course_2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import utils\n",
    "utils.set_pretty_prints()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We have PyTorch version 1.4.0\n"
     ]
    }
   ],
   "source": [
    "import torch as th\n",
    "print(\"We have PyTorch version\", th.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading dataset 'california_housing' using 'fetch_california_housing' with normalize=True...\n",
      "Data loaded:\n",
      "  x_train    (16512, 8)\n",
      "  y_train    (16512, 1)\n",
      "  x_dev      (2064, 8)\n",
      "  y_dev      (2064, 1)\n",
      "  x_test     (2064, 8)\n",
      "  y_test     (2064, 1)\n",
      "  df         (20640, 8)\n",
      "  desc       \".. _california_housing_dataset:California Housing dataset--------------------------**Data Set C\"\n"
     ]
    }
   ],
   "source": [
    "bd = utils.load_dataset('california_housing')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>MedInc</th>\n",
       "      <th>HouseAge</th>\n",
       "      <th>AveRooms</th>\n",
       "      <th>AveBedrms</th>\n",
       "      <th>Population</th>\n",
       "      <th>AveOccup</th>\n",
       "      <th>Latitude</th>\n",
       "      <th>Longitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.3252</td>\n",
       "      <td>41.0</td>\n",
       "      <td>6.9841</td>\n",
       "      <td>1.0238</td>\n",
       "      <td>322.0</td>\n",
       "      <td>2.5556</td>\n",
       "      <td>37.88</td>\n",
       "      <td>-122.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.3014</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6.2381</td>\n",
       "      <td>0.9719</td>\n",
       "      <td>2401.0</td>\n",
       "      <td>2.1098</td>\n",
       "      <td>37.86</td>\n",
       "      <td>-122.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.2574</td>\n",
       "      <td>52.0</td>\n",
       "      <td>8.2881</td>\n",
       "      <td>1.0734</td>\n",
       "      <td>496.0</td>\n",
       "      <td>2.8023</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.6431</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5.8174</td>\n",
       "      <td>1.0731</td>\n",
       "      <td>558.0</td>\n",
       "      <td>2.5479</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.8462</td>\n",
       "      <td>52.0</td>\n",
       "      <td>6.2819</td>\n",
       "      <td>1.0811</td>\n",
       "      <td>565.0</td>\n",
       "      <td>2.1815</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4.0368</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.7617</td>\n",
       "      <td>1.1036</td>\n",
       "      <td>413.0</td>\n",
       "      <td>2.1399</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.6591</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.9319</td>\n",
       "      <td>0.9514</td>\n",
       "      <td>1094.0</td>\n",
       "      <td>2.1284</td>\n",
       "      <td>37.84</td>\n",
       "      <td>-122.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.1200</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.7975</td>\n",
       "      <td>1.0618</td>\n",
       "      <td>1157.0</td>\n",
       "      <td>1.7883</td>\n",
       "      <td>37.84</td>\n",
       "      <td>-122.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2.0804</td>\n",
       "      <td>42.0</td>\n",
       "      <td>4.2941</td>\n",
       "      <td>1.1176</td>\n",
       "      <td>1206.0</td>\n",
       "      <td>2.0269</td>\n",
       "      <td>37.84</td>\n",
       "      <td>-122.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.6912</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.9706</td>\n",
       "      <td>0.9902</td>\n",
       "      <td>1551.0</td>\n",
       "      <td>2.1723</td>\n",
       "      <td>37.84</td>\n",
       "      <td>-122.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>3.2031</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5.4776</td>\n",
       "      <td>1.0796</td>\n",
       "      <td>910.0</td>\n",
       "      <td>2.2637</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>3.2705</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.7725</td>\n",
       "      <td>1.0245</td>\n",
       "      <td>1504.0</td>\n",
       "      <td>2.0490</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.0750</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5.3226</td>\n",
       "      <td>1.0128</td>\n",
       "      <td>1098.0</td>\n",
       "      <td>2.3462</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2.6736</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.0000</td>\n",
       "      <td>1.0977</td>\n",
       "      <td>345.0</td>\n",
       "      <td>1.9828</td>\n",
       "      <td>37.84</td>\n",
       "      <td>-122.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.9167</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.2629</td>\n",
       "      <td>1.0097</td>\n",
       "      <td>1212.0</td>\n",
       "      <td>1.9548</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2.1250</td>\n",
       "      <td>50.0</td>\n",
       "      <td>4.2424</td>\n",
       "      <td>1.0720</td>\n",
       "      <td>697.0</td>\n",
       "      <td>2.6402</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2.7750</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5.9396</td>\n",
       "      <td>1.0483</td>\n",
       "      <td>793.0</td>\n",
       "      <td>2.3958</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2.1202</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.0528</td>\n",
       "      <td>0.9670</td>\n",
       "      <td>648.0</td>\n",
       "      <td>2.1386</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1.9911</td>\n",
       "      <td>50.0</td>\n",
       "      <td>5.3437</td>\n",
       "      <td>1.0859</td>\n",
       "      <td>990.0</td>\n",
       "      <td>2.3628</td>\n",
       "      <td>37.84</td>\n",
       "      <td>-122.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2.6033</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5.4655</td>\n",
       "      <td>1.0836</td>\n",
       "      <td>690.0</td>\n",
       "      <td>2.5091</td>\n",
       "      <td>37.84</td>\n",
       "      <td>-122.27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    MedInc  HouseAge  AveRooms  AveBedrms  Population  AveOccup  Latitude  Longitude\n",
       "0   8.3252      41.0    6.9841     1.0238       322.0    2.5556     37.88    -122.23\n",
       "1   8.3014      21.0    6.2381     0.9719      2401.0    2.1098     37.86    -122.22\n",
       "2   7.2574      52.0    8.2881     1.0734       496.0    2.8023     37.85    -122.24\n",
       "3   5.6431      52.0    5.8174     1.0731       558.0    2.5479     37.85    -122.25\n",
       "4   3.8462      52.0    6.2819     1.0811       565.0    2.1815     37.85    -122.25\n",
       "5   4.0368      52.0    4.7617     1.1036       413.0    2.1399     37.85    -122.25\n",
       "6   3.6591      52.0    4.9319     0.9514      1094.0    2.1284     37.84    -122.25\n",
       "7   3.1200      52.0    4.7975     1.0618      1157.0    1.7883     37.84    -122.25\n",
       "8   2.0804      42.0    4.2941     1.1176      1206.0    2.0269     37.84    -122.26\n",
       "9   3.6912      52.0    4.9706     0.9902      1551.0    2.1723     37.84    -122.25\n",
       "10  3.2031      52.0    5.4776     1.0796       910.0    2.2637     37.85    -122.26\n",
       "11  3.2705      52.0    4.7725     1.0245      1504.0    2.0490     37.85    -122.26\n",
       "12  3.0750      52.0    5.3226     1.0128      1098.0    2.3462     37.85    -122.26\n",
       "13  2.6736      52.0    4.0000     1.0977       345.0    1.9828     37.84    -122.26\n",
       "14  1.9167      52.0    4.2629     1.0097      1212.0    1.9548     37.85    -122.26\n",
       "15  2.1250      50.0    4.2424     1.0720       697.0    2.6402     37.85    -122.26\n",
       "16  2.7750      52.0    5.9396     1.0483       793.0    2.3958     37.85    -122.27\n",
       "17  2.1202      52.0    4.0528     0.9670       648.0    2.1386     37.85    -122.27\n",
       "18  1.9911      50.0    5.3437     1.0859       990.0    2.3628     37.84    -122.26\n",
       "19  2.6033      52.0    5.4655     1.0836       690.0    2.5091     37.84    -122.27"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bd.df.iloc[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _california_housing_dataset:\n",
      "\n",
      "California Housing dataset\n",
      "--------------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 20640\n",
      "\n",
      "    :Number of Attributes: 8 numeric, predictive attributes and the target\n",
      "\n",
      "    :Attribute Information:\n",
      "        - MedInc        median income in block\n",
      "        - HouseAge      median house age in block\n",
      "        - AveRooms      average number of rooms\n",
      "        - AveBedrms     average number of bedrooms\n",
      "        - Population    block population\n",
      "        - AveOccup      average house occupancy\n",
      "        - Latitude      house block latitude\n",
      "        - Longitude     house block longitude\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "This dataset was obtained from the StatLib repository.\n",
      "http://lib.stat.cmu.edu/datasets/\n",
      "\n",
      "The target variable is the median house value for California districts.\n",
      "\n",
      "This dataset was derived from the 1990 U.S. census, using one row per census\n",
      "block group. A block group is the smallest geographical unit for which the U.S.\n",
      "Census Bureau publishes sample data (a block group typically has a population\n",
      "of 600 to 3,000 people).\n",
      "\n",
      "It can be downloaded/loaded using the\n",
      ":func:`sklearn.datasets.fetch_california_housing` function.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "    - Pace, R. Kelley and Ronald Barry, Sparse Spatial Autoregressions,\n",
      "      Statistics and Probability Letters, 33 (1997) 291-297\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(bd.desc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAF2CAYAAAC7w0Z9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO3df3RU9Z3/8ddkAoRkIM5MiJgAlkDYQ5A0lHAKqCSFcdmiVQSWIgtnAY/uGpfIDz0EreDWymYrkRh+HFrR4BHPtl2E1B577DGNCbtSjwn5IQVXQkUQAwQyEUhIwCT3+8d8nRgJZIB8MiF5Ps7hHOYzn3vnfd/5wYvPvTPXZlmWJQAAABgTEuwCAAAAejoCFwAAgGEELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4ALQqQoLC2Wz2XT8+PFgl3JT+Pzzz2Wz2fS///u//jGbzaYdO3YYfd3t27crNDTU6GsAaEXgAnqJRYsWyWazafbs2Zc9l5eXJ5vNZuQfYALYtTtx4oTmzJkT7DIAdCICF9CLDBs2TH/4wx906tSpNuO//vWvdfvttwepqu7t0qVLXf6agwcPVlhYWJe/LgBzCFxALxIfH6+JEydq+/bt/rFjx47pvffe0+LFiy+bv2/fPv393/+9HA6HBg0apFmzZuno0aNt5mzcuFFDhgxReHi4pk+frmPHjl21hm9WvN577z1NmTJF4eHhSkhI0J/+9Kc286qrq7V48WLdeuutCgsL09/93d/ptddeu+J+Fy1aJI/H4w+PAwcO1AMPPKDTp0+3mff6668rISFB/fr105AhQ/Szn/1MTU1N/udTU1P18MMP69lnn9Vtt92m2NhYSdL3vvc9Pfvss3rssccUGRmp6Ohobdq0SRcvXtTSpUvldDoVGxurTZs2tXm9l19+WUlJSXI4HBo8eLDmzZunEydOXLVH3z6l+Nxzz8lms132Z9GiRf757733nu688071799fsbGxWrx4sWpqavzPW5alZ599VtHR0XI4HJo3b55qa2uvWgOAzkXgAnqZRx99VNu2bdM3d/Xatm2bpk2bdtkK18GDB5WSkqJJkyappKREBQUFstvtuueee9TY2ChJ+v3vf6/ly5drxYoVKi8v19y5c/XUU08FVMeTTz6pp59+WhUVFUpOTtZPf/pTffXVV5KkhoYGpaSkqKKiQm+++aYOHjyojRs3Kjw8/Kr7LC4u1vvvv6933nlH7777rsrLy/Xkk0/6n3/nnXe0ZMkSLVy4UPv371dWVpY2b96sf//3f2+zn9/97nc6ffq0/vznP6ugoMA/vnHjRsXHx2vfvn1KT09Xenq6HnzwQQ0fPlzFxcX6t3/7N6Wnp+vgwYNt9rd+/Xrt379fu3fv1rFjxzRv3ryAevRNn06cOOH/8/bbbys0NFSpqamSpIKCAj3wwAOaN2+ePv74Y+Xl5enzzz/Xgw8+6P8a5+Tk6KWXXtKLL76o0tJS/eAHP7jsmAEYZgHoFf75n//ZmjZtmtXQ0GC5XC6roKDAampqsmJjY6233nrLys3Ntex2e5v5P/3pT9vso7Gx0erfv7+1e/duy7Is684777Tmz5/fZs7KlSstSdYXX3xhWZZlvf/+++0+fuutt/zbnDhxwpJkvfvuu5ZlWda2bdusfv36+bcJ9PiioqKsxsZG/9h//Md/WIMHD/Y/vuuuu6x//Md/bLNddna2FRYWZl28eNGyLMtKSUmx4uPjrebm5jbzbr/9duuBBx7wP25ubrYGDBhg3XfffW3GbrnlFmvjxo1XrLO0tNSSZB0/ftyyLMs6cuSIJcn6n//5H/8cSdYbb7xx2bbHjh2zBg8ebD311FP+sZSUFGvVqlVt5h09etSSZJWVlVmWZVmxsbHW008/3WbO7Nmz23y9AZjFChfQy4SFhWnhwoV65ZVX9M4776ipqUk/+clPLptXXFys3bt3y+Fw+P+43W41NjaqsrJSkm8VbPLkyW22u+uuuwKqIykpyf/3wYMHy263+68t27dvnxISEjRkyJBrOrbRo0erX79+/sexsbFtrlc7cOCApkyZ0mablJQUNTY26m9/+5t/bPz48QoJufzX4/e//33/30NCQjRo0CAlJia2GYuOjlZ1dbV/rLCwUNOnT9fQoUM1YMAAf3++e2q2I3V1dfrJT36iSZMmKTMz0z9eXFys7OzsNl+nhIQESVJlZaXOnTunL7/88rq/TgA6B+8JBnqhf/mXf9G4ceN07NgxLV68WH369LlsTktLixYuXKiMjIzLnnO73f6/22y266qhb9++7b7mjez3u/u02Wz+02pX2u83z397PCIiot39f7dPNput3bFvjuPYsWOaMWOGFi5cqDVr1igqKkrHjx+Xx+O5povxW1paNH/+fPXp00c7duxoEwZbWlq0atUqLVy48LLtBg8erObm5suOD0DXI3ABvdDo0aM1YcIEffDBB3r99dfbnZOcnKyPP/5YI0aMuOI/1gkJCfrggw+UlpbmH/vggw9uuL7x48frtdde0/Hjx695letqxowZo6KiIj3++OP+sT179qh///6Ki4vrtNf5RnFxsRoaGpSdna3+/ftL8q3eXasnn3xS5eXl+uijjy67ji05OVkHDhzQyJEjr7h9bGysPvjgA82YMcM/1hlfJwCB45Qi0Ev96U9/0pkzZzRixIh2n3/66af1ySefaMGCBfroo4905MgRvf/++3riiSf02WefSZJWrlyp3/72t3r55ZdVWVmp3NxcvfHGGzdc20MPPaTbb79d999/v/Lz83XkyBH9+c9/1m9/+9sb2u/q1av11ltvKTMzU4cOHdLvfvc7Pffcc1q5cmW7K243Kj4+XjabTVlZWTpy5Ijy8vL085///Jr2sX37dm3ZskXbtm2TJJ08eVInT57U2bNnJUk///nP/W9eKC8v19/+9je9++67evjhh9XQ0CDJ93V6+eWX9cYbb6iyslJZWVnKz8/v3IMFcFUELqCXCg8Pl8vluuLzo0eP1t69e1VXV6fp06crISFBjzzyiBoaGnTLLbdIkh588EFlZWXpl7/8pRITE/Xmm2/qP//zPzultqKiIt1xxx2aN2+eRo8erccff9wfIK7XjBkz9Nprr+n111/XHXfcoeXLlystLU1r16694Zrbk5iYqI0bN+pXv/qVEhIStH79emVnZ1/TPgoLC3Xx4kVNnz5dt912m//PE088IUn60Y9+pIKCAu3fv1933323EhMTtXz5cg0YMMB/uvOJJ55Qenq6li9frqSkJP3lL3/RmjVrOv14AVyZzfruBQ4AAADoVKxwAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMO6/SfNV1VVBTQvKipKZ86cMVxN90cfWtELH/rQil740Acf+tCKXvjcaB9iYmKu+BwrXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhAX0OV319vbZu3aovvvhCNptNjz32mGJiYrRhwwadPn1agwYN0vLly+VwOGRZlnJzc1VWVqZ+/fopLS1NcXFxkqTCwkLt2rVLkjRr1iylpqYaOzAAAIDuIqDAlZubq6SkJK1cuVJNTU26ePGidu/erbFjx2rmzJnKy8tTXl6eFixYoLKyMp08eVI5OTmqrKzUtm3btG7dOtXV1Wnnzp3KzMyUJGVkZCg5OVkOh8PoAQIAAARbh6cUL1y4oE8++URTp06VJIWGhioiIkLFxcVKSUmRJKWkpKi4uFiSVFJSoilTpshms2nUqFGqr69XbW2tysvLlZiYKIfDIYfDocTERJWXlxs8NAAAgO6hwxWu6upqDRw4UFu2bNHRo0cVFxenRYsW6ezZs3I6nZIkp9Opc+fOSZK8Xq+ioqL827vdbnm9Xnm9Xrndbv+4y+WS1+vt7OMBAADodjoMXM3NzTpy5IiWLFmi+Ph45ebmKi8v74rzLcu6bMxms7U7t73x/Px85efnS5IyMzPbhLerCQ0NDXhuT0YfWtELH/rQil740Acf+tCKXviY7EOHgcvtdsvtdis+Pl6SNHHiROXl5SkyMlK1tbVyOp2qra3VwIED/fO/fePHmpoaOZ1OuVwuHTx40D/u9XqVkJBw2et5PB55PB7/40BvIsmNN33oQyt64UMfWtELH/rgQx9a0Qsfkzev7jBw3XLLLXK73aqqqlJMTIz279+vIUOGaMiQISoqKtLMmTNVVFSkCRMmSJKSk5P17rvv6s4771RlZaXCw8PldDqVlJSk//qv/1JdXZ0kqaKiQvPnz7/ug8Llmh+5X6eCXUQnsb/ydrBLAACg0wT0LsUlS5YoJydHTU1Nio6OVlpamizL0oYNG1RQUKCoqCitWLFCkjRu3DiVlpYqPT1dffv2VVpamiTJ4XBo9uzZWr16tSRpzpw5vEMRAAD0CjarvYuuupGqqqqA5rEc6lvh6ik6Y4WL7wkf+tCKXvjQBx/60Ipe+Jg8pcgnzQMAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGEbgAgAAMIzABQAAYBiBCwAAwLDQQCY9/vjjCgsLU0hIiOx2uzIzM1VXV6cNGzbo9OnTGjRokJYvXy6HwyHLspSbm6uysjL169dPaWlpiouLkyQVFhZq165dkqRZs2YpNTXV2IEBAAB0FwEFLklau3atBg4c6H+cl5ensWPHaubMmcrLy1NeXp4WLFigsrIynTx5Ujk5OaqsrNS2bdu0bt061dXVaefOncrMzJQkZWRkKDk5WQ6Ho/OPCgAAoBu57lOKxcXFSklJkSSlpKSouLhYklRSUqIpU6bIZrNp1KhRqq+vV21trcrLy5WYmCiHwyGHw6HExESVl5d3zlEAAAB0YwGvcL3wwguSpHvuuUcej0dnz56V0+mUJDmdTp07d06S5PV6FRUV5d/O7XbL6/XK6/XK7Xb7x10ul7xe72Wvk5+fr/z8fElSZmZmm31d9UBCQwOe21OdCnYBnagzvpZ8T/jQh1b0woc++NCHVvTCx2QfAgpczz//vFwul86ePatf/OIXiomJueJcy7IuG7PZbO3ObW/c4/HI4/H4H585cyaQEhUVFRXwXHR/nfG15HvChz60ohc+9MGHPrSiFz432oer5aOATim6XC5JUmRkpCZMmKDDhw8rMjJStbW1kqTa2lr/9V1ut7tNsTU1NXI6nXK5XKqpqfGPe71e/woZAABAT9Zh4GpsbFRDQ4P/7x9//LGGDRum5ORkFRUVSZKKioo0YcIESVJycrL27Nkjy7J06NAhhYeHy+l0KikpSRUVFaqrq1NdXZ0qKiqUlJRk8NAAAAC6hw5PKZ49e1br16+XJDU3N+uuu+5SUlKSRowYoQ0bNqigoEBRUVFasWKFJGncuHEqLS1Venq6+vbtq7S0NEmSw+HQ7NmztXr1aknSnDlzeIciAADoFWxWexdddSNVVVUBzeP8s9T8yP3BLqHT2F95+4b3wfeED31oRS986IMPfWhFL3xMXsMV8LsUga7UGeGxu7xrszPCIwDg5satfQAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGBYa6MSWlhZlZGTI5XIpIyND1dXVys7OVl1dnYYPH66lS5cqNDRUX3/9tTZt2qTPPvtMAwYM0LJlyxQdHS1J2r17twoKChQSEqLFixcrKSnJ2IEBAAB0FwGvcP3xj39UbGys//GOHTt07733KicnRxERESooKJAkFRQUKCIiQhs3btS9996rN998U5J0/Phx7d27Vy+99JKeeeYZvfrqq2ppaenkwwEAAOh+AgpcNTU1Ki0t1bRp0yRJlmXpwIEDmjhxoiQpNTVVxcXFkqSSkhKlpqZKkiZOnKi//vWvsixLxcXFmjx5svr06aPo6GgNHjxYhw8fNnBIAAAA3UtApxS3b9+uBQsWqKGhQZJ0/vx5hYeHy263S5JcLpe8Xq8kyev1yu12S5LsdrvCw8N1/vx5eb1excfH+/f57W2+LT8/X/n5+ZKkzMxMRUVFBXYgoaEBz+2pTgW7ALQr2N+X/Gy0ohc+9MGHPrSiFz4m+9Bh4Nq3b58iIyMVFxenAwcOdLhDy7IuG7PZbO2Ot8fj8cjj8fgfnzlzJqDtoqKiAp4LdKVgf1/ys9GKXvjQBx/60Ipe+NxoH2JiYq74XIeB69NPP1VJSYnKysp06dIlNTQ0aPv27bpw4YKam5tlt9vl9XrlcrkkSW63WzU1NXK73WpubtaFCxfkcDj849/49jYAAAA9WYfXcM2fP19bt27V5s2btWzZMt1xxx1KT0/XmDFj9OGHH0qSCgsLlZycLEkaP368CgsLJUkffvihxowZI5vNpuTkZO3du1dff/21qqurdeLECY0cOdLckQEAAHQTAX8sxHf90z/9k7Kzs/Wb3/xGw4cP19SpUyVJU6dO1aZNm7R06VI5HA4tW7ZMkjR06FBNmjRJK1asUEhIiB5++GGFhPAxYAAAoOezWYFeXBUkVVVVAc3j/LPU/Mj9wS4B7bC/8nZQX5+fjVb0woc++NCHVvTCx+Q1XCwxAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgWGhHEy5duqS1a9eqqalJzc3NmjhxoubOnavq6mplZ2errq5Ow4cP19KlSxUaGqqvv/5amzZt0meffaYBAwZo2bJlio6OliTt3r1bBQUFCgkJ0eLFi5WUlGT8AAEAAIKtwxWuPn36aO3atXrxxRf1y1/+UuXl5Tp06JB27Nihe++9Vzk5OYqIiFBBQYEkqaCgQBEREdq4caPuvfdevfnmm5Kk48ePa+/evXrppZf0zDPP6NVXX1VLS4vZowMAAOgGOgxcNptNYWFhkqTm5mY1NzfLZrPpwIEDmjhxoiQpNTVVxcXFkqSSkhKlpqZKkiZOnKi//vWvsixLxcXFmjx5svr06aPo6GgNHjxYhw8fNnRYAAAA3UeHpxQlqaWlRatWrdLJkyc1ffp03XrrrQoPD5fdbpckuVwueb1eSZLX65Xb7ZYk2e12hYeH6/z58/J6vYqPj/fv89vbfFt+fr7y8/MlSZmZmYqKigrsQEJDA57bU50KdgFoV7C/L/nZaEUvfOiDD31oRS98TPYhoMAVEhKiF198UfX19Vq/fr2+/PLLK861LOuyMZvN1u54ezwejzwej//xmTNnAtouKioq4LlAVwr29yU/G63ohQ998KEPreiFz432ISYm5orPXdO7FCMiIpSQkKDKykpduHBBzc3NknyrWi6XS5LkdrtVU1MjyXcK8sKFC3I4HG3Gv7sNAABAT9Zh4Dp37pzq6+sl+d6xuH//fsXGxmrMmDH68MMPJUmFhYVKTk6WJI0fP16FhYWSpA8//FBjxoyRzWZTcnKy9u7dq6+//lrV1dU6ceKERo4caeiwAAAAuo8OTynW1tZq8+bNamlpkWVZmjRpksaPH68hQ4YoOztbv/nNbzR8+HBNnTpVkjR16lRt2rRJS5culcPh0LJlyyRJQ4cO1aRJk7RixQqFhITo4YcfVkgIHwMGAAB6PpsV6MVVQVJVVRXQPM4/S82P3B/sEtAO+ytvB/X1+dloRS986IMPfWhFL3y6zTVcAAAAuHYELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMNCg10A0NM1P3J/UF//VCfuy/7K2524NwDoPVjhAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYFtrRhDNnzmjz5s366quvZLPZ5PF4NGPGDNXV1WnDhg06ffq0Bg0apOXLl8vhcMiyLOXm5qqsrEz9+vVTWlqa4uLiJEmFhYXatWuXJGnWrFlKTU01enAAAADdQYeBy263a+HChYqLi1NDQ4MyMjKUmJiowsJCjR07VjNnzlReXp7y8vK0YMEClZWV6eTJk8rJyVFlZaW2bdumdevWqa6uTjt37lRmZqYkKSMjQ8nJyXI4HMYPEgAAIJg6PKXodDr9K1T9+/dXbGysvF6viouLlZKSIklKSUlRcXGxJKmkpERTpkyRzWbTqFGjVF9fr9raWpWXlysxMVEOh0MOh0OJiYkqLy83eGgAAADdwzVdw1VdXa0jR45o5MiROnv2rJxOpyRfKDt37pwkyev1Kioqyr+N2+2W1+uV1+uV2+32j7tcLnm93s44BgAAgG6tw1OK32hsbFRWVpYWLVqk8PDwK86zLOuyMZvN1u7c9sbz8/OVn58vScrMzGwT3q4mNDQ04Lk91algF4Ae72b/GeP3hA998KEPreiFj8k+BBS4mpqalJWVpbvvvls//OEPJUmRkZGqra2V0+lUbW2tBg4cKMm3onXmzBn/tjU1NXI6nXK5XDp48KB/3Ov1KiEh4bLX8ng88ng8/sff3tfVREVFBTwXwPW52X/G+D3hQx986EMreuFzo32IiYm54nMdnlK0LEtbt25VbGys7rvvPv94cnKyioqKJElFRUWaMGGCf3zPnj2yLEuHDh1SeHi4nE6nkpKSVFFRobq6OtXV1amiokJJSUnXfVAAAAA3iw5XuD799FPt2bNHw4YN01NPPSVJeuihhzRz5kxt2LBBBQUFioqK0ooVKyRJ48aNU2lpqdLT09W3b1+lpaVJkhwOh2bPnq3Vq1dLkubMmcM7FAEAQK9gs9q76KobqaqqCmgey6FS8yP3B7sE9HD2V94Odgk3hN8TPvTBhz60ohc+QT2lCAAAgBtD4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhAX/SfE/Gu/sAAIBJrHABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGGhHU3YsmWLSktLFRkZqaysLElSXV2dNmzYoNOnT2vQoEFavny5HA6HLMtSbm6uysrK1K9fP6WlpSkuLk6SVFhYqF27dkmSZs2apdTUVHNHBQAA0I10uMKVmpqqp59+us1YXl6exo4dq5ycHI0dO1Z5eXmSpLKyMp08eVI5OTl69NFHtW3bNkm+gLZz506tW7dO69at086dO1VXV2fgcAAAALqfDgNXQkKCHA5Hm7Hi4mKlpKRIklJSUlRcXCxJKikp0ZQpU2Sz2TRq1CjV19ertrZW5eXlSkxMlMPhkMPhUGJiosrLyw0cDgAAQPdzXddwnT17Vk6nU5LkdDp17tw5SZLX61VUVJR/ntvtltfrldfrldvt9o+7XC55vd4bqRsAAOCm0eE1XNfCsqzLxmw2W7tzrzSen5+v/Px8SVJmZmabAHc1oaGhAc/9rlPXtRXQ+1zvz1h3cSO/J3oS+uBDH1rRCx+TfbiuwBUZGana2lo5nU7V1tZq4MCBknwrWmfOnPHPq6mpkdPplMvl0sGDB/3jXq9XCQkJ7e7b4/HI4/H4H397f1cTFRUV8FwA1+dm/xnj94QPffChD63ohc+N9iEmJuaKz13XKcXk5GQVFRVJkoqKijRhwgT/+J49e2RZlg4dOqTw8HA5nU4lJSWpoqJCdXV1qqurU0VFhZKSkq7npQEAAG46Ha5wZWdn6+DBgzp//rz+9V//VXPnztXMmTO1YcMGFRQUKCoqSitWrJAkjRs3TqWlpUpPT1ffvn2VlpYmSXI4HJo9e7ZWr14tSZozZ85lF+IDAAD0VDarvQuvupGqqqqA5t3IMmDzI/df13ZAb2N/5e1gl3BDOG3iQx986EMreuHT7U4pAgAAIC4ErDsAAAeuSURBVHAELgAAAMMIXAAAAIZ16udwAejZbvbrHb/5zL2b/Vo0ADcfVrgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYQQuAAAAwwhcAAAAhhG4AAAADCNwAQAAGEbgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMMIXAAAAIYRuAAAAAwjcAEAABhG4AIAADCMwAUAAGAYgQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMCw12AQDQ1ZofuT/YJXQa+ytvB7sEAAFghQsAAMAwAhcAAIBhBC4AAADDCFwAAACGEbgAAAAMI3ABAAAYRuACAAAwjMAFAABgGIELAADAMAIXAACAYdzaBwBuYtdzm6JTBuroDNymCD0ZK1wAAACGEbgAAAAM6/JTiuXl5crNzVVLS4umTZummTNndnUJAIBu6HpOj94Ik6dWOT2K7+rSwNXS0qJXX31VP/vZz+R2u7V69WolJydryJAhXVkGAAAIQFeHYJOCHYK7NHAdPnxYgwcP1q233ipJmjx5soqLiwlcAIAe5WYLKt31jRQ9SZdew+X1euV2u/2P3W63vF5vV5YAAADQ5bp0hcuyrMvGbDZbm8f5+fnKz8+XJGVmZiomJibg/V/L3DbeKbm+7QAAQI9y3VmiA126wuV2u1VTU+N/XFNTI6fT2WaOx+NRZmamMjMzr2nfGRkZnVLjzY4+tKIXPvShFb3woQ8+9KEVvfAx2YcuDVwjRozQiRMnVF1draamJu3du1fJycldWQIAAECX69JTina7XUuWLNELL7yglpYW/ehHP9LQoUO7sgQAAIAuZ3/uueee68oXvO222/TjH/9YM2bM0OjRozt133FxcZ26v5sVfWhFL3zoQyt64UMffOhDK3rhY6oPNqu9K9kBAADQabi1DwAAgGFdfmsfU9544w3t27dPoaGhuvXWW5WWlqaIiIhglxUUf/nLX/Tf//3f+vLLL7Vu3TqNGDEi2CV1KW4f5bNlyxaVlpYqMjJSWVlZwS4naM6cOaPNmzfrq6++ks1mk8fj0YwZM4JdVlBcunRJa9euVVNTk5qbmzVx4kTNnTs32GUFTUtLizIyMuRyuXr1u/Qef/xxhYWFKSQkRHa7/Zo/JaCnqK+v19atW/XFF1/IZrPpscce06hRozpt/z0mcCUmJmr+/Pmy2+3asWOHdu/erQULFgS7rKAYOnSonnzySf36178OdildjttHtUpNTdU//MM/aPPmzcEuJajsdrsWLlyouLg4NTQ0KCMjQ4mJib3ye6JPnz5au3atwsLC1NTUpDVr1igpKalT/1G5mfzxj39UbGysGhoagl1K0K1du1YDBw4MdhlBlZubq6SkJK1cuVJNTU26ePFip+6/x5xS/P73vy+73S5JGjVqVK/+BPshQ4YY++C27u7bt48KDQ313z6qN0pISJDD4Qh2GUHndDr9F8H2799fsbGxvfb3g81mU1hYmCSpublZzc3Nl334dG9RU1Oj0tJSTZs2LdiloBu4cOGCPvnkE02dOlWSFBoa2ulnyXrMCte3FRQUaPLkycEuA0HQ3u2jKisrg1gRupPq6modOXJEI0eODHYpQdPS0qJVq1bp5MmTmj59uuLj44NdUlBs375dCxYsYHXr/3vhhRckSffcc488Hk+Qq+l61dXVGjhwoLZs2aKjR48qLi5OixYt8v8HpTPcVIHr+eef11dffXXZ+Lx58zRhwgRJ0q5du2S323X33Xd3dXldKpBe9EaB3D4KvVNjY6OysrK0aNEihYeHB7ucoAkJCdGLL76o+vp6rV+/XseOHdOwYcOCXVaX2rdvnyIjIxUXF6cDBw4Eu5yge/755+VyuXT27Fn94he/UExMjBISEoJdVpdqbm7WkSNHtGTJEsXHxys3N1d5eXmaN29ep73GTRW4nn322as+X1hYqH379mnNmjU9/h/ZjnrRWwVy+yj0Pk1NTcrKytLdd9+tH/7wh8Eup1uIiIhQQkKCysvLe13g+vTTT1VSUqKysjJdunRJDQ0NysnJUXp6erBLCwqXyyVJioyM1IQJE3T48OFeF7jcbrfcbrd/xXfixInKy8vr1NfoMddwlZeX6/e//71WrVqlfv36BbscBAm3j8J3WZalrVu3KjY2Vvfdd1+wywmqc+fOqb6+XpLvHYv79+9XbGxskKvqevPnz9fWrVu1efNmLVu2THfccUevDVuNjY3+06qNjY36+OOPe10Al6RbbrlFbrdbVVVVkqT9+/d3+htreswHny5dulRNTU3+i4Tj4+P16KOPBrmq4Pjoo4/02muv6dy5c4qIiND3vvc9PfPMM8Euq8uUlpbq9ddf998+atasWcEuKSiys7N18OBBnT9/XpGRkZo7d67/gtDe5P/+7/+0Zs0aDRs2zL/y/dBDD+kHP/hBkCvrekePHtXmzZvV0tIiy7I0adIkzZkzJ9hlBdWBAwf0hz/8odd+LMSpU6e0fv16Sb7TanfddVev/Z35+eefa+vWrWpqalJ0dLTS0tI69Y1HPSZwAQAAdFc95pQiAABAd0XgAgAAMIzABQAAYBiBCwAAwDACFwAAgGEELgAAAMMIXAAAAIYRuAAAAAz7fyX5Obb6pm7iAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmIAAAF2CAYAAADN+fT2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO3de3CU5aHH8d8myy1ZCLsbAgZQEwFrUmKwQS6nQoRte0ZEOcjBC2q5KGIsiKiVS4899cKk1ZAYIdUCAwqdgx4GkNbW9qQx5AiDBkIoJCog2IEmISQbLkuAQPY9fzDsMRIE8iY8IXw/M8y4T55993l+s21+875vdh2WZVkCAADAFRdmegEAAADXKooYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRA9Bivv76azkcDn3yySe2jzVx4kT5fL5mWFXb9e2M/vM//1N9+vRp8de98cYb9corr7T46wBtEUUMaGMmTpwoh8Mhh8Mhp9OpG264QdOmTVN1dbXppV2SlStXyuFwnDf+xhtv6L//+78NrOjq9dxzz2nz5s2mlwHgOzhNLwBA87vjjjv0/vvv68yZM9q6dasee+wx7d+/Xx9++KHppTVZVFSU6SXYVldXp/bt21+x13O5XHK5XFfs9QBcPs6IAW1Q+/bt1aNHD/Xq1Uv33nuvZs6cqY8++kgnTpyQJH355ZcaNWpU6Bf16NGjtWfPntDzly9fLqfTqdzcXCUmJqpjx466/fbbVVRUdN6cbzpw4IAcDofy8/MvuLZ58+bplltuUUREhHr37q1p06bpyJEjkqT8/Hw98sgjkhQ6qzdx4kRJ5192syxLr7/+uuLj49W+fXvddNNNysrKavBaN954o1588UU9/fTT8ng86t69u5577jnV19dfcH3nLqe+//77Gj16tCIiIhQfH68VK1Y0mFdeXq4HHnhAXbt2VadOnZSamqotW7aEfp6fny+Hw6EPP/xQP/zhD9WxY0f97ne/C+X28ccfq3///urUqZOGDx+usrIyFRQUaMCAAYqMjJTP59M///nP0PH27dunsWPHKjY2VhEREerfv/95a/q2b1+aPJfpt/99/fXXkqRAIKCnn35aPXv2VEREhAYMGKA1a9Y0OOb27ds1dOhQdezYUf369dP777//nWsA8N0oYsA1oFOnTgoGgzpz5oxOnDihH//4xzp58qQ2bNigDRs2KBAI6F//9V9VV1cXek4wGNTPf/5z5eTk6LPPPlNMTIxGjRql2tpa22v53e9+p9LSUi1fvlz5+fmaMWOGJGno0KFauHChpLNFp7y8XG+88Uajx8nJydF//Md/aPbs2SopKdHzzz+v2bNna+nSpQ3mvfnmm7ruuuv06aefKjs7W1lZWXr33Xcvus7Zs2frkUce0d///neNHz9ekyZN0u7duyWdLYFjxozRF198oT/+8Y/67LPP1L17d/3oRz9SVVVVg+M8++yz+vnPf67PP/9cY8aMkXQ221/96ldasmSJNm7cqLKyMt1///168cUX9dvf/laffPKJDhw4oFmzZoWOEwgENHLkSH300UfasWOHpk6dqkmTJunjjz++xOT/P9Py8nKVlZXJ5/PplltuUffu3WVZlkaPHq3t27frvffe086dO/Xkk0/qgQce0N/+9jdJ0okTJ3TXXXepa9eu+vTTT/XOO+/otddeU2Vl5SWvAcC3WADalJ/+9KfWyJEjQ49LSkqs+Ph4a9CgQZZlWdaSJUusTp06WYcOHQrNqaiosDp27Gi98847lmVZ1rJlyyxJVm5ubmiO3++3IiMjrcWLF4fmhIeHN3jt/fv3W5Ksjz/+2LIsy9q3b58lyfrf//3fC653zZo1Vvv27a36+nrLsixrxYoVVmP/1/TtffXq1ct6/vnnG8yZOXOmFRcXF3p8ww03WKNHj24w5yc/+Yn1wAMPXHA959ackZERGjt9+rQVGRlpvfXWW5ZlWVZubq4lySopKQnNOXnypNWjRw/rV7/6lWVZlvXxxx9bkqx33323wfHPZbtt27bQ2G9+8xtLkrVly5bQ2IIFCyyv13vBdVqWZd1zzz3WY489Fnr87Yx++ctfWjfddFOjz507d64VExNj7d27N7TeDh06WIcPH24wb9KkSda9995rWZZlLV682IqMjLT8fn/o5zt27LAkWS+//PJ3rhVA47hHDGiD8vPz5XK5VF9fr1OnTmnkyJF6++23JUklJSVKSEhQdHR0aH737t118803q6SkpMFxhgwZEvpvt9utW265RaWlpbbWtmbNGmVlZWnPnj06evSogsGg6urqVFFRodjY2Es6xtGjR3XgwAENGzaswfjw4cP1xhtvqLa2VhEREZKk5OTkBnN69uypffv2XfQ1vvk8p9Op7t276+DBg5LOZuj1epWQkBCa06FDBw0aNOi8DG+//fbzju1wONS/f//Q4x49ekiSkpKSGoxVV1ervr5e4eHhqq2t1UsvvaQ//OEPKi8vV11dnU6dOqU777zzonv5thUrVmjBggXKy8tTXFycJKmwsFB1dXXq2bNng7l1dXXq27evJKm0tFS33HKL3G536Off//7328T9e4ApFDGgDRo0aJDeeecdOZ1OXXfdderQoUODnzf2V4mWZTU6/u0554SFnX9nw+nTp7/z+Z9++qn+/d//XXPmzNFrr70mt9utzZs366c//WmDy6KX6tvr/eb6zvn2zfEOh0PBYPCix77Y8y41w8jIyPPmhYWFKTw8/LxjtWvX7ryxc3t6/vnn9cEHHygjI0Pf+973FBkZqWeffTZ0f92l+uSTTzR16lQtX768QdEOBoOKiopSYWHhec85l8WlvEcAXB7uEQPaoE6dOqlPnz668cYbzythiYmJKikpaXAv08GDB7Vr1y4lJiY2mPvNjz44fPiwvvjiC91yyy2SpJiYGNXX14fOEklqcDN/Yz755BNFR0frlVde0aBBg9SvXz8dOHCgwZxzv/S/64b6Ll26qFevXtqwYUOD8YKCAsXFxYXOhrWUxMREVVVVNTg7eOrUKX322WfnZdhcCgoKNGHCBN1///269dZbFR8fr127dl3WMfbu3at/+7d/0y9+8Qvdf//9DX6WkpKiw4cP6+TJk+rTp0+Df9dff72ks/suLS3V4cOHQ88rKSm57DII4P9RxIBrzEMPPaRu3brp/vvvV1FRkbZu3aoHHnhAPXv2bPDL2eFw6Oc//7kKCgq0Y8cOPfroo4qMjNRDDz0k6ewlt86dO2v27NnavXu3PvroI7300kvf+do333yzDh06pKVLl2rv3r169913lZOT02DOuUtl69ev16FDhxQIBBo91pw5c/Tmm29q8eLF2r17t95++2399re/1dy5c+3Ec0lGjBih22+/XQ899JA2btyonTt36tFHH9XJkyf15JNPtshr3nzzzfrggw/02WefqbS0VFOnTlVZWdklP//EiRO6++67NWTIEE2ZMkUVFRWhf/X19RoxYoR8Pp/Gjh2rtWvXau/evdq6dWsoY+nse6dz5856+OGHtX37dm3evFmTJ09Wp06dWmTPwLWAIgZcYzp16qS//vWv6tChg4YNG6bhw4crMjJSH330UYPLcWFhYZo/f76eeOIJpaSkqLy8XB9++GHoUpvH49F//dd/afPmzUpKStLLL7+s3/zmN9/52nfffbfmzZunuXPnqn///lq1apVee+21BnMGDhyop59+WtOmTVP37t31s5/9rNFjPfnkk3rppZc0f/58JSQk6Ne//rXS09M1ZcoUmwldnMPh0Lp16/S9731Po0aN0sCBA1VRUaH/+Z//aXDvXXPKzMzUDTfcoDvvvFMjR45Uz549NW7cuEt+/sGDB/X555/rD3/4g6677roG//bv3y+Hw6H169dr7NixmjVrVmhvH374oW666SZJUkREhP70pz+purpat99+uyZMmKBnnnlGMTExLbJn4FrgsBq7qQLANW358uV67LHHdObMGdNLAYA2jTNiAAAAhlDEAAAADOHSJAAAgCGcEQMAADCEIgYAAGAIRQwAAMCQq/orji7nwwxbg+jo6AafZo7LR4b2kJ99ZGgP+dlHhvaYyu9C36XLGTEAAABDKGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAkIt+jlhOTo6KiooUFRWljIyM0Pif//xnffTRRwoPD9dtt92mhx9+WJK0du1a5eXlKSwsTJMmTVJycrIkqbi4WMuWLVMwGNTIkSM1ZswYSVJlZaWysrIUCAQUFxen6dOny+m8qj/eDAAA4JJc9IxYamqq5s6d22Bs586d2rJli15//XUtWLBAo0ePliQdOHBAmzZt0oIFCzRv3jwtXbpUwWBQwWBQS5cu1dy5c5WZmamNGzfqwIEDkqSVK1dq1KhRys7OVmRkpPLy8lpgmwAAAK3PRYtYQkKCXC5Xg7G//vWvuvfee9WuXTtJUlRUlCSpsLBQQ4cOVbt27RQTE6MePXpoz5492rNnj3r06KHu3bvL6XRq6NChKiwslGVZKikp0eDBgyWdLX2FhYXNvUcAAIBWqUnXAMvLy/XFF19o1apVateunR555BH16dNHfr9fffv2Dc3zeDzy+/2SJK/XGxr3er3avXu3jh07poiICIWHh583vzG5ubnKzc2VJKWnpys6OropyzfG6XRedWtubcjQHvKzjwztIT/7yNCe1pZfk4pYMBhUIBDQq6++qq+++kqZmZlauHChLMtqdH5j4w6H47Jf1+fzyefzhR5fbd+1xfeD2UeG9pCffWRoD/nZR4b2tLbvmmxSEfN4PBo0aJAcDof69OmjsLAwHTt2TF6vV9XV1aF5fr9fHo9HkhqMV1dXy+12q3PnzqqtrVV9fb3Cw8MbzAcAAGjrmlTEBg4cqJ07dyoxMVFlZWU6c+aMOnfurJSUFGVnZ+vuu+9WTU2NysvL1adPH1mWpfLyclVWVsrj8WjTpk2aMWOGHA6HEhMTtXnzZv3Lv/yL8vPzlZKS0tx7bLL6x+9p1uMdbNajXZ7wxesNvjoAAGjMRYtYVlaWSktLdezYMU2bNk3jx4/XiBEjlJOTo2effVZOp1NPPfWUHA6HevfurSFDhmjWrFkKCwvTlClTFBZ29u8BJk+erFdffVXBYFB33nmnevfuLUmaMGGCsrKytGrVKsXFxWnEiBEtu2MAAIBWwmFd6Mauq0BZWVmLHr+5z4iZ1FbOiHFvhD3kZx8Z2kN+9pGhPa3tHjE+WR8AAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAEIoYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMoYgBAAAY4rzYhJycHBUVFSkqKkoZGRkNfrZ+/XqtXLlSS5YsUZcuXWRZlpYtW6Zt27apQ4cOSktLU3x8vCQpPz9fa9askSSNHTtWqampkqS9e/dq0aJFqqur04ABAzRp0iQ5HI5m3iYAAEDrc9EzYqmpqZo7d+5541VVVdqxY4eio6NDY9u2bVNFRYWys7M1depULVmyRJIUCAS0evVqzZ8/X/Pnz9fq1asVCAQkSYsXL9YTTzyh7OxsVVRUqLi4uLn2BgAA0KpdtIglJCTI5XKdN/7OO+9owoQJDc5ebdmyRcOGDZPD4VC/fv10/Phx1dTUqLi4WElJSXK5XHK5XEpKSlJxcbFqamp04sQJ9evXTw6HQ8OGDVNhYWHz7hAAAKCVuuilycZs2bJFHo9HN954Y4Nxv9/f4AyZ1+uV3++X3++X1+sNjXs8nkbHz82/kNzcXOXm5kqS0tPTG7xWSzjYoke/slo6qyvF6XS2mb2YQH72kaE95GcfGdrT2vK77CJ26tQprVmzRr/4xS/O+5llWeeNXeh+L4fD0ej87+Lz+eTz+UKPq6qqLuv517K2klV0dHSb2YsJ5GcfGdpDfvaRoT2m8ouNjW10/LL/avLgwYOqrKzU888/r6eeekrV1dV64YUXdPjwYXm93gabq66ultvtlsfjUXV1dWjc7/fL7XbL6/U2GK+urpbH47ncJQEAAFyVLruIXX/99VqyZIkWLVqkRYsWyev16te//rW6du2qlJQUFRQUyLIs7dq1SxEREXK73UpOTtb27dsVCAQUCAS0fft2JScny+12q1OnTtq1a5csy1JBQYFSUlJaYp8AAACtzkUvTWZlZam0tFTHjh3TtGnTNH78eI0YMaLRuQMGDFBRUZFmzJih9u3bKy0tTZLkcrl03333ac6cOZKkcePGhf4A4LHHHlNOTo7q6uqUnJysAQMGNNfeAAAAWjWHdbk3arUiZWVlLXr8+sfvadHjX0nhi9ebXkKz4N4Ie8jPPjK0h/zsI0N7rvp7xAAAANA8KGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAEIoYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgiPNiE3JyclRUVKSoqChlZGRIklasWKGtW7fK6XSqe/fuSktLU2RkpCRp7dq1ysvLU1hYmCZNmqTk5GRJUnFxsZYtW6ZgMKiRI0dqzJgxkqTKykplZWUpEAgoLi5O06dPl9N50WUBAABc9S56Riw1NVVz585tMJaUlKSMjAy9/vrruu6667R27VpJ0oEDB7Rp0yYtWLBA8+bN09KlSxUMBhUMBrV06VLNnTtXmZmZ2rhxow4cOCBJWrlypUaNGqXs7GxFRkYqLy+vBbYJAADQ+ly0iCUkJMjlcjUYu/XWWxUeHi5J6tevn/x+vySpsLBQQ4cOVbt27RQTE6MePXpoz5492rNnj3r06KHu3bvL6XRq6NChKiwslGVZKikp0eDBgyWdLX2FhYXNvUcAAIBWyfY9Ynl5eaHLj36/X16vN/Qzj8cjv99/3rjX65Xf79exY8cUERERKnXn5gMAAFwLbN2MtWbNGoWHh+uOO+6QJFmW1ei8xsYdDsdlv15ubq5yc3MlSenp6YqOjr7sY1yOgy169CurpbO6UpxOZ5vZiwnkZx8Z2kN+9pGhPa0tvyYXsfz8fG3dulUvvvhiqFR5vV5VV1eH5vj9fnk8HklqMF5dXS23263OnTurtrZW9fX1Cg8PbzC/MT6fTz6fL/S4qqqqqcu/5rSVrKKjo9vMXkwgP/vI0B7ys48M7TGVX2xsbKPjTbo0WVxcrA8++EAvvPCCOnToEBpPSUnRpk2bdPr0aVVWVqq8vFx9+vTRTTfdpPLyclVWVurMmTPatGmTUlJS5HA4lJiYqM2bN0s6W+5SUlKasiQAAICrzkXPiGVlZam0tFTHjh3TtGnTNH78eK1du1ZnzpzRyy+/LEnq27evpk6dqt69e2vIkCGaNWuWwsLCNGXKFIWFne16kydP1quvvqpgMKg777xTvXv3liRNmDBBWVlZWrVqleLi4jRixIgW3C4AAEDr4bAudGPXVaCsrKxFj1//+D0tevwrKXzxetNLaBackreH/OwjQ3vIzz4ytKdNXJoEAACAfRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAEIoYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMMR5sQk5OTkqKipSVFSUMjIyJEmBQECZmZk6dOiQunXrpmeeeUYul0uWZWnZsmXatm2bOnTooLS0NMXHx0uS8vPztWbNGknS2LFjlZqaKknau3evFi1apLq6Og0YMECTJk2Sw+Fooe0CAAC0Hhc9I5aamqq5c+c2GFu3bp369++v7Oxs9e/fX+vWrZMkbdu2TRUVFcrOztbUqVO1ZMkSSWeL2+rVqzV//nzNnz9fq1evViAQkCQtXrxYTzzxhLKzs1VRUaHi4uLm3iMAAECrdNEilpCQIJfL1WCssLBQw4cPlyQNHz5chYWFkqQtW7Zo2LBhcjgc6tevn44fP66amhoVFxcrKSlJLpdLLpdLSUlJKi4uVk1NjU6cOKF+/frJ4XBo2LBhoWMBAAC0dU26R+zIkSNyu92SJLfbraNHj0qS/H6/oqOjQ/O8Xq/8fr/8fr+8Xm9o3OPxNDp+bj4AAMC14KL3iF0Oy7LOG7vQ/V4Oh6PR+d8lNzdXubm5kqT09PQGpa8lHGzRo19ZLZ3VleJ0OtvMXkwgP/vI0B7ys48M7Wlt+TWpiEVFRammpkZut1s1NTXq0qWLpLNntKqqqkLzqqur5Xa75fF4VFpaGhr3+/1KSEiQ1+tVdXV1g/kej+eCr+vz+eTz+UKPv/la+G5tJavo6Og2sxcTyM8+MrSH/OwjQ3tM5RcbG9voeJMuTaakpGjDhg2SpA0bNmjgwIGh8YKCAlmWpV27dikiIkJut1vJycnavn27AoGAAoGAtm/fruTkZLndbnXq1Em7du2SZVkqKChQSkpKE7cIAABwdbnoGbGsrCyVlpbq2LFjmjZtmsaPH68xY8YoMzNTeXl5io6O1qxZsyRJAwYMUFFRkWbMmKH27dsrLS1NkuRyuXTfffdpzpw5kqRx48aF/gDgscceU05Ojurq6pScnKwBAwa01F4BAABaFYd1uTdqtSJlZWUtevz6x+9p0eNfSeGL15teQrPglLw95GcfGdpDfvaRoT1t4tIkAAAA7KOIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAEIoYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEOcdp78xz/+UXl5eXI4HOrdu7fS0tJ0+PBhZWVlKRAIKC4uTtOnT5fT6dTp06e1cOFC7d27V507d9bMmTMVExMjSVq7dq3y8vIUFhamSZMmKTk5uVk2BwAA0Jo1+YyY3+/Xn//8Z6WnpysjI0PBYFCbNm3SypUrNWrUKGVnZysyMlJ5eXmSpLy8PEVGRurNN9/UqFGj9Pvf/16SdODAAW3atEkLFizQvHnztHTpUgWDwebZHQAAQCtm69JkMBhUXV2d6uvrVVdXp65du6qkpESDBw+WJKWmpqqwsFCStGXLFqWmpkqSBg8erJ07d8qyLBUWFmro0KFq166dYmJi1KNHD+3Zs8fergAAAK4CTb406fF4NHr0aD355JNq3769br31VsXHxysiIkLh4eGhOX6/X9LZM2her1eSFB4eroiICB07dkx+v199+/ZtcNxzz/m23Nxc5ebmSpLS09MVHR3d1OVfkoMtevQrq6WzulKcTmeb2YsJ5GcfGdpDfvaRoT2tLb8mF7FAIKDCwkItWrRIERERWrBggYqLiy8437Ks88YcDkej4xfi8/nk8/lCj6uqqi5v0dewtpJVdHR0m9mLCeRnHxnaQ372kaE9pvKLjY1tdLzJlyZ37NihmJgYdenSRU6nU4MGDdKXX36p2tpa1dfXSzp7Fszj8UiSvF6vqqurJUn19fWqra2Vy+VqMP7t5wAAALRlTS5i0dHR2r17t06dOiXLsrRjxw716tVLiYmJ2rx5syQpPz9fKSkpkqQf/OAHys/PlyRt3rxZiYmJcjgcSklJ0aZNm3T69GlVVlaqvLxcffr0sb8zAACAVq7Jlyb79u2rwYMH64UXXlB4eLhuvPFG+Xw+3XbbbcrKytKqVasUFxenESNGSJJGjBihhQsXavr06XK5XJo5c6YkqXfv3hoyZIhmzZqlsLAwTZkyRWFhfLwZAABo+xzW5dyk1cqUlZW16PHrH7+nRY9/JYUvXm96Cc2CeyPsIT/7yNAe8rOPDO1pM/eIAQAAwB6KGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAEIoYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABjitPPk48eP66233tL+/fvlcDj05JNPKjY2VpmZmTp06JC6deumZ555Ri6XS5ZladmyZdq2bZs6dOigtLQ0xcfHS5Ly8/O1Zs0aSdLYsWOVmppqe2MAAACtna0itmzZMiUnJ+vZZ5/VmTNndOrUKa1du1b9+/fXmDFjtG7dOq1bt04PP/ywtm3bpoqKCmVnZ2v37t1asmSJ5s+fr0AgoNWrVys9PV2SNHv2bKWkpMjlcjXLBgEAAFqrJl+arK2t1eeff64RI0ZIkpxOpyIjI1VYWKjhw4dLkoYPH67CwkJJ0pYtWzRs2DA5HA7169dPx48fV01NjYqLi5WUlCSXyyWXy6WkpCQVFxc3w9YAAABatyafEausrFSXLl2Uk5Ojf/zjH4qPj9fEiRN15MgRud1uSZLb7dbRo0clSX6/X9HR0aHne71e+f1++f1+eb3e0LjH45Hf72/0NXNzc5WbmytJSk9Pb3C8lnCwRY9+ZbV0VleK0+lsM3sxgfzsI0N7yM8+MrSnteXX5CJWX1+vffv2afLkyerbtw4ktrQAAA87SURBVK+WLVumdevWXXC+ZVnnjTkcjkbnXmjc5/PJ5/OFHldVVV3mqq9dbSWr6OjoNrMXE8jPPjK0h/zsI0N7TOUXGxvb6HiTL016vV55vV717dtXkjR48GDt27dPUVFRqqmpkSTV1NSoS5cuofnf3Hh1dbXcbrc8Ho+qq6tD436/P3RGDQAAoC1rchHr2rWrvF6vysrKJEk7duxQr169lJKSog0bNkiSNmzYoIEDB0qSUlJSVFBQIMuytGvXLkVERMjtdis5OVnbt29XIBBQIBDQ9u3blZyc3AxbAwAAaN1s/dXk5MmTlZ2drTNnzigmJkZpaWmyLEuZmZnKy8tTdHS0Zs2aJUkaMGCAioqKNGPGDLVv315paWmSJJfLpfvuu09z5syRJI0bN46/mAQAANcEh9XYzVtXiXNn41pK/eP3tOjxr6TwxetNL6FZcG+EPeRnHxnaQ372kaE9beYeMQAAANhDEQMAADCEIgYAAGAIRQwAAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAEIoYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMAQihgAAIAhFDEAAABDnHYPEAwGNXv2bHk8Hs2ePVuVlZXKyspSIBBQXFycpk+fLqfTqdOnT2vhwoXau3evOnfurJkzZyomJkaStHbtWuXl5SksLEyTJk1ScnKy7Y0BAAC0drbPiP3pT39Sz549Q49XrlypUaNGKTs7W5GRkcrLy5Mk5eXlKTIyUm+++aZGjRql3//+95KkAwcOaNOmTVqwYIHmzZunpUuXKhgM2l0WAABAq2eriFVXV6uoqEgjR46UJFmWpZKSEg0ePFiSlJqaqsLCQknSli1blJqaKkkaPHiwdu7cKcuyVFhYqKFDh6pdu3aKiYlRjx49tGfPHjvLAgAAuCrYujS5fPlyPfzwwzpx4oQk6dixY4qIiFB4eLgkyePxyO/3S5L8fr+8Xq8kKTw8XBERETp27Jj8fr/69u0bOuY3n/Ntubm5ys3NlSSlp6crOjrazvIv6mCLHv3KaumsrhSn09lm9mIC+dlHhvaQn31kaE9ry6/JRWzr1q2KiopSfHy8SkpKLjrfsqzzxhwOR6PjF+Lz+eTz+UKPq6qqLvm517q2klV0dHSb2YsJ5GcfGdpDfvaRoT2m8ouNjW10vMlF7Msvv9SWLVu0bds21dXV6cSJE1q+fLlqa2tVX1+v8PBw+f1+eTweSZLX61V1dbW8Xq/q6+tVW1srl8sVGj/nm88BAABoy5p8j9hDDz2kt956S4sWLdLMmTP1/e9/XzNmzFBiYqI2b94sScrPz1dKSook6Qc/+IHy8/MlSZs3b1ZiYqIcDodSUlK0adMmnT59WpWVlSovL1efPn3s7wwAAKCVs/3xFd82YcIEZWVladWqVYqLi9OIESMkSSNGjNDChQs1ffp0uVwuzZw5U5LUu3dvDRkyRLNmzVJYWJimTJmisDA+3gwAALR9DutybtJqZcrKylr0+PWP39Oix7+SwhevN72EZsG9EfaQn31kaA/52UeG9rS2e8Q49QQAAGAIRQwAAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAEIoYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMAQihgAAIAhFDEAAABDKGIAAACGUMQAAAAMcTb1iVVVVVq0aJEOHz4sh8Mhn8+nu+66S4FAQJmZmTp06JC6deumZ555Ri6XS5ZladmyZdq2bZs6dOigtLQ0xcfHS5Ly8/O1Zs0aSdLYsWOVmpraLJsDAABozZpcxMLDw/XII48oPj5eJ06c0OzZs5WUlKT8/Hz1799fY8aM0bp167Ru3To9/PDD2rZtmyoqKpSdna3du3dryZIlmj9/vgKBgFavXq309HRJ0uzZs5WSkiKXy9VsmwQAAGiNmnxp0u12h85oderUST179pTf71dhYaGGDx8uSRo+fLgKCwslSVu2bNGwYcPkcDjUr18/HT9+XDU1NSouLlZSUpJcLpdcLpeSkpJUXFzcDFsDAABo3ZrlHrHKykrt27dPffr00ZEjR+R2uyWdLWtHjx6VJPn9fkVHR4ee4/V65ff75ff75fV6Q+Mej0d+v785lgUAANCqNfnS5DknT55URkaGJk6cqIiIiAvOsyzrvDGHw9Ho3AuN5+bmKjc3V5KUnp7eoNi1hIMtevQrq6WzulKcTmeb2YsJ5GcfGdpDfvaRoT2tLT9bRezMmTPKyMjQHXfcoUGDBkmSoqKiVFNTI7fbrZqaGnXp0kXS2TNgVVVVoedWV1fL7XbL4/GotLQ0NO73+5WQkNDo6/l8Pvl8vtDjbx4P362tZBUdHd1m9mIC+dlHhvaQn31kaI+p/GJjYxsdb/KlScuy9NZbb6lnz566++67Q+MpKSnasGGDJGnDhg0aOHBgaLygoECWZWnXrl2KiIiQ2+1WcnKytm/frkAgoEAgoO3btys5ObmpywIAALhqNPmM2JdffqmCggJdf/31ev755yVJDz74oMaMGaPMzEzl5eUpOjpas2bNkiQNGDBARUVFmjFjhtq3b6+0tDRJksvl0n333ac5c+ZIksaNG8dfTAIAgGuCw2rs5q2rRFlZWYsev/7xe1r0+FdS+OL1ppfQLDglbw/52UeG9pCffWRoT5u5NAkAAAB7KGIAAACGUMQAAAAMoYgBAAAYQhEDAAAwhCIGAABgCEUMAADAEIoYAACAIRQxAAAAQyhiAAAAhlDEAAAADKGIAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMAQp+kF4Mqof/we00toFgclhS9eb3oZAAA0C86IAQAAGEIRAwAAMIQiBgAAYAhFDAAAwBCKGAAAgCEUMQAAAENazcdXFBcXa9myZQoGgxo5cqTGjBljekkAAAAtqlWcEQsGg1q6dKnmzp2rzMxMbdy4UQcOHDC9LAAAgBbVKs6I7dmzRz169FD37t0lSUOHDlVhYaF69epleGVojdrKh9PywbQAgFZxRszv98vr9YYee71e+f1+gysCAABoea3ijJhlWeeNORyO88Zyc3OVm5srSUpPT1dsbGzLLuzDLS17fMCAFv/fzTWADO0hP/vI0J7WlF+rOCPm9XpVXV0delxdXS23233ePJ/Pp/T0dKWnp1/J5TWb2bNnm17CVY8M7SE/+8jQHvKzjwztaW35tYoidtNNN6m8vFyVlZU6c+aMNm3apJSUFNPLAgAAaFGt4tJkeHi4Jk+erFdffVXBYFB33nmnevfubXpZAAAALapVFDFJuu2223TbbbeZXkaL8vl8ppdw1SNDe8jPPjK0h/zsI0N7Wlt+DquxO+UBAADQ4lrFPWIAAADXolZzabKt4yuc7HnqqafUsWNHhYWFKTw8/Kr9y9krKScnR0VFRYqKilJGRoYkKRAIKDMzU4cOHVK3bt30zDPPyOVyGV5p69VYhu+//77+9re/qUuXLpKkBx98sM3fVtFUVVVVWrRokQ4fPiyHwyGfz6e77rqL9+ElulB+vAcvXV1dnX75y1/qzJkzqq+v1+DBgzV+/HhVVlYqKytLgUBAcXFxmj59upxOQ5XIQourr6+3fvazn1kVFRXW6dOnreeee87av3+/6WVdVdLS0qwjR46YXsZVpaSkxPrqq6+sWbNmhcZWrFhhrV271rIsy1q7dq21YsUKU8u7KjSW4XvvvWd98MEHBld19fD7/dZXX31lWZZl1dbWWjNmzLD279/P+/ASXSg/3oOXLhgMWidOnLAsy7JOnz5tzZkzx/ryyy+tjIwM65NPPrEsy7Lefvtt6y9/+YuxNXJp8gr45lc4OZ3O0Fc4AS0pISHhvLMMhYWFGj58uCRp+PDhvA8vorEMcencbrfi4+MlSZ06dVLPnj3l9/t5H16iC+WHS+dwONSxY0dJUn19verr6+VwOFRSUqLBgwdLklJTU42+B7k0eQU09hVOu3fvNriiq9Orr74qSfrRj37U6v7q5Wpx5MiR0Iclu91uHT161PCKrk5/+ctfVFBQoPj4eD366KOUtUtQWVmpffv2qU+fPrwPm+Cb+X3xxRe8By9DMBjUCy+8oIqKCv3kJz9R9+7dFRERofDwcEmSx+MxWnApYleAdYlf4YQLe/nll+XxeHTkyBG98sorio2NVUJCgull4Rr04x//WOPGjZMkvffee3r33XeVlpZmeFWt28mTJ5WRkaGJEycqIiLC9HKuOt/Oj/fg5QkLC9Nrr72m48eP6/XXX9c///lP00tqgEuTV8ClfoUTLszj8UiSoqKiNHDgQO3Zs8fwiq5OUVFRqqmpkSTV1NSEbvbFpevatavCwsIUFhamkSNH6quvvjK9pFbtzJkzysjI0B133KFBgwZJ4n14ORrLj/dg00RGRiohIUG7d+9WbW2t6uvrJZ29anXud4wJFLErgK9wsufkyZM6ceJE6L///ve/6/rrrze8qqtTSkqKNmzYIEnasGGDBg4caHhFV59zBUKSPvvsM74F5DtYlqW33npLPXv21N133x0a5314aS6UH+/BS3f06FEdP35c0tm/oNyxY4d69uypxMREbd68WZKUn59v9HcyH+h6hRQVFemdd94JfYXT2LFjTS/pqnHw4EG9/vrrks7ebPnDH/6Q/C5BVlaWSktLdezYMUVFRWn8+PEaOHCgMjMzVVVVpejoaM2aNYt7S75DYxmWlJTo66+/lsPhULdu3TR16lTOcF/AF198oRdffFHXX3996HaMBx98UH379uV9eAkulN/GjRt5D16if/zjH1q0aJGCwaAsy9KQIUM0btw4HTx48LyPr2jXrp2RNVLEAAAADOHSJAAAgCEUMQAAAEMoYgAAAIZQxAAAAAyhiAEAABhCEQMAADCEIgYAAGAIRQwAAMCQ/wPOl+Dbu1TAEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i, column in enumerate(bd.df.columns):\n",
    "    plt.figure(figsize=(10,6))\n",
    "    bd.df[column].hist()    \n",
    "    plt.title(column + ' un-normalized')\n",
    "    plt.figure(figsize=(10,6))\n",
    "    pd.Series(bd.x_train[:,i]).hist()\n",
    "    plt.title(column + ' normalized')\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Price histogram')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlwAAAF2CAYAAAC7w0Z9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO3de3BU5cHH8d8m4RZWwl4gMSEoIUIbIEYN5TJcglnRAkMpMLQoWPBCnXgZRCkgTKMiTCqEIArDjFAsiqMORbRTL53IJWBkCJcghlbAgkoJxmRjIDEUkj3vH7xuiSRshDzZTfh+Zpxhzz579jmeYfPlnJOzNsuyLAEAAMCYsGBPAAAAoLUjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAA0qePHj8tms2nnzp1G3yctLU0PPPDAZcc8/fTTSkxMNDoPAGgMggtAvaZNmyabzSabzaaIiAjdcMMNeuihh1RWVnbZ18XHx6u4uFgDBgxoppk27Mknn9SuXbsaPT4xMVFPP/20uQkBuGZFBHsCAELX0KFD9dZbb6mmpkZ79+7VAw88oK+//lp///vf6x1/7tw5tW3bVjExMc080/rZ7XbZ7fZgT6NelmWppqZGbdq0CfZUADQDjnABaNAP8dStWzf96le/0syZM/XBBx+ourraf+pww4YNGjVqlDp27Kinnnqq3lOKJSUlmj59uqKjo9W+fXv17t1bf/7zn/3PHz16VBMmTFDnzp3lcDg0cuRIHTx4sFFzXLhwoWJiYuR0OjVt2jRVVVX5n/vxKcUTJ05owoQJcrvd6tChgxISErRkyRJJF05RfvHFF3rmmWf8R/aOHz8uSdq1a5eGDRumDh06yOFw6O6771ZJSUmdeSxfvlzdunVTZGSk7rzzTr366quy2Ww6ceKEJOmVV15RRESEtm7dqltuuUXt2rXThx9+qGPHjmn8+PGKjY1VZGSk+vXrp1dffbXOutPS0nT//fdrwYIF6tq1qzp37qz58+fL5/Pp2WefVXR0tLp06aL58+c36v8ZgOZHcAFotA4dOsjn86mmpsa/bM6cObr77rt18OBBPfzww5e8prq6WsOHD9eBAwe0YcMGHTp0SC+++KIiIyMlSd98842GDBmirl27aseOHdq1a5d69+6ttLQ0ffvtt5edz8aNG+X1erVt2za9/vrr2rx5s55//vkGx2dkZKiiokK5ubn65z//qbVr16pbt26SpE2bNunGG2/UE088oeLiYhUXFys+Pl6nTp3SyJEj1a1bN+3evVt/+9vf9Nlnn2nChAn+9W7atElPPvmkZs+erQMHDmjy5MmaM2fOJe/v8/n0hz/8QdnZ2frXv/6lAQMGqLKyUunp6frggw908OBBzZgxQ9OnT9fWrVsv2dbz589r586dWrZsmRYvXqwxY8aosrJSO3bs0NKlS7V48WK9//77l/1/BiBILACox+9+9zsrPT3d/7ioqMhKSEiwBgwYYFmWZR07dsySZD377LN1XvfD8h07dliWZVlr1qyx2rVrZ3399df1vk9mZqZ/nT/w+XxWQkKClZOT0+D8hg8fbvXr16/Ost///vfWwIED66y7Z8+e/sfJyclWZmZmg+vs2bPnJc8vWLDAiouLs/773//6lxUWFlqSrO3bt1uWZVmDBw+2pkyZUud1c+bMsST5t3vdunWWJCsvL6/B9//B2LFjrQceeKDOtt588811xiQlJVl9+/atsyw5Odl64oknAq4fQPPjCBeABm3btk12u10dOnRQ3759lZCQoNdff73OmF/84heXXcfevXuVlJTkP5L0YwUFBdq7d6//eiu73a7rrrtOx48f15EjRy677pSUlDqP4+Li9M033zQ4fubMmVq8eLEGDBigOXPmKC8v77Lrl6SioiINHDhQbdu29S+7+eabFRUVpaKiIknSoUOHNHDgwDqvGzRoUL3r69+/f53H33//vebOnas+ffrI6XTKbrfrvffe05dfflln3M0331zncUxMjJKTky9Z9uNTnQBCAxfNA2jQgAED9Je//EURERG6/vrr1a5du0vGdOzYMeB6bDZbg8/5fD6lp6frpZdeuuS5qKioy6734gj64X18Pl+D46dPn6677rpLH3zwgbZu3apf/vKX+vWvf63XXnvtiuZ/8fLLbeMPwsPD1b59+zrLZs+erXfeeUfZ2dn62c9+po4dO+qJJ55QRUVFnXE/vrjeZrPVu+xy2w8geDjCBaBBHTp0UGJiom688cZ6Y6sxbrvtNhUVFfkvHv+x1NRUFRUVKS4uTomJiXX+69Kly9VMv17XX3+9pk+frvXr12vt2rXasGGDTp8+LelCwNXW1tYZ36dPH33yySc6d+6cf9mBAwdUUVGhPn36SJKSkpL0ySef1HldY29HkZeXp3vuuUe/+c1vdPPNNyshIUGHDx++mk0EEIIILgBGTZ48WTfccIPGjh2r3NxcHTt2TB999JHefPNNSdIjjzyi2tpajRs3Tjt27NDx48e1c+dOzZ8/X/n5+U06l0ceeUTvvfeevvjiCxUVFWnTpk2Kj4/XddddJ0nq0aOHPv74Y3311VcqLS2Vz+fTI488otOnT2vatGn67LPPtHPnTk2dOlVDhgzR0KFDJUlPPPGE3njjDb344os6evSo1q9fr/Xr10sKfOSrd+/eeuedd7R7924dOnRIM2bM0MmTJ5t0uwEEH8EFwKjIyEht375dffv21W9/+1v9/Oc/18MPP6zq6mpJUnR0tD755BO53W6NHz9evXv31j333KMvv/xS119/fZPOxbIszZw5U3379tWwYcNUVVWl999/3x9FzzzzjCoqKtS7d2916dJFX331laKjo/WPf/xDJ06cUP/+/TVmzBj17dtXf/3rX/3rHT9+vJ5//nllZWWpX79+2rBhgzIzMyXpklOIP5aTk6MbbrhBI0aMUHp6uuLi4jRx4sQm3W4AwWezLMsK9iQAoLV59tln9cILLwS8Mz+AawMXzQPAVTp//ryys7P9N4DdunWrlixZUu99yQBcmzjCBQBXqaamRmPGjNHevXt15swZ9ejRQ/fee69mz56tiAj+XQuA4AIAADCOi+YBAAAMI7gAAAAMI7gAAAAMC/mrORtzA0C3263S0tJmmA2uFPsotLF/Qh/7KLSxf0Jfc+yj2NjYBp/jCBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhEcGeAFCf2gfHBnsKTSb85XeDPQUAQJBxhAsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMAwggsAAMCwiEADzp07p8zMTNXU1Ki2tlYDBw7UpEmTVFJSouXLl6uyslI9evTQo48+qoiICJ0/f14vvfSS/v3vf+u6667TzJkz1bVrV0nS22+/rS1btigsLEzTp09XSkqK8Q0EAAAItoBHuNq0aaPMzEwtWbJEzz//vAoLC3X48GG99tprGj16tFasWKGOHTtqy5YtkqQtW7aoY8eOevHFFzV69Ght2LBBknTixAnl5+dr2bJlmj9/vtauXSufz2d26wAAAEJAwOCy2Wxq3769JKm2tla1tbWy2WwqKirSwIEDJUlpaWkqKCiQJO3Zs0dpaWmSpIEDB+qzzz6TZVkqKCjQ4MGD1aZNG3Xt2lUxMTE6evSooc0CAAAIHQFPKUqSz+fTnDlzdOrUKd15552Kjo5WZGSkwsPDJUlOp1Ner1eS5PV65XK5JEnh4eGKjIzUmTNn5PV6ddNNN/nXefFrgNas9sGxwZ5CQN80clz4y+8anQcAtFaNCq6wsDAtWbJEVVVVWrp0qf7zn/80ONayrEuW2Wy2epfXJzc3V7m5uZKkrKwsud3ugK+JiIho1DgEz0/dR40NADQv/p4FD59zoY39E/qCvY8aFVw/6Nixo5KSknTkyBF9//33qq2tVXh4uLxer5xOpyTJ5XKprKxMLpdLtbW1+v7772W32/3Lf3Dxay7m8Xjk8Xj8j0tLSwPOy+12N2ocgod91DqwD4OHv0Ohjf0T+ppjH8XGxjb4XMBruE6fPq2qqipJF35j8eDBg4qLi1OfPn20a9cuSdK2bduUmpoqSbrtttu0bds2SdKuXbvUp08f2Ww2paamKj8/X+fPn1dJSYmKi4uVmJh4tdsGAAAQ8gIe4SovL9fKlSvl8/lkWZYGDRqk2267Td26ddPy5cv1xhtvqEePHrr99tslSbfffrteeuklPfroo7Lb7Zo5c6YkKT4+XoMGDdKsWbMUFham+++/X2Fh3AYMAAC0fjarsRdXBcnJkycDjuFQbuj7qfuoJVxofi3iovng4XMutLF/Ql/In1IEAADA1SG4AAAADCO4AAAADCO4AAAADCO4AAAADPtJNz5F6AvV3+7jzvEAgGsZR7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMiwg0oLS0VCtXrtR3330nm80mj8ejUaNG6a233tJHH32kTp06SZImT56sW2+9VZL09ttva8uWLQoLC9P06dOVkpIiSSosLNS6devk8/mUnp6ucePGGdw0AACA0BAwuMLDwzV16lQlJCSourpac+fOVXJysiRp9OjRGjt2bJ3xJ06cUH5+vpYtW6by8nItXLhQL7zwgiRp7dq1WrBggVwul+bNm6fU1FR169bNwGYBAACEjoDB5XA45HA4JEkdOnRQXFycvF5vg+MLCgo0ePBgtWnTRl27dlVMTIyOHj0qSYqJiVF0dLQkafDgwSooKCC4AABAq/eTruEqKSnRsWPHlJiYKEn68MMP9eSTT2rVqlWqrKyUJHm9XrlcLv9rnE6nvF7vJctdLtdlww0AAKC1CHiE6wdnz55Vdna2pk2bpsjISI0cOVITJ06UJL355ptav369MjIyZFlWva+vb7nNZrtkWW5urnJzcyVJWVlZcrvdgTciIqJR464F3wR7AmjV+HsWPHzOhTb2T+gL9j5qVHDV1NQoOztbQ4cO1YABAyRJnTt39j+fnp6uP/3pT5IuHLkqKyvzP+f1euV0OiWpzvKysjL/qcqLeTweeTwe/+PS0tKA83O73Y0aB+Dq8PcsePicC23sn9DXHPsoNja2wecCnlK0LEurV69WXFycxowZ419eXl7u//Pu3bsVHx8vSUpNTVV+fr7Onz+vkpISFRcXKzExUT179lRxcbFKSkpUU1Oj/Px8paamXs12AQAAtAgBj3B9/vnnysvLU/fu3TV79mxJF24B8fHHH+v48eOy2Wzq0qWLZsyYIUmKj4/XoEGDNGvWLIWFhen+++9XWNiFrrvvvvu0aNEi+Xw+jRgxwh9pAAAArZnNauiiqxBx8uTJgGM4lPs/tQ+ODTwIuELhL78b7Clcs/icC23sn9AX8qcUAQAAcHUILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMILgAAAMMigj0BAC1H7YNjgz2FJhH+8rvBngKAawxHuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAwjuAAAAAyLCDSgtLRUK1eu1HfffSebzSaPx6NRo0apsrJSOTk5+vbbb9WlSxc9/vjjstvtsixL69at0/79+9WuXTtlZGQoISFBkrRt2zZt2rRJkjR+/HilpaUZ3TgAAIBQEDC4wsPDNXXqVCUkJKi6ulpz585VcnKytm3bpn79+mncuHHavHmzNm/erClTpmj//v06deqUVqxYoSNHjmjNmjVavHixKisrtXHjRmVlZUmS5s6dq9TUVNntduMbCQAAEEwBTyk6HA7/EaoOHTooLi5OXq9XBQUFGj58uCRp+PDhKigokCTt2bNHw4YNk81mU69evVRVVaXy8nIVFhYqOTlZdrtddrtdycnJKiwsNLhpAAAAoSHgEa6LlZSU6NixY0pMTFRFRYUcDoekC1F2+vRpSZLX65Xb7fa/xuVyyev1yuv1yuVy+Zc7nU55vd5L3iM3N1e5ubmSpKysrDrranAjIiIaNe5a8E2wJwC0AC3x84LPudDG/gl9wd5HjQ6us2fPKjs7W9OmTVNkZGSD4yzLumSZzWard2x9yz0ejzwej/9xaWlpwLm53e5GjQMAqXGfK6GGz7nQxv4Jfc2xj2JjYxt8rlG/pVhTU6Ps7GwNHTpUAwYMkCRFRUWpvLxcklReXq5OnTpJunBE6+INKisrk8PhkNPpVFlZmX+51+v1HyEDAABozQIGl2VZWr16teLi4jRmzBj/8tTUVG3fvl2StH37dvXv39+/PC8vT5Zl6fDhw4qMjJTD4VBKSooOHDigyspKVVZW6sCBA0pJSTG0WQAAAKEj4CnFzz//XHl5eerevbtmz54tSZo8ebLGjRunnJwcbdmyRW63W7NmzZIk3XLLLdq3b58ee+wxtW3bVhkZGZIku92uCRMmaN68eZKkiRMn8huKAADgmmCz6rvoKoScPHky4BjOnf9P7YNjgz0FIOSFv/xusKfwk/E5F9rYP6GvRVzDBQAAgCtHcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABgWEWjAqlWrtG/fPkVFRSk7O1uS9NZbb+mjjz5Sp06dJEmTJ0/WrbfeKkl6++23tWXLFoWFhWn69OlKSUmRJBUWFmrdunXy+XxKT0/XuHHjTG0TAABASAkYXGlpabrrrru0cuXKOstHjx6tsWPH1ll24sQJ5efna9myZSovL9fChQv1wgsvSJLWrl2rBQsWyOVyad68eUpNTVW3bt2acFMAAABCU8DgSkpKUklJSaNWVlBQoMGDB6tNmzbq2rWrYmJidPToUUlSTEyMoqOjJUmDBw9WQUEBwQUAAK4JAYOrIR9++KHy8vKUkJCge++9V3a7XV6vVzfddJN/jNPplNfrlSS5XC7/cpfLpSNHjtS73tzcXOXm5kqSsrKy5Ha7A29ERESjxl0Lvgn2BIAWoCV+XvA5F9rYP6Ev2PvoioJr5MiRmjhxoiTpzTff1Pr165WRkSHLsuodX99ym81W71iPxyOPx+N/XFpaGnA+bre7UeMAQGrc50qo4XMutLF/Ql9z7KPY2NgGn7ui31Ls3LmzwsLCFBYWpvT0dH3xxReSLhy5Kisr84/zer1yOp2XLC8rK5PD4biStwYAAGhxrii4ysvL/X/evXu34uPjJUmpqanKz8/X+fPnVVJSouLiYiUmJqpnz54qLi5WSUmJampqlJ+fr9TU1KbZAgAAgBAX8JTi8uXLdejQIZ05c0YPPfSQJk2apKKiIh0/flw2m01dunTRjBkzJEnx8fEaNGiQZs2apbCwMN1///0KC7vQdPfdd58WLVokn8+nESNG+CMNAACgtbNZDV14FSJOnjwZcAznzv+n9sGxgQcB17jwl98N9hR+Mj7nQhv7J/S1yGu4AAAA0HgEFwAAgGFXfB8uAGipWuKp94busdcST48C1yKOcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABhGcAEAABgWEWjAqlWrtG/fPkVFRSk7O1uSVFlZqZycHH377bfq0qWLHn/8cdntdlmWpXXr1mn//v1q166dMjIylJCQIEnatm2bNm3aJEkaP3680tLSzG0VAABACAl4hCstLU1PPfVUnWWbN29Wv379tGLFCvXr10+bN2+WJO3fv1+nTp3SihUrNGPGDK1Zs0bShUDbuHGjFi9erMWLF2vjxo2qrKw0sDkAAAChJ2BwJSUlyW6311lWUFCg4cOHS5KGDx+ugoICSdKePXs0bNgw2Ww29erVS1VVVSovL1dhYaGSk5Nlt9tlt9uVnJyswsJCA5sDAAAQegKeUqxPRUWFHA6HJMnhcOj06dOSJK/XK7fb7R/ncrnk9Xrl9Xrlcrn8y51Op7xeb73rzs3NVW5uriQpKyurzvoa3IiIiEaNuxZ8E+wJAGhWfPaFBn4Ohb5g76MrCq6GWJZ1yTKbzVbv2IaWezweeTwe/+PS0tKA7+t2uxs1DgBaGz77QkNr/TlU++DYYE+hyUS/nW98H8XGxjb43BUFV1RUlMrLy+VwOFReXq5OnTpJunBE6+KNKSsrk8PhkNPp1KFDh/zLvV6vkpKSruStAQAXaU0/EMNffjfYUwCMuaLbQqSmpmr79u2SpO3bt6t///7+5Xl5ebIsS4cPH1ZkZKQcDodSUlJ04MABVVZWqrKyUgcOHFBKSkrTbQUAAEAIC3iEa/ny5Tp06JDOnDmjhx56SJMmTdK4ceOUk5OjLVu2yO12a9asWZKkW265Rfv27dNjjz2mtm3bKiMjQ5Jkt9s1YcIEzZs3T5I0ceLESy7EBwAAaK1sVn0XXoWQkydPBhzTWs+dX4nWdHoBwLWlJZ9SbK0/h1rTz5RgX8PFneYBAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMI7gAAAAMiwj2BEJB7YNjgz0FAADQinGECwAAwDCCCwAAwDCCCwAAwDCCCwAAwDCCCwAAwDCCCwAAwDCCCwAAwDCCCwAAwDCCCwAAwDCCCwAAwDC+2gcAEBJa8tesffOjx+EvvxuUeSB0cYQLAADAMIILAADAMIILAADAsKu6huvhhx9W+/btFRYWpvDwcGVlZamyslI5OTn69ttv1aVLFz3++OOy2+2yLEvr1q3T/v371a5dO2VkZCghIaGptgMAACBkXfVF85mZmerUqZP/8ebNm9WvXz+NGzdOmzdv1ubNmzVlyhTt379fp06d0ooVK3TkyBGtWbNGixcvvtq3BwAACHlNfkqxoKBAw4cPlyQNHz5cBQUFkqQ9e/Zo2LBhstls6tWrl6qqqlReXt7Ubw8AABByrvoI16JFiyRJd9xxhzwejyoqKuRwOCRJDodDp0+fliR5vV653W7/61wul7xer38sAABAa3VVwbVw4UI5nU5VVFToueeeU2xsbINjLcu6ZJnNZrtkWW5urnJzcyVJWVlZdSKtIREREY0a15Af3z8FAICrcTU/k0JJa/r5eLWtcNXvfzUvdjqdkqSoqCj1799fR48eVVRUlMrLy+VwOFReXu6/vsvlcqm0tNT/2rKysnqPbnk8Hnk8Hv/ji1/TELfb3ahxAAA0B34mhZ6amhrj++VyB56u+Bqus2fPqrq62v/nTz/9VN27d1dqaqq2b98uSdq+fbv69+8vSUpNTVVeXp4sy9Lhw4cVGRnJ6UQAAHBNuOIjXBUVFVq6dKkkqba2VkOGDFFKSop69uypnJwcbdmyRW63W7NmzZIk3XLLLdq3b58ee+wxtW3bVhkZGU2zBQAAACHOZtV3cVUIOXnyZMAxV3tKsSV/fxcAIPS0lu9SbE0/H6Pfzm+ZpxQBAADQOAQXAACAYQQXAACAYQQXAACAYQQXAACAYQQXAACAYVf9XYoAAKCu1nQ7BTQNjnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYRnABAAAYFtHcb1hYWKh169bJ5/MpPT1d48aNa+4pAAAANKtmPcLl8/m0du1aPfXUU8rJydHHH3+sEydONOcUAAAAml2zBtfRo0cVExOj6OhoRUREaPDgwSooKGjOKQAAADS7Zg0ur9crl8vlf+xyueT1eptzCgAAAM2uWa/hsizrkmU2m63O49zcXOXm5kqSsrKyFBsb26h1N3Zcvf6+58pfCwAAWoSraoWr1KxHuFwul8rKyvyPy8rK5HA46ozxeIrCSNAAAAPdSURBVDzKyspSVlZWo9c7d+7cJpsjzGAfhTb2T+hjH4U29k/oC/Y+atbg6tmzp4qLi1VSUqKamhrl5+crNTW1OacAAADQ7Jr1lGJ4eLjuu+8+LVq0SD6fTyNGjFB8fHxzTgEAAKDZNft9uG699VbdeuutTbpOj8fTpOtD02MfhTb2T+hjH4U29k/oC/Y+sln1XckOAACAJsNX+wAAABjW7KcUmxpfFRTaVq1apX379ikqKkrZ2dnBng5+pLS0VCtXrtR3330nm80mj8ejUaNGBXtauMi5c+eUmZmpmpoa1dbWauDAgZo0aVKwp4Uf8fl8mjt3rpxOZ9B/Gw6Xevjhh9W+fXuFhYUpPDz8J90Joam06OD64auCFixYIJfLpXnz5ik1NVXdunUL9tTw/9LS0nTXXXdp5cqVwZ4K6hEeHq6pU6cqISFB1dXVmjt3rpKTk/k7FELatGmjzMxMtW/fXjU1NfrjH/+olJQU9erVK9hTw0Xee+89xcXFqbq6OthTQQMyMzPVqVOnoL1/iz6lyFcFhb6kpCTZ7fZgTwMNcDgcSkhIkCR16NBBcXFxfPtDiLHZbGrfvr0kqba2VrW1tZfcMBrBVVZWpn379ik9PT3YU0EIa9FHuOr7qqAjR44EcUZAy1VSUqJjx44pMTEx2FPBj/h8Ps2ZM0enTp3SnXfeqZtuuinYU8JFXnnlFU2ZMoWjWyFu0aJFkqQ77rgjKL+x2KKDqzFfFQQgsLNnzyo7O1vTpk1TZGRksKeDHwkLC9OSJUtUVVWlpUuX6quvvlL37t2DPS1I2rt3r6KiopSQkKCioqJgTwcNWLhwoZxOpyoqKvTcc88pNjZWSUlJzTqHFh1cjfmqIACXV1NTo+zsbA0dOlQDBgwI9nRwGR07dlRSUpIKCwsJrhDx+eefa8+ePdq/f7/OnTun6upqrVixQo899liwp4aLOJ1OSVJUVJT69++vo0ePNntwtehruPiqIODqWJal1atXKy4uTmPGjAn2dFCP06dPq6qqStKF31g8ePCg4uLigjwr/ODuu+/W6tWrtXLlSs2cOVN9+/YltkLM2bNn/ad7z549q08//TQo/2Bp0Ue4+Kqg0Ld8+XIdOnRIZ86c0UMPPaRJkybp9ttvD/a08P8+//xz5eXlqXv37po9e7YkafLkyU3+bRC4cuXl5Vq5cqV8Pp8sy9KgQYN02223BXtaQItRUVGhpUuXSrrwiydDhgxRSkpKs8+DO80DAAAY1qJPKQIAALQEBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBhBBcAAIBh/wc15qG0KUbimQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "pd.Series(bd.y_train.reshape(-1)).hist()\n",
    "plt.title('Price histogram')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_results(pred, gold, label=''):\n",
    "    pred = pred.ravel()\n",
    "    gold = gold.ravel()\n",
    "    df_snapshot = pd.DataFrame({'PRED' : pred, 'TRUTH' : gold, 'AERR' : np.abs(gold-pred)})\n",
    "    print(\"\\nResults so far {}:\\n{}\".format(label, df_snapshot.iloc[:20]))\n",
    "    print(\"Overall abs average error: {:.2f}\".format(df_snapshot['AERR'].mean()))\n",
    "    return df_snapshot\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "nr_feats = bd.x_train.shape[1]\n",
    "th_coefs = th.zeros((nr_feats,1), requires_grad=True)\n",
    "th_bias = th.zeros(1, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "th_x_train = th.tensor(bd.x_train)\n",
    "th_y_train = th.tensor(bd.y_train)\n",
    "\n",
    "\n",
    "def predict(X):\n",
    "    with th.no_grad():\n",
    "        th_x = th.tensor(X)\n",
    "        th_yh = th.mm(th_x, th_coefs) + th_bias\n",
    "        yhat = th_yh.cpu().numpy()\n",
    "        return yhat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "th_ds = th.utils.data.TensorDataset(th_x_train, th_y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 10\n",
    "th_dl = th.utils.data.DataLoader(th_ds, batch_size=batch_size)\n",
    "epoch_len = bd.x_train.shape[0] // batch_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results so far RANDOM paras on TRAIN:\n",
      "    PRED  TRUTH   AERR\n",
      "0    0.0  1.125  1.125\n",
      "1    0.0  4.024  4.024\n",
      "2    0.0  3.034  3.034\n",
      "3    0.0  1.582  1.582\n",
      "4    0.0  2.822  2.822\n",
      "5    0.0  1.865  1.865\n",
      "6    0.0  2.250  2.250\n",
      "7    0.0  0.756  0.756\n",
      "8    0.0  0.662  0.662\n",
      "9    0.0  0.911  0.911\n",
      "10   0.0  1.625  1.625\n",
      "11   0.0  2.424  2.424\n",
      "12   0.0  1.342  1.342\n",
      "13   0.0  2.464  2.464\n",
      "14   0.0  3.455  3.455\n",
      "15   0.0  3.386  3.386\n",
      "16   0.0  2.579  2.579\n",
      "17   0.0  2.445  2.445\n",
      "18   0.0  4.833  4.833\n",
      "19   0.0  5.000  5.000\n",
      "Overall abs average error: 2.07\n",
      "Epoch 1 done 100.0% - avg loss: 0.635\n",
      "Epoch 2 done 100.0% - avg loss: 0.518\n",
      "Epoch 3 done 100.0% - avg loss: 0.516\n",
      "Epoch 4 done 100.0% - avg loss: 0.516\n",
      "Epoch 5 done 100.0% - avg loss: 0.516\n",
      "Results so far at epoch 5 on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.2442  1.125  0.8808\n",
      "1   3.4900  4.024  0.5340\n",
      "2   2.6592  3.034  0.3748\n",
      "3   1.2610  1.582  0.3210\n",
      "4   2.9171  2.822  0.0951\n",
      "5   1.9278  1.865  0.0628\n",
      "6   2.3231  2.250  0.0731\n",
      "7   1.0979  0.756  0.3419\n",
      "8   0.9783  0.662  0.3163\n",
      "9   0.6947  0.911  0.2163\n",
      "10  1.7872  1.625  0.1622\n",
      "11  2.0916  2.424  0.3324\n",
      "12  1.8139  1.342  0.4719\n",
      "13  2.1607  2.464  0.3033\n",
      "14  2.3755  3.455  1.0795\n",
      "15  2.5373  3.386  0.8487\n",
      "16  1.9504  2.579  0.6286\n",
      "17  2.4237  2.445  0.0213\n",
      "18  4.3435  4.833  0.4895\n",
      "19  4.5269  5.000  0.4731\n",
      "Overall abs average error: 0.52\n",
      "Results so far at epoch 5 on DEV:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.9085  1.136  0.2275\n",
      "1   2.8592  5.000  2.1408\n",
      "2   2.1883  3.431  1.2427\n",
      "3   0.4404  0.941  0.5006\n",
      "4   2.7192  2.417  0.3022\n",
      "5   1.8192  2.250  0.4308\n",
      "6   3.6987  4.225  0.5263\n",
      "7   1.3495  1.482  0.1325\n",
      "8   3.5155  4.050  0.5345\n",
      "9   1.5045  1.279  0.2255\n",
      "10  0.7070  0.619  0.0880\n",
      "11  1.8668  1.175  0.6918\n",
      "12  2.0428  2.208  0.1652\n",
      "13  0.4110  0.541  0.1300\n",
      "14  2.4235  1.909  0.5145\n",
      "15  2.3678  2.849  0.4812\n",
      "16  0.9127  1.625  0.7123\n",
      "17  0.6335  0.875  0.2415\n",
      "18  0.5788  1.391  0.8122\n",
      "19  1.7905  1.841  0.0505\n",
      "Overall abs average error: 0.51\n",
      "Epoch 6 done 100.0% - avg loss: 0.516\n",
      "Epoch 7 done 100.0% - avg loss: 0.516\n",
      "Epoch 8 done 100.0% - avg loss: 0.516\n",
      "Epoch 9 done 100.0% - avg loss: 0.516\n",
      "Epoch 10 done 100.0% - avg loss: 0.516\n",
      "Results so far at epoch 10 on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.2357  1.125  0.8893\n",
      "1   3.4961  4.024  0.5279\n",
      "2   2.6565  3.034  0.3775\n",
      "3   1.2722  1.582  0.3098\n",
      "4   2.9216  2.822  0.0996\n",
      "5   1.9480  1.865  0.0830\n",
      "6   2.3331  2.250  0.0831\n",
      "7   1.1150  0.756  0.3590\n",
      "8   0.9897  0.662  0.3277\n",
      "9   0.7057  0.911  0.2053\n",
      "10  1.7803  1.625  0.1553\n",
      "11  2.0947  2.424  0.3293\n",
      "12  1.8265  1.342  0.4845\n",
      "13  2.1704  2.464  0.2936\n",
      "14  2.3697  3.455  1.0853\n",
      "15  2.5401  3.386  0.8459\n",
      "16  1.9557  2.579  0.6233\n",
      "17  2.4380  2.445  0.0070\n",
      "18  4.3221  4.833  0.5109\n",
      "19  4.5115  5.000  0.4885\n",
      "Overall abs average error: 0.51\n",
      "Results so far at epoch 10 on DEV:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.9291  1.136  0.2069\n",
      "1   2.8795  5.000  2.1205\n",
      "2   2.2004  3.431  1.2306\n",
      "3   0.4557  0.941  0.4853\n",
      "4   2.7103  2.417  0.2933\n",
      "5   1.8592  2.250  0.3908\n",
      "6   3.7031  4.225  0.5219\n",
      "7   1.3446  1.482  0.1374\n",
      "8   3.5182  4.050  0.5318\n",
      "9   1.5183  1.279  0.2393\n",
      "10  0.7127  0.619  0.0937\n",
      "11  1.8655  1.175  0.6905\n",
      "12  2.0549  2.208  0.1531\n",
      "13  0.4241  0.541  0.1169\n",
      "14  2.4367  1.909  0.5277\n",
      "15  2.3839  2.849  0.4651\n",
      "16  0.9083  1.625  0.7167\n",
      "17  0.6382  0.875  0.2368\n",
      "18  0.5932  1.391  0.7978\n",
      "19  1.7846  1.841  0.0564\n",
      "Overall abs average error: 0.50\n",
      "Epoch 11 done 100.0% - avg loss: 0.516\n",
      "Epoch 12 done 100.0% - avg loss: 0.516\n",
      "Epoch 13 done 100.0% - avg loss: 0.516\n",
      "Epoch 14 done 100.0% - avg loss: 0.516\n",
      "Epoch 15 done 100.0% - avg loss: 0.516\n",
      "Results so far at epoch 15 on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.2443  1.125  0.8807\n",
      "1   3.4940  4.024  0.5300\n",
      "2   2.6602  3.034  0.3738\n",
      "3   1.2795  1.582  0.3025\n",
      "4   2.9159  2.822  0.0939\n",
      "5   1.9616  1.865  0.0966\n",
      "6   2.3399  2.250  0.0899\n",
      "7   1.1168  0.756  0.3608\n",
      "8   0.9939  0.662  0.3319\n",
      "9   0.7079  0.911  0.2031\n",
      "10  1.7636  1.625  0.1386\n",
      "11  2.0959  2.424  0.3281\n",
      "12  1.8262  1.342  0.4842\n",
      "13  2.1737  2.464  0.2903\n",
      "14  2.3735  3.455  1.0815\n",
      "15  2.5430  3.386  0.8430\n",
      "16  1.9558  2.579  0.6232\n",
      "17  2.4425  2.445  0.0025\n",
      "18  4.3043  4.833  0.5287\n",
      "19  4.5024  5.000  0.4976\n",
      "Overall abs average error: 0.51\n",
      "Results so far at epoch 15 on DEV:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.9353  1.136  0.2007\n",
      "1   2.8806  5.000  2.1194\n",
      "2   2.2053  3.431  1.2257\n",
      "3   0.4665  0.941  0.4745\n",
      "4   2.7054  2.417  0.2884\n",
      "5   1.8573  2.250  0.3927\n",
      "6   3.6989  4.225  0.5261\n",
      "7   1.3493  1.482  0.1327\n",
      "8   3.5120  4.050  0.5380\n",
      "9   1.5212  1.279  0.2422\n",
      "10  0.7162  0.619  0.0972\n",
      "11  1.8754  1.175  0.7004\n",
      "12  2.0516  2.208  0.1564\n",
      "13  0.4242  0.541  0.1168\n",
      "14  2.4339  1.909  0.5249\n",
      "15  2.3820  2.849  0.4670\n",
      "16  0.9074  1.625  0.7176\n",
      "17  0.6380  0.875  0.2370\n",
      "18  0.5989  1.391  0.7921\n",
      "19  1.7762  1.841  0.0648\n",
      "Overall abs average error: 0.50\n",
      "Epoch 16 done 100.0% - avg loss: 0.516\n",
      "Epoch 17 done 100.0% - avg loss: 0.516\n",
      "Epoch 18 done 100.0% - avg loss: 0.515\n",
      "Epoch 19 done 100.0% - avg loss: 0.515\n",
      "Epoch 20 done 100.0% - avg loss: 0.516\n",
      "Results so far at epoch 20 on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.2453  1.125  0.8797\n",
      "1   3.4901  4.024  0.5339\n",
      "2   2.6598  3.034  0.3742\n",
      "3   1.2824  1.582  0.2996\n",
      "4   2.9129  2.822  0.0909\n",
      "5   1.9648  1.865  0.0998\n",
      "6   2.3435  2.250  0.0935\n",
      "7   1.1145  0.756  0.3585\n",
      "8   0.9972  0.662  0.3352\n",
      "9   0.7125  0.911  0.1985\n",
      "10  1.7692  1.625  0.1442\n",
      "11  2.0990  2.424  0.3250\n",
      "12  1.8231  1.342  0.4811\n",
      "13  2.1781  2.464  0.2859\n",
      "14  2.3700  3.455  1.0850\n",
      "15  2.5435  3.386  0.8425\n",
      "16  1.9620  2.579  0.6170\n",
      "17  2.4489  2.445  0.0039\n",
      "18  4.2976  4.833  0.5354\n",
      "19  4.4953  5.000  0.5047\n",
      "Overall abs average error: 0.51\n",
      "Results so far at epoch 20 on DEV:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.9407  1.136  0.1953\n",
      "1   2.8857  5.000  2.1143\n",
      "2   2.2078  3.431  1.2232\n",
      "3   0.4726  0.941  0.4684\n",
      "4   2.7037  2.417  0.2867\n",
      "5   1.8732  2.250  0.3768\n",
      "6   3.6915  4.225  0.5335\n",
      "7   1.3460  1.482  0.1360\n",
      "8   3.5061  4.050  0.5439\n",
      "9   1.5217  1.279  0.2427\n",
      "10  0.7153  0.619  0.0963\n",
      "11  1.8757  1.175  0.7007\n",
      "12  2.0554  2.208  0.1526\n",
      "13  0.4253  0.541  0.1157\n",
      "14  2.4330  1.909  0.5240\n",
      "15  2.3867  2.849  0.4623\n",
      "16  0.9086  1.625  0.7164\n",
      "17  0.6305  0.875  0.2445\n",
      "18  0.5989  1.391  0.7921\n",
      "19  1.7772  1.841  0.0638\n",
      "Overall abs average error: 0.50\n",
      "Results so far at epoch 20 on TEST:\n",
      "      PRED  TRUTH    AERR\n",
      "0   2.6425  2.776  0.1335\n",
      "1   2.0295  2.247  0.2175\n",
      "2   1.0732  0.926  0.1472\n",
      "3   1.6597  1.936  0.2763\n",
      "4   2.7058  3.550  0.8442\n",
      "5   0.7842  0.758  0.0262\n",
      "6   1.7371  1.595  0.1421\n",
      "7   1.5817  1.706  0.1243\n",
      "8   2.2131  2.029  0.1841\n",
      "9   2.7246  2.180  0.5446\n",
      "10  2.6077  3.905  1.2973\n",
      "11  1.7174  2.181  0.4636\n",
      "12  2.1888  2.540  0.3512\n",
      "13  1.6801  0.375  1.3051\n",
      "14  6.8995  5.000  1.8995\n",
      "15  1.4056  0.968  0.4376\n",
      "16  1.9001  2.440  0.5399\n",
      "17  4.5334  3.818  0.7154\n",
      "18  1.5048  1.603  0.0982\n",
      "19  2.5624  2.706  0.1436\n",
      "Overall abs average error: 0.51\n"
     ]
    }
   ],
   "source": [
    "nr_epochs = 20\n",
    "lr = 0.01\n",
    "y_rnd_preds = predict(bd.x_train)\n",
    "res = show_results(y_rnd_preds, bd.y_train, label='RANDOM paras on TRAIN'.format(epoch))    \n",
    "\n",
    "for epoch in range(1, nr_epochs + 1):\n",
    "    epoch_losses = []\n",
    "    for i, batch_data in enumerate(th_dl):\n",
    "        th_x_batch, th_y_batch = batch_data\n",
    "        th_preds = th.mm(th_x_batch, th_coefs) + th_bias\n",
    "        th_batch_loss = (th_preds  - th_y_batch).abs()\n",
    "        th_loss = th_batch_loss.mean()\n",
    "        th_loss.backward()        \n",
    "        with th.no_grad():\n",
    "            th_coefs -= lr * th_coefs.grad\n",
    "            th_bias -= lr * th_bias.grad\n",
    "            th_coefs.grad.zero_()\n",
    "            th_bias.grad.zero_()\n",
    "            epoch_losses.append(th_loss.cpu().item())\n",
    "        print(\"\\rEpoch {} done {:.1f}% - avg loss: {:.3f}\".format(epoch, i/epoch_len * 100, np.mean(epoch_losses)),\n",
    "             end='', flush=True)\n",
    "    print(\"\")\n",
    "    if (epoch % 5) == 0:  \n",
    "        y_train_hat = predict(bd.x_train)\n",
    "        res = show_results(y_train_hat, bd.y_train, label='at epoch {} on TRAIN'.format(epoch))    \n",
    "\n",
    "        y_dev_hat = predict(bd.x_dev)\n",
    "        res = show_results(y_dev_hat, bd.y_dev, label='at epoch {} on DEV'.format(epoch))    \n",
    "        \n",
    "y_test_hat = predict(bd.x_test)\n",
    "res = show_results(y_test_hat, bd.y_test, label='at epoch {} on TEST'.format(epoch))            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results so far RANDOM paras on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.4458  1.125  0.6792\n",
      "1   0.0295  4.024  3.9945\n",
      "2   0.4715  3.034  2.5625\n",
      "3  -0.1587  1.582  1.7407\n",
      "4  -0.1147  2.822  2.9367\n",
      "5  -0.6288  1.865  2.4938\n",
      "6   0.0304  2.250  2.2196\n",
      "7  -0.4407  0.756  1.1967\n",
      "8   0.1776  0.662  0.4844\n",
      "9  -0.8445  0.911  1.7555\n",
      "10 -0.0252  1.625  1.6502\n",
      "11  0.4494  2.424  1.9746\n",
      "12 -0.4946  1.342  1.8366\n",
      "13 -0.0156  2.464  2.4796\n",
      "14  0.4006  3.455  3.0544\n",
      "15  0.0021  3.386  3.3839\n",
      "16  0.4481  2.579  2.1309\n",
      "17 -0.1146  2.445  2.5596\n",
      "18  1.0185  4.833  3.8145\n",
      "19  0.4790  5.000  4.5210\n",
      "Overall abs average error: 2.11\n",
      "Epoch 1 done 100.0% - avg loss: 0.620\n",
      "Epoch 2 done 100.0% - avg loss: 0.521\n",
      "Epoch 3 done 100.0% - avg loss: 0.521\n",
      "Epoch 4 done 100.0% - avg loss: 0.521\n",
      "Epoch 5 done 100.0% - avg loss: 0.521\n",
      "Results so far at epoch 5 on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.2755  1.125  0.8495\n",
      "1   3.4959  4.024  0.5281\n",
      "2   2.7493  3.034  0.2847\n",
      "3   1.3463  1.582  0.2357\n",
      "4   2.8868  2.822  0.0648\n",
      "5   1.9609  1.865  0.0959\n",
      "6   2.4181  2.250  0.1681\n",
      "7   1.0136  0.756  0.2576\n",
      "8   0.9774  0.662  0.3154\n",
      "9   0.7219  0.911  0.1891\n",
      "10  1.7413  1.625  0.1163\n",
      "11  2.1303  2.424  0.2937\n",
      "12  1.7515  1.342  0.4095\n",
      "13  2.2151  2.464  0.2489\n",
      "14  2.4753  3.455  0.9797\n",
      "15  2.5956  3.386  0.7904\n",
      "16  1.9948  2.579  0.5842\n",
      "17  2.4844  2.445  0.0394\n",
      "18  4.3863  4.833  0.4467\n",
      "19  4.6285  5.000  0.3716\n",
      "Overall abs average error: 0.52\n",
      "Results so far at epoch 5 on DEV:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.9004  1.136  0.2356\n",
      "1   2.8782  5.000  2.1218\n",
      "2   2.3126  3.431  1.1184\n",
      "3   0.5098  0.941  0.4312\n",
      "4   2.7537  2.417  0.3367\n",
      "5   1.8337  2.250  0.4163\n",
      "6   3.7026  4.225  0.5224\n",
      "7   1.3815  1.482  0.1005\n",
      "8   3.5096  4.050  0.5404\n",
      "9   1.4998  1.279  0.2208\n",
      "10  0.6616  0.619  0.0426\n",
      "11  1.9831  1.175  0.8081\n",
      "12  1.9960  2.208  0.2120\n",
      "13  0.3407  0.541  0.2003\n",
      "14  2.3986  1.909  0.4896\n",
      "15  2.3467  2.849  0.5023\n",
      "16  0.8669  1.625  0.7581\n",
      "17  0.5443  0.875  0.3307\n",
      "18  0.5715  1.391  0.8195\n",
      "19  1.7610  1.841  0.0800\n",
      "Overall abs average error: 0.50\n",
      "Epoch 6 done 100.0% - avg loss: 0.521\n",
      "Epoch 7 done 100.0% - avg loss: 0.521\n",
      "Epoch 8 done 100.0% - avg loss: 0.521\n",
      "Epoch 9 done 100.0% - avg loss: 0.521\n",
      "Epoch 10 done 100.0% - avg loss: 0.521\n",
      "Results so far at epoch 10 on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.2696  1.125  0.8554\n",
      "1   3.4956  4.024  0.5284\n",
      "2   2.7538  3.034  0.2802\n",
      "3   1.3480  1.582  0.2340\n",
      "4   2.8860  2.822  0.0640\n",
      "5   1.9724  1.865  0.1074\n",
      "6   2.4288  2.250  0.1788\n",
      "7   1.0030  0.756  0.2470\n",
      "8   0.9677  0.662  0.3057\n",
      "9   0.7226  0.911  0.1884\n",
      "10  1.7278  1.625  0.1028\n",
      "11  2.1289  2.424  0.2951\n",
      "12  1.7457  1.342  0.4037\n",
      "13  2.2165  2.464  0.2475\n",
      "14  2.4867  3.455  0.9683\n",
      "15  2.6036  3.386  0.7824\n",
      "16  1.9874  2.579  0.5916\n",
      "17  2.4882  2.445  0.0432\n",
      "18  4.3876  4.833  0.4454\n",
      "19  4.6439  5.000  0.3561\n",
      "Overall abs average error: 0.52\n",
      "Results so far at epoch 10 on DEV:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.8862  1.136  0.2498\n",
      "1   2.8717  5.000  2.1283\n",
      "2   2.3184  3.431  1.1126\n",
      "3   0.5084  0.941  0.4326\n",
      "4   2.7499  2.417  0.3329\n",
      "5   1.8208  2.250  0.4292\n",
      "6   3.7117  4.225  0.5133\n",
      "7   1.3874  1.482  0.0946\n",
      "8   3.5122  4.050  0.5378\n",
      "9   1.4963  1.279  0.2173\n",
      "10  0.6558  0.619  0.0368\n",
      "11  1.9823  1.175  0.8073\n",
      "12  1.9836  2.208  0.2244\n",
      "13  0.3180  0.541  0.2230\n",
      "14  2.3982  1.909  0.4892\n",
      "15  2.3359  2.849  0.5131\n",
      "16  0.8650  1.625  0.7600\n",
      "17  0.5335  0.875  0.3415\n",
      "18  0.5612  1.391  0.8298\n",
      "19  1.7600  1.841  0.0810\n",
      "Overall abs average error: 0.50\n",
      "Epoch 11 done 100.0% - avg loss: 0.521\n",
      "Epoch 12 done 100.0% - avg loss: 0.521\n",
      "Epoch 13 done 100.0% - avg loss: 0.521\n",
      "Epoch 14 done 100.0% - avg loss: 0.521\n",
      "Epoch 15 done 100.0% - avg loss: 0.521\n",
      "Results so far at epoch 15 on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.2403  1.125  0.8847\n",
      "1   3.5196  4.024  0.5044\n",
      "2   2.7426  3.034  0.2914\n",
      "3   1.3601  1.582  0.2219\n",
      "4   2.9098  2.822  0.0878\n",
      "5   1.9649  1.865  0.0999\n",
      "6   2.4181  2.250  0.1681\n",
      "7   1.0475  0.756  0.2915\n",
      "8   0.9811  0.662  0.3191\n",
      "9   0.7370  0.911  0.1740\n",
      "10  1.7306  1.625  0.1056\n",
      "11  2.1212  2.424  0.3028\n",
      "12  1.7842  1.342  0.4422\n",
      "13  2.2153  2.464  0.2487\n",
      "14  2.4765  3.455  0.9785\n",
      "15  2.5955  3.386  0.7905\n",
      "16  1.9814  2.579  0.5976\n",
      "17  2.4824  2.445  0.0374\n",
      "18  4.3943  4.833  0.4387\n",
      "19  4.6430  5.000  0.3570\n",
      "Overall abs average error: 0.52\n",
      "Results so far at epoch 15 on DEV:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.9095  1.136  0.2265\n",
      "1   2.8926  5.000  2.1074\n",
      "2   2.3407  3.431  1.0903\n",
      "3   0.5125  0.941  0.4285\n",
      "4   2.7477  2.417  0.3307\n",
      "5   1.8661  2.250  0.3839\n",
      "6   3.7443  4.225  0.4807\n",
      "7   1.3789  1.482  0.1031\n",
      "8   3.5450  4.050  0.5050\n",
      "9   1.5223  1.279  0.2433\n",
      "10  0.6657  0.619  0.0467\n",
      "11  1.9697  1.175  0.7947\n",
      "12  2.0016  2.208  0.2064\n",
      "13  0.3598  0.541  0.1812\n",
      "14  2.4323  1.909  0.5233\n",
      "15  2.3574  2.849  0.4916\n",
      "16  0.8481  1.625  0.7769\n",
      "17  0.5787  0.875  0.2963\n",
      "18  0.5955  1.391  0.7955\n",
      "19  1.7556  1.841  0.0854\n",
      "Overall abs average error: 0.50\n",
      "Epoch 16 done 100.0% - avg loss: 0.521\n",
      "Epoch 17 done 100.0% - avg loss: 0.521\n",
      "Epoch 18 done 100.0% - avg loss: 0.521\n",
      "Epoch 19 done 100.0% - avg loss: 0.521\n",
      "Epoch 20 done 100.0% - avg loss: 0.521\n",
      "Results so far at epoch 20 on TRAIN:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.2684  1.125  0.8566\n",
      "1   3.4894  4.024  0.5346\n",
      "2   2.7545  3.034  0.2795\n",
      "3   1.3646  1.582  0.2174\n",
      "4   2.8890  2.822  0.0670\n",
      "5   1.9735  1.865  0.1085\n",
      "6   2.4343  2.250  0.1843\n",
      "7   1.0091  0.756  0.2531\n",
      "8   0.9761  0.662  0.3141\n",
      "9   0.7482  0.911  0.1628\n",
      "10  1.7450  1.625  0.1200\n",
      "11  2.1340  2.424  0.2900\n",
      "12  1.7515  1.342  0.4095\n",
      "13  2.2241  2.464  0.2399\n",
      "14  2.4881  3.455  0.9669\n",
      "15  2.6059  3.386  0.7801\n",
      "16  1.9931  2.579  0.5859\n",
      "17  2.4933  2.445  0.0483\n",
      "18  4.3880  4.833  0.4450\n",
      "19  4.6446  5.000  0.3555\n",
      "Overall abs average error: 0.52\n",
      "Results so far at epoch 20 on DEV:\n",
      "      PRED  TRUTH    AERR\n",
      "0   0.8931  1.136  0.2429\n",
      "1   2.8734  5.000  2.1266\n",
      "2   2.3340  3.431  1.0970\n",
      "3   0.5252  0.941  0.4158\n",
      "4   2.7491  2.417  0.3321\n",
      "5   1.8495  2.250  0.4005\n",
      "6   3.7132  4.225  0.5118\n",
      "7   1.3927  1.482  0.0893\n",
      "8   3.5154  4.050  0.5346\n",
      "9   1.5061  1.279  0.2271\n",
      "10  0.6635  0.619  0.0445\n",
      "11  1.9739  1.175  0.7989\n",
      "12  1.9867  2.208  0.2213\n",
      "13  0.3278  0.541  0.2132\n",
      "14  2.4096  1.909  0.5006\n",
      "15  2.3395  2.849  0.5095\n",
      "16  0.8711  1.625  0.7539\n",
      "17  0.5420  0.875  0.3330\n",
      "18  0.5707  1.391  0.8203\n",
      "19  1.7715  1.841  0.0695\n",
      "Overall abs average error: 0.50\n",
      "Results so far at epoch 20 on TEST:\n",
      "      PRED  TRUTH    AERR\n",
      "0   2.6888  2.776  0.0872\n",
      "1   2.0607  2.247  0.1863\n",
      "2   0.9590  0.926  0.0330\n",
      "3   1.6143  1.936  0.3217\n",
      "4   2.6709  3.550  0.8791\n",
      "5   0.8056  0.758  0.0476\n",
      "6   1.6813  1.595  0.0863\n",
      "7   1.5506  1.706  0.1554\n",
      "8   2.2489  2.029  0.2199\n",
      "9   2.7791  2.180  0.5991\n",
      "10  2.6936  3.905  1.2114\n",
      "11  1.7694  2.181  0.4116\n",
      "12  2.2556  2.540  0.2844\n",
      "13  1.6882  0.375  1.3132\n",
      "14  7.0977  5.000  2.0977\n",
      "15  1.4004  0.968  0.4324\n",
      "16  1.8466  2.440  0.5934\n",
      "17  4.6871  3.818  0.8691\n",
      "18  1.5062  1.603  0.0968\n",
      "19  2.4953  2.706  0.2107\n",
      "Overall abs average error: 0.51\n"
     ]
    }
   ],
   "source": [
    "lin_func = th.nn.Linear(8,1)\n",
    "opt = th.optim.Adam(lin_func.parameters(), lr=0.01)\n",
    "\n",
    "def predict2(X):\n",
    "    with th.no_grad():\n",
    "        th_x = th.tensor(X)\n",
    "        th_yh = lin_func(th_x)\n",
    "        return th_yh.cpu().numpy()\n",
    "    \n",
    "nr_epochs = 20\n",
    "y_rnd_preds = predict2(bd.x_train)\n",
    "res = show_results(y_rnd_preds, bd.y_train, label='RANDOM paras on TRAIN'.format(epoch))    \n",
    "\n",
    "for epoch in range(1, nr_epochs + 1):\n",
    "    epoch_losses = []\n",
    "    for i, batch_data in enumerate(th_dl):\n",
    "        th_x_batch, th_y_batch = batch_data\n",
    "        th_preds = lin_func(th_x_batch)\n",
    "        th_batch_loss = (th_preds  - th_y_batch).abs()\n",
    "        th_loss = th_batch_loss.mean()\n",
    "        opt.zero_grad()\n",
    "        th_loss.backward()        \n",
    "        opt.step()\n",
    "        epoch_losses.append(th_loss.cpu().detach().numpy())\n",
    "        print(\"\\rEpoch {} done {:.1f}% - avg loss: {:.3f}\".format(epoch, i/epoch_len * 100, np.mean(epoch_losses)),\n",
    "             end='', flush=True)\n",
    "    print(\"\")\n",
    "    if (epoch % 5) == 0:  \n",
    "        y_train_hat = predict2(bd.x_train)\n",
    "        res = show_results(y_train_hat, bd.y_train, label='at epoch {} on TRAIN'.format(epoch))    \n",
    "\n",
    "        y_dev_hat = predict2(bd.x_dev)\n",
    "        res = show_results(y_dev_hat, bd.y_dev, label='at epoch {} on DEV'.format(epoch))    \n",
    "        \n",
    "y_test_hat = predict2(bd.x_test)\n",
    "res = show_results(y_test_hat, bd.y_test, label='at epoch {} on TEST'.format(epoch))            \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.18, -0.77,  0.58,  0.33, -1.08,  0.05, -1.35,  1.96,  1.  ],\n",
       "       [ 1.52,  0.58,  0.7 ,  0.11, -0.76, -0.08,  1.06, -1.49,  1.  ],\n",
       "       [ 1.29, -0.29,  1.04, -0.17, -0.2 , -0.02, -1.34,  1.31,  1.  ],\n",
       "       [ 0.14, -1.24,  0.39, -0.11,  0.91, -0.04, -0.52,  1.16,  1.  ]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_trn = np.hstack((bd.x_train,np.ones((bd.x_train.shape[0], 1))))\n",
    "x_trn[:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "np_coefs = np.linalg.pinv(x_trn.T.dot(x_trn)).dot(x_trn.T).dot(bd.y_train)\n",
    "def show_feats(np_feats, caption):\n",
    "    plt.figure(figsize=(10,6))\n",
    "    plt.bar(np.arange(np_feats.shape[0]), np_feats, tick_label=list(bd.df.columns))\n",
    "    plt.title(caption)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_feats(np_coefs.ravel()[:-1], \"Normal equation feats\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_feats(th_coefs.detach().numpy().ravel(), \"th_coefs feats\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_feats(lin_func.weight.detach().numpy().ravel(), \"lin_func feats\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Parameter containing:\n",
       "tensor([[ 0.9204,  0.0889, -0.3335,  0.4577,  0.0135, -1.2184, -0.7714, -0.7117]],\n",
       "       requires_grad=True)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_func.weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}