03_Secant.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (1.20.1)\n",
      "\u001b[33mWARNING: You are using pip version 20.2.4; however, version 21.0.1 is available.\n",
      "You should consider upgrading via the '/usr/local/Cellar/jupyterlab/2.2.9_1/libexec/bin/python -m pip install --upgrade pip' command.\u001b[0m\n",
      "Requirement already satisfied: matplotlib in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (3.3.4)\n",
      "Requirement already satisfied: cycler>=0.10 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (0.10.0)\n",
      "Requirement already satisfied: numpy>=1.15 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (1.20.1)\n",
      "Requirement already satisfied: pillow>=6.2.0 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (8.1.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (1.3.1)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (2.8.1)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.3 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (2.4.7)\n",
      "Requirement already satisfied: six in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from cycler>=0.10->matplotlib) (1.15.0)\n",
      "\u001b[33mWARNING: You are using pip version 20.2.4; however, version 21.0.1 is available.\n",
      "You should consider upgrading via the '/usr/local/Cellar/jupyterlab/2.2.9_1/libexec/bin/python -m pip install --upgrade pip' command.\u001b[0m\n",
      "Requirement already satisfied: scipy in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (1.6.1)\n",
      "Requirement already satisfied: numpy>=1.16.5 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from scipy) (1.20.1)\n",
      "\u001b[33mWARNING: You are using pip version 20.2.4; however, version 21.0.1 is available.\n",
      "You should consider upgrading via the '/usr/local/Cellar/jupyterlab/2.2.9_1/libexec/bin/python -m pip install --upgrade pip' command.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "!{sys.executable} -m pip install numpy\n",
    "!{sys.executable} -m pip install matplotlib\n",
    "!{sys.executable} -m pip install scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definicja funkcji f(x):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fun(x):\n",
    "    return(x**3 - 2*x**2 -3)\n",
    "\n",
    "plt.figure()\n",
    "x=np.linspace(-2,3,num=100)\n",
    "y=fun(x)\n",
    "plt.plot(x,y)\n",
    "plt.grid()\n",
    "step=0\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Metoda siecznych:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$x_{n+1}=x_{n}-\\frac{f(x_{n})(x_{n}-x_{n-1})}{f(x_{n})-f(x_{n-1})}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteracja-0, x2 = 1.000000 and f(x2) =         -4.000000\n",
      "Iteracja-1, x2 = 5.000000 and f(x2) =         72.000000\n",
      "Iteracja-2, x2 = 1.210526 and f(x2) =         -4.156874\n",
      "Iteracja-3, x2 = 1.417367 and f(x2) =         -4.170468\n",
      "Iteracja-4, x2 = -62.038133 and f(x2) =         -246468.477668\n",
      "Iteracja-5, x2 = 1.418441 and f(x2) =         -4.170082\n",
      "Iteracja-6, x2 = 1.419515 and f(x2) =         -4.169691\n",
      "Iteracja-7, x2 = 12.856373 and f(x2) =         1791.410225\n",
      "Iteracja-8, x2 = 1.446073 and f(x2) =         -4.158332\n",
      "Iteracja-9, x2 = 1.472498 and f(x2) =         -4.143756\n",
      "Iteracja-10, x2 = 8.985063 and f(x2) =         560.913661\n",
      "Iteracja-11, x2 = 1.527590 and f(x2) =         -4.102383\n",
      "Iteracja-12, x2 = 1.581737 and f(x2) =         -4.046449\n",
      "Iteracja-13, x2 = 5.498862 and f(x2) =         102.796793\n",
      "Iteracja-14, x2 = 1.730089 and f(x2) =         -3.807900\n",
      "Iteracja-15, x2 = 1.864709 and f(x2) =         -3.470426\n",
      "Iteracja-16, x2 = 3.249079 and f(x2) =         10.185914\n",
      "Iteracja-17, x2 = 2.216513 and f(x2) =         -1.936288\n",
      "Iteracja-18, x2 = 2.381445 and f(x2) =         -0.836717\n",
      "Iteracja-19, x2 = 2.506950 and f(x2) =         0.186081\n",
      "Iteracja-20, x2 = 2.484117 and f(x2) =         -0.012595\n",
      "Iteracja-21, x2 = 2.485564 and f(x2) =         -0.000170\n",
      "Iteracja-22, x2 = 2.485584 and f(x2) =         0.000000\n",
      "Iteracja-23, x2 = 2.485584 and f(x2) =         -0.000000\n",
      "Iteracja-24, x2 = 2.485584 and f(x2) =         0.000000\n",
      "Iteracja-25, x2 = 2.485584 and f(x2) =         0.000000\n",
      "Iteracje przerwane. Odnaleziono dokładny pierwiastek\n",
      "Pierwiastek:  2.4855839976886003\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def secant_method(f, x0, x1, iterations):\n",
    "    \n",
    "    plt.figure()\n",
    "    x=np.linspace(-2,4,num=100)\n",
    "    y=fun(x)\n",
    "    plt.plot(x,y)\n",
    "    plt.grid()\n",
    "    step=0\n",
    "    plt.scatter(x0,fun(x0))\n",
    "    plt.scatter(x1,fun(x1))\n",
    "\n",
    "    for i in range(iterations):\n",
    "        print('Iteracja-%d, x2 = %0.6f and f(x2) = \\\n",
    "        %0.6f'% (step, x1, f(x1)))\n",
    "        step+=1\n",
    "        \n",
    "        if f(x1)==f(x0): \n",
    "            print(\"Iteracje przerwane. Odnaleziono dokładny pierwiastek\")\n",
    "            return x2\n",
    "        else:\n",
    "            x2 = x1 - f(x1) * (x1 - x0) / float(f(x1) - f(x0))\n",
    "            \n",
    "            plt.scatter(x2,fun(x2))\n",
    "            plt.scatter(x1,fun(x1))\n",
    "            plt.xlim([-2,4])\n",
    "            plt.ylim([-20,5])\n",
    "            x0, x1 = x1, x2\n",
    "    return x2\n",
    "\n",
    "root = secant_method(fun, -1, 1, 200)\n",
    "\n",
    "print(\"Pierwiastek: \",root)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zastosowanie funkcji root z pakietu numpy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.485584+0.j         -0.242792+1.07145315j -0.242792-1.07145315j]\n"
     ]
    }
   ],
   "source": [
    "coef=[1,-2,0,-3]\n",
    "print(np.roots(coef))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}