{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "11f16ac1",
   "metadata": {},
   "source": [
    "### Część podstawowa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "38487b50",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted amount of thefts for 50 fires: 82.70999487819813\n",
      "Predicted amount of thefts for 100 fires: 148.45251499453076\n",
      "Predicted amount of thefts for 200 fires: 279.93755522719596\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "data = pd.read_csv('fires_thefts.csv', names = ['fires', 'thefts'])\n",
    "\n",
    "x = data[['fires']].to_numpy().flatten()\n",
    "y = data[['thefts']].to_numpy().flatten()\n",
    "\n",
    "def gradient_descent(h, cost_fun, theta, x, y, alpha, eps, max_steps = 1000000):\n",
    "    current_cost = cost_fun(h, theta, x, y)\n",
    "    log = [[current_cost, theta]]\n",
    "    m = len(y)\n",
    "    steps_counter = 0\n",
    "    while True and steps_counter < max_steps:\n",
    "        steps_counter += 1\n",
    "        new_theta = [\n",
    "            theta[0] - alpha/float(m) * sum(h(theta, x[i]) - y[i]\n",
    "                                            for i in range(m)),   \n",
    "            theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i]\n",
    "                                            for i in range(m))]\n",
    "        theta = new_theta\n",
    "        prev_cost = current_cost\n",
    "        current_cost = cost_fun(h, theta, x, y)\n",
    "        if abs(prev_cost - current_cost) <= eps:\n",
    "            break\n",
    "        log.append([current_cost, theta])\n",
    "    return theta, log\n",
    "\n",
    "def J(h, theta, x, y):\n",
    "    m = len(y)\n",
    "    return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i])**2 for i in range(m))\n",
    "\n",
    "def h(theta, x):\n",
    "    return theta[0] + theta[1] * x\n",
    "\n",
    "def mse(expected, predicted):\n",
    "    m = len(expected)\n",
    "    if len(predicted) != m:\n",
    "        raise Exception('Wektory mają różne długości!')\n",
    "    return 1.0 / (2 * m) * sum((expected[i] - predicted[i])**2 for i in range(m))\n",
    "\n",
    "best_theta, log = gradient_descent(h, J, [0.0, 0.0], x, y, alpha=0.001, eps=0.0000001, max_steps = 1000000)\n",
    "\n",
    "predicted_50 = h(best_theta, 50)\n",
    "predicted_100 = h(best_theta, 100)\n",
    "predicted_200 = h(best_theta, 200)\n",
    "print(f'Predicted amount of thefts for 50 fires: {predicted_50}')\n",
    "print(f'Predicted amount of thefts for 100 fires: {predicted_100}')\n",
    "print(f'Predicted amount of thefts for 200 fires: {predicted_200}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2126b66",
   "metadata": {},
   "source": [
    "### Część zaawansowana"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e98cdca2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:32: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i])**2 for i in range(m))\n",
      "/var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:25: RuntimeWarning: invalid value encountered in scalar subtract\n",
      "  if abs(prev_cost - current_cost) <= eps:\n",
      "/var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:20: RuntimeWarning: overflow encountered in scalar add\n",
      "  theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i]\n",
      "/var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:20: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i]\n",
      "/var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:20: RuntimeWarning: invalid value encountered in scalar subtract\n",
      "  theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i]\n",
      "/var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:32: RuntimeWarning: overflow encountered in scalar add\n",
      "  return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i])**2 for i in range(m))\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "best_theta_01, log_01 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.1, eps = 0.0000001, max_steps = 1000)\n",
    "best_theta_001, log_001 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.01, eps = 0.0000001, max_steps = 1000)\n",
    "best_theta_0001, log_0001 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.001, eps = 0.0000001, max_steps = 1000)\n",
    "\n",
    "steps_range = np.arange(0, 200, 1)\n",
    "y_01, y_001, y_0001 = [], [], []\n",
    "for step in steps_range:\n",
    "    y_01.append(log_01[step][0])\n",
    "    y_001.append(log_001[step][0])\n",
    "    y_0001.append(log_0001[step][0])\n",
    "\n",
    "fig = plt.figure(figsize=(8, 7))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(steps_range, y_01, label='alpha = 0.1')\n",
    "ax.plot(steps_range, y_001, label='alpha = 0.01')\n",
    "ax.plot(steps_range, y_0001, label='alpha = 0.001')\n",
    "ax.legend(loc='best')\n",
    "ax.set_xlabel('krok')\n",
    "ax.set_ylabel(r'$J(\\theta)$')\n",
    "# plt.ylim([0, 800])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}