Atividade 11 - Equações não lineares.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ------\n",
    "# Questão 0: Utilize o algoritmo do método da Bissecção, com tolerância 0.000001, para resolver os seguintes casos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bissec(f, a, b, tol = 1e-6, maxIt = 50):\n",
    "    fa = f(a)\n",
    "    fb = f(b)\n",
    "    \n",
    "    if(np.abs(fa) <= tol):\n",
    "        return a, 0\n",
    "    if(np.abs(fb) <= tol):\n",
    "        return b, 0\n",
    "    if(fa*fb > 0):\n",
    "        print(\"Intervalo é inválido\")\n",
    "        return 0, -1\n",
    "    \n",
    "    for it in range(maxIt):\n",
    "        x = (a + b)/2\n",
    "        fx = f(x)\n",
    "        \n",
    "        if(np.abs(fx) <= tol):\n",
    "            return x, it+1\n",
    "        \n",
    "        if(fa*fx < 0):\n",
    "            b = x\n",
    "            fb = fx\n",
    "        else: #fb*fx < 0\n",
    "            a = x\n",
    "            fa = fx\n",
    "    \n",
    "    print(\"O método não convergiu nas iterações, ou seja, não atingiu a tolerância\")\n",
    "    return x, maxIt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## x - 2^(-x) = 0, considerando o intervalo 0<=x<=1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  0.6411857604980469 2.3100954371635396e-08 18\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: x - 2**(-x)\n",
    "x, it = bissec(f, 0, 1)\n",
    "print('> ', x, f(x), it)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exp(x) - x² + 3x - 2 = 0, considerando o intervalo 0<=x<=1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  0.25753021240234375 -2.759847070876731e-07 17\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: np.exp(x) - x**2 + 3*x - 2\n",
    "x, it = bissec(f, 0, 1)\n",
    "print('> ', x, f(x), it)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2xcos(2x) - (x+1)² = 0, considerando os intervalos -3<=x<=-2, -1<=x<=0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  -2.19130802154541 -9.775346199170087e-08 20\n",
      ">  -0.7981600761413574 4.1836280610663135e-07 21\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: 2*x*np.cos(2*x) - (x + 1)**2\n",
    "x, it = bissec(f, -3, -2)\n",
    "print('> ', x, f(x), it)\n",
    "x, it = bissec(f, -1, 0)\n",
    "print('> ', x, f(x), it)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## xcos(x) - 2x² + 3x - 1 = 0, considerando os intervalos 0.2<=x<=0.3, 1.2<=x<=1.3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  0.29753036499023444 3.517655073892456e-07 17\n",
      ">  1.2566230773925782 7.139104405418095e-07 17\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: x*np.cos(x) - 2*x**2 + 3*x - 1\n",
    "x, it = bissec(f, 0.2, 0.3)\n",
    "print('> ', x, f(x), it)\n",
    "x, it = bissec(f, 1.2, 1.3)\n",
    "print('> ', x, f(x), it)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ------\n",
    "# Questão 1: Utilize o algoritmo do método de Newton, com tolerância 0.000001, para resolver os seguintes casos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def metNewt(f, df, x0, tol = 1e-6, maxIt = 50):\n",
    "    for it in range(maxIt):\n",
    "        fx = f(x0)\n",
    "        if(np.abs(fx) <= tol):\n",
    "            return x0, it\n",
    "        \n",
    "        if(df(x0) == 0):\n",
    "            print(\"A derivada zerou\")\n",
    "            return x, it\n",
    "        \n",
    "        x0 = x0 - f(x0)/df(x0)\n",
    "    \n",
    "    print(\"O método não atingiu a tolerância!\")\n",
    "    return x0, maxIt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = [] #Vetor para armazenar os resultados e plotar na Questão 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exp(x) + 2^(-x) + 2cos(x) - 6 = 0, considerando o intervalo 1<=x<=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  1.829383602512459 2.3731692166961693e-09 7\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: np.exp(x) + 2**(-x) + 2*np.cos(x) - 6\n",
    "df = lambda x: np.exp(x) - 2**(-x)*np.log(2) - 2*np.sin(x)\n",
    "\n",
    "x, it = metNewt(f, df, 1)\n",
    "print('> ', x, f(x), it)\n",
    "result.append(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ln(x-1) + cos(x-1) = 0, considerando o intervalo 1.3<=x<=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  1.3977481644736214 -6.624694446344392e-07 3\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: np.log(x - 1) + np.cos(x - 1)\n",
    "df = lambda x: 1/(x - 1) - np.sin(x - 1)\n",
    "\n",
    "x, it = metNewt(f, df, 1.3)\n",
    "print('> ', x, f(x), it)\n",
    "result.append(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2xcos(2x) - (x-2)² = 0, considerando os intervalos 2<=x<=3, 3<=x<=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  2.3706869176622676 5.2513549064769904e-14 4\n",
      ">  2.3706870165845224 8.70056168222888e-07 5\n",
      ">  3.7221127731388566 -6.043472389194449e-10 10\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: 2*x*np.cos(2*x) - (x - 2)**2\n",
    "df = lambda x: 2*np.cos(2*x) - 4*x*np.sin(2*x) - 2*(x - 2)\n",
    "\n",
    "x, it = metNewt(f, df, 2)\n",
    "print('> ', x, f(x), it)\n",
    "result.append(x)\n",
    "x, it = metNewt(f, df, 3)\n",
    "print('> ', x, f(x), it)\n",
    "\n",
    "x, it = metNewt(f, df, 3.001)\n",
    "print('> ', x, f(x), it)\n",
    "result.append(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sin(x) - exp(-x) = 0, considerando os intervalos 0<=x<=1, 3<=x<=4, 6<=x<=7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  0.5885327439774188 -6.160960630552381e-12 4\n",
      ">  3.0963639608966513 -2.7168927836662693e-08 2\n",
      ">  6.285049004142744 -2.6974122881509577e-07 2\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: np.sin(x) - np.exp(-x)\n",
    "df = lambda x: np.cos(x) + np.exp(-x)\n",
    "\n",
    "x, it = metNewt(f, df, 0)\n",
    "print('> ', x, f(x), it)\n",
    "result.append(x)\n",
    "x, it = metNewt(f, df, 3)\n",
    "print('> ', x, f(x), it)\n",
    "result.append(x)\n",
    "x, it = metNewt(f, df, 6)\n",
    "print('> ', x, f(x), it)\n",
    "result.append(x)"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ------\n",
    "# Questão 2: Uma forma de evitar o uso do cálculo da derivada da função f(x) no algoritmo do método de Newton é substituir o valor da derivada por uma aproximação. Ou seja, no lugar de calcular a cada passo o termo f'(x^(k)) podemos usar:\n",
    "![image.png](attachment:image.png)\n",
    "# Esse método é conhecido como método da secante.\n",
    "# • Utilize o método da secante para resolver os mesmos exercícios do item anterior, com a mesma tolerância. Observe que você deve escolher dois chutes iniciais! Para cada caso, compare o número de iterações do método de Newton e o da secante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def metSec(f, xAnt, x0, tol = 1e-6, maxIt = 50):\n",
    "    for it in range(maxIt):\n",
    "        fx = f(x0)\n",
    "        if(np.abs(fx) <= tol):\n",
    "            return x0, it\n",
    "        \n",
    "        #Aproximando o valor da derivada\n",
    "        dfx0 = (f(x0) - f(xAnt))/(x0 - xAnt)\n",
    "        if(dfx0 == 0):\n",
    "            print(\"A derivada zerou\")\n",
    "            return x, it\n",
    "        \n",
    "        x = x0\n",
    "        x0 = x0 - f(x0)/dfx0\n",
    "    \n",
    "    print(\"O método não atingiu a tolerância!\")\n",
    "    return x0, maxIt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exp(x) + 2^(-x) + 2cos(x) - 6 = 0, considerando o intervalo 1<=x<=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  1.8293834294825584 -7.073088301723374e-07 42\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: np.exp(x) + 2**(-x) + 2*np.cos(x) - 6\n",
    "df = lambda x: np.exp(x) - 2**(-x)*np.log(2) - 2*np.sin(x)\n",
    "\n",
    "x, it = metSec(f, 1.2, 1.3)\n",
    "print('> ', x, f(x), it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# O método de Newton utilizou 7 iterações para obter o resultado da equação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ln(x-1) + cos(x-1) = 0, considerando o intervalo 1.3<=x<=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  1.3977482001017572 -5.866951604538428e-07 7\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: np.log(x - 1) + np.cos(x - 1)\n",
    "df = lambda x: 1/(x - 1) - np.sin(x - 1)\n",
    "\n",
    "x, it = metSec(f, 1.3, 1.31)\n",
    "print('> ', x, f(x), it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# O método de Newton utilizou 3 iterações para obter o resultado da equação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2xcos(2x) - (x-2)² = 0, considerando os intervalos 2<=x<=3, 3<=x<=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  2.370686995098252 6.810768372333964e-07 11\n",
      ">  2.370686894515888 -2.0358050981106324e-07 12\n",
      ">  3.7221128300150053 -9.27879550971511e-07 23\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: 2*x*np.cos(2*x) - (x - 2)**2\n",
    "df = lambda x: 2*np.cos(2*x) - 4*x*np.sin(2*x) - 2*(x - 2)\n",
    "\n",
    "x, it = metSec(f, 2, 2.1)\n",
    "print('> ', x, f(x), it)\n",
    "x, it = metSec(f, 3, 3.1)\n",
    "print('> ', x, f(x), it)\n",
    "\n",
    "x, it = metSec(f, 3.3, 3.4)\n",
    "print('> ', x, f(x), it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# O método de Newton utilizou respectivamente 4, 5 e 10 iterações para obter o resultado da equação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sin(x) - exp(-x) = 0, considerando os intervalos 0<=x<=1, 3<=x<=4, 6<=x<=7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">  0.5885322269626375 -7.170527293043349e-07 8\n",
      ">  3.096364075287336 -1.362706516030987e-07 2\n",
      ">  6.28504996483996 6.927450236272632e-07 3\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: np.sin(x) - np.exp(-x)\n",
    "df = lambda x: np.cos(x) + np.exp(-x)\n",
    "\n",
    "x, it = metSec(f, 0, 0.1)\n",
    "print('> ', x, f(x), it)\n",
    "x, it = metSec(f, 3, 3.1)\n",
    "print('> ', x, f(x), it)\n",
    "x, it = metSec(f, 6, 6.1)\n",
    "print('> ', x, f(x), it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# O método de Newton utilizou respectivamente 4, 2 e 2 iterações para obter o resultado da equação"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dessa forma, observa-se que o método de Newton utiliza menos iterações que o método da secante. Isso se deve ao fato de que, para o método de Newton, é necessário saber a derivada exata. Já no método da secante, esse valor é calculado via aproximação."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Questão 3: Esse exercício deve ser feito apenas após o termino dos anteriores. Utilize os comandos do Octave de construir gráficos, e faça os plots das funções do exercício 1, de acordo com intervalo dado."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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": [
    "f = lambda x: np.exp(x) + 2**(-x) + 2*np.cos(x) - 6\n",
    "x = np.linspace(1, 2, 1000)\n",
    "plt.plot(x, f(x), 'r-')\n",
    "plt.plot(result[0], f(result[0]), 'bo')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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": [
    "f = lambda x: np.log(x - 1) + np.cos(x - 1)\n",
    "x = np.linspace(1.3, 2, 1000)\n",
    "plt.plot(x, f(x), 'r-')\n",
    "plt.plot(result[1], f(result[1]), 'bo')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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": [
    "f = lambda x: 2*x*np.cos(2*x) - (x - 2)**2\n",
    "x = np.linspace(2, 4, 1000)\n",
    "plt.plot(x, f(x), 'r-')\n",
    "plt.plot(result[2], f(result[2]), 'bo')\n",
    "plt.plot(result[3], f(result[3]), 'bo')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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": [
    "f = lambda x: np.sin(x) - np.exp(-x)\n",
    "x = np.linspace(0, 7, 1000)\n",
    "plt.plot(x, f(x), 'r-')\n",
    "plt.plot(result[4], f(result[4]), 'bo')\n",
    "plt.plot(result[5], f(result[5]), 'bo')\n",
    "plt.plot(result[6], f(result[6]), 'bo')\n",
    "plt.grid()"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}