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   "cell_type": "code",
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   "id": "fc2a6be1",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted amount of thefts for 50 fires: 100.5454538681846\n",
      "Predicted amount of thefts for 100 fires: 195.86844057898603\n",
      "Predicted amount of thefts for 200 fires: 386.5144140005889\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 = 200)\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}')"
   ]
  }
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