From 95e840682355896b8be4fd4ddd0c9de004329867 Mon Sep 17 00:00:00 2001 From: yrjose Date: Tue, 21 Jan 2025 18:07:21 -0300 Subject: [PATCH] adicao de pasta com arquivo .ipynb --- ...lgoritmos_comeco_de_Calculo_numerico.ipynb | 953 ++++++++++++++++++ 1 file changed, 953 insertions(+) create mode 100644 cap_python/Metodos numericos/Algoritmos_comeco_de_Calculo_numerico.ipynb diff --git a/cap_python/Metodos numericos/Algoritmos_comeco_de_Calculo_numerico.ipynb b/cap_python/Metodos numericos/Algoritmos_comeco_de_Calculo_numerico.ipynb new file mode 100644 index 00000000..6c83e9e9 --- /dev/null +++ b/cap_python/Metodos numericos/Algoritmos_comeco_de_Calculo_numerico.ipynb @@ -0,0 +1,953 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "source": [ + "### Método da bisseção:" + ], + "metadata": { + "id": "Ex1QzWsjadfX" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Pelo [teorema do valor intermediário](https://https://pt.wikipedia.org/wiki/Teorema_do_valor_intermedi%C3%A1rio), se dois pontos $a$ e $b$ satisfazem $f(a)f(b) < 0$, então existe um ponto $c$ no intervalo $(a, b)$ t.q. $f(c) = 0$.\n", + "\n", + "####![](https://upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Teorema_de_Bolzano.svg/330px-Teorema_de_Bolzano.svg.png)\n", + "\n", + "#### O método da bisseção busca encontrar $c$ através da redução do intervalo $(a, b)$" + ], + "metadata": { + "id": "rQroF_vli2HJ" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Recursivo:" + ], + "metadata": { + "id": "ToirClRnbQJF" + } + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "JTSQviCsv0j2", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "fb998003-89dc-4a2e-e4af-c0b0598c8a12" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "a raiz se encontra em x = 0.6417143708729327; convergiu em 42 iterações\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "6.117328865684613e-14" + ] + }, + "metadata": {}, + "execution_count": 1 + } + ], + "source": [ + "#Metodo da bisseção\n", + "import numpy as np\n", + "\n", + "def fun(x):\n", + " #exemplos de funções\n", + " #y = np.e**x - np.sin(x) - 2\n", + " #y = x + np.log(x) - 2\n", + " y = np.sqrt(x) - np.cos(x)\n", + " return y\n", + "\n", + "#variáveis globais\n", + "counter = 0\n", + "epsilon = 1E-13\n", + "\n", + "def bisec(a, b):\n", + "\n", + " c = (a + b) / 2\n", + " y = fun(c)\n", + "\n", + " global counter\n", + " counter += 1\n", + "\n", + " if abs(y) <= epsilon:\n", + " print('a raiz se encontra em x = {}; convergiu em {} iterações'.format(c, counter))\n", + " return c\n", + " if y > 0:\n", + " if fun(a) < fun(b): return bisec(a, c)\n", + " else: return bisec(c, b)\n", + " if y < 0:\n", + " if fun(a) > fun(b): return bisec(a, c)\n", + " else:\n", + " #print(y)\n", + " return bisec(c, b)\n", + "\n", + "fun(bisec(0, 1))" + ] + }, + { + "cell_type": "markdown", + "source": [ + "#### Iterado:" + ], + "metadata": { + "id": "sT5yawi5bUcd" + } + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "cb98c943-2494-4621-cb20-a3fae3f89565", + "id": "wKXzEQkIbY14" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "a raiz se encontra em x = 0.6417143708729327; convergiu em 30 iterações\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "6.117328865684613e-14" + ] + }, + "metadata": {}, + "execution_count": 7 + } + ], + "source": [ + "#Metodo da bisseção\n", + "import numpy as np\n", + "\n", + "def fun(x):\n", + " #exemplos de funções\n", + " #y = np.e**x - np.sin(x) - 2\n", + " #y = x + np.log(x) - 2\n", + " y = np.sqrt(x) - np.cos(x)\n", + " return y\n", + "\n", + "#variáveis globais\n", + "epsilon = 1E-13\n", + "\n", + "def bisec(a, b):\n", + "\n", + " c = (a + b) / 2\n", + " y = fun(c)\n", + "\n", + " counter = 0\n", + "\n", + " while abs(y) >= epsilon:\n", + " counter += 1\n", + "\n", + " if y > 0:\n", + " if fun(a) < fun(b):\n", + " a = a\n", + " b = c\n", + " c = (a + b) / 2\n", + " y = fun(c)\n", + " else:\n", + " a = c\n", + " b = b\n", + " c = (a + b) / 2\n", + " y = fun(c)\n", + " if y < 0:\n", + " if fun(a) > fun(b):\n", + " a = a\n", + " b = c\n", + " c = (a + b) / 2\n", + " y = fun(c)\n", + " else:\n", + " a = c\n", + " b = b\n", + " c = (a + b) / 2\n", + " y = fun(c)\n", + "\n", + " print('a raiz se encontra em x = {}; convergiu em {} iterações'.format(c, counter))\n", + " return c\n", + "\n", + "fun(bisec(0, 1))" + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Método de Newton" + ], + "metadata": { + "id": "5LoBmc_ujFq_" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Uma reta tangente à uma função pode ser uma boa simplificação desta. O [método de newton](https://pt.wikipedia.org/wiki/M%C3%A9todo_de_Newton%E2%80%93Raphson) consiste em buscar o valor $x_1$ onde a reta tangente a um ponto $(x_0, f(x_0))$ é igual a zero. A repetição dessa ideia consiste em substituir $(x_0, f(x_0))$ por $(x_1, f(x_1))$ a cada iteração.\n", + "####![](https://upload.wikimedia.org/wikipedia/commons/4/4c/Ganzhi001.jpg)" + ], + "metadata": { + "id": "KzSM8S4KjVtp" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Recursivo" + ], + "metadata": { + "id": "JxU6WcExjS9w" + } + }, + { + "cell_type": "code", + "source": [ + "#Metodo de Newton\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import sympy as sp\n", + "#sympy está aqui como uma forma do usuário não ter que derivar\n", + "#manualmente, mas é importante levar em cosideração os problemas\n", + "#da derivação numérica ao pensar na precisão\n", + "\n", + "#função simbólica, aqui se escreve a função a ser trabalhada\n", + "def fun_N():\n", + "\n", + " x = sp.symbols('x')\n", + " #exemplos de funções\n", + " #y = x**3 + x + 1\n", + " #y = x**3 - x**2 + 2*x -1\n", + " #y = sp.cos(x) - x\n", + " y = x**2 - 6\n", + " return y\n", + "\n", + "#derivação, o resultado também\n", + "#é uma função simbólica\n", + "def D_fun_N():\n", + "\n", + " x = sp.symbols('x')\n", + " dx = sp.diff(fun_N(), x)\n", + "\n", + " return dx\n", + "\n", + "#aplica a função simbólica num ponto,\n", + "#devolve um float\n", + "def F_pontual(f, x0):\n", + "\n", + " x = sp.symbols('x')\n", + "\n", + " y = f.subs(x, x0)\n", + "\n", + " #print(x0, y)\n", + "\n", + " return y\n", + "\n", + "#variáveis globais\n", + "past=[]\n", + "contador = 0\n", + "\n", + "def Met_Newton(x0, tol, maxit):\n", + " '''\n", + " x0 é o chute inicial,\n", + " tol é a tolerância,\n", + " maxit é o n máximo de iterações.\n", + " '''\n", + " #variáveis globais\n", + " global contador\n", + " contador += 1\n", + "\n", + " past.append(x0) #armazena os valores para examinar depois\n", + "\n", + " y = F_pontual(fun_N(), x0)\n", + " dy = F_pontual(D_fun_N(), x0)\n", + " x = float(x0 - y/dy)\n", + "\n", + " if contador >= maxit:\n", + " print('não convergiu a tempo', x)\n", + " return x\n", + "\n", + " if abs(x - x0)/abs(x0) <= tol:\n", + " print('a raiz se encontra em x = {}; convergiu em {} iterações'.format(x, contador))\n", + " return x\n", + " else:\n", + " Met_Newton(x, tol, maxit)\n", + "\n", + "Met_Newton(1, 1e-12, 200)\n", + "\n", + "#plots:\n", + "\n", + "#função\n", + "dominio = np.linspace(min(past), max(past), 50)\n", + "imagem = [F_pontual(fun_N(), i) for i in dominio]\n", + "plt.plot(dominio, imagem, 'r')\n", + "\n", + "#iterações\n", + "plt.plot(past, [F_pontual(fun_N(), im) for im in past], 'o--')\n", + "for i, (x, y) in enumerate(zip(past, [F_pontual(fun_N(), im) for im in past])):\n", + " plt.text(x, y, f'{i+1}', fontsize=12, ha='right', color='darkblue')\n", + "plt.xlabel('x')\n", + "plt.ylabel('f(x)')\n", + "plt.title('Método de Newton: Iterações na Função')\n", + "plt.grid(True)\n", + "\n", + "plt.show()\n", + "\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 489 + }, + "id": "7_iRU8VbKaot", + "outputId": "2356ec62-0bd0-42c7-c302-8f5ae3c5e288" + }, + "execution_count": 29, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "a raiz se encontra em x = 2.449489742783178; convergiu em 7 iterações\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "#### Iterativo" + ], + "metadata": { + "id": "uvBHqlJVzESx" + } + }, + { + "cell_type": "code", + "source": [ + "#Metodo de Newton\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import sympy as sp\n", + "#sympy está aqui como uma forma do usuário não ter que derivar\n", + "#manualmente, mas é importante levar em cosideração os problemas\n", + "#da derivação numérica ao pensar na precisão\n", + "\n", + "#função simbólica\n", + "def fun_N():\n", + "\n", + " x = sp.symbols('x')\n", + " #exemplos de funções\n", + " #y = x**3 + x + 1\n", + " #y = x**3 - x**2 + 2*x -1\n", + " #y = sp.cos(x) - x\n", + " y = x**2 - 6\n", + " return y\n", + "\n", + "#derivação, o resultado também\n", + "#é uma função simbólica\n", + "def D_fun_N():\n", + "\n", + " x = sp.symbols('x')\n", + " dx = sp.diff(fun_N(), x)\n", + "\n", + " return dx\n", + "\n", + "#aplica a função simbólica num ponto,\n", + "#devolve um float\n", + "def F_pontual(f, x0):\n", + "\n", + " x = sp.symbols('x')\n", + "\n", + " y = f.subs(x, x0)\n", + "\n", + " #print(x0, y)\n", + "\n", + " return y\n", + "\n", + "#variáveis globais\n", + "past=[]\n", + "\n", + "def Met_Newton(x0, tol, maxit):\n", + "\n", + " '''\n", + " x0 é o chute inicial,\n", + " tol é a tolerância,\n", + " maxit é o n máximo de iterações.\n", + " '''\n", + "\n", + " #variáveis globais\n", + " contador = 0\n", + "\n", + " y = F_pontual(fun_N(), x0)\n", + " dy = F_pontual(D_fun_N(), x0)\n", + " x = float(x0 - y/dy)\n", + "\n", + " while abs(x - x0)/abs(x0) >= tol:\n", + " contador += 1\n", + " past.append(x0) #armazena os valores para examinar depois\n", + " if contador >= maxit:\n", + " print('não convergiu a tempo', x)\n", + " return x\n", + "\n", + " x0 = x\n", + " y = F_pontual(fun_N(), x0)\n", + " dy = F_pontual(D_fun_N(), x0)\n", + " x = float(x - y/dy)\n", + "\n", + " print('a raiz se encontra em x = {}; convergiu em {} iterações'.format(x, contador))\n", + " return y\n", + "\n", + "\n", + "print(Met_Newton(1, 1e-12, 200))\n", + "\n", + "#plots:\n", + "\n", + "#função\n", + "dominio = np.linspace(min(past), max(past), 50)\n", + "imagem = [F_pontual(fun_N(), i) for i in dominio]\n", + "plt.plot(dominio, imagem, 'r')\n", + "\n", + "#iterações\n", + "plt.plot(past, [F_pontual(fun_N(), im) for im in past], 'o--')\n", + "for i, (x, y) in enumerate(zip(past, [F_pontual(fun_N(), im) for im in past])):\n", + " plt.text(x, y, f'{i+1}', fontsize=12, ha='right', color='darkblue')\n", + "plt.xlabel('x')\n", + "plt.ylabel('f(x)')\n", + "plt.title('Método de Newton: Iterações na Função')\n", + "plt.grid(True)\n", + "\n", + "plt.show()\n", + "\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 507 + }, + "id": "yX04PV-dzGaJ", + "outputId": "a895fb66-e085-48fc-bbf7-261d04747e4d" + }, + "execution_count": 30, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "a raiz se encontra em x = 2.449489742783178; convergiu em 6 iterações\n", + "-8.88178419700125e-16\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "#### Cálculo de raizes quadradas" + ], + "metadata": { + "id": "xXRabOJY7-0r" + } + }, + { + "cell_type": "markdown", + "source": [ + "##### Digamos que queremos calcular a raiz quadrada $x = \\sqrt{x_0}$ de algum número $x_0$, como $x_{n+1} = x_{n} - \\frac{f(x_n)}{f'(x_n)}$, então com problema equivalente $x^2 = x_0$, escrevemos $x^2-x_0 = 0 = f(x)$. Logo, transformamos o problema de achar a raiz quadrada em achar um $x^*$ raiz de $f(x)$, isto é: $x_{n+1} = x_{n} - \\frac{x_n^2-x_0}{2x_n} = -\\frac{-2x_n^2+x_n^2-x_0}{2x_n} = \\frac{x_n}{2}+\\frac{x_0}{2x_n}$." + ], + "metadata": { + "id": "ThVH8jD5FzQQ" + } + }, + { + "cell_type": "code", + "source": [ + "#raizes secant\n", + "#Metodo da secante\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def Met_Raiz_Newton(x0, tol, maxit, raiz):\n", + " #queremos resolver o problema x = sqrt(raiz)\n", + " contador = 0\n", + " x = x0/2 + raiz/(2*x0)\n", + "\n", + " while abs(x - x0)/abs(x0) >= tol:\n", + " past.append(x0)\n", + " contador += 1\n", + " if contador >= maxit:\n", + " print('não convergiu a tempo', x)\n", + " return x\n", + " x0 = x\n", + " x = x0/2 + raiz/(2*x0)\n", + " print('ITERAÇÕES:', contador, '\\n A RAIZ É:', x)\n", + " return x\n", + "\n", + "past = []\n", + "\n", + "print(Met_Raiz_Newton(5, 1e-19, 200, 25.4) - np.sqrt(25.4))\n", + "print(*past)" + ], + "metadata": { + "id": "tp2iegXa8CpU", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "8bb3de41-d12a-4755-f420-c8d4c2f10f4a" + }, + "execution_count": 31, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "ITERAÇÕES: 3 \n", + " A RAIZ É: 5.039841267341661\n", + "0.0\n", + "5 5.04 5.03984126984127\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Método da secante" + ], + "metadata": { + "id": "_AEgovIGe4ye" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Ao invés de exigir a derivada explicitamente, aproxima-a e aplica o método de Newton, exige dois chutes iniciais" + ], + "metadata": { + "id": "OE2WNyHvi82w" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Recursivo" + ], + "metadata": { + "id": "Bm9E97zqjCvQ" + } + }, + { + "cell_type": "code", + "source": [ + "#Metodo da secante\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def fun_S(x):\n", + "\n", + " y = np.cos(x) - x\n", + "\n", + " return y\n", + "\n", + "past=[]\n", + "\n", + "def Met_Secante(x0, x1, tol, maxit):\n", + "\n", + " global contador\n", + "\n", + " contador += 1\n", + " past.append(x0)\n", + "\n", + " y0 = fun_S(x0)\n", + " y1 = fun_S(x1)\n", + "\n", + " x = x1 - (y1)*(x1 - x0)/(y1 - y0)\n", + "\n", + " if contador >= maxit:\n", + " print('não convergiu a tempo', x)\n", + " return x\n", + "\n", + " if abs(x - x1)/abs(x1) <= tol:\n", + " print(contador, x)\n", + " return x\n", + " else:\n", + " Met_Secante(x1, x, tol, maxit)\n", + "\n", + "contador = 0\n", + "epsilon = 1e-40\n", + "maxiteracoes = 200\n", + "\n", + "Met_Secante(0, 5, epsilon, maxiteracoes)\n", + "\n", + "#plots\n", + "dom = np.linspace(min(past), max(past))\n", + "plt.plot(dom, [fun_S(im) for im in dom], 'r')\n", + "\n", + "plt.plot(past, [fun_S(im) for im in past], 'o--')\n", + "\n", + "for i, (x, y) in enumerate(zip(past, [fun_S(im) for im in past])):\n", + " plt.text(x, y, f'{i+1}', fontsize=12, ha='right', color='darkblue')\n", + "\n", + "plt.grid(True)\n", + "plt.show()\n", + "\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "fLBy0SNOAtrh", + "outputId": "71a35fe1-19ed-48d7-97bd-4f2bc3557703" + }, + "execution_count": 32, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "8 0.7390851332151607\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "#### Iterado" + ], + "metadata": { + "id": "XaFDgsXEmWTX" + } + }, + { + "cell_type": "code", + "source": [ + "#Metodo da secante\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def fun_S(x):\n", + "\n", + " y = np.cos(x) - x\n", + "\n", + " return y\n", + "\n", + "past=[]\n", + "\n", + "def Met_Secante(x0, x1, tol, maxit):\n", + "\n", + " y0 = fun_S(x0)\n", + " y1 = fun_S(x1)\n", + "\n", + " x = x1 - (y1)*(x1 - x0)/(y1 - y0)\n", + "\n", + " contador = 0\n", + " while abs(x - x1)/abs(x1) >= tol:\n", + " contador += 1\n", + " past.append(x0)\n", + " if contador >= maxit:\n", + " print('não convergiu a tempo', x)\n", + " return x\n", + " x0 = x1\n", + " x1 = x\n", + " y0 = fun_S(x0)\n", + " y1 = fun_S(x1)\n", + " x = x1 - (y1)*(x1 - x0)/(y1 - y0)\n", + "\n", + " print(contador, x)\n", + " return x\n", + "\n", + "epsilon = 1e-40\n", + "maxiteracoes = 200\n", + "\n", + "Met_Secante(0, 5, epsilon, maxiteracoes)\n", + "\n", + "#plots\n", + "dom = np.linspace(min(past), max(past))\n", + "plt.plot(dom, [fun_S(im) for im in dom], 'r')\n", + "\n", + "plt.plot(past, [fun_S(im) for im in past], 'o--')\n", + "\n", + "for i, (x, y) in enumerate(zip(past, [fun_S(im) for im in past])):\n", + " plt.text(x, y, f'{i+1}', fontsize=12, ha='right', color='darkblue')\n", + "\n", + "plt.grid(True)\n", + "plt.show()\n", + "\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "zOHR2zEpmTre", + "outputId": "bd38968e-60a2-4ba1-c872-1bcb44b5bffe" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "7 0.7390851332151607\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Iteração do ponto fixo" + ], + "metadata": { + "id": "BwPSqWfujayQ" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Um ponto fixo de uma função $f(x)$ é um ponto $x^*$ que satisfaz $f(x^*) = x^*$; isto é, a função aplicada em $x^*$ devolve o proprio $x^*$.\n", + "![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Fixed_Point_Graph.png/330px-Fixed_Point_Graph.png)\n", + "#### O método do ponto fixo consiste em iterar a função $f(x)$ t.q. $x_{n+1} = f(x_{n})$ e esperar que ela convirga a um ponto com as propriedades do ponto fixo. Existem algumas formas de [garantir que isso aconteça](https://pt.wikipedia.org/wiki/Itera%C3%A7%C3%A3o_de_ponto_fixo), com condições que relacionam o chute inicial $x_0$ e a função $f(x)$.\n", + "![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Cosine_fixed_point.svg/270px-Cosine_fixed_point.svg.png)" + ], + "metadata": { + "id": "7jWpUtdgvWD9" + } + }, + { + "cell_type": "markdown", + "source": [ + "#### Recursivo" + ], + "metadata": { + "id": "zMaNiS3sy8eu" + } + }, + { + "cell_type": "code", + "source": [ + "#Método do ponto fixo\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def F_g(x):\n", + " #exemplo x = cos(x)\n", + " y = np.cos(x)\n", + "\n", + " return y\n", + "\n", + "counter = 0\n", + "epsilon = 1E-13\n", + "\n", + "past=[]\n", + "\n", + "def pto_fixo(x):\n", + "\n", + " global counter\n", + "\n", + " past.append(x)\n", + " counter += 1\n", + "\n", + " if abs(F_g(x) - x) / abs(x) <= epsilon:\n", + " print('a raiz se encontra em x = {}; convergiu em {} iterações'.format(x, counter))\n", + " return x\n", + " else:\n", + " pto_fixo(F_g(x))\n", + " return\n", + "\n", + "pto_fixo(0.7)\n", + "\n", + "#plots\n", + "dom = np.linspace(min(past), max(past))\n", + "plt.plot(dom, [F_g(im) for im in dom], 'r')\n", + "\n", + "plt.plot(past, [F_g(im) for im in past], 'o--')\n", + "\n", + "for i, (x, y) in enumerate(zip(past, [F_g(im) for im in past])):\n", + " plt.text(x, y, f'{i+1}', fontsize=12, ha='right', color='darkblue')\n", + "\n", + "plt.grid(True)\n", + "plt.show()" + ], + "metadata": { + "id": "oL0tZhdxD-2o", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "outputId": "dd1993ae-aa64-4beb-c2f8-437e3ba3e246" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "a raiz se encontra em x = 0.7390851332151231; convergiu em 71 iterações\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "#### Iterativo" + ], + "metadata": { + "id": "FJuE1B2m2puv" + } + }, + { + "cell_type": "code", + "source": [ + "#Método do ponto fixo\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def F_g(x):\n", + " #exemplo x = cos(x)\n", + " y = np.cos(x)\n", + "\n", + " return y\n", + "\n", + "epsilon = 1E-13\n", + "past=[]\n", + "\n", + "def pto_fixo(x_0):\n", + " x = F_g(x_0) #inicializar\n", + " counter = 0\n", + " while abs(x - x_0) / abs(x_0) >= epsilon:\n", + " past.append(x_0)\n", + " counter += 1\n", + " x_0 = x\n", + " x = F_g(x_0)\n", + "\n", + " print('a raiz se encontra em x = {}; convergiu em {} iterações'.format(x, counter))\n", + " return x\n", + "\n", + "pto_fixo(0.7)\n", + "\n", + "#plots\n", + "dom = np.linspace(min(past), max(past))\n", + "plt.plot(dom, [F_g(im) for im in dom], 'r')\n", + "\n", + "plt.plot(past, [F_g(im) for im in past], 'o--')\n", + "\n", + "for i, (x, y) in enumerate(zip(past, [F_g(im) for im in past])):\n", + " plt.text(x, y, f'{i+1}', fontsize=12, ha='right', color='darkblue')\n", + "\n", + "plt.grid(True)\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "x2cNRqMK2r5D", + "outputId": "30e14361-182c-4243-b5e9-e9eeb3be98e1" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "a raiz se encontra em x = 0.7390851332151859; convergiu em 70 iterações\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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