From d191de2cef3b6bac2d59930c48f7beb7f336834f Mon Sep 17 00:00:00 2001
From: Wlad <ulazho@st.amu.edu.pl>
Date: Tue, 15 Nov 2022 13:06:57 +0100
Subject: [PATCH] Added test

---
 Ans.ipynb | 231 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 231 insertions(+)
 create mode 100644 Ans.ipynb

diff --git a/Ans.ipynb b/Ans.ipynb
new file mode 100644
index 0000000..d4bcd81
--- /dev/null
+++ b/Ans.ipynb
@@ -0,0 +1,231 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import pandas as pd\n",
+    "\n",
+    "%matplotlib inline\n",
+    "%config InlineBackend.figure_format = \"svg\"\n",
+    "\n",
+    "from IPython.display import display, Math, Latex\n",
+    "\n",
+    "data = pd.read_csv(\"fires_thefts.csv\", names=[\"x\", \"y\"])\n",
+    "\n",
+    "x = data[\"x\"].to_numpy()\n",
+    "y = data[\"y\"].to_numpy()\n",
+    "\n",
+    "# Hipoteza: funkcja liniowa jednej zmiennej\n",
+    "def h(theta, x):\n",
+    "    return theta[0] + theta[1] * x\n",
+    "\n",
+    "#  Funkcja kosztu\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",
+    "# Wyświetlanie macierzy w LaTeX-u\n",
+    "def LatexMatrix(matrix):\n",
+    "    ltx = r\"\\left[\\begin{array}\"\n",
+    "    m, n = matrix.shape\n",
+    "    ltx += \"{\" + (\"r\" * n) + \"}\"\n",
+    "    for i in range(m):\n",
+    "        ltx += r\" & \".join([(\"%.4f\" % j.item()) for j in matrix[i]]) + r\" \\\\ \"\n",
+    "    ltx += r\"\\end{array}\\right]\"\n",
+    "    return ltx\n",
+    "\n",
+    "def gradient_descent(h, cost_fun, theta, x, y, alpha, eps):\n",
+    "    current_cost = cost_fun(h, theta, x, y)\n",
+    "    history = [\n",
+    "        [current_cost, theta]\n",
+    "    ]  # zapiszmy wartości kosztu i parametrów, by potem zrobić wykres\n",
+    "    m = len(y)\n",
+    "    while True:\n",
+    "        new_theta = [\n",
+    "            theta[0] - alpha / float(m) * sum(h(theta, x[i]) - y[i] for i in range(m)),\n",
+    "            theta[1]\n",
+    "            - alpha / float(m) * sum((h(theta, x[i]) - y[i]) * x[i] for i in range(m)),\n",
+    "        ]\n",
+    "        theta = new_theta  # jednoczesna aktualizacja - używamy zmiennej tymczasowej\n",
+    "        try:\n",
+    "            prev_cost = current_cost\n",
+    "            current_cost = cost_fun(h, theta, x, y)\n",
+    "        except OverflowError:\n",
+    "            break\n",
+    "        if abs(prev_cost - current_cost) <= eps:\n",
+    "            break\n",
+    "        history.append([current_cost, theta])\n",
+    "    return theta, history\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\large\\textrm{Wynik:}\\quad \\theta = \\left[\\begin{array}{r}16.9446 \\\\ 1.3160 \\\\ \\end{array}\\right] \\quad J(\\theta) = 180.4105 \\quad \\textrm{po 5369 iteracjach}$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "best_theta, history = gradient_descent(h, J, [0.0, 0.0], x, y, alpha=0.003, eps=0.000001)\n",
+    "\n",
+    "display(\n",
+    "    Math(\n",
+    "        r\"\\large\\textrm{Wynik:}\\quad \\theta = \"\n",
+    "        + LatexMatrix(np.matrix(best_theta).reshape(2, 1))\n",
+    "        + (r\" \\quad J(\\theta) = %.4f\" % history[-1][0])\n",
+    "        + r\" \\quad \\textrm{po %d iteracjach}\" % len(history)\n",
+    "    )\n",
+    ")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "eps=    1.0,  cost=        231.741,  steps=     4\n",
+      "eps=    0.1,  cost=        226.569,  steps=    52\n",
+      "eps=   0.01,  cost=        185.031,  steps=  1115\n",
+      "eps=  0.001,  cost=        180.872,  steps=  2179\n",
+      "eps= 0.0001,  cost=        180.456,  steps=  3242\n",
+      "eps=  1e-05,  cost=        180.415,  steps=  4306\n",
+      "eps=  1e-06,  cost=        180.411,  steps=  5369\n",
+      "eps=  1e-07,  cost=        180.410,  steps=  6433\n",
+      "eps=  1e-08,  cost=        180.410,  steps=  7496\n",
+      "eps=  1e-09,  cost=        180.410,  steps=  8560\n",
+      "eps=  1e-10,  cost=        180.410,  steps=  9623\n",
+      "eps=  1e-11,  cost=        180.410,  steps= 10687\n"
+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "epss = [10.0**(-n) for n in range(0, 12)]\n",
+    "alpha=0.003\n",
+    "costs = []\n",
+    "lengths = []\n",
+    "for eps in epss:\n",
+    "    theta_best, history = gradient_descent(\n",
+    "        h, J, [0.0, 0.0], x, y, alpha, eps)\n",
+    "    cost = history[-1][0]\n",
+    "    steps = len(history)\n",
+    "    print(f\"{eps=:7},  {cost=:15.3f},  {steps=:6}\")\n",
+    "    costs.append(cost)\n",
+    "    lengths.append(steps)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def eps_cost_steps_plot(eps, costs, steps):\n",
+    "    \"\"\"Wykres kosztu i liczby kroków w zależności od eps\"\"\"\n",
+    "    fig, ax1 = plt.subplots()\n",
+    "    ax2 = ax1.twinx()\n",
+    "    ax1.plot(eps, steps, \"--s\", color=\"green\")\n",
+    "    ax2.plot(eps, costs, \":o\", color=\"orange\")\n",
+    "    ax1.set_xscale(\"log\")\n",
+    "    ax1.set_xlabel(\"eps\")\n",
+    "    ax1.set_ylabel(\"liczba kroków\", color=\"green\")\n",
+    "    ax2.set_ylabel(\"koszt\", color=\"orange\")\n",
+    "    plt.show()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
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+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "eps_cost_steps_plot(epss, costs, lengths)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[16.835521154474677, 1.3214970549417684]\n",
+      "Liczba pozarów - 50 Przewidywalna liczba włamań - 82.91037390156309\n",
+      "Liczba pozarów - 100 Przewidywalna liczba włamań - 148.98522664865152\n",
+      "Liczba pozarów - 200 Przewidywalna liczba włamań - 281.13493214282835\n"
+     ]
+    }
+   ],
+   "source": [
+    "example_x = [50, 100, 200]\n",
+    "print(best_theta)\n",
+    "example_y = [h(best_theta, ex) for ex in example_x]\n",
+    "for i in range(3):\n",
+    "    print(f\"Liczba pozarów - {example_x[i]} \"\n",
+    "    f\"Przewidywalna liczba włamań - {example_y[i]}\")"
+   ]
+  }
+ ],
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