.110       1.360\n",
      "Dest[T.Southwark]                       2.3374      0.055     42.630      0.000       2.230       2.445\n",
      "Dest[T.St James Street]                -0.5143      0.091     -5.622      0.000      -0.694      -0.335\n",
      "Dest[T.St. James's Park]                2.6150      0.055     47.865      0.000       2.508       2.722\n",
      "Dest[T.St. John's Wood]                 1.6816      0.056     29.907      0.000       1.571       1.792\n",
      "Dest[T.St. Paul's]                      2.6118      0.055     47.815      0.000       2.505       2.719\n",
      "Dest[T.Stamford Brook]                  0.3837      0.065      5.929      0.000       0.257       0.511\n",
      "Dest[T.Stamford Hill]                   0.1984      0.076      2.609      0.009       0.049       0.347\n",
      "Dest[T.Stanmore]                        1.5825      0.063     25.195      0.000       1.459       1.706\n",
      "Dest[T.Star Lane]                       1.0261      0.062     16.536      0.000       0.904       1.148\n",
      "Dest[T.Stepney Green]                   0.7830      0.059     13.349      0.000       0.668       0.898\n",
      "Dest[T.Stockwell]                       0.7328      0.059     12.340      0.000       0.616       0.849\n",
      "Dest[T.Stoke Newington]                 0.3097      0.071      4.372      0.000       0.171       0.449\n",
      "Dest[T.Stonebridge Park]                0.5830      0.065      8.902      0.000       0.455       0.711\n",
      "Dest[T.Stratford]                       3.6360      0.054     67.186      0.000       3.530       3.742\n",
      "Dest[T.Stratford High Street]           0.9198      0.065     14.246      0.000       0.793       1.046\n",
      "Dest[T.Stratford International]         1.6389      0.060     27.518      0.000       1.522       1.756\n",
      "Dest[T.Sudbury Hill]                   -0.1956      0.081     -2.420      0.016      -0.354      -0.037\n",
      "Dest[T.Sudbury Town]                   -0.2893      0.087     -3.338      0.001      -0.459      -0.119\n",
      "Dest[T.Surrey Quays]                    0.8376      0.063     13.367      0.000       0.715       0.960\n",
      "Dest[T.Swiss Cottage]                   1.3552      0.057     23.605      0.000       1.243       1.468\n",
      "Dest[T.Sydenham]                        0.4568      0.070      6.508      0.000       0.319       0.594\n",
      "Dest[T.Temple]                          1.9429      0.055     35.141      0.000       1.835       2.051\n",
      "Dest[T.Theobalds Grove]                 0.2637      0.093      2.845      0.004       0.082       0.445\n",
      "Dest[T.Theydon Bois]                   -0.8585      0.115     -7.469      0.000      -1.084      -0.633\n",
      "Dest[T.Tooting Bec]                     0.9531      0.061     15.628      0.000       0.834       1.073\n",
      "Dest[T.Tooting Broadway]                2.3663      0.056     42.260      0.000       2.257       2.476\n",
      "Dest[T.Tottenham Court Road]            2.9102      0.054     53.472      0.000       2.803       3.017\n",
      "Dest[T.Tottenham Hale]                  1.8436      0.057     32.488      0.000       1.732       1.955\n",
      "Dest[T.Totteridge & Whetstone]          0.2980      0.080      3.722      0.000       0.141       0.455\n",
      "Dest[T.Tower Gateway]                   2.5489      0.057     45.048      0.000       2.438       2.660\n",
      "Dest[T.Tower Hill]                      2.1673      0.055     39.375      0.000       2.059       2.275\n",
      "Dest[T.Tufnell Park]                   -0.1063      0.069     -1.549      0.121      -0.241       0.028\n",
      "Dest[T.Turkey Street]                   1.0356      0.072     14.301      0.000       0.894       1.178\n",
      "Dest[T.Turnham Green]                   0.9811      0.060     16.415      0.000       0.864       1.098\n",
      "Dest[T.Turnpike Lane]                   0.6714      0.063     10.724      0.000       0.549       0.794\n",
      "Dest[T.Upminster]                       1.0273      0.063     16.291      0.000       0.904       1.151\n",
      "Dest[T.Upminster Bridge]                1.1568      0.069     16.813      0.000       1.022       1.292\n",
      "Dest[T.Upney]                           0.2362      0.071      3.348      0.001       0.098       0.374\n",
      "Dest[T.Upper Holloway]                  1.2636      0.064     19.870      0.000       1.139       1.388\n",
      "Dest[T.Upton Park]                      1.0213      0.059     17.222      0.000       0.905       1.138\n",
      "Dest[T.Uxbridge]                        3.2380      0.056     57.436      0.000       3.128       3.348\n",
      "Dest[T.Vauxhall]                        3.0447      0.055     55.849      0.000       2.938       3.152\n",
      "Dest[T.Victoria]                        3.5676      0.054     65.795      0.000       3.461       3.674\n",
      "Dest[T.Walthamstow Central]             2.2599      0.056     40.534      0.000       2.151       2.369\n",
      "Dest[T.Walthamstow Queens Road]         2.2529      0.062     36.544      0.000       2.132       2.374\n",
      "Dest[T.Wandsworth Road]                 0.7311      0.070     10.376      0.000       0.593       0.869\n",
      "Dest[T.Wanstead]                       -0.1248      0.073     -1.715      0.086      -0.267       0.018\n",
      "Dest[T.Wanstead Park]                   0.8472      0.073     11.538      0.000       0.703       0.991\n",
      "Dest[T.Wapping]                         0.9908      0.062     15.929      0.000       0.869       1.113\n",
      "Dest[T.Warren Street]                   2.8394      0.054     52.123      0.000       2.733       2.946\n",
      "Dest[T.Warwick Avenue]                  0.5632      0.061      9.181      0.000       0.443       0.683\n",
      "Dest[T.Waterloo]                        3.2029      0.054     58.947      0.000       3.096       3.309\n",
      "Dest[T.Watford]                         1.6647      0.064     26.167      0.000       1.540       1.789\n",
      "Dest[T.Watford High Street]             2.1939      0.067     32.568      0.000       2.062       2.326\n",
      "Dest[T.Watford Junction]                3.0124      0.063     47.849      0.000       2.889       3.136\n",
      "Dest[T.Wembley Central]                 1.3158      0.061     21.713      0.000       1.197       1.435\n",
      "Dest[T.Wembley Park]                    2.4788      0.056     44.588      0.000       2.370       2.588\n",
      "Dest[T.West Acton]                      0.4021      0.070      5.707      0.000       0.264       0.540\n",
      "Dest[T.West Brompton]                   1.8432      0.056     33.198      0.000       1.734       1.952\n",
      "Dest[T.West Croydon]                    2.7095      0.059     45.829      0.000       2.594       2.825\n",
      "Dest[T.West Finchley]                  -1.0590      0.118     -8.979      0.000      -1.290      -0.828\n",
      "Dest[T.West Ham]                        1.7716      0.056     31.892      0.000       1.663       1.881\n",
      "Dest[T.West Hampstead]                  1.9471      0.056     35.067      0.000       1.838       2.056\n",
      "Dest[T.West Harrow]                    -1.2927      0.105    -12.257      0.000      -1.499      -1.086\n",
      "Dest[T.West India Quay]                 0.0098      0.073      0.133      0.894      -0.134       0.154\n",
      "Dest[T.West Kensington]                 0.6595      0.060     10.909      0.000       0.541       0.778\n",
      "Dest[T.West Ruislip]                    0.6237      0.090      6.918      0.000       0.447       0.800\n",
      "Dest[T.West Silvertown]                 0.9658      0.063     15.231      0.000       0.841       1.090\n",
      "Dest[T.Westbourne Park]                 0.7381      0.060     12.211      0.000       0.620       0.857\n",
      "Dest[T.Westferry]                       1.1740      0.061     19.296      0.000       1.055       1.293\n",
      "Dest[T.Westminster]                     2.7250      0.055     49.966      0.000       2.618       2.832\n",
      "Dest[T.White City]                      2.3848      0.055     42.975      0.000       2.276       2.494\n",
      "Dest[T.White Hart Lane]                 0.5046      0.067      7.516      0.000       0.373       0.636\n",
      "Dest[T.Whitechapel]                     2.6807      0.054     49.218      0.000       2.574       2.787\n",
      "Dest[T.Willesden Green]                 0.4086      0.064      6.367      0.000       0.283       0.534\n",
      "Dest[T.Willesden Junction]              1.8420      0.056     32.799      0.000       1.732       1.952\n",
      "Dest[T.Wimbledon]                       3.3415      0.055     60.261      0.000       3.233       3.450\n",
      "Dest[T.Wimbledon Park]                  0.7715      0.068     11.382      0.000       0.639       0.904\n",
      "Dest[T.Wood Green]                      1.5359      0.058     26.426      0.000       1.422       1.650\n",
      "Dest[T.Wood Lane]                       1.1181      0.060     18.778      0.000       1.001       1.235\n",
      "Dest[T.Wood Street]                     0.2131      0.074      2.895      0.004       0.069       0.357\n",
      "Dest[T.Woodford]                        0.5565      0.066      8.453      0.000       0.427       0.686\n",
      "Dest[T.Woodgrange Park]                 0.4017      0.084      4.759      0.000       0.236       0.567\n",
      "Dest[T.Woodside Park]                   1.1069      0.065     16.951      0.000       0.979       1.235\n",
      "Dest[T.Woolwich Arsenal]                3.4932      0.056     62.428      0.000       3.384       3.603\n",
      "Dist                                   -0.0002   1.85e-07   -835.998      0.000      -0.000      -0.000\n",
      "=======================================================================================================\n"
     ]
    }
   ],
   "source": [
    "# Run a doubly constrained SIM with a negative exponential cost function.\n",
    "doubsim_form = \"Total ~ Orig + Dest + Dist -1\"\n",
    "doubsim_exp = smf.glm(formula=doubsim_form, data = london_flows, family = sm.families.Poisson()).fit()\n",
    "print(doubsim_exp.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [],
   "source": [
    "london_flows[\"doubsimfitted1\"] = np.round(doubsim_exp.mu,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "93.399"
      ]
     },
     "execution_count": 264,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRMSE(london_flows['Total'],london_flows['doubsimfitted1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4978623570468335"
      ]
     },
     "execution_count": 265,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRSqaured(london_flows['Total'],london_flows['doubsimfitted1'])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## From Poisson Regression back to Entropy\n",
    "\n",
    "As with the earlier models, I have shown you how you can plug the parameter estimates back into Wilson’s entropy maximising multiplicative models in order to generate estimates and tweak things still further.\n",
    "\n",
    "If you remember from Equations 11 and 12 above, the key to the doubly constrained models is the $A_i$ and $B_j$ balancing factors and as they rely on each other, they need to be calculated iteratively. We can do this using [Senior’s algorthim](http://journals.sagepub.com/doi/abs/10.1177/030913257900300218) also mentioned earlier.\n",
    "\n",
    "Here is the code as provided by [Dan Lewis](https://github.com/danlewis85/UCL_CASA_Urban_Simulation/blob/master/Constrained%20SIM.ipynb) who in a departure from Dennet rewrites the algorithm as a function, which can then be called subject to the required parameters. In order for it to work it requires:\n",
    "\n",
    "- pd - a pandas dataframe of origin-destination pairwise flows and associated data.\n",
    "- orig_field - the name of the dataframe field in pd that uniquely labels origin zones.\n",
    "- dest_field - the name of the dataframe field in pd that uniquely labels destination zones.\n",
    "- Oi_field - the name of the dataframe field that stores total flows from a given origin $i$\n",
    "- Dj_field - the name of the dataframe field that stores total flows to a given destination $j$\n",
    "- cij_field - the name of the dataframe field that stores the pairwise cost (e.g. distance) between $i$ and $j$\n",
    "- beta - a constant for the beta parameter you wish to use in the model\n",
    "- cost_function - a string representing the cost function, either 'power' or 'exponential'\n",
    "- Ainame - What you want to call the new field in pd that will hold $A_{i}$ values, defaults to \"Ai_new\"\n",
    "- Bjname - What you want to call the new field in pd that will hold $B_{j}$ values, defaults to \"Bj_new\"\n",
    "- converge - A threshold value at which a model can be said to have converged, the default of 0.001 seems to work fine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create some Oi and Dj columns in the dataframe and store row and column totals in them:\n",
    "#to create O_i, take london_flows ...then... group by origcodenew ...then... summarise by calculating the sum of Total\n",
    "O_i = pd.DataFrame(london_flows.groupby([\"Orig\"])[\"Total\"].agg(np.sum))\n",
    "O_i.rename(columns={\"Total\":\"O_i\"}, inplace = True)\n",
    "london_flows = london_flows.merge(O_i, on = \"Orig\", how = \"left\" )\n",
    "\n",
    "D_j = pd.DataFrame(london_flows.groupby([\"Dest\"])[\"Total\"].agg(np.sum))\n",
    "D_j.rename(columns={\"Total\":\"D_j\"}, inplace = True)\n",
    "london_flows = london_flows.merge(D_j, on = \"Dest\", how = \"left\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Here is the entropy maximising approach for a known beta.\n",
    "# Plug in the required values in this function to solve.\n",
    "\n",
    "def balance_doubly_constrained(pd, orig_field, dest_field, Oi_field, Dj_field, cij_field, beta, \n",
    "                               cost_function, Ai_name = \"Ai_new\", Bj_name = \"Bj_new\", converge=0.001):\n",
    "    # Define some variables\n",
    "    Oi = pd[[orig_field, Oi_field]]\n",
    "    Dj = pd[[dest_field,Dj_field]]    \n",
    "    if cost_function.lower() in ['power','pow']:\n",
    "        beta_cij = np.exp(beta * np.log(pd[cij_field]))\n",
    "    elif cost_function.lower() in ['exponential','exp']:\n",
    "        beta_cij = np.exp(beta * pd[cij_field])\n",
    "    else:\n",
    "        return \"Cost function not specified properly, use 'exp' or 'pow'\"\n",
    "    \n",
    "    # Create some helper variables\n",
    "    cnvg = 1\n",
    "    iteration = 0\n",
    "    # Now iteratively rebalance the Ai and Bj terms until convergence\n",
    "    while cnvg > converge:\n",
    "        if iteration == 0:\n",
    "            # This first condition sets starting values for Ai and Bj\n",
    "            # NB sets starting value of Ai assuming Bj is a vector of 1s.\n",
    "            # We've already established beta_cij with the appropriate cost function, so...\n",
    "            Oi = Oi.assign(Ai = Dj[Dj_field] * beta_cij)\n",
    "            # Aggregate Ai and take inverse\n",
    "            Ai = 1.0/Oi.groupby(orig_field)['Ai'].sum().to_frame()\n",
    "            # Merge new Ais \n",
    "            Oi = Oi.merge(Ai,left_on = orig_field, right_index = True, suffixes = ('','_old'))\n",
    "            # Drop the temporary Ai field we created, leaving Ai_old\n",
    "            Oi.drop('Ai', axis=1, inplace=True)\n",
    "            \n",
    "            # Now set up Bjs using starting values of Ai\n",
    "            Dj = Dj.assign(Bj = Oi['Ai_old'] * Oi[Oi_field] * beta_cij)\n",
    "            # Aggregate Bj and take inverse\n",
    "            Bj = 1.0/Dj.groupby(dest_field)['Bj'].sum().to_frame()\n",
    "            # Merge new Bjs\n",
    "            Dj = Dj.merge(Bj,left_on = dest_field, right_index = True, suffixes = ('','_old'))\n",
    "            # Drop the temporary Bj field we created, leaving Bj_old\n",
    "            Dj.drop('Bj', axis=1, inplace=True)\n",
    "            \n",
    "            # Increment loop\n",
    "            iteration += 1\n",
    "        else:\n",
    "            # This bit is the iterated bit of the loop which refines the values of Ai and Bj\n",
    "            # First Ai\n",
    "            Oi['Ai'] = Dj['Bj_old'] * Dj[Dj_field] * beta_cij\n",
    "            # Aggregate Ai and take inverse\n",
    "            Ai = 1.0/Oi.groupby(orig_field)['Ai'].sum().to_frame()\n",
    "            # Drop temporary Ai\n",
    "            Oi.drop('Ai', axis=1, inplace=True)\n",
    "            # Merge new Ais \n",
    "            Oi = Oi.merge(Ai,left_on = orig_field, right_index = True)\n",
    "            # Calculate the difference between old and new Ais\n",
    "            Oi['diff'] = np.absolute((Oi['Ai_old'] - Oi['Ai'])/Oi['Ai_old'])\n",
    "            # Set new Ais to Ai_old\n",
    "            Oi['Ai_old'] = Oi['Ai']\n",
    "            # Drop the temporary Ai field we created, leaving Ai_old\n",
    "            Oi.drop('Ai', axis=1, inplace=True)\n",
    "            \n",
    "            # Then Bj\n",
    "            Dj['Bj'] = Oi['Ai_old'] * Oi[Oi_field] * beta_cij\n",
    "            # Aggregate Bj and take inverse\n",
    "            Bj = 1.0/Dj.groupby(dest_field)['Bj'].sum().to_frame()\n",
    "            # Drop temporary Bj\n",
    "            Dj.drop('Bj', axis=1, inplace=True)\n",
    "            # Merge new Bjs\n",
    "            Dj = Dj.merge(Bj,left_on = dest_field, right_index = True)\n",
    "            # Calculate the difference between old and new Bjs\n",
    "            Dj['diff'] = np.absolute((Dj['Bj_old'] - Dj['Bj'])/Dj['Bj_old'])\n",
    "            # Set new Bjs to Bj_old\n",
    "            Dj['Bj_old'] = Dj['Bj']\n",
    "            # Drop the temporary Bj field we created, leaving Bj_old\n",
    "            Dj.drop('Bj', axis=1, inplace=True)\n",
    "            \n",
    "            # Assign higher sum difference from Ai or Bj to cnvg\n",
    "            cnvg = np.maximum(Oi['diff'].sum(),Dj['diff'].sum())\n",
    "            \n",
    "            # Print and increment loop\n",
    "            print(\"Iteration:\", iteration)\n",
    "            iteration += 1\n",
    "\n",
    "    # When the while loop finishes add the computed Ai_old and Bj_old to the dataframe and return\n",
    "    pd[Ai_name] = Oi['Ai_old']\n",
    "    pd[Bj_name] = Dj['Bj_old']\n",
    "    return pd"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Using the function above we can calculate $A_{i}$ and $B_{j}$ for the previous Poisson model by plugging in the estimate of beta that we generated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "Iteration: 2\n",
      "Iteration: 3\n",
      "Iteration: 4\n",
      "Iteration: 5\n",
      "Iteration: 6\n",
      "Iteration: 7\n",
      "Iteration: 8\n",
      "Iteration: 9\n",
      "Iteration: 10\n",
      "Iteration: 11\n",
      "Iteration: 12\n",
      "Iteration: 13\n",
      "Iteration: 14\n",
      "Iteration: 15\n",
      "Iteration: 16\n",
      "Iteration: 17\n",
      "Iteration: 18\n",
      "Iteration: 19\n",
      "Iteration: 20\n",
      "Iteration: 21\n",
      "Iteration: 22\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1224.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>...</td>\n",
       "      <td>30</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>3747.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>42</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2873.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>21</td>\n",
       "      <td>...</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3172.0</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",
       "      <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>Woodford</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>31</td>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>29</td>\n",
       "      <td>...</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4862.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>530.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>18</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>...</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3093.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7893.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>346</td>\n",
       "      <td>751</td>\n",
       "      <td>2198</td>\n",
       "      <td>7788</td>\n",
       "      <td>7934</td>\n",
       "      <td>446</td>\n",
       "      <td>741</td>\n",
       "      <td>256</td>\n",
       "      <td>174</td>\n",
       "      <td>8108</td>\n",
       "      <td>...</td>\n",
       "      <td>6278</td>\n",
       "      <td>599</td>\n",
       "      <td>2141</td>\n",
       "      <td>1576</td>\n",
       "      <td>402</td>\n",
       "      <td>700</td>\n",
       "      <td>240</td>\n",
       "      <td>740</td>\n",
       "      <td>4427</td>\n",
       "      <td>1541959.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road                 0              0           0        0   \n",
       "Acton Central              0              0           0        0   \n",
       "Acton Town                 0              0           0       15   \n",
       "Aldgate                    0              0           2        0   \n",
       "Aldgate East               0              0           2       49   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                   0              0           7       31   \n",
       "Woodgrange Park            0              6           0        0   \n",
       "Woodside Park              0              0           5       18   \n",
       "Woolwich Arsenal          20              0           0        0   \n",
       "All                      346            751        2198     7788   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                   0           0         0         0        0   \n",
       "Acton Central                0           0         0         0        0   \n",
       "Acton Town                  15           0        11         1        0   \n",
       "Aldgate                     42           0         0         0        0   \n",
       "Aldgate East                 0           0         1         0        0   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                    33           0         0         0        0   \n",
       "Woodgrange Park              0           0         0         0        0   \n",
       "Woodside Park               17           0         3         0        0   \n",
       "Woolwich Arsenal             0          28         0         0        0   \n",
       "All                       7934         446       741       256      174   \n",
       "\n",
       "Dest              Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                     ...                                          \n",
       "Abbey Road            0  ...          0               0           0   \n",
       "Acton Central         0  ...          0               0           0   \n",
       "Acton Town           17  ...         30               3           5   \n",
       "Aldgate              19  ...          7               0           2   \n",
       "Aldgate East         21  ...          8               1           3   \n",
       "...                 ...  ...        ...             ...         ...   \n",
       "Woodford             29  ...         29               0          10   \n",
       "Woodgrange Park       0  ...          0               0           0   \n",
       "Woodside Park        22  ...         21               0           6   \n",
       "Woolwich Arsenal      0  ...          0               0           0   \n",
       "All                8108  ...       6278             599        2141   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road                0            0         0                0   \n",
       "Acton Central             0            0         0                2   \n",
       "Acton Town               12            0         2                0   \n",
       "Aldgate                   2            0         1                0   \n",
       "Aldgate East              2            0         1                0   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                  0            0         0                0   \n",
       "Woodgrange Park           0            0         0                0   \n",
       "Woodside Park             0            0         0                0   \n",
       "Woolwich Arsenal          0            0         0                0   \n",
       "All                    1576          402       700              240   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                    0                26      600.0  \n",
       "Acton Central                 0                 0     1224.0  \n",
       "Acton Town                    2                 0     3747.0  \n",
       "Aldgate                       1                 0     2873.0  \n",
       "Aldgate East                  1                 0     3172.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                      0                 0     4862.0  \n",
       "Woodgrange Park               0                 0      530.0  \n",
       "Woodside Park                 0                 0     3093.0  \n",
       "Woolwich Arsenal              0                 0     7893.0  \n",
       "All                         740              4427  1541959.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 303,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the beta we got from the inverse power model\n",
    "beta = -doubSim_pow.params[-1]\n",
    "\n",
    "# Get the balancing factors.Oi_origpop\tDj_destjobOi_origpop\tDj_destjobOi_origpop\tDj_destjobOi_origpop\tDj_destjobOi_origpop\tDj_destjobOi_origpop\tDj_destjob\n",
    "london_flows = balance_doubly_constrained(london_flows,'Orig','Dest','O_i','D_j','Dist',-beta,'power')\n",
    "\n",
    "# Now predict the model again using the new Ai and Dj fields.\n",
    "london_flows['SIM_est_pow'] = np.round(london_flows['O_i'] * london_flows['Ai_new'] * london_flows['D_j'] * london_flows['Bj_new'] * \n",
    "                                   np.exp(np.log(london_flows['Dist'])*-beta))\n",
    "# Check out the matrix\n",
    "pd.pivot_table(london_flows,values='SIM_est_pow',index ='Orig',columns='Dest',fill_value=0,aggfunc=sum,margins=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "93.399"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRMSE(london_flows['Total'],london_flows['SIM_est_exp'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101.331"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CalcRMSE(london_flows['Total'],london_flows['SIM_est_pow'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00015436845765696853"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "Iteration: 2\n",
      "Iteration: 3\n",
      "Iteration: 4\n",
      "Iteration: 5\n",
      "Iteration: 6\n",
      "Iteration: 7\n",
      "Iteration: 8\n",
      "Iteration: 9\n",
      "Iteration: 10\n",
      "Iteration: 11\n",
      "Iteration: 12\n",
      "Iteration: 13\n",
      "Iteration: 14\n",
      "Iteration: 15\n",
      "Iteration: 16\n",
      "Iteration: 17\n",
      "Iteration: 18\n",
      "Iteration: 19\n",
      "Iteration: 20\n",
      "Iteration: 21\n",
      "Iteration: 22\n",
      "Iteration: 23\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>31</td>\n",
       "      <td>603.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1221.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>12</td>\n",
       "      <td>...</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3752.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2883.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>38</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>24</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3167.0</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",
       "      <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>Woodford</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>38</td>\n",
       "      <td>44</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>25</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4862.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>528.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>17</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>25</td>\n",
       "      <td>...</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3093.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>28</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7896.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>344</td>\n",
       "      <td>750</td>\n",
       "      <td>2204</td>\n",
       "      <td>7776</td>\n",
       "      <td>7933</td>\n",
       "      <td>442</td>\n",
       "      <td>739</td>\n",
       "      <td>249</td>\n",
       "      <td>175</td>\n",
       "      <td>8097</td>\n",
       "      <td>...</td>\n",
       "      <td>6296</td>\n",
       "      <td>594</td>\n",
       "      <td>2140</td>\n",
       "      <td>1578</td>\n",
       "      <td>402</td>\n",
       "      <td>692</td>\n",
       "      <td>242</td>\n",
       "      <td>747</td>\n",
       "      <td>4426</td>\n",
       "      <td>1541437.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road                 0              0           0        0   \n",
       "Acton Central              0              0           0        0   \n",
       "Acton Town                 0              0           0       11   \n",
       "Aldgate                    0              0           1        0   \n",
       "Aldgate East               0              0           2       38   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                   0              0           2       38   \n",
       "Woodgrange Park            0              2           0        0   \n",
       "Woodside Park              0              0           2       17   \n",
       "Woolwich Arsenal          28              0           0        0   \n",
       "All                      344            750        2204     7776   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                   0           0         0         0        0   \n",
       "Acton Central                0           0         0         0        0   \n",
       "Acton Town                  10           0        17         0        0   \n",
       "Aldgate                     32           0         0         0        0   \n",
       "Aldgate East                 0           0         0         0        0   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                    44           0         0         0        0   \n",
       "Woodgrange Park              0           0         0         0        0   \n",
       "Woodside Park               15           0         0         0        0   \n",
       "Woolwich Arsenal             0          29         0         0        0   \n",
       "All                       7933         442       739       249      175   \n",
       "\n",
       "Dest              Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                     ...                                          \n",
       "Abbey Road            0  ...          0               0           0   \n",
       "Acton Central         0  ...          0               0           0   \n",
       "Acton Town           12  ...         40               4           2   \n",
       "Aldgate              23  ...          7               0           3   \n",
       "Aldgate East         24  ...          7               1           3   \n",
       "...                 ...  ...        ...             ...         ...   \n",
       "Woodford             25  ...          7               0           7   \n",
       "Woodgrange Park       0  ...          0               0           0   \n",
       "Woodside Park        25  ...         10               0           4   \n",
       "Woolwich Arsenal      0  ...          0               0           0   \n",
       "All                8097  ...       6296             594        2140   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road                0            0         0                0   \n",
       "Acton Central             0            0         0                0   \n",
       "Acton Town               19            0         0                0   \n",
       "Aldgate                   2            0         1                0   \n",
       "Aldgate East              2            0         1                0   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                  0            0         0                0   \n",
       "Woodgrange Park           0            0         0                0   \n",
       "Woodside Park             0            0         0                0   \n",
       "Woolwich Arsenal          0            0         0                0   \n",
       "All                    1578          402       692              242   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                    0                31      603.0  \n",
       "Acton Central                 0                 0     1221.0  \n",
       "Acton Town                    1                 0     3752.0  \n",
       "Aldgate                       1                 0     2883.0  \n",
       "Aldgate East                  1                 0     3167.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                      0                 0     4862.0  \n",
       "Woodgrange Park               0                 0      528.0  \n",
       "Woodside Park                 0                 0     3093.0  \n",
       "Woolwich Arsenal              0                 0     7896.0  \n",
       "All                         747              4426  1541437.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the beta we got from the negative exponential model\n",
    "beta = -doubsim_exp.params[-1]\n",
    "\n",
    "\n",
    "# Get the balancing factors. NB Setting of new field names for Ai and Bj.\n",
    "london_flows = balance_doubly_constrained(london_flows,'Orig','Dest','O_i','D_j','Dist',-beta,'exponential','Ai_exp','Bj_exp')\n",
    "\n",
    "# Now predict the model again using the new Ai and Dj fields.\n",
    "london_flows['SIM_est_exp'] = np.round(london_flows['O_i'] * london_flows['Ai_exp'] * london_flows['D_j'] * london_flows['Bj_exp'] * \n",
    "                                   np.exp(london_flows['Dist']*-beta))\n",
    "# Check out the matrix\n",
    "pd.pivot_table(london_flows,values='SIM_est_exp',index ='Orig',columns='Dest',fill_value=0,aggfunc=sum,margins=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1\n",
      "Iteration: 2\n",
      "Iteration: 3\n",
      "Iteration: 4\n",
      "Iteration: 5\n",
      "Iteration: 6\n",
      "Iteration: 7\n",
      "Iteration: 8\n",
      "Iteration: 9\n",
      "Iteration: 10\n",
      "Iteration: 11\n",
      "Iteration: 12\n",
      "Iteration: 13\n",
      "Iteration: 14\n",
      "Iteration: 15\n",
      "Iteration: 16\n",
      "Iteration: 17\n",
      "Iteration: 18\n",
      "Iteration: 19\n",
      "Iteration: 20\n",
      "Iteration: 21\n",
      "Iteration: 22\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>599.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1224.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>...</td>\n",
       "      <td>30</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>3747.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>42</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2873.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>49</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>21</td>\n",
       "      <td>...</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3172.0</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",
       "      <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>Woodford</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>31</td>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>29</td>\n",
       "      <td>...</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4862.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>530.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>18</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>...</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3093.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>28</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7893.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>346</td>\n",
       "      <td>751</td>\n",
       "      <td>2198</td>\n",
       "      <td>7788</td>\n",
       "      <td>7934</td>\n",
       "      <td>447</td>\n",
       "      <td>741</td>\n",
       "      <td>256</td>\n",
       "      <td>174</td>\n",
       "      <td>8109</td>\n",
       "      <td>...</td>\n",
       "      <td>6278</td>\n",
       "      <td>599</td>\n",
       "      <td>2141</td>\n",
       "      <td>1575</td>\n",
       "      <td>402</td>\n",
       "      <td>700</td>\n",
       "      <td>240</td>\n",
       "      <td>740</td>\n",
       "      <td>4427</td>\n",
       "      <td>1542079.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road                 0              0           0        0   \n",
       "Acton Central              0              0           0        0   \n",
       "Acton Town                 0              0           0       15   \n",
       "Aldgate                    0              0           2        0   \n",
       "Aldgate East               0              0           2       49   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                   0              0           7       31   \n",
       "Woodgrange Park            0              6           0        0   \n",
       "Woodside Park              0              0           5       18   \n",
       "Woolwich Arsenal          20              0           0        0   \n",
       "All                      346            751        2198     7788   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                   0           0         0         0        0   \n",
       "Acton Central                0           0         0         0        0   \n",
       "Acton Town                  15           0        11         1        0   \n",
       "Aldgate                     42           0         0         0        0   \n",
       "Aldgate East                 0           0         1         0        0   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                    33           0         0         0        0   \n",
       "Woodgrange Park              0           0         0         0        0   \n",
       "Woodside Park               17           0         3         0        0   \n",
       "Woolwich Arsenal             0          28         0         0        0   \n",
       "All                       7934         447       741       256      174   \n",
       "\n",
       "Dest              Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                     ...                                          \n",
       "Abbey Road            0  ...          0               0           0   \n",
       "Acton Central         0  ...          0               0           0   \n",
       "Acton Town           17  ...         30               3           5   \n",
       "Aldgate              19  ...          7               0           2   \n",
       "Aldgate East         21  ...          8               1           3   \n",
       "...                 ...  ...        ...             ...         ...   \n",
       "Woodford             29  ...         29               0          10   \n",
       "Woodgrange Park       0  ...          0               0           0   \n",
       "Woodside Park        22  ...         21               0           6   \n",
       "Woolwich Arsenal      0  ...          0               0           0   \n",
       "All                8109  ...       6278             599        2141   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road                0            0         0                0   \n",
       "Acton Central             0            0         0                2   \n",
       "Acton Town               12            0         2                0   \n",
       "Aldgate                   2            0         1                0   \n",
       "Aldgate East              2            0         1                0   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                  0            0         0                0   \n",
       "Woodgrange Park           0            0         0                0   \n",
       "Woodside Park             0            0         0                0   \n",
       "Woolwich Arsenal          0            0         0                0   \n",
       "All                    1575          402       700              240   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                    0                26      599.0  \n",
       "Acton Central                 0                 0     1224.0  \n",
       "Acton Town                    2                 0     3747.0  \n",
       "Aldgate                       1                 0     2873.0  \n",
       "Aldgate East                  1                 0     3172.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                      0                 0     4862.0  \n",
       "Woodgrange Park               0                 0      530.0  \n",
       "Woodside Park                 0                 0     3093.0  \n",
       "Woolwich Arsenal              0                 0     7893.0  \n",
       "All                         740              4427  1542079.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the beta we got from the inverse power model\n",
    "beta = -doubSim.params[-1]\n",
    "\n",
    "# Get the balancing factors.Oi_origpop\tDj_destjobOi_origpop\tDj_destjobOi_origpop\tDj_destjobOi_origpop\tDj_destjobOi_origpop\tDj_destjobOi_origpop\tDj_destjob\n",
    "london_flows_db = balance_doubly_constrained(london_flows.copy(),'Orig','Dest','Oi_origpop','Dj_destjob','Dist',-beta,'power')\n",
    "\n",
    "# Now predict the model again using the new Ai and Dj fields.\n",
    "london_flows_db['SIM_est_pow_1'] = np.round(london_flows_db['Oi_origpop'] * london_flows_db['Ai_new'] * london_flows_db['Dj_destjob'] * london_flows_db['Bj_new'] * \n",
    "                                   np.exp(np.log(london_flows_db['Dist'])*-beta))\n",
    "# Check out the matrix\n",
    "pd.pivot_table(london_flows_db,values='SIM_est_pow_1',index ='Orig',columns='Dest',fill_value=0,aggfunc=sum,margins=True)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scenarios\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scenario A: assume that **Canary Wharf** has a 50% decrease in jobs after Brexit. Using the \n",
    "calibrated parameter $\\beta$, compute the new flows for scenario A. Make sure the number of commuters is conserved, and explain how you ensured this.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8781569676332593"
      ]
     },
     "execution_count": 304,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set beta as the calibration result of production constration model\n",
    "beta=-prodSim.params[-1]\n",
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new variable with the altered jobs\n",
    "def new_job(row):\n",
    "    if row[\"Dest\"] == \"Canary Wharf\":\n",
    "        val = 0.5*row[\"Dj_destjob\"]\n",
    "    else:\n",
    "        val = row[\"Dj_destjob\"]\n",
    "    return val\n",
    "        \n",
    "london_flows[\"Dj_destjobSceA\"] = london_flows.apply(new_job, axis =1)\n",
    "#london_flows.head(10)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now plug the new values into new model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>572.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1223.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>...</td>\n",
       "      <td>16.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3719.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>47.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>21.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2859.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>23.0</td>\n",
       "      <td>...</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3134.0</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",
       "      <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>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32.0</td>\n",
       "      <td>...</td>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4790.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>532.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25.0</td>\n",
       "      <td>...</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3060.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>29.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>33.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>445.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>2156.0</td>\n",
       "      <td>8753.0</td>\n",
       "      <td>9308.0</td>\n",
       "      <td>504.0</td>\n",
       "      <td>582.0</td>\n",
       "      <td>108.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>9202.0</td>\n",
       "      <td>...</td>\n",
       "      <td>3426.0</td>\n",
       "      <td>523.0</td>\n",
       "      <td>2161.0</td>\n",
       "      <td>1647.0</td>\n",
       "      <td>341.0</td>\n",
       "      <td>654.0</td>\n",
       "      <td>156.0</td>\n",
       "      <td>603.0</td>\n",
       "      <td>1009.0</td>\n",
       "      <td>1520944.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN     18.0   \n",
       "Aldgate                  NaN            NaN         2.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0     52.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         7.0     35.0   \n",
       "Woodgrange Park          NaN            4.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         5.0     20.0   \n",
       "Woolwich Arsenal        29.0            NaN         NaN      NaN   \n",
       "All                    445.0          391.0      2156.0   8753.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                18.0         NaN       9.0       1.0      NaN   \n",
       "Aldgate                   47.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       1.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  39.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             20.0         NaN       2.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN        33.0       NaN       NaN      NaN   \n",
       "All                     9308.0       504.0     582.0     108.0    140.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          20.0  ...       16.0             3.0         5.0   \n",
       "Aldgate             21.0  ...        4.0             NaN         3.0   \n",
       "Aldgate East        23.0  ...        5.0             1.0         3.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            32.0  ...       15.0             NaN        10.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       25.0  ...       11.0             NaN         6.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               9202.0  ...     3426.0           523.0      2161.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              1.0   \n",
       "Acton Town             13.0          NaN       2.0              NaN   \n",
       "Aldgate                 2.0          NaN       1.0              NaN   \n",
       "Aldgate East            2.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1647.0        341.0     654.0            156.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                  NaN               5.0      572.0  \n",
       "Acton Central               NaN               NaN     1223.0  \n",
       "Acton Town                  2.0               NaN     3719.0  \n",
       "Aldgate                     1.0               NaN     2859.0  \n",
       "Aldgate East                1.0               NaN     3134.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                    NaN               NaN     4790.0  \n",
       "Woodgrange Park             NaN               NaN      532.0  \n",
       "Woodside Park               NaN               NaN     3060.0  \n",
       "Woolwich Arsenal            NaN               NaN     7297.0  \n",
       "All                       603.0            1009.0  1520944.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 356,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows[\"prodsimest_a\"] = np.exp(london_flows[\"alpha_i\"]+gamma*np.log(london_flows[\"Dj_destjobSceA\"]) - beta*london_flows[\"log_Dist\"])\n",
    "\n",
    "london_flows[\"prodsimest_a\"] = round(london_flows[\"prodsimest_a\"],0)\n",
    "#now we can convert the pivot table into a matrix\n",
    "ldf_submat_prod_a = london_flows.pivot_table(values =\"prodsimest_a\", index=\"Orig\", columns = \"Dest\",\n",
    "                            aggfunc=np.sum, margins=True)\n",
    "ldf_submat_prod_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8781569676332593"
      ]
     },
     "execution_count": 288,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate some new Dj^gamma and d_ij^beta values\n",
    "Dj_gamma_b1 = london_flows[\"Dj_destjob\"]**gamma\n",
    "dist_beta = london_flows[\"Dist\"]**-beta\n",
    "#calcualte the first stage of the Ai values\n",
    "london_flows[\"Ai1\"] = Dj2_gamma * dist_beta\n",
    "#now do the sum over all js bit\n",
    "A_i = pd.DataFrame(london_flows.groupby([\"Orig\"])[\"Ai1\"].agg(np.sum))\n",
    "#now divide into 1\n",
    "A_i[\"Ai1\"] = 1/A_i[\"Ai1\"]\n",
    "A_i.rename(columns={\"Ai1\":\"A_i\"}, inplace=True)\n",
    "#and write the A_i values back into the dataframe\n",
    "london_flows = london_flows.merge(A_i, left_on=\"Orig\", right_index=True, how=\"left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>prodsimest1</th>\n",
       "      <th>prodsimest_a_1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>55.0</td>\n",
       "      <td>55.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>66.0</td>\n",
       "      <td>66.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>49.0</td>\n",
       "      <td>49.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61408</th>\n",
       "      <td>121.0</td>\n",
       "      <td>121.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61409</th>\n",
       "      <td>259.0</td>\n",
       "      <td>259.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61410</th>\n",
       "      <td>32.0</td>\n",
       "      <td>32.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61411</th>\n",
       "      <td>98.0</td>\n",
       "      <td>98.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61412</th>\n",
       "      <td>74.0</td>\n",
       "      <td>74.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>61413 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       prodsimest1  prodsimest_a_1\n",
       "0             55.0            55.0\n",
       "1              1.0             1.0\n",
       "2              3.0             3.0\n",
       "3             66.0            66.0\n",
       "4             49.0            49.0\n",
       "...            ...             ...\n",
       "61408        121.0           121.0\n",
       "61409        259.0           259.0\n",
       "61410         32.0            32.0\n",
       "61411         98.0            98.0\n",
       "61412         74.0            74.0\n",
       "\n",
       "[61413 rows x 2 columns]"
      ]
     },
     "execution_count": 360,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#to check everything works, recreate the original estimates\n",
    "london_flows[\"prodsimest_a_1\"] = london_flows[\"A_i\"]*london_flows[\"O_i\"]*Dj2_gamma*dist_beta\n",
    "#round\n",
    "london_flows[\"prodsimest_a_1\"] = round(london_flows[\"prodsimest_a_1\"])\n",
    "#check\n",
    "london_flows[[\"prodsimest1\", \"prodsimest_a_1\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate some new Dj^gamma and d_ij^beta values\n",
    "Dj_gamma_a = london_flows[\"Dj_destjobSceA\"]**gamma\n",
    "\n",
    "#calcualte the first stage of the Ai values\n",
    "london_flows[\"Ai1\"] = Dj3_gamma * dist_beta\n",
    "#now do the sum over all js bit\n",
    "A_i = pd.DataFrame(london_flows.groupby([\"Orig\"])[\"Ai1\"].agg(np.sum))\n",
    "#now divide into 1\n",
    "A_i[\"Ai1\"] = 1/A_i[\"Ai1\"]\n",
    "A_i.rename(columns={\"Ai1\":\"A_i\"}, inplace=True)\n",
    "#and write the A_i values back into the dataframe\n",
    "london_flows = london_flows.merge(A_i, left_on=\"Orig\", right_index=True, how=\"left\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modelling the scenario\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate new scenatio flow estimates based on new $A_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [],
   "source": [
    "#to check everything works, recreate the original estimates\n",
    "london_flows[\"prodsimest_a\"] = london_flows[\"A_i\"]*london_flows[\"O_i\"]*Dj_gamma_a*dist_beta\n",
    "#round\n",
    "london_flows[\"prodsimest_a\"] = round(london_flows[\"prodsimest_a\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>600.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1223.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>...</td>\n",
       "      <td>17.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3744.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>47.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2884.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>23.0</td>\n",
       "      <td>...</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3166.0</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",
       "      <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>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>33.0</td>\n",
       "      <td>...</td>\n",
       "      <td>16.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4863.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>532.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25.0</td>\n",
       "      <td>...</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3091.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>32.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>36.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7893.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>470.0</td>\n",
       "      <td>393.0</td>\n",
       "      <td>2182.0</td>\n",
       "      <td>8837.0</td>\n",
       "      <td>9400.0</td>\n",
       "      <td>547.0</td>\n",
       "      <td>588.0</td>\n",
       "      <td>109.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>9302.0</td>\n",
       "      <td>...</td>\n",
       "      <td>3461.0</td>\n",
       "      <td>527.0</td>\n",
       "      <td>2185.0</td>\n",
       "      <td>1664.0</td>\n",
       "      <td>342.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>156.0</td>\n",
       "      <td>609.0</td>\n",
       "      <td>1081.0</td>\n",
       "      <td>1541949.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN     18.0   \n",
       "Aldgate                  NaN            NaN         2.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0     53.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         7.0     36.0   \n",
       "Woodgrange Park          NaN            4.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         5.0     21.0   \n",
       "Woolwich Arsenal        32.0            NaN         NaN      NaN   \n",
       "All                    470.0          393.0      2182.0   8837.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                18.0         NaN       9.0       1.0      NaN   \n",
       "Aldgate                   47.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       1.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  39.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             21.0         NaN       2.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN        36.0       NaN       NaN      NaN   \n",
       "All                     9400.0       547.0     588.0     109.0    140.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          20.0  ...       17.0             3.0         5.0   \n",
       "Aldgate             22.0  ...        4.0             NaN         3.0   \n",
       "Aldgate East        23.0  ...        5.0             1.0         3.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            33.0  ...       16.0             NaN        10.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       25.0  ...       11.0             NaN         6.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               9302.0  ...     3461.0           527.0      2185.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              1.0   \n",
       "Acton Town             13.0          NaN       2.0              NaN   \n",
       "Aldgate                 2.0          NaN       1.0              NaN   \n",
       "Aldgate East            2.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1664.0        342.0     666.0            156.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                  NaN               6.0      600.0  \n",
       "Acton Central               NaN               NaN     1223.0  \n",
       "Acton Town                  2.0               NaN     3744.0  \n",
       "Aldgate                     1.0               NaN     2884.0  \n",
       "Aldgate East                1.0               NaN     3166.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                    NaN               NaN     4863.0  \n",
       "Woodgrange Park             NaN               NaN      532.0  \n",
       "Woodside Park               NaN               NaN     3091.0  \n",
       "Woolwich Arsenal            NaN               NaN     7893.0  \n",
       "All                       609.0            1081.0  1541949.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 365,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "ldf_submat_prod_a= london_flows.pivot_table(values =\"prodsimest_a\", index=\"Orig\", columns = \"Dest\",\n",
    "                            aggfunc=np.sum, margins=True)\n",
    "ldf_submat_prod_a"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Investigate changes\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Total</th>\n",
       "      <th>prodsimest_a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>61413.000000</td>\n",
       "      <td>61413.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>25.113298</td>\n",
       "      <td>25.107860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>131.479668</td>\n",
       "      <td>84.478902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>13.000000</td>\n",
       "      <td>20.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>15946.000000</td>\n",
       "      <td>4480.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Total  prodsimest_a\n",
       "count  61413.000000  61413.000000\n",
       "mean      25.113298     25.107860\n",
       "std      131.479668     84.478902\n",
       "min        0.000000      0.000000\n",
       "25%        0.000000      2.000000\n",
       "50%        3.000000      7.000000\n",
       "75%       13.000000     20.000000\n",
       "max    15946.000000   4480.000000"
      ]
     },
     "execution_count": 366,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows[['Total','prodsimest_a']].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    61413.000000\n",
       "mean        -0.005439\n",
       "std        104.105595\n",
       "min     -12303.000000\n",
       "25%          0.000000\n",
       "50%          2.000000\n",
       "75%          7.000000\n",
       "max       4035.000000\n",
       "Name: diff_a, dtype: float64"
      ]
     },
     "execution_count": 367,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows['diff_a']=london_flows['prodsimest_a']-london_flows['Total']\n",
    "london_flows['diff_a'].describe()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Orig</th>\n",
       "      <th>Dest</th>\n",
       "      <th>Total</th>\n",
       "      <th>prodsimest_a</th>\n",
       "      <th>diff_a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>32584</th>\n",
       "      <td>London Bridge</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>445</td>\n",
       "      <td>4480.0</td>\n",
       "      <td>4035.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32282</th>\n",
       "      <td>Liverpool Street</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>812</td>\n",
       "      <td>4220.0</td>\n",
       "      <td>3408.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32441</th>\n",
       "      <td>Liverpool Street</td>\n",
       "      <td>Moorgate</td>\n",
       "      <td>172</td>\n",
       "      <td>3089.0</td>\n",
       "      <td>2917.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56086</th>\n",
       "      <td>Waterloo</td>\n",
       "      <td>Southwark</td>\n",
       "      <td>109</td>\n",
       "      <td>2516.0</td>\n",
       "      <td>2407.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56133</th>\n",
       "      <td>Waterloo</td>\n",
       "      <td>Westminster</td>\n",
       "      <td>717</td>\n",
       "      <td>2734.0</td>\n",
       "      <td>2017.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Orig               Dest  Total  prodsimest_a  diff_a\n",
       "32584     London Bridge  Bank and Monument    445        4480.0  4035.0\n",
       "32282  Liverpool Street  Bank and Monument    812        4220.0  3408.0\n",
       "32441  Liverpool Street           Moorgate    172        3089.0  2917.0\n",
       "56086          Waterloo          Southwark    109        2516.0  2407.0\n",
       "56133          Waterloo        Westminster    717        2734.0  2017.0"
      ]
     },
     "execution_count": 368,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff_a_max=london_flows.nlargest(5,'diff_a')\n",
    "diff_a_max[['Orig','Dest','Total','prodsimest_a','diff_a']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Orig</th>\n",
       "      <th>Dest</th>\n",
       "      <th>Total</th>\n",
       "      <th>prodsimest_a</th>\n",
       "      <th>diff_a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>55890</th>\n",
       "      <td>Waterloo</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>15946</td>\n",
       "      <td>3643.0</td>\n",
       "      <td>-12303.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55915</th>\n",
       "      <td>Waterloo</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>8085</td>\n",
       "      <td>667.0</td>\n",
       "      <td>-7418.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32609</th>\n",
       "      <td>London Bridge</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>6165</td>\n",
       "      <td>412.0</td>\n",
       "      <td>-5753.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50041</th>\n",
       "      <td>Stratford</td>\n",
       "      <td>Liverpool Street</td>\n",
       "      <td>6946</td>\n",
       "      <td>2135.0</td>\n",
       "      <td>-4811.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54769</th>\n",
       "      <td>Victoria</td>\n",
       "      <td>Oxford Circus</td>\n",
       "      <td>5181</td>\n",
       "      <td>1678.0</td>\n",
       "      <td>-3503.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Orig               Dest  Total  prodsimest_a   diff_a\n",
       "55890       Waterloo  Bank and Monument  15946        3643.0 -12303.0\n",
       "55915       Waterloo       Canary Wharf   8085         667.0  -7418.0\n",
       "32609  London Bridge       Canary Wharf   6165         412.0  -5753.0\n",
       "50041      Stratford   Liverpool Street   6946        2135.0  -4811.0\n",
       "54769       Victoria      Oxford Circus   5181        1678.0  -3503.0"
      ]
     },
     "execution_count": 369,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff_a_min=london_flows.nsmallest(5,'diff_a')\n",
    "diff_a_min[['Orig','Dest','Total','prodsimest_a','diff_a']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1542283"
      ]
     },
     "execution_count": 352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(london_flows['Total'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1541949.0"
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(london_flows['prodsimest_a'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {},
   "outputs": [],
   "source": [
    "def heatmap_plotter(smallest_diff,largest_diff):\n",
    "# plot heatmap of smallest differences\n",
    "    plt.figure(figsize=(6,6))\n",
    "    # Create a pivot table for significant flows\n",
    "    pt_s = pd.pivot_table(smallest_diff, values='diff_a', index='Orig', columns='Dest', aggfunc=np.sum)\n",
    "    sns.heatmap(pt_s, annot=True, cmap=\"YlGnBu\")\n",
    "    plt.title(\"Heatmap of Smallest Differences\")\n",
    "    plt.xlabel(\"Destination\")\n",
    "    plt.ylabel(\"Origin\")\n",
    "    plt.show()\n",
    "\n",
    "    # plot heatmap of largest differences\n",
    "    plt.figure(figsize=(6, 6))\n",
    "    pt_l = pd.pivot_table(largest_diff, values='diff_a', index='Orig', columns='Dest', aggfunc=np.sum)\n",
    "    sns.heatmap(pt_l, annot=True,  cmap=\"YlGnBu\")\n",
    "    plt.title(\"Heatmap of Largest Differences\")\n",
    "    plt.xlabel(\"Destination\")\n",
    "    plt.ylabel(\"Origin\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(15,5))\n",
    "sns.histplot(london_flows['Total'], ax=ax[0])\n",
    "ax[0].set_title('Observed Flows')\n",
    "sns.histplot(london_flows['prodsimest_a'], ax=ax[1])\n",
    "ax[1].set_title('Flows in scenario A')\n",
    "#sns.histplot(london_flows['prediction_2'], ax=ax[2])\n",
    "#ax[2].set_title('Prediction 2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot heatmap of smallest differences\n",
    "plt.figure(figsize=(12, 8))\n",
    "sns.heatmap(smallest_diff, annot=True, fmt=\".1f\", cmap=\"YlGnBu\")\n",
    "plt.title(\"Heatmap of Smallest Differences\")\n",
    "plt.xlabel(\"Destination\")\n",
    "plt.ylabel(\"Origin\")\n",
    "plt.show()\n",
    "\n",
    "# plot heatmap of largest differences\n",
    "plt.figure(figsize=(12, 8))\n",
    "sns.heatmap(largest_diff, annot=True, fmt=\".1f\", cmap=\"YlGnBu\")\n",
    "plt.title(\"Heatmap of Largest Differences\")\n",
    "plt.xlabel(\"Destination\")\n",
    "plt.ylabel(\"Origin\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Filter the flows that have changed significantly\n",
    "significant_flows =london_flows [abs(london_flows['diff_a']) > 1000]\n",
    "\n",
    "# Create a pivot table for significant flows\n",
    "pivot_table = pd.pivot_table(significant_flows, values='diff_a', index='Orig', columns='Dest', aggfunc=np.sum)\n",
    "\n",
    "# Create a heatmap\n",
    "sns.heatmap(pivot_table,  cmap='coolwarm')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Canary Wharf</th>\n",
       "      <th>Canary Wharf</th>\n",
       "      <th>Canary Wharf</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>66.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>73.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>43.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>57.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>34.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>81.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>48.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodford</th>\n",
       "      <td>185.0</td>\n",
       "      <td>109.0</td>\n",
       "      <td>110.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>77.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>46.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>1437.0</td>\n",
       "      <td>844.0</td>\n",
       "      <td>912.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>50534.0</td>\n",
       "      <td>29666.0</td>\n",
       "      <td>31309.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Canary Wharf  Canary Wharf  Canary Wharf\n",
       "Orig                                                      \n",
       "Abbey Road                66.0          39.0          41.0\n",
       "Acton Central              NaN           NaN           NaN\n",
       "Acton Town                73.0          43.0          43.0\n",
       "Aldgate                   57.0          34.0          34.0\n",
       "Aldgate East              81.0          48.0          48.0\n",
       "...                        ...           ...           ...\n",
       "Woodford                 185.0         109.0         110.0\n",
       "Woodgrange Park            NaN           NaN           NaN\n",
       "Woodside Park             77.0          45.0          46.0\n",
       "Woolwich Arsenal        1437.0         844.0         912.0\n",
       "All                    50534.0       29666.0       31309.0\n",
       "\n",
       "[399 rows x 3 columns]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check flows into Canary Wharf\n",
    "# Check the flow ends in canary wharf\n",
    "res_ori=ldf_submat_prodc['Canary Wharf']\n",
    "\n",
    "res_a=ldf_submat_prod_a['Canary Wharf']\n",
    "res_a_1=ldf_submat_prod_a_1['Canary Wharf']\n",
    "pd.concat([res_ori,res_a,res_a_1],axis=1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scenario B: assume that there is a significant increase **in the cost of transport**. Select 2 values for the parameter in the cost function reflecting scenario B. Recompute the distribution of flows."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "set up the adjusted $\\beta$, we assume that $k$ is the increase in cost of transport, meaning the original cost is $c$ and new cost is $kc$\n",
    "\n",
    "According to research (nature of transport cost and pricing), the  transport costs are proportional to distance\n",
    "$f(d)=kd_{i j}$\n",
    "Given a cost function that aligns with power law\n",
    "$f(d)=d_{i j}^{-\\beta}$\n",
    "To adjust the parameter $\\beta$ in the cost function reflecting the increase in cost of transport\n",
    "\n",
    "$(kd_{i j})^{-\\beta}=d_{i j}^{-\\beta_{adjusted}}$\n",
    "\n",
    "After taking logarithmic of both sides, the equation will look like the following \n",
    "\n",
    "$ \\beta(log(k)+ log(d_{i j})=\\beta_{adjusted}log(d_{ij})$\n",
    "\n",
    "\n",
    "So $\\beta_{adjusted}=\\beta \\frac{ log(d_{i j})+log(k)}{log(d_{i j})}$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scenario B parameter 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8781569676332593"
      ]
     },
     "execution_count": 312,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta=-prodSim.params[-1]\n",
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8988100402866469"
      ]
     },
     "execution_count": 376,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta*(london_flows['log_Dist'].mean()+np.log(1.25))/london_flows['log_Dist'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8989477824802116"
      ]
     },
     "execution_count": 313,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_adj_25=beta*(london_flows['log_Dist']+np.log(1.25))/london_flows['log_Dist']\n",
    "beta_adj_25.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [],
   "source": [
    "london_flows_b=london_flows.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use the new parameter to predict flow\n",
    "# first recalculate the balanceing factor to ensure convergence\n",
    "#calculate some new Dj^gamma and d_ij^beta values\n",
    "Dj_gamma = london_flows[\"Dj_destjob\"]**gamma\n",
    "dist_beta_25 = london_flows[\"Dist\"]**-beta_adj_25\n",
    "\n",
    "#calcualte the first stage of the Ai values\n",
    "london_flows_b[\"Ai1\"] = Dj_gamma * dist_beta_25\n",
    "#now do the sum over all js bit\n",
    "A_i = pd.DataFrame(london_flows_b.groupby([\"Orig\"])[\"Ai1\"].agg(np.sum))\n",
    "#now divide into 1\n",
    "A_i[\"Ai1\"] = 1/A_i[\"Ai1\"]\n",
    "A_i.rename(columns={\"Ai1\":\"A_i1\"}, inplace=True)\n",
    "#and write the A_i values back into the dataframe\n",
    "london_flows_b = london_flows_b.merge(A_i, left_on=\"Orig\", right_index=True, how=\"left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now generate new scenario estimate \n",
    "london_flows_b['prodsimest_b1']=london_flows_b['A_i1']*london_flows_b['O_i']*Dj_gamma*dist_beta_25\n",
    "# round\n",
    "london_flows_b['prodsimest_b1']=round(london_flows_b['prodsimest_b1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>601.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1226.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>...</td>\n",
       "      <td>17.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3744.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>47.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>22.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2886.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>24.0</td>\n",
       "      <td>...</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3165.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>33.0</td>\n",
       "      <td>...</td>\n",
       "      <td>16.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4866.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>530.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25.0</td>\n",
       "      <td>...</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3095.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>32.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>36.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7892.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>488.0</td>\n",
       "      <td>410.0</td>\n",
       "      <td>2236.0</td>\n",
       "      <td>8837.0</td>\n",
       "      <td>9377.0</td>\n",
       "      <td>544.0</td>\n",
       "      <td>623.0</td>\n",
       "      <td>117.0</td>\n",
       "      <td>153.0</td>\n",
       "      <td>9280.0</td>\n",
       "      <td>...</td>\n",
       "      <td>3465.0</td>\n",
       "      <td>571.0</td>\n",
       "      <td>2249.0</td>\n",
       "      <td>1718.0</td>\n",
       "      <td>361.0</td>\n",
       "      <td>693.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>645.0</td>\n",
       "      <td>1036.0</td>\n",
       "      <td>1541832.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN     18.0   \n",
       "Aldgate                  NaN            NaN         2.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0     53.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         8.0     35.0   \n",
       "Woodgrange Park          NaN            4.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         6.0     21.0   \n",
       "Woolwich Arsenal        32.0            NaN         NaN      NaN   \n",
       "All                    488.0          410.0      2236.0   8837.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                18.0         NaN       9.0       1.0      NaN   \n",
       "Aldgate                   47.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       1.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  39.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             21.0         NaN       2.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN        36.0       NaN       NaN      NaN   \n",
       "All                     9377.0       544.0     623.0     117.0    153.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          20.0  ...       17.0             3.0         5.0   \n",
       "Aldgate             22.0  ...        4.0             NaN         3.0   \n",
       "Aldgate East        24.0  ...        5.0             1.0         3.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            33.0  ...       16.0             NaN        10.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       25.0  ...       11.0             NaN         6.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               9280.0  ...     3465.0           571.0      2249.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              1.0   \n",
       "Acton Town             13.0          NaN       2.0              NaN   \n",
       "Aldgate                 2.0          NaN       1.0              NaN   \n",
       "Aldgate East            2.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1718.0        361.0     693.0            161.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                  NaN               6.0      601.0  \n",
       "Acton Central               NaN               NaN     1226.0  \n",
       "Acton Town                  2.0               NaN     3744.0  \n",
       "Aldgate                     1.0               NaN     2886.0  \n",
       "Aldgate East                1.0               NaN     3165.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                    NaN               NaN     4866.0  \n",
       "Woodgrange Park             NaN               NaN      530.0  \n",
       "Woodside Park               NaN               NaN     3095.0  \n",
       "Woolwich Arsenal            NaN               NaN     7892.0  \n",
       "All                       645.0            1036.0  1541832.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 379,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldf_submat_prod_b1=london_flows_b.pivot_table(values =\"prodsimest_b1\", index=\"Orig\", columns = \"Dest\",\n",
    "                            aggfunc=np.sum, margins=True)\n",
    "ldf_submat_prod_b1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now you have estimate new flows! GOOD JOBBBB!"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scenario B parameter 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9159351151079581"
      ]
     },
     "execution_count": 380,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_adj_50=beta*(london_flows['log_Dist']+np.log(1.50))/london_flows['log_Dist']\n",
    "beta_adj_50.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use the new parameter to predict flow\n",
    "# first recalculate the balanceing factor to ensure convergence\n",
    "#calculate some new Dj^gamma and d_ij^beta values\n",
    "Dj_gamma = london_flows[\"Dj_destjob\"]**gamma\n",
    "dist_beta_50 = london_flows[\"Dist\"]**-beta_adj_50\n",
    "\n",
    "#calcualte the first stage of the Ai values\n",
    "london_flows_b[\"Ai1\"] = Dj_gamma * dist_beta_50\n",
    "#now do the sum over all js bit\n",
    "A_i = pd.DataFrame(london_flows_b.groupby([\"Orig\"])[\"Ai1\"].agg(np.sum))\n",
    "#now divide into 1\n",
    "A_i[\"Ai1\"] = 1/A_i[\"Ai1\"]\n",
    "A_i.rename(columns={\"Ai1\":\"A_i2\"}, inplace=True)\n",
    "#and write the A_i values back into the dataframe\n",
    "london_flows_b = london_flows_b.merge(A_i, left_on=\"Orig\", right_index=True, how=\"left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now generate new scenario estimate \n",
    "london_flows_b['prodsimest_b2']=london_flows_b['A_i2']*london_flows_b['O_i']*Dj_gamma*dist_beta_50\n",
    "# round\n",
    "london_flows_b['prodsimest_b2']=round(london_flows_b['prodsimest_b2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Dest</th>\n",
       "      <th>Abbey Road</th>\n",
       "      <th>Acton Central</th>\n",
       "      <th>Acton Town</th>\n",
       "      <th>Aldgate</th>\n",
       "      <th>Aldgate East</th>\n",
       "      <th>All Saints</th>\n",
       "      <th>Alperton</th>\n",
       "      <th>Amersham</th>\n",
       "      <th>Anerley</th>\n",
       "      <th>Angel</th>\n",
       "      <th>...</th>\n",
       "      <th>Wimbledon</th>\n",
       "      <th>Wimbledon Park</th>\n",
       "      <th>Wood Green</th>\n",
       "      <th>Wood Lane</th>\n",
       "      <th>Wood Street</th>\n",
       "      <th>Woodford</th>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <th>Woodside Park</th>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Orig</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Abbey Road</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>599.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Central</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1223.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Acton Town</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>18.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>20.0</td>\n",
       "      <td>...</td>\n",
       "      <td>16.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3749.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>47.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>21.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2882.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Aldgate East</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>23.0</td>\n",
       "      <td>...</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3167.0</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",
       "      <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>Woodford</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>39.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32.0</td>\n",
       "      <td>...</td>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4866.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodgrange Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>532.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woodside Park</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>25.0</td>\n",
       "      <td>...</td>\n",
       "      <td>11.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3092.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Woolwich Arsenal</th>\n",
       "      <td>29.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>33.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7890.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>445.0</td>\n",
       "      <td>391.0</td>\n",
       "      <td>2156.0</td>\n",
       "      <td>8753.0</td>\n",
       "      <td>9308.0</td>\n",
       "      <td>504.0</td>\n",
       "      <td>582.0</td>\n",
       "      <td>108.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>9202.0</td>\n",
       "      <td>...</td>\n",
       "      <td>3426.0</td>\n",
       "      <td>523.0</td>\n",
       "      <td>2161.0</td>\n",
       "      <td>1647.0</td>\n",
       "      <td>341.0</td>\n",
       "      <td>654.0</td>\n",
       "      <td>156.0</td>\n",
       "      <td>603.0</td>\n",
       "      <td>1009.0</td>\n",
       "      <td>1541812.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>399 rows × 399 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Dest              Abbey Road  Acton Central  Acton Town  Aldgate  \\\n",
       "Orig                                                               \n",
       "Abbey Road               NaN            NaN         NaN      NaN   \n",
       "Acton Central            NaN            NaN         NaN      NaN   \n",
       "Acton Town               NaN            NaN         NaN     18.0   \n",
       "Aldgate                  NaN            NaN         2.0      NaN   \n",
       "Aldgate East             NaN            NaN         2.0     52.0   \n",
       "...                      ...            ...         ...      ...   \n",
       "Woodford                 NaN            NaN         7.0     35.0   \n",
       "Woodgrange Park          NaN            4.0         NaN      NaN   \n",
       "Woodside Park            NaN            NaN         5.0     20.0   \n",
       "Woolwich Arsenal        29.0            NaN         NaN      NaN   \n",
       "All                    445.0          391.0      2156.0   8753.0   \n",
       "\n",
       "Dest              Aldgate East  All Saints  Alperton  Amersham  Anerley  \\\n",
       "Orig                                                                      \n",
       "Abbey Road                 NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Central              NaN         NaN       NaN       NaN      NaN   \n",
       "Acton Town                18.0         NaN       9.0       1.0      NaN   \n",
       "Aldgate                   47.0         NaN       NaN       0.0      NaN   \n",
       "Aldgate East               NaN         NaN       1.0       0.0      NaN   \n",
       "...                        ...         ...       ...       ...      ...   \n",
       "Woodford                  39.0         NaN       NaN       NaN      NaN   \n",
       "Woodgrange Park            NaN         NaN       NaN       NaN      NaN   \n",
       "Woodside Park             20.0         NaN       2.0       NaN      NaN   \n",
       "Woolwich Arsenal           NaN        33.0       NaN       NaN      NaN   \n",
       "All                     9308.0       504.0     582.0     108.0    140.0   \n",
       "\n",
       "Dest               Angel  ...  Wimbledon  Wimbledon Park  Wood Green  \\\n",
       "Orig                      ...                                          \n",
       "Abbey Road           NaN  ...        NaN             NaN         NaN   \n",
       "Acton Central        NaN  ...        NaN             NaN         NaN   \n",
       "Acton Town          20.0  ...       16.0             3.0         5.0   \n",
       "Aldgate             21.0  ...        4.0             NaN         3.0   \n",
       "Aldgate East        23.0  ...        5.0             1.0         3.0   \n",
       "...                  ...  ...        ...             ...         ...   \n",
       "Woodford            32.0  ...       15.0             NaN        10.0   \n",
       "Woodgrange Park      NaN  ...        NaN             NaN         NaN   \n",
       "Woodside Park       25.0  ...       11.0             NaN         6.0   \n",
       "Woolwich Arsenal     NaN  ...        NaN             NaN         NaN   \n",
       "All               9202.0  ...     3426.0           523.0      2161.0   \n",
       "\n",
       "Dest              Wood Lane  Wood Street  Woodford  Woodgrange Park  \\\n",
       "Orig                                                                  \n",
       "Abbey Road              NaN          NaN       NaN              NaN   \n",
       "Acton Central           NaN          NaN       NaN              1.0   \n",
       "Acton Town             13.0          NaN       2.0              NaN   \n",
       "Aldgate                 2.0          NaN       1.0              NaN   \n",
       "Aldgate East            2.0          NaN       1.0              NaN   \n",
       "...                     ...          ...       ...              ...   \n",
       "Woodford                NaN          NaN       NaN              NaN   \n",
       "Woodgrange Park         NaN          NaN       NaN              NaN   \n",
       "Woodside Park           NaN          NaN       NaN              NaN   \n",
       "Woolwich Arsenal        NaN          NaN       NaN              NaN   \n",
       "All                  1647.0        341.0     654.0            156.0   \n",
       "\n",
       "Dest              Woodside Park  Woolwich Arsenal        All  \n",
       "Orig                                                          \n",
       "Abbey Road                  NaN               5.0      599.0  \n",
       "Acton Central               NaN               NaN     1223.0  \n",
       "Acton Town                  2.0               NaN     3749.0  \n",
       "Aldgate                     1.0               NaN     2882.0  \n",
       "Aldgate East                1.0               NaN     3167.0  \n",
       "...                         ...               ...        ...  \n",
       "Woodford                    NaN               NaN     4866.0  \n",
       "Woodgrange Park             NaN               NaN      532.0  \n",
       "Woodside Park               NaN               NaN     3092.0  \n",
       "Woolwich Arsenal            NaN               NaN     7890.0  \n",
       "All                       603.0            1009.0  1541812.0  \n",
       "\n",
       "[399 rows x 399 columns]"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldf_submat_prod_b2=london_flows_b.pivot_table(values =\"prodsimest_b2\", index=\"Orig\", columns = \"Dest\",\n",
    "                            aggfunc=np.sum, margins=True)\n",
    "ldf_submat_prod_b2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9427391373075978"
      ]
     },
     "execution_count": 386,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_adj_2=beta*(london_flows['log_Dist']+np.log(2))/london_flows['log_Dist']\n",
    "beta_adj_2.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use the new parameter to predict flow\n",
    "# first recalculate the balanceing factor to ensure convergence\n",
    "#calculate some new Dj^gamma and d_ij^beta values\n",
    "Dj_gamma = london_flows[\"Dj_destjob\"]**gamma\n",
    "dist_beta_50 = london_flows[\"Dist\"]**-beta_adj_2\n",
    "\n",
    "#calcualte the first stage of the Ai values\n",
    "london_flows_b[\"Ai1\"] = Dj_gamma * dist_beta_50\n",
    "#now do the sum over all js bit\n",
    "A_i = pd.DataFrame(london_flows_b.groupby([\"Orig\"])[\"Ai1\"].agg(np.sum))\n",
    "#now divide into 1\n",
    "A_i[\"Ai1\"] = 1/A_i[\"Ai1\"]\n",
    "A_i.rename(columns={\"Ai1\":\"A_i3\"}, inplace=True)\n",
    "#and write the A_i values back into the dataframe\n",
    "london_flows_b = london_flows_b.merge(A_i, left_on=\"Orig\", right_index=True, how=\"left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now generate new scenario estimate \n",
    "london_flows_b['prodsimest_b3']=london_flows_b['A_i3']*london_flows_b['O_i']*Dj_gamma*dist_beta_50\n",
    "# round\n",
    "london_flows_b['prodsimest_b3']=round(london_flows_b['prodsimest_b3'])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Investigate the change\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    61413.000000\n",
       "mean        -0.007344\n",
       "std        103.140603\n",
       "min     -12479.000000\n",
       "25%          0.000000\n",
       "50%          2.000000\n",
       "75%          7.000000\n",
       "max       3829.000000\n",
       "Name: diff_b1, dtype: float64"
      ]
     },
     "execution_count": 392,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows_b['diff_b1']=london_flows_b['prodsimest_b1']-london_flows_b['Total']\n",
    "london_flows_b['diff_b1'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Orig</th>\n",
       "      <th>Dest</th>\n",
       "      <th>Total</th>\n",
       "      <th>Oi_origpop</th>\n",
       "      <th>Dj_destjob</th>\n",
       "      <th>Dist</th>\n",
       "      <th>unconstrainedEst1</th>\n",
       "      <th>log_Oi_origpop</th>\n",
       "      <th>log_Dj_destjob</th>\n",
       "      <th>log_Dist</th>\n",
       "      <th>...</th>\n",
       "      <th>A_i</th>\n",
       "      <th>A_i1</th>\n",
       "      <th>prodsimest_b1</th>\n",
       "      <th>A_i2_x</th>\n",
       "      <th>prodsimest_b2</th>\n",
       "      <th>A_i2_y</th>\n",
       "      <th>A_i2</th>\n",
       "      <th>A_i3</th>\n",
       "      <th>prodsimest_b3</th>\n",
       "      <th>diff_b1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>58127</th>\n",
       "      <td>West India Quay</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>0</td>\n",
       "      <td>162</td>\n",
       "      <td>58772</td>\n",
       "      <td>327.235548</td>\n",
       "      <td>1197</td>\n",
       "      <td>5.087596</td>\n",
       "      <td>10.981421</td>\n",
       "      <td>5.790680</td>\n",
       "      <td>...</td>\n",
       "      <td>0.026512</td>\n",
       "      <td>0.031079</td>\n",
       "      <td>92.0</td>\n",
       "      <td>0.036475</td>\n",
       "      <td>94.0</td>\n",
       "      <td>0.028811</td>\n",
       "      <td>0.028811</td>\n",
       "      <td>0.037091</td>\n",
       "      <td>94.0</td>\n",
       "      <td>92.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40970</th>\n",
       "      <td>Poplar</td>\n",
       "      <td>West India Quay</td>\n",
       "      <td>3</td>\n",
       "      <td>2271</td>\n",
       "      <td>400</td>\n",
       "      <td>260.856791</td>\n",
       "      <td>180</td>\n",
       "      <td>7.727976</td>\n",
       "      <td>5.991465</td>\n",
       "      <td>5.563972</td>\n",
       "      <td>...</td>\n",
       "      <td>0.033512</td>\n",
       "      <td>0.041477</td>\n",
       "      <td>51.0</td>\n",
       "      <td>0.048679</td>\n",
       "      <td>46.0</td>\n",
       "      <td>0.038678</td>\n",
       "      <td>0.038678</td>\n",
       "      <td>0.049794</td>\n",
       "      <td>46.0</td>\n",
       "      <td>48.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58147</th>\n",
       "      <td>West India Quay</td>\n",
       "      <td>Poplar</td>\n",
       "      <td>0</td>\n",
       "      <td>162</td>\n",
       "      <td>1301</td>\n",
       "      <td>260.856791</td>\n",
       "      <td>42</td>\n",
       "      <td>5.087596</td>\n",
       "      <td>7.170888</td>\n",
       "      <td>5.563972</td>\n",
       "      <td>...</td>\n",
       "      <td>0.026512</td>\n",
       "      <td>0.031079</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.036475</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.028811</td>\n",
       "      <td>0.028811</td>\n",
       "      <td>0.037091</td>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33545</th>\n",
       "      <td>Mansion House</td>\n",
       "      <td>Cannon Street</td>\n",
       "      <td>1</td>\n",
       "      <td>516</td>\n",
       "      <td>4698</td>\n",
       "      <td>248.175187</td>\n",
       "      <td>530</td>\n",
       "      <td>6.246107</td>\n",
       "      <td>8.454892</td>\n",
       "      <td>5.514135</td>\n",
       "      <td>...</td>\n",
       "      <td>0.008486</td>\n",
       "      <td>0.012892</td>\n",
       "      <td>23.0</td>\n",
       "      <td>0.015131</td>\n",
       "      <td>23.0</td>\n",
       "      <td>0.012021</td>\n",
       "      <td>0.012021</td>\n",
       "      <td>0.015476</td>\n",
       "      <td>23.0</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4 rows × 52 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Orig             Dest  Total  Oi_origpop  Dj_destjob  \\\n",
       "58127  West India Quay     Canary Wharf      0         162       58772   \n",
       "40970           Poplar  West India Quay      3        2271         400   \n",
       "58147  West India Quay           Poplar      0         162        1301   \n",
       "33545    Mansion House    Cannon Street      1         516        4698   \n",
       "\n",
       "             Dist  unconstrainedEst1  log_Oi_origpop  log_Dj_destjob  \\\n",
       "58127  327.235548               1197        5.087596       10.981421   \n",
       "40970  260.856791                180        7.727976        5.991465   \n",
       "58147  260.856791                 42        5.087596        7.170888   \n",
       "33545  248.175187                530        6.246107        8.454892   \n",
       "\n",
       "       log_Dist  ...       A_i      A_i1  prodsimest_b1    A_i2_x  \\\n",
       "58127  5.790680  ...  0.026512  0.031079           92.0  0.036475   \n",
       "40970  5.563972  ...  0.033512  0.041477           51.0  0.048679   \n",
       "58147  5.563972  ...  0.026512  0.031079            7.0  0.036475   \n",
       "33545  5.514135  ...  0.008486  0.012892           23.0  0.015131   \n",
       "\n",
       "       prodsimest_b2    A_i2_y      A_i2      A_i3  prodsimest_b3  diff_b1  \n",
       "58127           94.0  0.028811  0.028811  0.037091           94.0     92.0  \n",
       "40970           46.0  0.038678  0.038678  0.049794           46.0     48.0  \n",
       "58147            6.0  0.028811  0.028811  0.037091            6.0      7.0  \n",
       "33545           23.0  0.012021  0.012021  0.015476           23.0     22.0  \n",
       "\n",
       "[4 rows x 52 columns]"
      ]
     },
     "execution_count": 399,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows_dist= london_flows_b.sort_values([\"Dist\"], ascending=False)\n",
    "london_flows_dist[-5:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Orig</th>\n",
       "      <th>Dest</th>\n",
       "      <th>Total</th>\n",
       "      <th>Dist</th>\n",
       "      <th>prodsimest_b1</th>\n",
       "      <th>diff_b1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>32584</th>\n",
       "      <td>London Bridge</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>445</td>\n",
       "      <td>886.711434</td>\n",
       "      <td>4274.0</td>\n",
       "      <td>3829.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32282</th>\n",
       "      <td>Liverpool Street</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>812</td>\n",
       "      <td>841.490882</td>\n",
       "      <td>4025.0</td>\n",
       "      <td>3213.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32441</th>\n",
       "      <td>Liverpool Street</td>\n",
       "      <td>Moorgate</td>\n",
       "      <td>172</td>\n",
       "      <td>434.080019</td>\n",
       "      <td>3028.0</td>\n",
       "      <td>2856.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56086</th>\n",
       "      <td>Waterloo</td>\n",
       "      <td>Southwark</td>\n",
       "      <td>109</td>\n",
       "      <td>656.415167</td>\n",
       "      <td>2511.0</td>\n",
       "      <td>2402.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56133</th>\n",
       "      <td>Waterloo</td>\n",
       "      <td>Westminster</td>\n",
       "      <td>717</td>\n",
       "      <td>850.342561</td>\n",
       "      <td>2703.0</td>\n",
       "      <td>1986.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Orig               Dest  Total        Dist  prodsimest_b1  \\\n",
       "32584     London Bridge  Bank and Monument    445  886.711434         4274.0   \n",
       "32282  Liverpool Street  Bank and Monument    812  841.490882         4025.0   \n",
       "32441  Liverpool Street           Moorgate    172  434.080019         3028.0   \n",
       "56086          Waterloo          Southwark    109  656.415167         2511.0   \n",
       "56133          Waterloo        Westminster    717  850.342561         2703.0   \n",
       "\n",
       "       diff_b1  \n",
       "32584   3829.0  \n",
       "32282   3213.0  \n",
       "32441   2856.0  \n",
       "56086   2402.0  \n",
       "56133   1986.0  "
      ]
     },
     "execution_count": 397,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff_b_max=london_flows_b.nlargest(5,'diff_b1')\n",
    "diff_b_max[['Orig','Dest','Total','Dist','prodsimest_b1','diff_b1']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Orig</th>\n",
       "      <th>Dest</th>\n",
       "      <th>Dist</th>\n",
       "      <th>Total</th>\n",
       "      <th>prodsimest_b1</th>\n",
       "      <th>diff_b1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>55890</th>\n",
       "      <td>Waterloo</td>\n",
       "      <td>Bank and Monument</td>\n",
       "      <td>2542.900106</td>\n",
       "      <td>15946</td>\n",
       "      <td>3467.0</td>\n",
       "      <td>-12479.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55915</th>\n",
       "      <td>Waterloo</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>7433.856719</td>\n",
       "      <td>8085</td>\n",
       "      <td>1089.0</td>\n",
       "      <td>-6996.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32609</th>\n",
       "      <td>London Bridge</td>\n",
       "      <td>Canary Wharf</td>\n",
       "      <td>5679.110688</td>\n",
       "      <td>6165</td>\n",
       "      <td>674.0</td>\n",
       "      <td>-5491.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50041</th>\n",
       "      <td>Stratford</td>\n",
       "      <td>Liverpool Street</td>\n",
       "      <td>6698.344174</td>\n",
       "      <td>6946</td>\n",
       "      <td>1997.0</td>\n",
       "      <td>-4949.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54769</th>\n",
       "      <td>Victoria</td>\n",
       "      <td>Oxford Circus</td>\n",
       "      <td>2220.118547</td>\n",
       "      <td>5181</td>\n",
       "      <td>1617.0</td>\n",
       "      <td>-3564.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Orig               Dest         Dist  Total  prodsimest_b1  \\\n",
       "55890       Waterloo  Bank and Monument  2542.900106  15946         3467.0   \n",
       "55915       Waterloo       Canary Wharf  7433.856719   8085         1089.0   \n",
       "32609  London Bridge       Canary Wharf  5679.110688   6165          674.0   \n",
       "50041      Stratford   Liverpool Street  6698.344174   6946         1997.0   \n",
       "54769       Victoria      Oxford Circus  2220.118547   5181         1617.0   \n",
       "\n",
       "       diff_b1  \n",
       "55890 -12479.0  \n",
       "55915  -6996.0  \n",
       "32609  -5491.0  \n",
       "50041  -4949.0  \n",
       "54769  -3564.0  "
      ]
     },
     "execution_count": 396,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff_b_min=london_flows_b.nsmallest(5,'diff_b1')\n",
    "diff_b_min[['Orig','Dest','Dist','Total','prodsimest_b1','diff_b1']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Total</th>\n",
       "      <th>prodsimest_b1</th>\n",
       "      <th>prodsimest_b2</th>\n",
       "      <th>prodsimest_b3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>61413.000000</td>\n",
       "      <td>61413.000000</td>\n",
       "      <td>61413.000000</td>\n",
       "      <td>61413.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>25.113298</td>\n",
       "      <td>25.105955</td>\n",
       "      <td>25.105629</td>\n",
       "      <td>25.105629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>131.479668</td>\n",
       "      <td>83.564952</td>\n",
       "      <td>85.431747</td>\n",
       "      <td>85.431747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>7.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>13.000000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>20.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>15946.000000</td>\n",
       "      <td>4274.000000</td>\n",
       "      <td>4441.000000</td>\n",
       "      <td>4441.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Total  prodsimest_b1  prodsimest_b2  prodsimest_b3\n",
       "count  61413.000000   61413.000000   61413.000000   61413.000000\n",
       "mean      25.113298      25.105955      25.105629      25.105629\n",
       "std      131.479668      83.564952      85.431747      85.431747\n",
       "min        0.000000       0.000000       0.000000       0.000000\n",
       "25%        0.000000       2.000000       2.000000       2.000000\n",
       "50%        3.000000       7.000000       7.000000       7.000000\n",
       "75%       13.000000      20.000000      20.000000      20.000000\n",
       "max    15946.000000    4274.000000    4441.000000    4441.000000"
      ]
     },
     "execution_count": 389,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "london_flows_b[['Total','prodsimest_b1','prodsimest_b2','prodsimest_b3']].describe()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Which scenario would have more impact in the redistribution of flows? \n",
    "Explain and justify your answers using the results of the analysis"
   ]
  }
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