lista-5-solucoes.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lista de Exercícios 5\n",
    "\n",
    "Solucionário matemático e computacional de exercícios selecionados da Lista de Exercícios 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# importação de módulos\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ajuste de curvas\n",
    "\n",
    "**Obs.:**: função `polyfit` retorna coeficientes da curva de ajuste na ordem: \n",
    "```python \n",
    "P = p[0] + p[1]*x + p[2]*x**2 + p[3]*x**3 + ...\n",
    "```"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemplo: solução fechada 2D "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# tabela de dados\n",
    "x = np.array([1,2,3,4])\n",
    "y = np.array([0.5,2.5,2.0,4.0])\n",
    "\n",
    "# min quad\n",
    "m = np.size(x)\n",
    "alpha1 = (m*np.dot(x,y) - np.sum(x)*np.sum(y))/(m*np.dot(x,x)-np.sum(x)**2)\n",
    "alpha0 = np.mean(y) - alpha1*np.mean(x)\n",
    "\n",
    "# plot\n",
    "plt.scatter(x,y)\n",
    "y2 = alpha0 + alpha1*x\n",
    "plt.plot(x,y2,'r:');"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resolução da Lista 5"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Função-base para computar ajuste e plotar resultados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Resolve problema de ajuste polinomial discreto e plota resultado\n",
    "\n",
    "    entrada: \n",
    "        x,y : tabela de valores (numpy arrays)\n",
    "        g   : grau do polinômio de ajuste (int)\n",
    "\"\"\"\n",
    "def resolve_ajuste(x,y,g):\n",
    "    \n",
    "    c = np.polyfit(x, y, g) # ajuste\n",
    "    p = np.poly1d(c) \n",
    "    plt.plot(x,y,'d',x,p(x),'o-')\n",
    "    plt.xlabel(str(x))\n",
    "    for i in range(g+1):\n",
    "        print('Coeficiente de ajuste p[' + str(i) + ']: ' + str(c[i]))\n",
    "\n",
    "    return p"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### L5-Q2\n",
    "\n",
    "Ajuste os dados abaixo pelo método dos mínimos quadrados:\n",
    "\n",
    "\\begin{array}{c|cccccccc}\n",
    "x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\\\n",
    "\\hline\n",
    "y & 0.5 & 0.6  & 0.9 & 0.8 & 1.2 & 1.5 &  1.7 & 2.0\n",
    "\\end{array}\n",
    "\n",
    "a) por reta \n",
    "\n",
    "b) por parábola do tipo $ax^2 + bx + c$; "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "#### Metodologia matemática"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a)\n",
    "\n",
    "$$g_1(x) = x$$$$ g_2(x)=1$$\n",
    "\n",
    "\\begin{array}{c|cccccccc}\n",
    "g_1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\\\n",
    "\\hline\n",
    "g_2 & 1 & 1 & 1& 1& 1 & 1 & 1 & 1 \\\\\n",
    "\\hline\n",
    "f & 0.5 & 0.6  & 0.9 & 0.8 & 1.2 & 1.5 &  1.7 & 2.0\n",
    "\\end{array}\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "a_{11} &=& <g_1,g_1> &= 204\\\\\n",
    "a_{12} &=& <g_1,g_2> &= 36 \\\\\n",
    "a_{21} &=& a_{12}  \\\\\n",
    "a_{22} &=& <g_2,g_2> &= 8\\\\\n",
    "b_{1} &=&  <g_1,f>   &= 50.5\\\\\n",
    "b_{2} &=&  <g_2,f>  &= 9.2\n",
    "\\end{eqnarray*}\n",
    "\n",
    "\n",
    "$$\\begin{bmatrix}\n",
    "204 & 36 \\\\\n",
    "36 &  8\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "\\alpha_1 \\\\\n",
    "\\alpha_2 \n",
    "\\end{bmatrix} = \n",
    "\\begin{bmatrix}\n",
    "50.5 \\\\\n",
    "9.2\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "$$\\begin{align*}\n",
    "204\\alpha_1+36\\alpha_2 &= 50.5 \\\\\n",
    "36\\alpha_1+8\\alpha_2 &= 9.2\n",
    "\\end{align*}$$\n",
    "\n",
    "\n",
    "$$\\alpha_1 = 0.2166 ,\\  \\alpha_2 = 0.175$$\n",
    "\n",
    "$$f(x) = 0.1749x + 0.2167$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) \n",
    "\n",
    "$g_1(x) = x^2$; $g_2(x)=x$; $g_3(x)=1$ \n",
    "\n",
    "\\begin{array}{c|cccccccc}\n",
    "g_1 & 1 & 4 & 9 & 16 & 25 & 36 & 49 & 64 \\\\\n",
    "\\hline\n",
    "g_2 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\\\n",
    "\\hline\n",
    "g_3 & 1 & 1 & 1& 1& 1 & 1 & 1 & 1 \\\\\n",
    "\\hline\n",
    "f & 0.5 & 0.6  & 0.9 & 0.8 & 1.2 & 1.5 &  1.7 & 2.0\n",
    "\\end{array}\n",
    "\n",
    "\\begin{align*}\n",
    "a_{11}=\\ <g_1,g_1> \\ &= 8772\\\\\n",
    "a_{12}=\\ a_{21}   =\\  <g_1,g_2> \\ &= 1296 \\\\\n",
    "a_{13}=\\ a_{31}   =\\  <g_1,g_3> \\ &= 204 \\\\\n",
    "a_{22}=\\ <g_2,g_2> \\ &= 204\\\\\n",
    "a_{23}=\\ a_{32}   =\\  <g_2,g_3> \\ &= 36 \\\\\n",
    "a_{33}=\\ <g_3,g_3> \\ &= 8 \\\\\n",
    "b_{1}=\\  <g_1,f>  \\ &= 319.1\\\\\n",
    "b_{2}=\\  <g_2,f>  \\ &= 50.5\\\\\n",
    "b_{3}=\\  <g_3,f>  \\ &= 9.2\n",
    "\\end{align*}\n",
    "\n",
    "$$\\begin{bmatrix}\n",
    "8872 & 1296 & 204 \\\\\n",
    "1296 &  204 & 36 \\\\\n",
    "204 &  36 & 8\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "\\alpha_1 \\\\\n",
    "\\alpha_2 \\\\\n",
    "\\alpha_3 \n",
    "\\end{bmatrix} = \n",
    "\\begin{bmatrix}\n",
    "319.1\\\\\n",
    "50.5 \\\\\n",
    "9.2 \n",
    "\\end{bmatrix}$$\n",
    "\n",
    "$$\\begin{align*}\n",
    "8872\\alpha_1+1296\\alpha_2 + 204\\alpha_3 &= 319.1 \\\\\n",
    "1296\\alpha_1+204\\alpha_2 + 36\\alpha_3 &= 50.5 \\\\\n",
    "204\\alpha_1+36\\alpha_2 + 8\\alpha_3 &= 9.2\n",
    "\\end{align*}$$\n",
    "\n",
    "$$\\alpha_1 = 0.4071 ,\\  \\alpha_2 = 0.07738, \\  \\alpha_3 = 0.01547$$ \n",
    "\n",
    "$$f(x) = 0.01547 + 0.07738x + 0.4071x^2$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Metodologia computacional"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 0.2166666666666667\n",
      "Coeficiente de ajuste p[1]: 0.17499999999999996\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# tabela de dados\n",
    "x = np.arange(1,9)\n",
    "y = np.array([0.5,.6,.9,.8,1.2,1.5,1.7,2.])\n",
    "\n",
    "# grau 1\n",
    "g = 1\n",
    "p = resolve_ajuste(x,y,g)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 0.015476190476190437\n",
      "Coeficiente de ajuste p[1]: 0.07738095238095268\n",
      "Coeficiente de ajuste p[2]: 0.407142857142857\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# grau 2\n",
    "g = 2\n",
    "p = resolve_ajuste(x,y,g)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### L5-Q3\n",
    "\n",
    "Dada a tabela abaixo, faça o gráfico de dispersão dos dados e ajuste uma curva da melhor maneira possı́vel:\n",
    "\n",
    "\\begin{array}{c|cccccc}\n",
    "x & 0.5 & 0.75 & 1 & 1.5 & 2.0 & 2.5 & 3.0  \\\\\n",
    "\\hline\n",
    "y & -2.8 & -0.6 & 1& 3.2& 4.8 & 6.0 & 7.0 \n",
    "\\end{array}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "#### Metodologia matemática\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$g_1(x) = 1$; $g_2(x)=x$; $g_3(x)=x^2$; $g_4(x)=x^3$\n",
    "\n",
    "\\begin{array}{c|cccccc}\n",
    "g_1 & 1 & 1 & 1& 1& 1 & 1 & 1 \\\\\n",
    "g_2 & 0.5 & 0.75 & 1 & 1.5 & 2.0 & 2.5 & 3.0  \\\\\n",
    "\\hline\n",
    "g_3 & 0.25 & 0.5625& 1& 2.25& 4 & 6.25 & 9.0\\\\\n",
    "\\hline\n",
    "g_4 & 0.1250 & 0.4219 & 1& 3.375& 8 &15. 625 & 27 \\\\\n",
    "f & -2.8 & -0.6 & 1& 3.2& 4.8 & 6.0 & 7.0 \n",
    "\\end{array}\n",
    "\n",
    "\\begin{align*}\n",
    "a_{11}=\\ <g_1,g_1> \\ &= 7\\\\\n",
    "a_{12}=\\ a_{21}   =\\  <g_1,g_2> \\ &= 11.25 \\\\\n",
    "a_{13}=\\ a_{31}   =\\  <g_1,g_3> \\ &= 23.3125 \\\\\n",
    "a_{14}=\\ a_{41}   =\\  <g_1,g_4> \\ &= 55.5468 \\\\\n",
    "a_{22}=\\ <g_2,g_2> \\ &= 23.3125\\\\\n",
    "a_{23}=\\ a_{32}   =\\  <g_2,g_3> \\ &= 55.5468 \\\\\n",
    "a_{24}=\\ a_{42}   =\\  <g_2,g_4> \\ &= 142.5039 \\\\\n",
    "a_{33}=\\ <g_3,g_3> \\ &= 142.5039 \\\\\n",
    "a_{34}=\\ <g_3,g_4> \\ &= 381.5185 \\\\\n",
    "a_{44}=\\ <g_4,g_4> \\ &= 1049.7248 \\\\\n",
    "b_{1}=\\  <g_1,f>  \\ &= 18.6\\\\\n",
    "b_{2}=\\  <g_2,f>  \\ &= 49.55\\\\\n",
    "b_{3}=\\  <g_3,f>  \\ &= 126.86\\\\\n",
    "b_{4}=\\  <g_4,f>  \\ &= 332.34\n",
    "\\end{align*}\n",
    "\n",
    "$$\\begin{bmatrix}\n",
    "7 & 11.25 & 23.3125 & 55.5468 \\\\\n",
    "11.25 &  23.3125 & 55.5468 & 142.5039 \\\\\n",
    "23.3125 &  55.5468 & 142.5039 & 381.5185\\\\\n",
    "55.5468 &  142.5039 & 381.5185 & 1049.7248\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "\\alpha_1 \\\\\n",
    "\\alpha_2 \\\\\n",
    "\\alpha_3 \\\\\n",
    "\\alpha_4 \n",
    "\\end{bmatrix} = \n",
    "\\begin{bmatrix}\n",
    "18.6\\\\\n",
    "49.55 \\\\\n",
    "126.8625\\\\\n",
    "332.3468\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "$$\\alpha_1 = -8.1043 ,\\  \\alpha_2 = 12.7882 \\  \\alpha_3 = -4.3250 , \\  \\alpha_4 = 0.5813$$\n",
    "\n",
    "$$f(x) = 0.5813  - 4.3250x + 12.79x^2 - 8.1043x^3$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Metodologia computacional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 0.588808229974697\n",
      "Coeficiente de ajuste p[1]: -4.365386461549416\n",
      "Coeficiente de ajuste p[2]: 12.85159200943416\n",
      "Coeficiente de ajuste p[3]: -8.131256481519904\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.040251260748212274"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# tabela\n",
    "x = np.array([0.5,0.75,1,1.5,2.0,2.5,3.0])\n",
    "y = np.array([-2.8,-0.6,1,3.2,4.8,6.0,7.0])\n",
    "\n",
    "# grau (teste para g = 2,3,4,5 e veja o erro)\n",
    "g = 3\n",
    "p = resolve_ajuste(x,y,g)\n",
    "\n",
    "# erro \n",
    "np.sum((p(x)-y)**2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### L5-Q4\n",
    "\n",
    "A tabela abaixo mostra as alturas e pesos de nove homens entre as idades de 25 a 29 anos extraı́da ao acaso entre funcionários de uma grande indústria:\n",
    "\n",
    "\\begin{array}{c|ccccccccc}\n",
    "\\text{Altura/cm} & 183& 173 & 168 & 188  & 158 & 163 & 193 &163 &178 \\\\\n",
    "\\hline\n",
    "\\text{Peso/kg} & 79 & 69 & 70& 81  & 61 &63 &79 & 71 & 73\n",
    "\\end{array}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Metodologia matemática \n",
    "\n",
    "$g_1(x) = 1$; $g_2(x)=x$\n",
    "\n",
    "\\begin{array}{c|cccccccc}\n",
    "g_1 & 1 & 1 & 1& 1& 1 & 1 & 1 & 1&1\\\\\n",
    "\\hline\n",
    "g_2 & 183& 173 & 168 & 188  & 158 & 163 & 193 &163 &178 \\\\\n",
    "\\hline\n",
    "f &  79 & 69 & 70& 81  & 61 &63 &79 & 71 & 73\n",
    "\\end{array}\n",
    "\n",
    "\\begin{align*}\n",
    "a_{11}=\\ <g_1,g_1> \\ &= 9\\\\\n",
    "a_{12}=\\ a_{21}   =  <g_1,g_2> \\ &= 1567 \\\\\n",
    "a_{22}=\\ <g_2,g_2> \\ &= 274.021\\\\\n",
    "b_{1}=\\ <g_1,f>  \\ &= 646\\\\\n",
    "b_{2}=\\ <g_2,f>  \\ &= 113.103\n",
    "\\end{align*}\n",
    "\n",
    "$$\\begin{bmatrix}\n",
    "9 & 1567 \\\\\n",
    "1567 &  274.021\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "\\alpha_1 \\\\\n",
    "\\alpha_2 \n",
    "\\end{bmatrix} = \n",
    "\\begin{bmatrix}\n",
    "646 \\\\\n",
    "113.103\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "$$\\alpha_1 = -20.0832 ,\\  \\alpha_2 = 0.5276$$\n",
    "\n",
    "$$f(x) = 0.5276x - 20.0832$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Metodologia computacional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fc4720ed610>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "altura = np.array([183,173,168,188,158,163,193,163,178])\n",
    "peso = np.array([79,69,70,81,61,63,79,71,73])\n",
    "\n",
    "# gráfico de dispersão \n",
    "plt.scatter(altura,peso)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q4-b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 0.527570093457944\n",
      "Coeficiente de ajuste p[1]: -20.078037383177612\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ajuste da reta \n",
    "p = resolve_ajuste(altura,peso,1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q4-c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.2467289719626\n",
      "189.69619131975205\n"
     ]
    }
   ],
   "source": [
    "# estimativa de peso (kg)\n",
    "alt = 175 \n",
    "p_c = p(alt)\n",
    "print(p_c)\n",
    "\n",
    "# estimativa de altura (cm)\n",
    "alt = 80\n",
    "a_c = (alt - p[0])/p[1]\n",
    "print(a_c)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q4-d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 1.5856741573033717\n",
      "Coeficiente de ajuste p[1]: 60.294943820224695\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p2 = resolve_ajuste(peso,altura,1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q4-e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.33835252435782\n",
      "0.09162355239521958\n"
     ]
    }
   ],
   "source": [
    "# estimativa de peso a partir de altura com novo ajuste \n",
    "alt = 175\n",
    "p_e = (alt - p2[0])/p2[1]\n",
    "print(p_e)\n",
    "\n",
    "# comparação com item (c): pesos \n",
    "# pequena diferença entre os valores\n",
    "dif = abs(p_c-p_e)\n",
    "print(dif)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q4-f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc4724d15d0>,\n",
       " <matplotlib.lines.Line2D at 0x7fc4724d1810>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# comparação das retas de ajuste\n",
    "# influência do resíduo => inclinações diferentes\n",
    "\n",
    "plt.plot(altura,p(altura),altura,(altura - p2[0])/p2[1])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## solucao-L5-Q5-a"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AJUSTE POR RETA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 1.7924185769967504\n",
      "Coeficiente de ajuste p[1]: -3420.8153029001523\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "208.83231551826748"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\" \n",
    "Nota: pesquisa no IBGE em maio de 2018 \n",
    "      mostra que a população já rompeu 209 mi. \n",
    "\"\"\"\n",
    "\n",
    "# tabela de dados\n",
    "ano = np.array([1900, 1920, 1940, 1950, 1960, 1970, 1980, 1991, 2000, 2010, 2015])\n",
    "hab = np.array([17.4, 30.6, 41.2, 51.9, 70.2, 93.1, 119.0, 146.2, 175.8, 198.6, 207.8])\n",
    "\n",
    "# plotagem\n",
    "fig,ax = plt.subplots(1,1)\n",
    "p = resolve_ajuste(ano,hab,1)\n",
    "ax.grid(axis='x')\n",
    "\n",
    "# plotagem do comportamento preditivo\n",
    "\n",
    "# linha tracejada e area  \n",
    "ano_m = np.linspace(2016, 2025, num=10, endpoint=True)\n",
    "v2 = np.ones(np.shape(ano_m))\n",
    "ax.fill_between(ano_m,200*v2,220*v2,facecolor='g',alpha=0.2)\n",
    "plt.plot(ano_m,p(ano_m),':')\n",
    "plt.plot(2025,p(2025),'go')\n",
    "\n",
    "# estimativa no ano 2025\n",
    "p(2025)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Marca de 100 milhões de pessoas: 1965\n",
      "Marca de 150 milhões de pessoas: 1993\n",
      "Marca de 200 milhões de pessoas: 2021\n"
     ]
    }
   ],
   "source": [
    "# abrindo vetor de 1900 a 2024\n",
    "anos = np.arange(ano[0],ano[-1]+10)\n",
    "pops = p(anos) # população\n",
    "\n",
    "# encontrando ano em que a populacao superou 100 mi\n",
    "lim100 = np.nonzero(pops>100)\n",
    "lim150 = np.nonzero(pops>150)\n",
    "lim200 = np.nonzero(pops>200)\n",
    "np.shape(lim100)\n",
    "print('Marca de 100 milhões de pessoas: ' + str(anos[lim100[0][0]]))\n",
    "print('Marca de 150 milhões de pessoas: ' + str(anos[lim150[0][0]]))\n",
    "print('Marca de 200 milhões de pessoas: ' + str(anos[lim200[0][0]]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 1.7924185769967504\n",
      "Coeficiente de ajuste p[1]: -3420.8153029001523\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7fc47246b410>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotagem por faixas de valores \n",
    "fig,ax = plt.subplots(1,1)\n",
    "p = resolve_ajuste(ano,hab,1)\n",
    "ax.grid(axis='x')\n",
    "v1 = np.ones(np.shape(ano))\n",
    "ax.fill_between(ano,100*v1,150*v1,alpha=0.1)\n",
    "ax.fill_between(ano,150*v1,200*v1,facecolor='r',alpha=0.1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AJUSTE POR PARÁBOLA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 0.01418349430843006\n",
      "Coeficiente de ajuste p[1]: -53.81354030390032\n",
      "Coeficiente de ajuste p[2]: 51061.1779002923\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "249.95013340016885"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# plotagem\n",
    "fig,ax = plt.subplots(1,1)\n",
    "p = resolve_ajuste(ano,hab,2)\n",
    "ax.grid(axis='x')\n",
    "\n",
    "# plotagem do comportamento preditivo\n",
    "\n",
    "# linha tracejada e area  \n",
    "ano_m = np.linspace(2016, 2025, num=10, endpoint=True)\n",
    "v2 = np.ones(np.shape(ano_m))\n",
    "ax.fill_between(ano_m,200*v2,260*v2,facecolor='g',alpha=0.2)\n",
    "plt.plot(ano_m,p(ano_m),':')\n",
    "plt.plot(2025,p(2025),'go')\n",
    "\n",
    "# estimativa no ano 2025\n",
    "p(2025)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Marca de 100 milhões de pessoas: 1974\n",
      "Marca de 150 milhões de pessoas: 1994\n",
      "Marca de 200 milhões de pessoas: 2011\n"
     ]
    }
   ],
   "source": [
    "# abrindo vetor de 1900 a 2024\n",
    "anos = np.arange(ano[0],ano[-1]+10)\n",
    "pops = p(anos) # população\n",
    "\n",
    "# encontrando ano em que a populacao superou 100 mi\n",
    "lim100 = np.nonzero(pops>100)\n",
    "lim150 = np.nonzero(pops>150)\n",
    "lim200 = np.nonzero(pops>200)\n",
    "np.shape(lim100)\n",
    "print('Marca de 100 milhões de pessoas: ' + str(anos[lim100[0][0]]))\n",
    "print('Marca de 150 milhões de pessoas: ' + str(anos[lim150[0][0]]))\n",
    "print('Marca de 200 milhões de pessoas: ' + str(anos[lim200[0][0]]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente de ajuste p[0]: 0.01418349430843006\n",
      "Coeficiente de ajuste p[1]: -53.81354030390032\n",
      "Coeficiente de ajuste p[2]: 51061.1779002923\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7fc471ff9310>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotagem por faixas de valores \n",
    "fig,ax = plt.subplots(1,1)\n",
    "p = resolve_ajuste(ano,hab,2)\n",
    "ax.grid(axis='x')\n",
    "v1 = np.ones(np.shape(ano))\n",
    "ax.fill_between(ano,100*v1,150*v1,alpha=0.1)\n",
    "ax.fill_between(ano,150*v1,200*v1,facecolor='r',alpha=0.1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integração Numérica"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Função-base para integrais de Newton-Cotes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def integral_newton_cotes(x,y,metodo):\n",
    "\n",
    "    # diff computa h = x[k+1] - x[k]; \n",
    "    # duplo diff retorna 0 se igualmente espaçado\n",
    "    h = np.diff(x)\n",
    "    hh = np.diff(h) \n",
    "\n",
    "    # verifica se vetor é, de fato, de zeros, dentro de tolerância\n",
    "    # se não, lança erro\n",
    "    np.testing.assert_allclose(hh, 0*hh, atol=1e-08)\n",
    "\n",
    "    # switch    \n",
    "    if metodo is 'trapezio':\n",
    "    \n",
    "        # montando vetor de somas y[k] + y[k+1]    \n",
    "        cs = np.cumsum(y)\n",
    "        u = np.concatenate((np.array([0]),cs[0:-2]))\n",
    "        ss = cs[1:]-u # somas \n",
    "\n",
    "        # integral (regra generalizada)\n",
    "        integral = h[0]/2*np.sum(ss)\n",
    "        \n",
    "    elif metodo is 'simpson13': \n",
    "        \n",
    "        if np.size(x) % 2 is 0:\n",
    "            raise ValueError('Regra de Simpson válida apenas para número ímpar de pontos.')    \n",
    "    \n",
    "        # constroi pesos \n",
    "        \n",
    "        # ignora primeiro e ultimo\n",
    "        ie = np.array(range(0,np.size(x)))\n",
    "        ie = ie[1:-1] % 2\n",
    "\n",
    "        # pesos para intermediarios\n",
    "        for v in range(np.size(ie)):\n",
    "            if ie[v] == 1:\n",
    "                ie[v] = 4\n",
    "            elif ie[v] == 0:\n",
    "                ie[v] = 1            \n",
    "    \n",
    "        # concatena para recriar \n",
    "        ie = np.concatenate(([1],ie,[1]))        \n",
    "        \n",
    "        # integral (regra generalizada)\n",
    "        integral = h[0]/3*(np.sum(y*ie))\n",
    "        \n",
    "            \n",
    "    return integral \n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemplo \n",
    "\n",
    "Integração numérica pela regra do trapézio para a função \n",
    "$$\\int_{a=0}^{b=\\pi} [ {\\rm sen}(3x + 2) + 0.5\\pi ] \\, dx \\approx I_T $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.799420241706493"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# função\n",
    "a = 0\n",
    "b = np.pi\n",
    "x = np.linspace(a,b,num=5,endpoint=True)\n",
    "f = lambda x: np.sin(3*x + 2) + np.pi/2\n",
    "y = f(x)\n",
    "\n",
    "# integração por trapézio\n",
    "integral_newton_cotes(x,y,'trapezio')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotagem dos trapézios\n",
    "plt.stem(x,y,'-ok',basefmt='k-',use_line_collection=True)\n",
    "plt.plot(x,y,'-k',label='$I_T$')\n",
    "plt.fill_between(x,0*y,y,facecolor='r',alpha=0.1)\n",
    "\n",
    "# \"imitação\" da função contínua\n",
    "xx = np.linspace(a,b,num=200,endpoint=True)\n",
    "plt.plot(xx,f(xx),color=[0.5,0.5,0.5],label='$f(x)$')\n",
    "plt.legend();"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemplo \n",
    "\n",
    "Idem, para regra 1/3 de Simpson $I_S$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.016218444253924"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# integração por 1/3 Simpson \n",
    "\n",
    "integral_newton_cotes(x,y,'simpson13')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Função residente em Python para integração"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.integrate as sp"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemplo\n",
    "Mesma função $f(x)$, agora calculada com o Scipy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.657370976179917, 1.5031433917569477e-13)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy::quad (erro absoluto)\n",
    "integral_ = sp.quad(f,a,b)\n",
    "integral_"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.32146250000000026\n",
      "0.2857383333333336\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.32148536841925296, 3.569204580991558e-15)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dados\n",
    "x = np.array([1.00, 1.05, 1.10, 1.15, 1.20, 1.25, 1.30])\n",
    "y = np.array([1.0000, 1.0247, 1.0488, 1.0723, 1.0954, 1.1180, 1.1401])\n",
    "\n",
    "# integral implementada: trapézio\n",
    "print(integral_newton_cotes(x,y,'trapezio'))\n",
    "\n",
    "# integral implementada: 1/3 Simpson\n",
    "print(integral_newton_cotes(x,y,'simpson13'))\n",
    "\n",
    "# integral scipy: 1/3 Simpson\n",
    "\n",
    "f = lambda x: np.sqrt(x) \n",
    "sp.quad(f,x[0],x[-1])\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8404750000000001\n",
      "0.7270900000000001\n",
      "(0.8414709848078965, 9.34220461887732e-15)\n",
      "0.83843\n",
      "0.6557999999999999\n",
      "(0.8414709848078965, 9.34220461887732e-15)\n"
     ]
    }
   ],
   "source": [
    "# caso h = 0.1\n",
    "x = np.array([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0])\n",
    "y = np.array([1, 0.995, 0.980, 0.955, 0.921, 0.877, 0.825, 0.764, 0.696, 0.6216, 0.5403])\n",
    "\n",
    "print(integral_newton_cotes(x,y,'trapezio'))\n",
    "\n",
    "# integral implementada: 1/3 Simpson\n",
    "print(integral_newton_cotes(x,y,'simpson13'))\n",
    "\n",
    "# residente\n",
    "f = lambda x: np.cos(x) \n",
    "print(sp.quad(f,x[0],x[-1]))\n",
    "\n",
    "\n",
    "# caso h = 0.2\n",
    "x2 = np.concatenate((x[0:-1:2],[1]))\n",
    "y2 = np.concatenate((y[0:-1:2],[0.5403]))\n",
    "\n",
    "print(integral_newton_cotes(x2,y2,'trapezio')) # TODO <=== CHECAR ISTO AQUI!\n",
    "\n",
    "# integral implementada: 1/3 Simpson\n",
    "print(integral_newton_cotes(x2[0:-1],y2[0:-1],'simpson13'))\n",
    "\n",
    "# residente \n",
    "print(sp.quad(f,x2[0],x2[-1]))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.39123050000000037\n",
      "0.35870866666666695\n",
      "(0.3915572767779624, 4.34715904138419e-15)\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1.2, 1.3, 1.4, 1.5, 1.6])\n",
    "y = np.array([0.93204, 0.96356, 0.98545, 0.99749, 0.99957])\n",
    "\n",
    "print(integral_newton_cotes(x,y,'trapezio'))\n",
    "\n",
    "# integral implementada: 1/3 Simpson\n",
    "print(integral_newton_cotes(x,y,'simpson13'))\n",
    "\n",
    "# residente\n",
    "f = lambda x: np.sin(x) \n",
    "\n",
    "print(sp.quad(f,x[0],x[-1]))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao L5-Q17 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0523917901871935\n",
      "3.0476097824918496\n"
     ]
    }
   ],
   "source": [
    "z = np.linspace(0,10,num=50,endpoint=True)\n",
    "f = lambda z: z/(4+z)*np.exp(-0.5*z)\n",
    "\n",
    "d = integral_newton_cotes(z,z*f(z),'trapezio')/integral_newton_cotes(z,f(z),'trapezio')\n",
    "print(d)\n",
    "\n",
    "# residente\n",
    "f2 = lambda z: ( z/(4+z)*np.exp(-0.5*z) )*z\n",
    "print(sp.quad(f2,0,10)[0]/sp.quad(f,0,10)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotagem da força\n",
    "plt.plot(f(z),z,label='$f(z)$')\n",
    "plt.plot(f(z),np.ones(np.shape(f(z)))*d,'--',label='$d$')\n",
    "plt.legend();"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### QUADRATURA GAUSSIANA\n",
    "\n",
    "Algumas informações:\n",
    "\n",
    "- A quadratura gaussiana pode ser chamada como \n",
    "\n",
    "```python\n",
    "from scipy.integrate import quadrature\n",
    "```\n",
    "Depois de importar, veja \n",
    "\n",
    "```python              \n",
    "help(quadrature)\n",
    "```\n",
    "\n",
    "- A tabela de pesos de quadratura pode ser acessada no Numpy através do comando \n",
    "\n",
    "```python\n",
    "np.polynomial.legendre.leggauss(ord)\n",
    "```\n",
    "Integra exatamente polinômios de grau até \n",
    "\n",
    "```python\n",
    "2*ord - 1\n",
    "```"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q18a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.6666666666666665, 0.0)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.integrate import quadrature\n",
    "\n",
    "# integração\n",
    "f = lambda z: z**3 + z**2 + z + 1\n",
    "quadrature(f, -1, 1,maxiter=3) # grau máximo = 3; erro = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6666666666666665"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verificando computação numérica x simbólica com Sympy\n",
    "import sympy as sy\n",
    "\n",
    "# cria símbolo para z\n",
    "zsym = sy.Symbol('z') \n",
    "\n",
    "# integração\n",
    "f = zsym**3 + zsym**2 + zsym + 1\n",
    "val = sy.integrate(f, (zsym,-1,1))\n",
    "float(val)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q18b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.666666666666667, 2.220446049250313e-16)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# integração\n",
    "f = lambda x: x**2 -1\n",
    "quadrature(f, -2, 0,maxiter=3) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6666666666666666"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# integração simbólica\n",
    "f = zsym**2 + -1\n",
    "val = sy.integrate(f, (zsym,-2,0))\n",
    "float(val)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exemplos de integrandos com singularidades \n",
    "\n",
    "Esses casos não são bem manipulados pelo submódulo `integrate`."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q18c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gustavo/anaconda3/lib/python3.7/site-packages/scipy/integrate/quadrature.py:251: AccuracyWarning: maxiter (50) exceeded. Latest difference = 6.973792e-04\n",
      "  AccuracyWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(1.1436022273829545, 0.0006973792417572788)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# função com singularidade\n",
    "\n",
    "# integração\n",
    "f = lambda x: ((1-x**2)**(-1/2))*x**2*x**2\n",
    "quadrature(f, -1, 1) "
   ]
  },
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   "metadata": {},
   "source": [
    "### solucao-L5-Q18d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/gustavo/anaconda3/lib/python3.7/site-packages/scipy/integrate/quadrature.py:251: AccuracyWarning: maxiter (3) exceeded. Latest difference = 1.333333e+00\n",
      "  AccuracyWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(3.3333333333333357, 1.333333333333336)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# função com singularidade \n",
    "\n",
    "# integração\n",
    "f = lambda x: (x**3 +2*x**2)/(4*(4-x**2)**1/2)\n",
    "quadrature(f, -2, 2,maxiter=3) "
   ]
  }
 ],
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    "author": "Gustavo P. Oliveira e Smith Lima",
    "email": "gustavo.oliveira@ci.ufpb.br",
    "institution": "Universidade Federal da Paraíba",
    "subtitle": "Soluções - Lista 05",
    "tagline": "Em preparação.",
    "title": "Cálculo Numérico"
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