{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costFunction(X, y, theta):\n",
    "    m = len(y)\n",
    "    hypothesis = X @ theta\n",
    "    err = hypothesis - y\n",
    "    return ((1 / (2 * m)) * (np.transpose(err) @ err).item((0, 0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run it against some fake housing data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With bad theta values  - cost: 2184583333333.3333\n",
      "With good theta values - cost: 0.0\n"
     ]
    }
   ],
   "source": [
    "X = np.array([\n",
    "    [1, 3000],\n",
    "    [1, 4000],\n",
    "    [1, 5000],\n",
    "])\n",
    "\n",
    "y = np.array([\n",
    "    [1550000],\n",
    "    [2050000],\n",
    "    [2550000],\n",
    "])\n",
    "\n",
    "bad_theta = np.array([\n",
    "    [0],\n",
    "    [0],\n",
    "])\n",
    "\n",
    "good_theta = np.array([\n",
    "    [50000],\n",
    "    [500],\n",
    "])\n",
    "\n",
    "print(\"With bad theta values  - cost:\", costFunction(X, y, bad_theta))\n",
    "\n",
    "print(\"With good theta values - cost:\", costFunction(X, y, good_theta))"
   ]
  }
 ],
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