weather_predictorNN.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\anaconda3\\lib\\site-packages\\pandas\\plotting\\_matplotlib\\core.py:1114: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored\n",
      "  scatter = ax.scatter(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: title={'center': 'Max Temp vs Max Temp Tomorrow'}, xlabel='tmax', ylabel='tmax_tomorrow'>"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# Load weather data and fill in any missing values\n",
    "weather = pd.read_csv('data/clean_weather.csv', index_col=0)\n",
    "weather = weather.ffill()\n",
    "\n",
    "weather.plot.scatter(\"tmax\", \"tmax_tomorrow\", title=\"Max Temp vs Max Temp Tomorrow\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   tmax      tmin      rain  tmax_tomorrow\n",
      "tmax           1.000000  0.615604 -0.219941       0.818561\n",
      "tmin           0.615604  1.000000 -0.019546       0.585572\n",
      "rain          -0.219941 -0.019546  1.000000      -0.211799\n",
      "tmax_tomorrow  0.818561  0.585572 -0.211799       1.000000\n"
     ]
    }
   ],
   "source": [
    "# Print the correlation matrix between the tmax and tmax_tomorrow columns. A perfect correlation would be +/-1.0, so this data is clearly not perfectly correlated.\n",
    "print(weather.corr())    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\anaconda3\\lib\\site-packages\\pandas\\plotting\\_matplotlib\\core.py:1114: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored\n",
      "  scatter = ax.scatter(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23eab29deb0>]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "weather.plot.scatter(\"tmax\", \"tmax_tomorrow\", title=\"Max Temp vs Max Temp Tomorrow\")\n",
    "\n",
    "# Add a line of best fit to the scatter plot for a given x (tmax) and y (tmax_tomorrow) using the equation y = x*w1 + b\n",
    "prediction = lambda x, w1=.82,b=11.99: x*w1+b\n",
    "# Plot from bottom left to top right, with value predicitons for 30 and 120\n",
    "plt.plot([30,120], [prediction(30), prediction(120)], color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE = 22.897335324598394\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "# Calculate the mean squared error for the line of best fit\n",
    "\n",
    "def mse(actual, predicted):\n",
    "    return np.mean((actual - predicted)**2)\n",
    "\n",
    "# Calculate the mean squared error for the line of best fit\n",
    "print(\"MSE =\",mse(weather.tmax_tomorrow, prediction(weather.tmax)))\n",
    "\n",
    "# Clearly, this is the best that a linear regression model can do with this data. We want to use NN to improve the model as it will allow us to represent the non-linear relationship \n",
    "# between tmax and tmax_tomorrow."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Key things that Neural Networks can do:\n",
    "1. Adds a non linear transformation on top of the linear transformation (using activation functions)\n",
    "2. Adds muldtiple layers, which can capture interactions between features (yhat = Wx + b)\n",
    "3. Adds multiple hidden units, which have slightly different linear and non linear transformations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23eab35a070>]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ReLu activation function\n",
    "def relu(x):\n",
    "    return max(0,x)\n",
    "\n",
    "temps = np.arange(-50, 50)\n",
    "# If the temperature is below 0, the output is 0, else, the output is the temperature itself. This adds non-linearity to the model -> y = relu(x*w1 + b)\n",
    "plt.plot(temps, [relu(x) for x in prediction(temps)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23eac5deac0>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1bdo0paamKjU1VdOmTVNoaKhGjhzZVPkBAKiz50iFxs3LVXWtS4M6x+qPV3c2OxJOoUHl4+DBgxo1apSKiooUGRmptLQ0LV26VIMGDZIkPfzww6qsrNSECRN07NgxXXrppfr8888VHh7eJOEBAPjJ8RPVGpNt09GKaqUlRurFm7vL349reXii877OR2PjOh8AgIZy1Do16s0f9EPBUV3QMkRLJvRTTESw2bGaFbdc5wMAAE9gGIYeeTdfPxQcVbg1QHMyMygeHo7yAQDwai98sV1L1u5XgJ9Fr9zWUx3j+Krf01E+AABe6928fXrxX9slSU8O76rLU9uYnAhng/IBAPBK3+08okfeWy9JmjDgIt2U0dbkRDhblA8AgNfZUVKu8fNzVeM09Ju0eP1ucEezI6EBKB8AAK9yuNyhMdk/yF5Vq17JrfQ/N3STH1NqvQrlAwDgNapqnBo3L1eFRyuV3DpUr9+eruBAf7NjoYEoHwAAr+ByGXpg8Tqt3XtcLUMDlZWZoaiwILNj4RxQPgAAXuHppVv06YZiBfn7afaodF3YpoXZkXCOKB8AAI/31vd79NrKXZKkGdenqXdKlMmJcD4oHwAAj7Z8a4n+/MFGSdKDgzro2h4XmJwI54vyAQDwWJuL7Jq0cK2cLkPX90rUvVe2NzsSGgHlAwDgkQ7aqzQ226ZyR636XdRa04ZfIouFKbW+gPIBAPA4FY5ajc22qai0Su1jWmjWbb0UFMBHlq/gvyQAwKM4XYbuW7RWGw/YFd0iSFmZGYoMCTQ7FhoR5QMA4DEMw9Bf/rlR/9pSImuAn16/PV1JUaFmx0Ijo3wAADzGnG93a+53e2SxSC/e3F092rYyOxKaAOUDAOARPttYrL99vEmSNGXoxRrSNd7kRGgqlA8AgOnW7zuu+3PWyjCkWy9tqzsvTzE7EpoQ5QMAYKp9x05obHauqmpcGtCxjZ74bRem1Po4ygcAwDT2qhqNzbbpcLlDneLCNXNkTwX489Hk6/gvDAAwRY3TpQkL1mjbwXLFRliVNSZDLawBZseCG1A+AABuZxiG/rhkg77ZcVihQf6ak5mh+MgQs2PBTSgfAAC3e2X5Ti3OLZSfRXp5ZE91SYg0OxLciPIBAHCrf/54QM98tlWS9MRvu2hgpxiTE8HdKB8AALfJ3X1UD739oyTpzstSNKpvO3MDwRSUDwCAW+w+XKFx83JVXevSVV1i9eivLzY7EkxC+QAANLljFdUak23TsRM16pYYqRdu6iF/P67l0VxRPgAATcpR69T4+XkqOFyhC1qG6I3RGQoJ8jc7FkxE+QAANBnDMPTwO+v1w+6jCg8OUPaYDLUJt5odCyajfAAAmsxzy7bpg3UHFOBn0au39VJqbLjZkeABKB8AgCbxj9xCvfTlDknStBGX6Bfto01OBE9B+QAANLpVOw5rynv5kqRJA9vrxvQkkxPBk1A+AACNavvBMo1fkKdal6HfdkvQQ4M7mB0JHobyAQBoNIfKHBqTbVNZVa0y2rXSMzekyWJhSi3qo3wAABpFZbVTd87L1b5jlUqJDtPsUemyBjClFiejfAAAzpvLZWjy4rX6sfC4WoYGak5mhlqFBZkdCx6K8gEAOG/TP92szzYeVJC/n16/PV0p0WFmR4IHo3wAAM7L/NV79PrXBZKkZ25IU0a7KJMTwdNRPgAA5+yrLSV6/IMNkqTfDe6ga7pfYHIieAPKBwDgnGw8UKpJC9fIZUg3pidq4sD2ZkeCl6B8AAAarKi0UmOzbaqoduoX7VvryeGXMKUWZ43yAQBokHJHrcZm5+qg3aHUmBZ65dZeCvTn4wRnj98WAMBZq3W6NGnhGm0usiu6hVVzMjMUGRJodix4GcoHAOCsGIahqf/cqOVbDyk40E9vjk5XUlSo2bHghSgfAICz8uY3BVqweq8sFumFm3qoW1JLsyPBS1E+AAA/a+mGYj35yWZJ0mO/vlhDusaZnAjejPIBADijdYXHNXnxWhmGNKpPsu64LMXsSPBylA8AwGkVHj2hO+faVFXj0sCObfT4sM5MqcV5o3wAAE6p9ESNxmTbdLi8Wp3jIzRzZE8FMKUWjYDfIgDASaprXbrnrTztKClXXESw5mRmKMwaYHYs+AjKBwCgHsMwNGVJvlbtPKKwIH/NycxQXGSw2bHgQygfAIB6Zn65Q+/k7ZO/n0Uzb+2pzgkRZkeCj2lQ+Zg+fboyMjIUHh6umJgYXXvttdq6dWu9fTIzM2WxWOotffr0adTQAICm8cG6/Xp22TZJ0hO/7aKBHWNMTgRf1KDysWLFCk2cOFGrV6/WsmXLVFtbq8GDB6uioqLefkOGDFFRUVHd8sknnzRqaABA4/uh4Kh+//Z6SdJdV1yo2/okm5wIvqpBZw8tXbq03uOsrCzFxMQoLy9PV1xxRd16q9WquDguQAMA3mLXoXLdNT9X1U6XhnSJ0yNDOpkdCT7svM75KC0tlSRFRUXVW798+XLFxMSoQ4cOGjdunEpKSk77Gg6HQ3a7vd4CAHCfoxXVGptt0/ETNeqW1FLP39Rdfn5cywNNx2IYhnEuTzQMQ9dcc42OHTumr7/+um794sWL1aJFCyUnJ6ugoEB/+tOfVFtbq7y8PFmt1pNeZ+rUqXriiSdOWl9aWqqICE5yAoCmVFXj1K1vfK+8PceU2CpESyb8Qm3CT36vBn6O3W5XZGTkWX1+n3P5mDhxoj7++GN98803SkxMPO1+RUVFSk5OVk5OjkaMGHHSdofDIYfDUS98UlIS5QMAmpjLZei+nLX6aH2RwoMDtGRCP7WPCTc7FrxUQ8rHOV0x5t5779WHH36olStXnrF4SFJ8fLySk5O1ffv2U263Wq2nPCICAGhazy7bqo/WFynAz6LXbutF8YDbNKh8GIahe++9V0uWLNHy5cuVkvLzNxc6cuSICgsLFR8ff84hAQCN6x+2Qr381U5J0lPXpalf+2iTE6E5adAJpxMnTtSCBQu0cOFChYeHq7i4WMXFxaqsrJQklZeX63e/+52+++477d69W8uXL9ewYcMUHR2t4cOHN8k/AADQMN9sP6wpS/IlSfdd2V7X9zrzEWygsTXoyMesWbMkSQMGDKi3PisrS5mZmfL391d+fr7mzZun48ePKz4+XgMHDtTixYsVHs7hPAAw29biMt2zIE+1LkPXdk/QA4M6mB0JzVCDv3Y5k5CQEH322WfnFQgA0DRK7FUam21TmaNWvdtF6enr02SxMKUW7se9XQCgGThRXas75+Vq//FKpUSH6bVRvWQN8Dc7FpopygcA+Diny9D9Oeu0fl+posKClJWZoVZhQWbHQjNG+QAAH/fkx5u1bNNBBQX46fXbe6lddJjZkdDMUT4AwIfNXbVbc74tkCQ9d2M39UqO+plnAE2P8gEAPupfmw/qiX9ulCT9/qqO+k1agsmJgH+jfACAD9qwv1T3LlorlyHdlJ6kCQMuMjsSUIfyAQA+5sDxSo3NtulEtVOXp0brb8O7MqUWHoXyAQA+pKyqRmOzbSopc6hjbLhevrWnAv15q4dn4TcSAHxEjdOliQvXaktxmdqEWzVnTIYiggPNjgWchPIBAD7AMAw9/uFGrdx2SCGB/npzdLouaBlidizglCgfAOADZq/cpYXf75XFIr14c3elJbY0OxJwWpQPAPByn+QXafqnWyRJf7q6swZ3iTM5EXBmlA8A8GJr9h7TA4vXSZIy+7XT2MtSzA0EnAXKBwB4qb1HTmjc3Fw5al361cUx+tNvOpsdCTgrlA8A8EKlJ2o0JvsHHamoVpeECL14cw/5+3EtD3gHygcAeJnqWpfGL8jVzkMVSogM1pzMDIVZA8yOBZw1ygcAeBHDMPTIu+u1etdRtbAGaM6YDMVGBJsdC2gQygcAeJEX/7Vd763dL38/i16+tac6xUWYHQloMMoHAHiJJWv36YUvtkuS/npNV/Xv0MbkRMC5oXwAgBdYveuIHn5nvSRpfP8LNfLStiYnAs4d5QMAPNzOQ+UaPz9PNU5Dv74kTn+4qpPZkYDzQvkAAA92pNyhMVk2lVbWqGfblnruxu7yY0otvBzlAwA8VFWNU+Pm5Wrv0RNqGxWq129PV3Cgv9mxgPNG+QAAD+RyGXroHz9qzd7jigwJ1JzMDLVuYTU7FtAoKB8A4IFmfLZVH+cXKdDfotdG9VL7mBZmRwIaDeUDADzMoh/26tUVOyVJT1+Xpj4XtjY5EdC4KB8A4EFWbDukP76/QZI0+VepGtEz0eREQOOjfACAh9hSbNfEt9bI6TI0oscFuv+XqWZHApoE5QMAPMBBe5XGZtlU7qjVpSlRmn7dJbJYmFIL30T5AACTVThqdcdcmw6UVunCNmGaPSpd1gCm1MJ3UT4AwEROl6H7c9Zqw367osKClJ3ZW5GhgWbHApoU5QMATPTXjzbpi80lsgb46Y3R6WrbOtTsSECTo3wAgEmyvi1Q9qrdkqTnbuyunm1bmRsIcBPKBwCYYNmmg/rLR5skSY8M7aSr0+JNTgS4D+UDANwsf1+p7lu0VoYh3dK7rcZfcaHZkQC3onwAgBvtO3ZCY+faVFnj1BUd2uiv13RhSi2aHcoHALiJvapGd2Tn6lCZQ53iwvXyyB4K8OdtGM0Pv/UA4AY1TpcmvrVGWw+WKSbcqjmZGQoPZkotmifKBwA0McMw9Kf3N+jr7YcVGuSvOZkZSmgZYnYswDSUDwBoYrNW7FSOrVB+FumlW3qo6wWRZkcCTEX5AIAm9M8fD2jG0q2SpMeHddEvL441ORFgPsoHADSRvD1H9dDbP0qSxvyinUb3a2duIMBDUD4AoAnsOVKhcfPyVF3r0qDOsfrj1Z3NjgR4DMoHADSyYxXVGpNl09GKaqUlRurFm7vL349reQA/oXwAQCNy1Do1fn6edh2u0AUtQ/TG6HSFBgWYHQvwKJQPAGgkhmHokXfz9cPuowq3BmhOZoZiwoPNjgV4HMoHADSS57/YriVr9yvAz6JXbuupjnHhZkcCPBLlAwAawTt5+/T3f22XJD05vKsuT21jciLAc1E+AOA8rdp5WI++t16SNGHARbopo63JiQDPRvkAgPOwo6RM4+fnqcZp6Ddp8frd4I5mRwI8HuUDAM7R4XKHMrNsKquqVa/kVvqfG7rJjym1wM+ifADAOaiqcerOubnad6xSya1DNXtULwUH+psdC/AKlA8AaCCXy9ADi9dpXeFxtQwNVFZmhlq3sJodC/AaDSof06dPV0ZGhsLDwxUTE6Nrr71WW7durbePYRiaOnWqEhISFBISogEDBmjjxo2NGhoAzPTU0i36dEOxgvz9NHtUui5s08LsSIBXaVD5WLFihSZOnKjVq1dr2bJlqq2t1eDBg1VRUVG3z4wZM/Tcc89p5syZstlsiouL06BBg1RWVtbo4QHA3Ras3qPZK3dJkp65IU29U6JMTgR4H4thGMa5PvnQoUOKiYnRihUrdMUVV8gwDCUkJGjy5Mn6wx/+IElyOByKjY3V008/rfHjx//sa9rtdkVGRqq0tFQRERHnGg0AGt3yrSW6Y26unC5DDw7qoPt+mWp2JMBjNOTz+7zO+SgtLZUkRUX9u/kXFBSouLhYgwcPrtvHarWqf//+WrVq1fn8KAAw1aYDdk18a42cLkPX90rUvVe2NzsS4LXO+W5HhmHowQcf1GWXXaauXbtKkoqLiyVJsbGx9faNjY3Vnj17Tvk6DodDDoej7rHdbj/XSADQJIpLqzQ226aKaqf6Xtha04ZfIouFKbXAuTrnIx+TJk3S+vXrtWjRopO2/fcfpWEYp/1DnT59uiIjI+uWpKSkc40EAI2u3FGrsdk2Fdur1D6mhV4d1UtBAUwUBM7HOf0F3Xvvvfrwww/11VdfKTExsW59XFycpP8/AvKTkpKSk46G/OTRRx9VaWlp3VJYWHgukQCg0dU6Xbp34RptKrIrukWQsjIzFBkSaHYswOs1qHwYhqFJkybpvffe05dffqmUlJR621NSUhQXF6dly5bVrauurtaKFSvUr1+/U76m1WpVREREvQUAzGYYhv7y0SZ9tfWQrAF+ev32dCVFhZodC/AJDTrnY+LEiVq4cKE++OADhYeH1x3hiIyMVEhIiCwWiyZPnqxp06YpNTVVqampmjZtmkJDQzVy5Mgm+QcAQFN485sCzftujywW6cWbu6tH21ZmRwJ8RoPKx6xZsyRJAwYMqLc+KytLmZmZkqSHH35YlZWVmjBhgo4dO6ZLL71Un3/+ucLDwxslMAA0taUbivXkJ5slSVOGXqwhXeNNTgT4lvO6zkdT4DofAMz0Y+Fx3TT7O1XVuHRbn7b66zVdmdkCnAW3XecDAHxJ4dETumNurqpqXBrQsY2mDutC8QCaAOUDACSVVtZobLZNh8sdujg+QjNH9lSAP2+RQFPgLwtAs1dd69KEt/K0vaRcsRFWzclMVwvrOV+DEcDPoHwAaNYMw9BjS/L17Y4jCg3y15zMDMVHhpgdC/BplA8Azdory3fq7bx98rNIL4/sqS4JkWZHAnwe5QNAs/XBuv165rOtkqQnfttFAzvFmJwIaB4oHwCaJdvuo/r92+slSXdelqJRfduZGwhoRigfAJqdgsMVumterqqdLl3VJVZTfn2x2ZGAZoXyAaBZOVpRrTFZP+jYiRp1S4zUCzf1kJ8f1/IA3InyAaDZqKpx6q55udp95IQuaBmiN0ZnKCTI3+xYQLND+QDQLLhchh5+Z71y9xxTeHCAssdkqE241exYQLNE+QDQLDy3bJs+/PGAAvwsevW2XkqN5WaXgFkoHwB83j9yCzXzqx2SpOkjLtEv2kebnAho3igfAHzatzsOa8p7+ZKke69srxvSk0xOBIDyAcBnbT9YprsX5KnWZei33RL04KAOZkcCIMoHAB9VUlalzCybyqpqldGulZ65IU0WC1NqAU9A+QDgcyqrnRo3N1f7j1cqJTpMs0elyxrAlFrAU1A+APgUp8vQ/Tlr9eO+UrUKDVRWZoZahQWZHQvAf6B8APAp0z/ZrM83HVSQv59m356udtFhZkcC8F8oHwB8xvzvduuNbwokSf9zYzdltIsyORGAU6F8APAJX245qMc/3ChJ+v1VHfXbbgkmJwJwOpQPAF5vw/5STVq4Vi5Duik9SRMGXGR2JABnQPkA4NWKSit1x1ybTlQ79Yv2rfW34V2ZUgt4OMoHAK9V7qjV2OxcHbQ7lBrTQq/c2kuB/rytAZ6Ov1IAXqnW6dLEt9Zoc5Fd0S2syhqTociQQLNjATgLlA8AXscwDD3+4Uat2HZIwYF+enN0uhJbhZodC8BZonwA8Dqvf71Lb32/VxaL9OLNPdQtqaXZkQA0AOUDgFf5NL9I0z7ZIkl67NcX66oucSYnAtBQlA8AXmPt3mOavHidJOn2vsm647IUcwMBOCeUDwBeofDoCd05N1eOWpeu7BSjP/+mM1NqAS9F+QDg8UpP1Cgz6wcdqahWl4QIvXRLDwUwpRbwWvz1AvBo1bUu3b0gTzsPVSg+MlhzMjMUZg0wOxaA80D5AOCxDMPQo+/l67tdRxQW5K83R2coNiLY7FgAzhPlA4DHeunLHXp3zT75+1n08q091TkhwuxIABoB5QOAR3p/7X49t2ybJOkv13TRgI4xJicC0FgoHwA8zve7jujhd9ZLku664kLdemmyyYkANCbKBwCPsvNQue6an6dqp0tDu8bpkSGdzI4EoJFRPgB4jCPlDo3Jsqm0skbdk1rq+Zu6y8+Pa3kAvobyAcAjVNU4NW5ervYePaGkqBC9MTpdwYH+ZscC0AQoHwBM53IZeujtH7Vm73FFBAcoKzND0S2sZscC0EQoHwBM98znW/Xx+iIF+lv06qheah8TbnYkAE2I8gHAVIt+2KtZy3dKkqaPSFO/i6JNTgSgqVE+AJhm5bZD+uP7GyRJ9/0yVdf3SjQ5EQB3oHwAMMWWYrsmvLVGTpeh4T0u0AO/SjU7EgA3oXwAcLsSe5XGZtlU7qhV75QoPXXdJbJYmFILNBeUDwBudaK6VmPn2nSgtEoXRodp9qhesgYwpRZoTigfANzG6TJ036K12rDfrqiwIGWNyVDL0CCzYwFwM8oHALf560eb9MXmEgUF+On123spuXWY2ZEAmIDyAcAtsr4tUPaq3ZKk52/srl7JUeYGAmAaygeAJrds00H95aNNkqQ/DOmkq9PiTU4EwEyUDwBNKn9fqe5btFaGId2ckaS7+19odiQAJqN8AGgy+49XauxcmyprnLo8NVp/vbYrU2oBUD4ANA17VY3GZtl0qMyhjrHhevnWngr05y0HAOUDQBOocbo08a012nqwTG3CrZozJkMRwYFmxwLgIRpcPlauXKlhw4YpISFBFotF77//fr3tmZmZslgs9ZY+ffo0Vl4AHs4wDP3p/Q36evthhQT6a87oDF3QMsTsWAA8SIPLR0VFhbp166aZM2eedp8hQ4aoqKiobvnkk0/OKyQA7/Hqil3KsRXKYpH+fksPXZIYaXYkAB4moKFPGDp0qIYOHXrGfaxWq+Li4s45FADv9NH6A3p66RZJ0p9/01mDOseanAiAJ2qScz6WL1+umJgYdejQQePGjVNJSclp93U4HLLb7fUWAN4nb89RPfiPHyVJmf3aacwvUkxOBMBTNXr5GDp0qN566y19+eWXevbZZ2Wz2XTllVfK4XCccv/p06crMjKybklKSmrsSACa2J4jFRo3L0/VtS796uIY/ek3nc2OBMCDWQzDMM75yRaLlixZomuvvfa0+xQVFSk5OVk5OTkaMWLESdsdDke9YmK325WUlKTS0lJFREScazQAbnL8RLVGzFqlXYcq1PWCCC2+q6/CrA3+RheAl7Pb7YqMjDyrz+8mf4eIj49XcnKytm/ffsrtVqtVVqu1qWMAaAKOWqfump+nXYcqlBAZrDmjMygeAH5Wk1/n48iRIyosLFR8PPdyAHyJYRh65N18/VBwVC2sAZozJkMxEcFmxwLgBRr8vyjl5eXasWNH3eOCggKtW7dOUVFRioqK0tSpU3XdddcpPj5eu3fv1pQpUxQdHa3hw4c3anAA5nr+i+1asna//P0seuXWnuoUx9ekAM5Og8tHbm6uBg4cWPf4wQcflCSNHj1as2bNUn5+vubNm6fjx48rPj5eAwcO1OLFixUeHt54qQGY6t28ffr7v/79Verfru2qKzq0MTkRAG/S4PIxYMAAnekc1c8+++y8AgHwbN/tPKJH3lsvSbq7/0W6pXdbkxMB8Dbc2wXAWdtRUq7x83NV4zR0dVq8Hr6qo9mRAHghygeAs3K43KEx2T/IXlWrnm1b6tkbusnPz2J2LABeiPIB4GdV1Th159xcFR6tVNuoUL1+e7qCA/3NjgXAS1E+AJyRy2XogcXrtK7wuCJDApU1JkOtW3BtHgDnjvIB4IyeXrpFn24oVqC/Ra+N6qWL2rQwOxIAL0f5AHBab32/R6+t3CVJmnF9mvpc2NrkRAB8AeUDwCkt31qiP3+wUZL0wK86aHiPRJMTAfAVlA8AJ9l0wK6Jb62R02VoRM8LdN8v25sdCYAPoXwAqOegvUp3zLWpotqpPhdG6akRabJYmFILoPFQPgDUqXDUamy2TUWlVbqoTZheuy1dQQG8TQBoXLyrAJAk1TpdunfRWm08YFfrsCBlZfZWZGig2bEA+CDKBwAZhqG/frRJX24pkTXAT2+MTlfb1qFmxwLgoygfADTn292a+90eSdLzN3VXj7atTE4EwJdRPoBm7rONxfrbx5skSY8O7aRfXxJvciIAvo7yATRjPxYe1/05a2UY0shL2+quKy40OxKAZoDyATRThUdP6I65uaqqcal/hzb6y2+7MKUWgFtQPoBmyF5Vozvm2nS43KFOceGaObKHAvx5OwDgHrzbAM1MjdOlCQvWaNvBcsWEWzUnM0PhwUypBeA+lA+gGTEMQ48tydc3Ow4rNMhfczIzlNAyxOxYAJoZygfQjLyyfKf+kbtPfhZp5sge6npBpNmRADRDlA+gmfhg3X4989lWSdLU33bRlZ1iTU4EoLmifADNQO7uo/r92+slSXdclqLb+7YzNxCAZo3yAfi43YcrNG5erqqdLg3qHKspv77Y7EgAmjnKB+DDjlVUa0y2TcdO1CgtMVIv3txd/n5cywOAuSgfgI+qqnHqrvm5KjhcoQtahuiN0ekKDQowOxYAUD4AX2QYhh5+Z71su48p3BqgrDEZigkPNjsWAEiifAA+6bll2/ThjwcU4GfRrNt6qUNsuNmRAKAO5QPwMf/ILdRLX+6QJE0bfokuS402OREA1Ef5AHzItzsOa8p7+ZKkiQMv0o0ZSSYnAoCTUT4AH7H9YJnuXpCnWpehYd0S9NCgjmZHAoBTonwAPuBQmUOZWTaVVdUqPbmVnrk+TX5MqQXgoSgfgJerrHbqzrk27T9eqXatQzX79nQFB/qbHQsATovyAXgxp8vQ5MVr9eO+UrUMDVTWmN6KCgsyOxYAnBHlA/Bi0z/ZrM82HlSQv59mj0pXSnSY2ZEA4GdRPgAvNf+73XrjmwJJ0jM3pKl3SpTJiQDg7FA+AC/01ZYSPf7hRknSQ4M66JruF5icCADOHuUD8DIbD5Rq0sI1chnS9b0SNenK9mZHAoAGoXwAXqSotFJjs22qqHaq30WtNW34JbJYmFILwLtQPgAvUe6o1djsXB20O5Qa00KzbuuloAD+hAF4H965AC9Q63Rp0sI12lxkV3SLIM3JzFBkSKDZsQDgnFA+AA9nGIam/nOjlm89pOBAP70xOkNJUaFmxwKAc0b5ADzcG18XaMHqvbJYpBdu6qHuSS3NjgQA54XyAXiwpRuKNO3TzZKkx359sYZ0jTM5EQCcP8oH4KHW7j2m+3PWyTCkUX2SdcdlKWZHAoBGQfkAPFDh0RMaNy9XjlqXBnRso8eHdWZKLQCfQfkAPEzpiRqNybbpcHm1OsdHaObIngrw508VgO/gHQ3wINW1Lt29IE87SsoVFxGsOZkZamENMDsWADQqygfgIQzD0JQl+fpu1xGFBflrTmaG4iKDzY4FAI2O8gF4iJlf7tA7efvk72fRzFt7qnNChNmRAKBJUD4AD/DBuv16dtk2SdITv+2igR1jTE4EAE2H8gGY7IeCo/r92+slSXddcaFu65NsciIAaFqUD8BEuw6V6675uap2ujSkS5weGdLJ7EgA0OQoH4BJjlZUa2y2TcdP1KhbUks9f1N3+flxLQ8Avq/B5WPlypUaNmyYEhISZLFY9P7779fbbhiGpk6dqoSEBIWEhGjAgAHauHFjY+UFfMJBe5XGZtu0+8gJJbYK0Ru3pyskyN/sWADgFg0uHxUVFerWrZtmzpx5yu0zZszQc889p5kzZ8pmsykuLk6DBg1SWVnZeYcFfMGyTQc15IWVWld4XBHBAcrKzFCbcKvZsQDAbRp89aKhQ4dq6NChp9xmGIZeeOEFPfbYYxoxYoQkae7cuYqNjdXChQs1fvz480sLeLGqGqee/Hiz5q/eI0nqkhChv9/SQxe1aWFyMgBwr0a9dGJBQYGKi4s1ePDgunVWq1X9+/fXqlWrTlk+HA6HHA5H3WO73d6YkerUOl168pPNTfLawNn4dsdhbTtYLkkad3mKfndVR1kD+KoFQPPTqOWjuLhYkhQbG1tvfWxsrPbs2XPK50yfPl1PPPFEY8Y4JZchZX27u8l/DnAm0S2sevbGburfoY3ZUQDANE1y04j/vvumYRinvSPno48+qgcffLDusd1uV1JSUqNn8rNIEwde1OivC5ytMGuAbkxPUnQLzu8A0Lw1avmIi4uT9O8jIPHx8XXrS0pKTjoa8hOr1SqrtenfjAP8/fT7q7iGAgAAZmvU63ykpKQoLi5Oy5Ytq1tXXV2tFStWqF+/fo35owAAgJdq8JGP8vJy7dixo+5xQUGB1q1bp6ioKLVt21aTJ0/WtGnTlJqaqtTUVE2bNk2hoaEaOXJkowYHAADeqcHlIzc3VwMHDqx7/NP5GqNHj1Z2drYefvhhVVZWasKECTp27JguvfRSff755woPD2+81AAAwGtZDMMwzA7xn+x2uyIjI1VaWqqICG4pDgCAN2jI5zf3dgEAAG5F+QAAAG5F+QAAAG5F+QAAAG5F+QAAAG5F+QAAAG5F+QAAAG5F+QAAAG5F+QAAAG7VqHe1bQw/XXDVbrebnAQAAJytnz63z+bC6R5XPsrKyiRJSUlJJicBAAANVVZWpsjIyDPu43H3dnG5XDpw4IDCw8NlsVjMjuMR7Ha7kpKSVFhYyP1umhhj7T6Mtfsw1u7TnMfaMAyVlZUpISFBfn5nPqvD4458+Pn5KTEx0ewYHikiIqLZ/TKbhbF2H8bafRhr92muY/1zRzx+wgmnAADArSgfAADArSgfXsBqterxxx+X1Wo1O4rPY6zdh7F2H8bafRjrs+NxJ5wCAADfxpEPAADgVpQPAADgVpQPAADgVpQPAADgVpQPL+BwONS9e3dZLBatW7eu3ra9e/dq2LBhCgsLU3R0tO677z5VV1ebE9RL7d69W3fccYdSUlIUEhKiiy66SI8//vhJ48hYN55XXnlFKSkpCg4OVq9evfT111+bHcnrTZ8+XRkZGQoPD1dMTIyuvfZabd26td4+hmFo6tSpSkhIUEhIiAYMGKCNGzealNh3TJ8+XRaLRZMnT65bx1ifGeXDCzz88MNKSEg4ab3T6dTVV1+tiooKffPNN8rJydG7776rhx56yISU3mvLli1yuVx67bXXtHHjRj3//PN69dVXNWXKlLp9GOvGs3jxYk2ePFmPPfaY1q5dq8svv1xDhw7V3r17zY7m1VasWKGJEydq9erVWrZsmWprazV48GBVVFTU7TNjxgw999xzmjlzpmw2m+Li4jRo0KC6e2qh4Ww2m2bPnq20tLR66xnrn2HAo33yySdGp06djI0bNxqSjLVr19bb5ufnZ+zfv79u3aJFiwyr1WqUlpaakNZ3zJgxw0hJSal7zFg3nt69ext33313vXWdOnUyHnnkEZMS+aaSkhJDkrFixQrDMAzD5XIZcXFxxlNPPVW3T1VVlREZGWm8+uqrZsX0amVlZUZqaqqxbNkyo3///sb9999vGAZjfTY48uHBDh48qHHjxmn+/PkKDQ09aft3332nrl271jsqctVVV8nhcCgvL8+dUX1OaWmpoqKi6h4z1o2jurpaeXl5Gjx4cL31gwcP1qpVq0xK5ZtKS0slqe73uKCgQMXFxfXG3mq1qn///oz9OZo4caKuvvpq/epXv6q3nrH+eR53Yzn8m2EYyszM1N1336309HTt3r37pH2Ki4sVGxtbb12rVq0UFBSk4uJiNyX1PTt37tRLL72kZ599tm4dY904Dh8+LKfTedJYxsbGMo6NyDAMPfjgg7rsssvUtWtXSaob31ON/Z49e9ye0dvl5ORozZo1stlsJ21jrH8eRz7cbOrUqbJYLGdccnNz9dJLL8lut+vRRx894+tZLJaT1hmGccr1zc3ZjvV/OnDggIYMGaIbbrhBd955Z71tjHXj+e8xYxwb16RJk7R+/XotWrTopG2M/fkrLCzU/fffrwULFig4OPi0+zHWp8eRDzebNGmSbr755jPu065dO/3tb3/T6tWrT7o/QHp6um699VbNnTtXcXFx+v777+ttP3bsmGpqak5q3M3R2Y71Tw4cOKCBAweqb9++mj17dr39GOvGER0dLX9//5OOcpSUlDCOjeTee+/Vhx9+qJUrVyoxMbFufVxcnKR//195fHx83XrGvuHy8vJUUlKiXr161a1zOp1auXKlZs6cWTfLiLE+AxPPN8EZ7Nmzx8jPz69bPvvsM0OS8c477xiFhYWGYfz/SZAHDhyoe15OTg4nQZ6Dffv2GampqcbNN99s1NbWnrSdsW48vXv3Nu6555566y6++GJOOD1PLpfLmDhxopGQkGBs27btlNvj4uKMp59+um6dw+HgJMhzYLfb670/5+fnG+np6cZtt91m5OfnM9ZngfLhJQoKCk6a7VJbW2t07drV+OUvf2msWbPG+OKLL4zExERj0qRJ5gX1Qvv37zfat29vXHnllca+ffuMoqKiuuUnjHXjycnJMQIDA40333zT2LRpkzF58mQjLCzM2L17t9nRvNo999xjREZGGsuXL6/3O3zixIm6fZ566ikjMjLSeO+994z8/HzjlltuMeLj4w273W5ict/wn7NdDIOx/jmUDy9xqvJhGP8+QnL11VcbISEhRlRUlDFp0iSjqqrKnJBeKisry5B0yuU/MdaN5+WXXzaSk5ONoKAgo2fPnnXTQXHuTvc7nJWVVbePy+UyHn/8cSMuLs6wWq3GFVdcYeTn55sX2of8d/lgrM/MYhiGYcK3PQAAoJlitgsAAHArygcAAHArygcAAHArygcAAHArygcAAHArygcAAHArygcAAHArygcAAHArygcAAHArygcAAHArygcAAHArygcAAHCr/wXxoGY2JNFcIAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Multiple layers: The output of one layer is the input to the next layer. This allows the model to learn more complex relationships between the input and output.\n",
    "# i.e: y = w2*(relu(w1*x + b1)) + b2 where w1 and b1 are the weights and biases of the first layer, and w2 and b2 are the weights and biases of the second layer.\n",
    "\n",
    "temps = np.arange(-50, 50)\n",
    "layer1 = np.maximum(0,prediction(temps)) # ReLu applied to first layer of linear transformation to create non-linearity\n",
    "layer2 = prediction(layer1, 0.5, 10) # Second layer of linear transformation\n",
    "\n",
    "plt.plot(temps, layer2)\n",
    "# We can see that we're now predicting 10 when the temperature is 0 based on our final bias term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23eab5087c0>]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Multiple hidden units\n",
    "layer1_1 = np.maximum(0, prediction(temps)) # Default weight and bias for first hidden unit\n",
    "layer1_2 = np.maximum(0, prediction(temps, 0.1, 10)) # Different weights and biases for second hidden unit\n",
    "\n",
    "plt.plot(temps, layer1_1)\n",
    "plt.plot(temps, layer1_2) # We can see that this weight and bias did not activate reLu at all based on having a really small weight and large bias."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23eab577730>]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Combine multiple hidden units\n",
    "plt.plot(temps, layer1_1 + layer1_2) # We can see that the output of the two hidden units is the sum of their outputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23eac5fe670>]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UKi4yTPcNTTU7jl+hoAAA0AScLrdeWr5DkvTrYV0VHxVuciL/QkEBAKAJLP6uWLsPValVdLh+yfTkrFFQAADwsjqXWy+vqJ+e3D+8m1pYw0xO5H8oKAAAeNn/rt+nvUeq1aZFhO66rLPZcfwSBQUAAC+yO1165fOdkqTfjOiu6AimJ+eCggIAgBf9v3WFKjpao8Q4q+4Y3MnsOH6LggIAgJfU1rk074v66cmkkd0VGR5qciL/RUEBAMBL/ufrvTpQbldyfKRuvSTF7Dh+jYICAIAXVDucen1l/fTkwVFpsoYxPTkfFBQAALzg3a8KdKjSoZSEKN00oKPZcfweBQUAgPNUaXfqjdxdkqSHrkxTeCgvr+eLIwgAwHl659/5KquuU9c2Mbqhfwez4wQECgoAAOfBVlOn+at2S5IeHp2mMKYnXsFRBADgPPx1db7Ka51Ka9dC112QbHacgOH1guJ0OvXkk08qNTVVUVFR6tq1q2bMmCG32+3ZxzAMTZ8+XcnJyYqKitKIESOUl5fn7SgAADSpo9UO/XV1viTpkYweCg2xmJwocHi9oMyaNUtvvPGG5s2bpx9//FGzZ8/Wf//3f+uVV17x7DN79mzNmTNH8+bN07p165SUlKSMjAxVVFR4Ow4AAE1m/qrdqrA71bt9nK7um2R2nIDi9YLy1Vdfady4cRozZoy6dOmim266SZmZmfr2228l1U9P5s6dq2nTpunGG29Uenq6FixYoOrqar3//vvejgMAQJM4XGnXO2v2SJIeGZ2mEKYnXuX1gjJ06FCtWLFC27dvlyR9//33Wr16ta699lpJUn5+vkpKSpSZmen5GqvVquHDh2vNmjXejgMAQJN4I3eXqh0uXdAxXhl9Es2OE3C8/hGLjz/+uGw2m3r16qXQ0FC5XC49//zzuv322yVJJSUlkqTExIa/zMTERBUUFJzwOe12u+x2u+d+eXm5t2MDAHDGSstr9bev6l+zHsnoIYuF6Ym3eX2C8uGHH+q9997T+++/rw0bNmjBggX605/+pAULFjTY7/hfpmEYJ/0FZ2dnKz4+3nNLSeHzDQAA5nlt5S7ZnW5d3KmlRvRoa3acgOT1gvK73/1OTzzxhG677Tb169dPv/jFL/TII48oOztbkpSUVH8R0c+TlJ+VlpY2mqr8bOrUqbLZbJ5bYWGht2MDAHBG9ttq9P7XeyVJj2b2ZHrSRLxeUKqrqxUS0vBpQ0NDPW8zTk1NVVJSknJycjyPOxwO5ebmasiQISd8TqvVqri4uAY3AADMMO/znXK43BqUmqAh3VqbHSdgef0alLFjx+r5559Xp06d1LdvX23cuFFz5szRvffeK6n+1E5WVpZmzpyptLQ0paWlaebMmYqOjtaECRO8HQcAAK8pPFKt//dt/RT/Ua49aVJeLyivvPKKnnrqKU2cOFGlpaVKTk7W/fffr6efftqzz2OPPaaamhpNnDhRZWVlGjx4sJYtW6bY2FhvxwEAwGte+XyH6lyGhnZvo8FdmZ40JYthGIbZIc5WeXm54uPjZbPZON0DAGgWew5VadScXLnchj6aOEQXd2pldiS/czav33wWDwAAZ+DlFTvkchsa2bMt5aQZUFAAADiNnaWVWvxdkaT6dU/Q9CgoAACcxtzl2+U2pIw+ibqgY0uz4wQFCgoAAKewtaRcn/ywX5I0helJs6GgAABwCi/m1H+23Jh+7dW7PW/MaC4UFAAATmJzkU2f5R2QxSJljU4zO05QoaAAAHASP09Prr8wWWmJrNXVnCgoAACcwMa9ZVqxtVQhFunhUUxPmhsFBQCAE5jz0/Tkxos7qmvbFianCT4UFAAAjrNuzxF9ueOQwkIsTE9MQkEBAOA4LyzbJkm6eWCKUhKiTU4TnCgoAAAcY82uQ1q7+4giQkM0+cruZscJWhQUAAB+YhiG5iyrv/bktkEp6tAyyuREwYuCAgDAT1btOKRvC8pkDQvRpJFMT8xEQQEAQD9PT+qvPbnz0s5KjIs0OVFwo6AAACBpxY+l+n6fTVHhoXpgeDez4wQ9CgoAIOgZhuFZ9+SuIZ3VNtZqciJQUAAAQe+zvBJt2V+umIhQ3X8F0xNfQEEBAAQ1t9vQizk7JEn3Dk1VQkyEyYkgUVAAAEHuk037te1AhWIjw/SroV3NjoOfUFAAAEHL6XJr7vL6a09+NbSr4qPDTU6En1FQAABBa8n3xdp9sEoto8N179AuZsfBMSgoAICgVOdy66UV9dee/NcVXRUbyfTEl1BQAABB6aMN+1RwuFqtYyJ092VdzI6D41BQAABBx+F06+UVOyVJvxnRTTHWMJMT4XgUFABA0Pnw20IVHa1R21ir7ry0s9lxcAIUFABAUKmtc+nVz+unJ5NGdFNkeKjJiXAiFBQAQFD54Ju9KimvVfv4SN02qJPZcXASFBQAQNCocbj02spdkqTJV3ZneuLDKCgAgKDx7to9OlhhV8dWUbp5QIrZcXAKFBQAQFCotDv1Ru5uSdJDo9IUEcZLoC/jtwMACAoL1uzRkSqHurSO1o39O5gdB6dBQQEABLzy2jrNX1U/PXl4dJrCQnn583X8hgAAAe+vq/Nlq6lT93YtdP2FTE/8AQUFABDQjlY79Jcv8yVJWaPTFBpiMTkRzgQFBQAQ0N76crcq7E71SorVtentzY6DM0RBAQAErCNVDr397z2SpEcyeiiE6YnfoKAAAALWm7m7VO1wKb1DnDL7JJodB2eBggIACEilFbVa8NUeSdKUjB6yWJie+BMKCgAgIL2+cpdq69y6KKWlRvZsZ3YcnCUKCgAg4Oy31eh/vt4rSXo0k+mJP6KgAAACzqtf7JTD6dagLgka2r2N2XFwDigoAICAsq+sWh+uK5RU/84dpif+iYICAAgo8z7fqTqXoSHdWuuybq3NjoNzREEBAASMgsNV+vv6fZLqrz2B/6KgAAACxksrdsjlNjS8R1sN6JxgdhycBwoKACAg7DpYqcUbiyTVr3sC/0ZBAQAEhJeW75DbkEb3bqcLU1qaHQfniYICAPB720oq9M8fiiXVv3MH/o+CAgDwe3OXb5dhSNekJ6lvcrzZceAFTVJQioqKdOedd6p169aKjo7WRRddpPXr13seNwxD06dPV3JysqKiojRixAjl5eU1RRQAQIDLK7bp080lsliYngQSrxeUsrIyXX755QoPD9enn36qLVu26IUXXlDLli09+8yePVtz5szRvHnztG7dOiUlJSkjI0MVFRXejgMACHAv5myXJI29IFk9EmNNTgNvCfP2E86aNUspKSl6++23Pdu6dOni+W/DMDR37lxNmzZNN954oyRpwYIFSkxM1Pvvv6/777/f25EAAAHq+8KjWv5jqUIs0sOj08yOAy/y+gRlyZIlGjhwoG6++Wa1a9dO/fv311tvveV5PD8/XyUlJcrMzPRss1qtGj58uNasWePtOACAADbnp+nJDf07qlvbFiangTd5vaDs3r1br7/+utLS0vTZZ5/pgQce0EMPPaS//e1vkqSSkhJJUmJiYoOvS0xM9Dx2PLvdrvLy8gY3AEBwW19wRLnbDyo0xKKHRnU3Ow68zOuneNxutwYOHKiZM2dKkvr376+8vDy9/vrruuuuuzz7Hf/hTYZhnPQDnbKzs/Xss896OyoAwI+9sKx+enLzgI7q3DrG5DTwNq9PUNq3b68+ffo02Na7d2/t3btXkpSUlCRJjaYlpaWljaYqP5s6dapsNpvnVlhY6O3YAAA/8tWuw1qz67DCQy2afCXTk0Dk9YJy+eWXa9u2bQ22bd++XZ07d5YkpaamKikpSTk5OZ7HHQ6HcnNzNWTIkBM+p9VqVVxcXIMbACA4GYbheefObZd0UsdW0SYnQlPw+imeRx55REOGDNHMmTN1yy236JtvvtH8+fM1f/58SfWndrKysjRz5kylpaUpLS1NM2fOVHR0tCZMmODtOACAALN65yF9s+eIIsJCNGkk05NA5fWCcskll2jRokWaOnWqZsyYodTUVM2dO1d33HGHZ5/HHntMNTU1mjhxosrKyjR48GAtW7ZMsbG8fx0AcHKGYXiuPblzcGclxUeanAhNxWIYhmF2iLNVXl6u+Ph42Ww2TvcAQBD5fOsB3fvOt4oMD9Gqx0aqXSwFxZ+czes3n8UDAPALhmF41j25+7IulJMAR0EBAPiFZVsOaHNRuWIiQnX/8G5mx0ETo6AAAHye2/2fd+788vJUJcREmJwITY2CAgDweUs379fWkgrFWsP062FdzY6DZkBBAQD4NJfb0NzlOyRJ9w1LVXx0uMmJ0BwoKAAAn7bk+yLtLK1UfFS47h2aanYcNBMKCgDAZzldbr300/Tkv67oqrhIpifBgoICAPBZH20o0p7D1WodE6F7hnQxOw6aEQUFAOCTHE63Xv68fnrywPBuirF6ffFz+DAKCgDAJ/19faH2ldWobaxVd17a2ew4aGYUFACAz6mtc2ne5zslSRNHdFNURKjJidDcKCgAAJ+z8Ju92m+rVfv4SN0+qJPZcWACCgoAwKfUOFx6deUuSdKkkd0VGc70JBhRUAAAPuW9tQU6WGFXh5ZRumVgitlxYBIKCgDAZ1TZnXojt3568tCo7ooI42UqWPGbBwD4jAVf7dHhKoc6t47WjRd3NDsOTERBAQD4hIraOs1ftVuS9PCoNIWH8hIVzPjtAwB8wl9X79HR6jp1axujcRd1MDsOTEZBAQCYzlZdpz+vrp+eZI3uodAQi8mJYDYKCgDAdH9evVsVtU71TIzVmH7tzY4DH0BBAQCY6kiVQ39dnS9JeiQjTSFMTyAKCgDAZG+u2qUqh0t9k+N0Vd8ks+PAR1BQAACmOVhh19/WFEiSpmT0kMXC9AT1KCgAANO8vnKXaupcujClpa7s1c7sOPAhFBQAgCkOlNfqva+ZnuDEKCgAAFO8+sVOOZxuDezcSlektTE7DnwMBQUA0OyKjtZo4TeFkqQpmUxP0BgFBQDQ7OZ9vkMOl1uXdW2tId2YnqAxCgoAoFntPVytv3+7T1L99AQ4EQoKAKBZvfz5DjndhoaltdElXRLMjgMfRUEBADSb3Qcr9dGGn6YnGUxPcHIUFABAs3lpxQ65DWlUr3bq36mV2XHgwygoAIBmsf1AhZZ8XyxJeoTpCU6DggIAaBZzl2+XYUhX901Seod4s+PAx1FQAABNbktxuZZuKpHFwvQEZ4aCAgBoci8u3y5JGtOvvXomxZqcBv6AggIAaFI/7DuqnC0HFGKRskYzPcGZoaAAAJrUnJz66cn4izqoe7sWJqeBv6CgAACazMptpVq57aBCQyx6aFSa2XHgR8LMDgAACDy26jrN+myrPvhmryTppos7qkubGJNTwZ9QUAAAXmMYhhZtLNLz//pRh6sckqSbBnTUU2P7mJwM/oaCAgDwip2llXpq8WZ9tfuwJCmtXQs9Nz5dg7u2NjkZ/BEFBQBwXmrrXHr1i516I3eX6lyGIsND9NCoNP1qaFdFhHGpI84NBQUAcM5WbivV0x/nae+RaknSyJ5tNWNculISok1OBn9HQQEAnLUSW63+8MkW/WvTfklSUlykpl/fR1f1TZLFYjE5HQIBBQUAcMacLrfeXVugF5ZtV6XdqRCLdO/lqcrK6KEWVl5S4D38aQIAnJHvC49q2uJN2lxULkm6KKWlnr8hXX2T+eA/eB8FBQBwSraaOv3ps2167+sCGYYUFxmmx6/ppdsv6aSQEE7noGlQUAAAJ2QYhpZ8X6w/fPKjDlXaJUk39O+g31/bW21jrSanQ6CjoAAAGsk/VKWnFm/W6p2HJEld28bouXHpGtK9jcnJECya/A3q2dnZslgsysrK8mwzDEPTp09XcnKyoqKiNGLECOXl5TV1FADAadTWuTR3+XZdNXeVVu88pIiwEE3J6KFPHx5GOUGzatKCsm7dOs2fP18XXHBBg+2zZ8/WnDlzNG/ePK1bt05JSUnKyMhQRUVFU8YBAJzC6h2HdM1LX2ru8h1yON26okdb5TxyhR4alSZrWKjZ8RBkmqygVFZW6o477tBbb72lVq1aebYbhqG5c+dq2rRpuvHGG5Wenq4FCxaourpa77//flPFAQCcRGlFrR76YKPu/MvXyj9UpXaxVr064WIt+OUl6tyaD/iDOZqsoEyaNEljxozR6NGjG2zPz89XSUmJMjMzPdusVquGDx+uNWvWNFUcAMBxXG5D7361R6NeyNWS74sVYpHuGdJFyx8drjEXtGfBNZiqSS6SXbhwoTZs2KB169Y1eqykpESSlJiY2GB7YmKiCgoKTvh8drtddrvdc7+8vNyLaQEg+Gwusmnaok36fp9NknRBx3g9P76f+nVkTRP4Bq8XlMLCQj388MNatmyZIiMjT7rf8c3cMIyTtvXs7Gw9++yzXs0JAMGoorZOc3K2a8GaPXIbUqw1TL+9qqfuvLSzQlnTBD7EYhiG4c0nXLx4sW644QaFhv7ngiqXyyWLxaKQkBBt27ZN3bt314YNG9S/f3/PPuPGjVPLli21YMGCRs95oglKSkqKbDab4uLivBkfAAKSYRhauqlEMz7J04Hy+r9Px16YrKfG9Fa7uJP/YxLwpvLycsXHx5/R67fXJyijRo3Spk2bGmz75S9/qV69eunxxx9X165dlZSUpJycHE9BcTgcys3N1axZs074nFarVVYriwIBwLkoOFylpz/OU+72g5KkLq2j9Yfx6RqW1tbkZMDJeb2gxMbGKj09vcG2mJgYtW7d2rM9KytLM2fOVFpamtLS0jRz5kxFR0drwoQJ3o4DAEHL7nTprVW79crnO2V3uhURGqIHRnTTxBHdFBnO24bh20xZSfaxxx5TTU2NJk6cqLKyMg0ePFjLli1TbGysGXEAIOB8teuwnly8SbsOVkmSLu/eWn8Yl66ubVuYnAw4M16/BqU5nM05LAAIJocq7Zr5rx/10cYiSVKbFhF66ro+uv7CZN42DNOZeg0KAKD5ud2GFq4r1B8//VHltU5ZLNIdgzvpd1f1UnxUuNnxgLNGQQEAP7eluFzTFm/Sxr1HJUl92sdp5o39dFFKS1NzAeeDggIAfqrK7tSLOdv19po9crkNxUSE6tHMnrrrss4KC23yz4IFmhQFBQD8jGEY+izvgJ79Z57222olSWP6tddT1/VRUjxrmiAwUFAAwI8UHqnW9CV5WrG1VJKUkhClGePSNbJnO5OTAd5FQQEAP+BwuvWX1fl6acV21da5FR5q0X9d0VWTR6YpKoI1TRB4KCgA4OO+yT+iaYs2aUdppSRpcGqCnr8hXd3bsXYUAhcFBQB81JEqh7KX/qi/r98nSUqIidC0a3vrxos7sKYJAh4FBQB8jNtt6B/r92nmpz/qaHWdJOn2QSl6/OpeahkdYXI6oHlQUADAh2wrqdCTizdp3Z4ySVKvpFg9f0O6BnROMDkZ0LwoKADgA6odTr28Yqf+/OVuOd2GoiNC9cjoHrrn8i4KZ00TBCEKCgCYbMWPB/T0x3kqOlojScrsk6hnru+rDi2jTE4GmIeCAgAmKT5ao+lL8rRsywFJUoeWUZp+fV9l9Ek0ORlgPgoKADSzOpdb7/x7j15cvl3VDpfCQiz61bCuemhUd0VH8NcyIFFQAKBZrS8o07RFm7S1pEKSNLBzKz1/Qz/1TGJNE+BYFBQAaAZHqx2a9X/b9ME3eyVJLaPD9ftreuumAR0VEsKaJsDxKCgA0IQMw9BHG4o0c+mPOlzlkCTdNKCjfn9tbyXEsKYJcDIUFABoIjtLK/Tk4s1au/uIJCmtXQs9f0M/DUplTRPgdCgoAOBltXUuzft8p95ctUt1LkOR4SF6eFQP3Tc0VRFhrGkCnAkKCgB40cptpXr64zztPVItSbqyVzs9e31fpSREm5wM8C8UFADwghJbrf7wyRb9a9N+SVL7+Eg9M7avruqbyAf7AeeAggIA58HpcutvXxVoTs52VdqdCg2x6JdDuigro4daWPkrFjhX/N8DAOfou8KjmrZok/KKyyVJ/Tu11PPj+6lPcpzJyQD/R0EBgLNkq6nTnz7bpve+LpBhSPFR4Xriml66dWAKa5oAXkJBAYAzZBiGlnxfrD988qMOVdolSTde3EG/v7a32rSwmpwOCCwUFAA4A/mHqvTU4s1avfOQJKlr2xg9Nz5dQ7q1MTkZEJgoKABwCrV1Lr2+cpdeX7lLDpdb1rAQTR7ZXf81vKusYaFmxwMCFgUFAE7iyx0H9dTizdpzuH5Nk+E92mrGuL7q3DrG5GRA4KOgAMBxSitq9dwnP2rJ98WSpHaxVj09to/G9GvPmiZAM6GgAMBPXG5D//N1gf77/7apwu5UiEW6e0gXTcnoodjIcLPjAUGFggIAkjYX2TRt0SZ9v88mSbqwY7yev6Gf0jvEm5wMCE4UFABBraK2Ti8s266/fbVHbkOKtYbpsat7asLgzgplTRPANBQUAEHJMAz9a9N+zfjnFpVW1K9pcv2FyXpyTG+1i4s0OR0ACgqAoFNwuEpPfZynVdsPSpJS28ToD+PSNTSNNU0AX0FBARA07E6X3szdrXlf7JTD6VZEaIgmjuymB4Z3U2Q4a5oAvoSCAiAorNl5SE9+vFm7D1ZJkoZ2b6MZ4/qqa9sWJicDcCIUFAAB7WCFXTOX/qhFG4skSW1a1K9pMvYC1jQBfBkFBUBAcrsNfbBur2Z9ulXltU5ZLNIvLu2sRzN7Kj6KNU0AX0dBARBwthSXa9riTdq496gkqW9ynJ6/oZ8uSmlpai4AZ46CAiBgVNqdmpuzXW+v2SOX21ALa5imZPTQXZd1VlhoiNnxAJwFCgoAv2cYhj7LO6Bn/5mn/bZaSdKYfu311HV9lBTPmiaAP6KgAPBrhUeq9cySPH2+tVSS1CkhWjPG9dWInu1MTgbgfFBQAPglh9OtP6/erZdX7FBtnVvhoRY9MLybJo3szpomQACgoADwO1/vPqwnF2/WjtJKSdKlXRP03Ph+6t6ONU2AQEFBAeA3Dlfalf3pVv1j/T5JUuuYCE0b01s39O/AmiZAgKGgAPB5brehv68vVPanW3W0uk6SdPugTnr86p5qGR1hcjoATYGCAsCnbSup0LRFm/RtQZkkqVdSrJ6/oZ8GdG5lcjIATYmCAsAnVTucemnFDv3ly3w53YaiI0I1JaOH7hnShTVNgCBAQQHgc3K2HND0JXkqOlojSbq6b5KeHttHyS2jTE4GoLlQUAD4jKKjNZq+JE85Ww5Ikjq0jNKz1/fV6D6JJicD0Ny8PifNzs7WJZdcotjYWLVr107jx4/Xtm3bGuxjGIamT5+u5ORkRUVFacSIEcrLy/N2FAB+os7l1pu5uzT6hVzlbDmgsJD6NU1yplxBOQGClNcLSm5uriZNmqS1a9cqJydHTqdTmZmZqqqq8uwze/ZszZkzR/PmzdO6deuUlJSkjIwMVVRUeDsOAB/37Z4juu7l1cr+dKtq6ly6pEsrLX14mJ64ppeiIxjyAsHKYhiG0ZTf4ODBg2rXrp1yc3N1xRVXyDAMJScnKysrS48//rgkyW63KzExUbNmzdL9999/2ucsLy9XfHy8bDab4uLimjI+gCZSVuXQrP/bqoXrCiVJraLDNfXa3rrp4o4KCWFNEyAQnc3rd5NfCm+z2SRJCQkJkqT8/HyVlJQoMzPTs4/VatXw4cO1Zs2apo4DwGSGYegf6/dp1JxcTzm5eUBHrXh0hG4ZmEI5ASCpiS+SNQxDU6ZM0dChQ5Weni5JKikpkSQlJjY8r5yYmKiCgoITPo/dbpfdbvfcLy8vb6LEAJrSjgMVmrZ4s77JPyJJ6pHYQs+N76dBqQkmJwPga5q0oEyePFk//PCDVq9e3eix45elNgzjpEtVZ2dn69lnn22SjACaXo3DpVc+36G3vtytOpehyPAQPTyqh+4bmqqIMNY0AdBYk/3N8OCDD2rJkiX64osv1LFjR8/2pKQkSf+ZpPystLS00VTlZ1OnTpXNZvPcCgsLmyo2AC/7YmupMl7M1Wsrd6nOZWhUr3bKeWS4fjOiG+UEwEl5fYJiGIYefPBBLVq0SCtXrlRqamqDx1NTU5WUlKScnBz1799fkuRwOJSbm6tZs2ad8DmtVqusVqu3owJoQvttNZrxzy36dHP9P0bax0dq+vV9ldknkQ/2A3BaXi8okyZN0vvvv6+PP/5YsbGxnklJfHy8oqKiZLFYlJWVpZkzZyotLU1paWmaOXOmoqOjNWHCBG/HAdDMnC63FnxVoDnLtqnK4VJoiEX3Xt5FWaN7KMbK24YBnBmv/23x+uuvS5JGjBjRYPvbb7+te+65R5L02GOPqaamRhMnTlRZWZkGDx6sZcuWKTY21ttxADSjjXvLNG3RZm3ZX38he/9OLfX8+H7qk8xyAADOTpOvg9IUWAcF8C226jrN/myr3v9mrwxDio8K1xPX9NKtvG0YwDHO5vWbeSuAc2YYhj7+rljP/WuLDlU6JEk3XtxBv7+2t9q04LoxAOeOggLgnOw6WKmnFm/Wml2HJUnd2sboufH9dFm31iYnAxAIKCgAzkptnUuvrdylN1buksPlljUsRA+NStOvh3XlbcMAvIaCAuCM5W4/qKc/3qyCw9WSpOE92uoP49LVqXW0yckABBoKCoDTKi2v1YxPtuiTH/ZLkhLjrHpmbF9dk57EmiYAmgQFBcBJudyG3ltboD99tk0VdqdCLNLdQ7poSkYPxUaGmx0PQACjoAA4oR/2HdW0RZu1qaj+E8kv7Biv52/op/QO8SYnAxAMKCgAGiivrdMLn23T39YWyDCkWGuYHru6pyYM7qxQ1jQB0EwoKAAk1a9p8skP+/WHT7aotMIuSRp3UbKmjemtdrGRJqcDEGwoKAC051CVnvp4s77ccUiSlNomRn8Yl66haW1MTgYgWFFQgCBmd7o0P3e3XvlipxxOtyLCQjRxRDc9MLybIsNDzY4HIIhRUIAgtWbnIT358WbtPlglSRqW1kYzxqUrtU2MyckAgIICBJ2DFXbNXPqjFm0skiS1jbXqqev6aOwF7VnTBIDPoKAAQcLtNvT+N3s1+/+2qrzWKYtF+sWlnfVoZk/FR7GmCQDfQkEBgkBesU3TFm3Wd4VHJUnpHeL0/Ph+ujClpam5AOBkKChAAKu0O/Vizna9/e98uQ2phTVMv83soV9c1oU1TQD4NAoKEIAMw9D/bS7Rs//copLyWknSmH7t9fTYPkqMY00TAL6PggIEmMIj1Xr64836YttBSVKnhGjNGNdXI3q2MzkZAJw5CgoQIBxOt976crde+XyHauvcCg+16DfDu2niyO6saQLA71BQgADw9e7DmrZ4s3aWVkqSLu2aoOfG91P3di1MTgYA54aCAvixw5V2ZX+6Vf9Yv0+S1DomQk9e11vjL+rAmiYA/BoFBfBDbrehv68vVPanW3W0uk6SNGFwJz1+VS/FR7OmCQD/R0EB/MzWknJNW7RZ6wvKJEm9kmL1/A39NKBzK5OTAYD3UFAAP1HtcOql5Tv059X5crkNRUeEakpGD90zpIvCQkPMjgcAXkVBAfxAzpYDmr4kT0VHayRJV/dN0tNj+yi5ZZTJyQCgaVBQAB9WdLRG05fkKWfLAUlSh5ZRmjGur0b1TjQ5GQA0LQoK4GMMw9C3BWX6n7UFWrqpRA6XW2EhFv36iq566Mo0RUWwpgmAwEdBAUzkdhuqqHXKVlMnW02dviss03tr92rbgQrPPpd2TdCMcenqkRhrYlIAaF4UFOA8ud2GKh1O2arrPEXj2NvRn7aX/3y/xlH/WHWdKuxOGUbj54wMD9G4Czvojks76YKOLZv9ZwIAs1FQANWfVqm0Oz2FovwEReNkt/KaOrlPUDLORlR4qOKjwpUYH6nxFyXrxos7Kj6K9UwABC8KCgKGYRiqcrg804n/lAjHKScatpo6ldc65TrPlmENC1F8VLjn1jI6XHHH3P95W3yDbRGKiwqTNYzrSgDgWBQU+BTDMFT9c8k4waTi2IJx/HZbTZ2c51kyIo4pGS2PKRLHF43jy0ZcVDgfyAcAXkRBgdcZhqHaOvcxEwvHGZ8qsdXUqc51fiUjPNTSqEx4btERp5xoUDIAwDdQUHBStXXHTTKqf77Is/Hk4vj9HC73eX3vsBDLCU+RnLx4/Oe/o8JD+aA8APBzFJQAZ3e6Gr275FSnSI4tIA7n+ZWM0BBLo1MkLY+bXpysgERHUDIAIJhRUPyAw+k+pkA4jptoOE/82E+32rrzKxkhFjUoDnFRJz89cnzZaGENo2QAAM4JBaWZ1Lncx6yD0fCUyYlOkRx7v6bOdV7f22KR4iIbTy5anmR6EXfMfpQMAIAZKChnwelyq7zW2eiiz0anSKobP1blOP+SEWsNa3CtRePTJxGNC0d0uGKtYQoJoWQAAPwHBeUYB8pr9ZfV+bJVH7PaZ43TUzIq7c7z/h6x1rAGE4oTXeQZf4LC0SIyTKGUDABAkKCgHKPS7tT8VbtPu18La9gp30nS4DqNY/47NjJMYaEhzfCTAADg3ygox2gba9Wvh6U2OHXS8rh1M+IoGQAANDkKyjHiIsM1bUwfs2MAABD0GAUAAACfQ0EBAAA+h4ICAAB8DgUFAAD4HAoKAADwORQUAADgcygoAADA51BQAACAzzG1oLz22mtKTU1VZGSkBgwYoC+//NLMOAAAwEeYVlA+/PBDZWVladq0adq4caOGDRuma665Rnv37jUrEgAA8BEWwzAMM77x4MGDdfHFF+v111/3bOvdu7fGjx+v7OzsU35teXm54uPjZbPZFBcX19RRAQCAF5zN67cpExSHw6H169crMzOzwfbMzEytWbPGjEgAAMCHmPJhgYcOHZLL5VJiYmKD7YmJiSopKWm0v91ul91u99wvLy9v8owAAMA8pn6ascViaXDfMIxG2yQpOztbzz77bKPtFBUAAPzHz6/bZ3J1iSkFpU2bNgoNDW00LSktLW00VZGkqVOnasqUKZ77RUVF6tOnj1JSUpo8KwAA8K6KigrFx8efch9TCkpERIQGDBignJwc3XDDDZ7tOTk5GjduXKP9rVarrFar536LFi1UWFio2NjYE05cgk15eblSUlJUWFjIRcPNgOPdfDjWzYdj3XyC+VgbhqGKigolJyefdl/TTvFMmTJFv/jFLzRw4EBddtllmj9/vvbu3asHHnjgtF8bEhKijh07NkNK/xIXFxd0f9jNxPFuPhzr5sOxbj7BeqxPNzn5mWkF5dZbb9Xhw4c1Y8YM7d+/X+np6Vq6dKk6d+5sViQAAOAjTL1IduLEiZo4caKZEQAAgA/is3gCgNVq1TPPPNPgOh00HY538+FYNx+OdfPhWJ8Z01aSBQAAOBkmKAAAwOdQUAAAgM+hoAAAAJ9DQQEAAD6HghIg7Ha7LrroIlksFn333XcNHtu7d6/Gjh2rmJgYtWnTRg899JAcDoc5Qf3Unj17dN999yk1NVVRUVHq1q2bnnnmmUbHkWPtPa+99ppSU1MVGRmpAQMG6MsvvzQ7kt/Lzs7WJZdcotjYWLVr107jx4/Xtm3bGuxjGIamT5+u5ORkRUVFacSIEcrLyzMpceDIzs6WxWJRVlaWZxvH+tQoKAHiscceO+HSwS6XS2PGjFFVVZVWr16thQsX6n//93/16KOPmpDSf23dulVut1tvvvmm8vLy9OKLL+qNN97Q73//e88+HGvv+fDDD5WVlaVp06Zp48aNGjZsmK655hrt3bvX7Gh+LTc3V5MmTdLatWuVk5Mjp9OpzMxMVVVVefaZPXu25syZo3nz5mndunVKSkpSRkaGKioqTEzu39atW6f58+frggsuaLCdY30aBvze0qVLjV69ehl5eXmGJGPjxo0NHgsJCTGKioo82z744APDarUaNpvNhLSBY/bs2UZqaqrnPsfaewYNGmQ88MADDbb16tXLeOKJJ0xKFJhKS0sNSUZubq5hGIbhdruNpKQk449//KNnn9raWiM+Pt544403zIrp1yoqKoy0tDQjJyfHGD58uPHwww8bhsGxPhNMUPzcgQMH9Otf/1rvvvuuoqOjGz3+1VdfKT09vcF05aqrrpLdbtf69eubM2rAsdlsSkhI8NznWHuHw+HQ+vXrlZmZ2WB7Zmam1qxZY1KqwGSz2STJ8+c4Pz9fJSUlDY691WrV8OHDOfbnaNKkSRozZoxGjx7dYDvH+vRMXeoe58cwDN1zzz164IEHNHDgQO3Zs6fRPiUlJUpMTGywrVWrVoqIiFBJSUkzJQ08u3bt0iuvvKIXXnjBs41j7R2HDh2Sy+VqdCwTExM5jl5kGIamTJmioUOHKj09XZI8x/dEx76goKDZM/q7hQsXasOGDVq3bl2jxzjWp8cExQdNnz5dFovllLdvv/1Wr7zyisrLyzV16tRTPp/FYmm0zTCME24PNmd6rI9VXFysq6++WjfffLN+9atfNXiMY+09xx8zjqN3TZ48WT/88IM++OCDRo9x7M9fYWGhHn74Yb333nuKjIw86X4c65NjguKDJk+erNtuu+2U+3Tp0kXPPfec1q5d2+jzHAYOHKg77rhDCxYsUFJSkr7++usGj5eVlamurq5Rcw9GZ3qsf1ZcXKyRI0fqsssu0/z58xvsx7H2jjZt2ig0NLTRtKS0tJTj6CUPPviglixZolWrVqljx46e7UlJSZLq/3Xfvn17z3aO/dlbv369SktLNWDAAM82l8ulVatWad68eZ53T3GsT8HE619wngoKCoxNmzZ5bp999pkhyfjHP/5hFBYWGobxnws3i4uLPV+3cOFCLtw8B/v27TPS0tKM2267zXA6nY0e51h7z6BBg4zf/OY3Dbb17t2bi2TPk9vtNiZNmmQkJycb27dvP+HjSUlJxqxZszzb7HY7F26eg/Ly8gZ/P2/atMkYOHCgceeddxqbNm3iWJ8BCkoAyc/Pb/QuHqfTaaSnpxujRo0yNmzYYCxfvtzo2LGjMXnyZPOC+qGioiKje/fuxpVXXmns27fP2L9/v+f2M4619yxcuNAIDw83/vKXvxhbtmwxsrKyjJiYGGPPnj1mR/Nrv/nNb4z4+Hhj5cqVDf4MV1dXe/b54x//aMTHxxsfffSRsWnTJuP222832rdvb5SXl5uYPDAc+y4ew+BYnw4FJYCcqKAYRv2kZcyYMUZUVJSRkJBgTJ482aitrTUnpJ96++23DUknvB2LY+09r776qtG5c2cjIiLCuPjiiz1vhcW5O9mf4bffftuzj9vtNp555hkjKSnJsFqtxhVXXGFs2rTJvNAB5PiCwrE+NYthGIYJZ5YAAABOinfxAAAAn0NBAQAAPoeCAgAAfA4FBQAA+BwKCgAA8DkUFAAA4HMoKAAAwOdQUAAAgM+hoAAAAJ9DQQEAAD6HggIAAHwOBQUAAPic/x93dWUkzn68hAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# As we add more hidden units with varying weights and biases, the relationship can grow in complexity\n",
    "layer1_3 = np.maximum(0,prediction(temps, 2, -50))\n",
    "plt.plot(temps, layer1_1 + layer1_2 + layer1_3)\n",
    "\n",
    "# We can create an output layer (layer 2) that is a linear combination of the outputs of the hidden layers (layer 1)\n",
    "# y = w3*[relu(w1*x + b1) + relu(w2*x + b2) + relu(w3*x + b3)] + b3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[76.79 18.  ]\n",
      " [84.89 19.  ]\n",
      " [92.99 20.  ]\n",
      " [ 0.    8.  ]\n",
      " [ 3.89  9.  ]]\n"
     ]
    }
   ],
   "source": [
    "# Forward Pass - The process of calculating the output of a neural network for a given input, weights and biases\n",
    "\n",
    "input = np.array([80, 90, 100, -20, -10]).reshape(-1,1) #5x1 -> reshape (row, column) allows you to specify -1 to automatically calculate the number of rows\n",
    "l1_weights = np.array([0.81, 0.1]).reshape(1,-1) \n",
    "l1_biases = np.array([11.99, 10]).reshape(1,-1)\n",
    "\n",
    "l1_output = np.maximum(0, np.dot(input, l1_weights) + l1_biases) # ReLu activation function applied to the linear transformation of the input\n",
    "print(l1_output) # End up with a 5x2 matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[46.995]\n",
      " [51.245]\n",
      " [55.495]\n",
      " [ 6.6  ]\n",
      " [ 8.745]]\n"
     ]
    }
   ],
   "source": [
    "# Add in second layer of weights and biases\n",
    "l2_weights = np.array([0.5, 0.2]).reshape(-1,1)\n",
    "l2_biases = np.array([5]).reshape(1,-1)\n",
    "\n",
    "# Apply the second layer of weights and biases to the output of the first layer - linear transformation\n",
    "l2_output = np.dot(l1_output, l2_weights) + l2_biases\n",
    "print(l2_output) # End up with a 5x1 matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-9574.3878]\n",
      " [-1767.03  ]] -13.383999999999997\n"
     ]
    }
   ],
   "source": [
    "# Backward Pass (backpropogation) - The process of calculating the gradient of the loss function with respect to the weights and biases of the neural network\n",
    "\n",
    "# If we don't have our weights and biases, we can use gradient descent to find the best weights and biases for our model.\n",
    "def mse(actual, predicted):\n",
    "    return (actual - predicted)**2\n",
    "    \n",
    "def mse_gradient(actual, predicted):\n",
    "    # Since the gradient of mse is 2*(predicted-actual), we can drop the 2 as it's a constant and doesn't change the direction of the gradient\n",
    "    return predicted-actual\n",
    "\n",
    "# Example set of weather data\n",
    "tmax = np.array([80, 90, 100, -20, -10]).reshape(-1,1)\n",
    "tmax_tomorrow = np.array([83, 89, 95, -22, -9]).reshape(-1,1)\n",
    "\n",
    "output_gradient = mse_gradient(tmax_tomorrow, l2_output)\n",
    "l2_weights_gradient = np.dot(l1_output.T, output_gradient) # dL/dw2 = dy/dw2 * dL/dy --> since y = w2*relu(w1*x + b1) + b2, dy/dw2 = relu(w1*x + b1) which is the output of the first layer\n",
    "l2_biases_gradient = np.mean(output_gradient) # dL/db2 = dy/db2 * dL/dy --> since y = w2*relu(w1*x + b1) + b2, dy/db2 = 1; dL/db2 = dL/dy\n",
    "print(l2_weights_gradient, l2_biases_gradient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pre descent:  [[0.5]\n",
      " [0.2]]\n",
      "Post descent:  [[0.59574388]\n",
      " [0.2176703 ]]\n"
     ]
    }
   ],
   "source": [
    "learning_rate = 1e-5\n",
    "print(\"Pre descent: \", l2_weights)\n",
    "# Update the weights and biases using gradient descent\n",
    "l2_weights = l2_weights - l2_weights_gradient*learning_rate\n",
    "l2_biases = l2_biases - l2_biases_gradient*learning_rate\n",
    "print(\"Post descent: \", l2_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-21.44975833  -7.83721915]\n",
      " [-22.49231011  -8.21814218]\n",
      " [-23.5348619   -8.5990652 ]\n",
      " [ 17.03827491   6.22537058]\n",
      " [ 10.57147512   3.86255947]]\n",
      "Pre descent:  [[0.81 0.1 ]]\n",
      "Post descent:  [[0.87540255 0.1238965 ]]\n"
     ]
    }
   ],
   "source": [
    "# Now that we have our layer 2 gradients, lets get our layer 1 gradients\n",
    "l1_output_gradient = np.dot(output_gradient, l2_weights.T) # dL/y1 = dy/dy1 * dL/dy --> since y = w2*y1 + b2, dy/dy1 = w2 * grad(Relu); dL/dw1 = dL/dy * w2 * grad(Relu)\n",
    "l1_output_gradient[l1_output < 0] = 0 # ReLu gradient is 0 if the input is less than 0\n",
    "print(l1_output_gradient)\n",
    "\n",
    "l1_weights_gradient = np.dot(tmax.T, l1_output_gradient) # dL/dw1 = dy/dw1 * dL/dy1 --> since y = w1*x + b1, dy/dw1 = x;\n",
    "l1_biases_gradient = np.mean(l1_output_gradient) # dL/db1 = dy/db1 * dL/dy1 --> since y = w1*x + b1, dy/db1 = 1;\n",
    "\n",
    "print(\"Pre descent: \", l1_weights)\n",
    "l1_weights = l1_weights - l1_weights_gradient*learning_rate\n",
    "l1_biases = l1_biases - l1_biases_gradient*learning_rate\n",
    "print(\"Post descent: \", l1_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's put it all together and estimate tomorrow's max temperature using a neural network\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "predictors = ['tmax', 'tmin', 'rain']\n",
    "target = 'tmax_tomorrow'\n",
    "\n",
    "# Normalize data\n",
    "scaler = StandardScaler()\n",
    "weather[predictors] = scaler.fit_transform(weather[predictors])\n",
    "\n",
    "# Split data into training, validation, and test sets\n",
    "split_data = np.split(weather, [int(0.7*len(weather)), int(0.85*len(weather))])\n",
    "(train_x, train_y), (val_x, val_y), (test_x, test_y) = [[d[predictors].to_numpy(), d[target].to_numpy()] for d in split_data]\n",
    "\n",
    "# Reshape the target data\n",
    "train_y = train_y.reshape(-1,1)\n",
    "val_y = val_y.reshape(-1,1)\n",
    "test_y = test_y.reshape(-1,1)\n",
    "\n",
    "# Initialize weights and biases\n",
    "def init_layers(inputs):\n",
    "    layers = []\n",
    "    for i in range(1,len(inputs)):\n",
    "        layers.append([np.random.rand(inputs[i-1], inputs[i])/5 - 0.1, # Weights array scaled to be between -0.1 and 0.1 with shape (inputs[i-1], inputs[i]) \n",
    "                                                                       # no. of columns in prev layer by no. of columns in current layer\n",
    "                       np.ones((1,inputs[i]))]) # Biases array initialized to 1\n",
    "    return layers\n",
    "\n",
    "layer_conf = [3,10,10,1] # 3 input features (predictors), 2 hidden layers with 10 hidden units each, and 1 output\n",
    "layers = init_layers(layer_conf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[array([[-0.04683171, -0.09187399,  0.0471197 ,  0.00870614, -0.04069896,\n",
       "           0.01847619, -0.06899341, -0.07830238,  0.02730239,  0.01996575],\n",
       "         [-0.07358389,  0.01177445,  0.01253273, -0.03946108,  0.08692133,\n",
       "           0.03877544, -0.03315102, -0.08358312, -0.06698391, -0.01039269],\n",
       "         [ 0.04119966,  0.03836001, -0.0639899 ,  0.03758877, -0.06861791,\n",
       "          -0.08547594,  0.0554395 , -0.03461599,  0.09480619,  0.06678746]]),\n",
       "  array([[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]])],\n",
       " [array([[-0.09544814, -0.0493713 ,  0.0371535 , -0.01460626,  0.00471483,\n",
       "           0.09995188, -0.02504427, -0.02454587,  0.00292758,  0.08997787],\n",
       "         [-0.06960028, -0.03566714, -0.05995642,  0.01356191, -0.05729504,\n",
       "           0.09388228,  0.02718565, -0.08447032,  0.06680774,  0.0924175 ],\n",
       "         [-0.06167065, -0.05472831, -0.0543751 , -0.04600411,  0.05504842,\n",
       "          -0.01066982,  0.05208734, -0.067403  , -0.02381136, -0.01966462],\n",
       "         [-0.0548346 ,  0.00765844, -0.01917609,  0.09969768, -0.0896381 ,\n",
       "           0.02266474, -0.07486668, -0.08124424, -0.04070344, -0.08028986],\n",
       "         [-0.03860535,  0.00746243,  0.0843883 ,  0.06221627, -0.09687645,\n",
       "          -0.03109066, -0.09572026,  0.01780718, -0.03592234,  0.02339983],\n",
       "         [-0.06527594, -0.07659676,  0.0398496 , -0.04716905, -0.03201947,\n",
       "           0.01449389,  0.04903372,  0.04573505, -0.0547201 , -0.03022489],\n",
       "         [-0.08864422, -0.0008229 ,  0.09092874,  0.03662042,  0.04296709,\n",
       "           0.02797567,  0.00851898,  0.02315276,  0.0319612 ,  0.04434161],\n",
       "         [ 0.02105168,  0.03375496,  0.0496883 ,  0.08312114, -0.06719199,\n",
       "          -0.09480696, -0.09281051,  0.08041672, -0.05915174, -0.03963126],\n",
       "         [ 0.00212457,  0.03124799,  0.06523327,  0.05509428, -0.02172279,\n",
       "           0.00447379,  0.06074512, -0.08221505, -0.05576449, -0.08803298],\n",
       "         [-0.09449775, -0.0875465 , -0.0316004 ,  0.01032027,  0.09921741,\n",
       "           0.03681117, -0.06113505,  0.01876759,  0.03976141, -0.06021782]]),\n",
       "  array([[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]])],\n",
       " [array([[-0.00741448],\n",
       "         [-0.02076868],\n",
       "         [-0.09422038],\n",
       "         [-0.02209572],\n",
       "         [-0.03272943],\n",
       "         [ 0.02898552],\n",
       "         [ 0.02187906],\n",
       "         [ 0.01736515],\n",
       "         [ 0.04240491],\n",
       "         [-0.03204999]]),\n",
       "  array([[1.]])]]"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Forward pass\n",
    "def forward(batch, layers):\n",
    "    hidden = [batch.copy()]\n",
    "    for i in range(len(layers)):\n",
    "        batch = np.matmul(batch, layers[i][0]) + layers[i][1] # Linear transformation\n",
    "        if i < len(layers) - 1:\n",
    "            batch = np.maximum(0, batch) # ReLu activation function if not the output layer\n",
    "        hidden.append(batch.copy())\n",
    "    return batch, hidden # Batch will be 1 value for each row (predictions), hidden will be the output of each layer for each row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loss function\n",
    "def mse(actual, predicted):\n",
    "    return (actual - predicted)**2\n",
    "    \n",
    "def mse_gradient(actual, predicted):\n",
    "    return predicted-actual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Backward pass\n",
    "def backward(layers, hidden, grad, learning_rate):\n",
    "    for i in range(len(layers)-1, -1, -1): # Loop through layers in reverse order\n",
    "        if i != len(layers)-1:\n",
    "            grad = np.multiply(grad, np.heaviside(hidden[i+1], 0)) # Multiply the gradient by the Heaviside step function (ReLu gradient); if we're not at the last layer, we have reLu to undo\n",
    "        w_grad = hidden[i].T @ grad # dL/dw = dy/dw * dL/dy\n",
    "        b_grad = np.mean(grad, axis=0)\n",
    "        layers[i][0] = layers[i][0] - w_grad*learning_rate # Update weights\n",
    "        layers[i][1] = layers[i][1] - b_grad*learning_rate # Update biases\n",
    "\n",
    "        grad = grad @ layers[i][0].T # Propogate the gradient back through the network as we update the weights (dL/dy_prev = dL/dy_current * dy_current/dy_prev) \n",
    "                                     # dy_current/dy_prev = w since y = w*x + b and the output of the previous layer is the input to the current layer\n",
    "\n",
    "    return layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1: Training MSE = 3364.8763204924235, Validation Loss = 1834.2466809743917\n",
      "Epoch 2: Training MSE = 388.2170889434792, Validation Loss = 26.990285044570893\n",
      "Epoch 3: Training MSE = 23.4576384588293, Validation Loss = 21.400642995598737\n",
      "Epoch 4: Training MSE = 22.46844708129027, Validation Loss = 20.890763838452823\n",
      "Epoch 5: Training MSE = 22.187284893966137, Validation Loss = 20.788440138006973\n",
      "Epoch 6: Training MSE = 22.114449888504595, Validation Loss = 20.773759182771688\n",
      "Epoch 7: Training MSE = 22.094744964432955, Validation Loss = 20.77546524686166\n",
      "Epoch 8: Training MSE = 22.088211587310795, Validation Loss = 20.778721997606\n",
      "Epoch 9: Training MSE = 22.085432195893944, Validation Loss = 20.78126232842669\n",
      "Epoch 10: Training MSE = 22.083679755167395, Validation Loss = 20.783057560690587\n"
     ]
    }
   ],
   "source": [
    "# Training loop\n",
    "from statistics import mean\n",
    "\n",
    "learning_rate = 1e-6\n",
    "epochs = 10\n",
    "batch_size = 8\n",
    "layer_conf = [3,10,10,1] # 3 input features (predictors), 2 hidden layers with 10 hidden units each, and 1 output\n",
    "\n",
    "layers = init_layers(layer_conf)\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    epoch_loss = []\n",
    "    for i in range(0, train_x.shape[0], batch_size):\n",
    "        batch_x = train_x[i:(i+batch_size)]\n",
    "        batch_y = train_y[i:(i+batch_size)]\n",
    "        \n",
    "        # Forward pass step\n",
    "        predictions, hidden = forward(batch_x, layers)\n",
    "        # Calculate loss and gradient\n",
    "        loss = mse_gradient(batch_y, predictions)\n",
    "        epoch_loss.append(np.mean(loss**2))\n",
    "        # Backward pass step\n",
    "        layers = backward(layers, hidden, loss, learning_rate)\n",
    "\n",
    "    valid_preds, _ = forward(val_x, layers) # Forward pass on validation set to see how well the model is doing for each epoch\n",
    "    print (f\"Epoch {epoch+1}: Training MSE = {mean(epoch_loss)}, Validation Loss = {np.mean(mse(val_y, valid_preds))}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "22.03309046110957\n"
     ]
    }
   ],
   "source": [
    "# Measure against test set using trained model (layers)\n",
    "predictions, _ = forward(test_x, layers)\n",
    "print(np.mean(mse(test_y, predictions)))"
   ]
  }
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