lista-5-solucoes.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "init_cell": true,
    "ipub": {
     "ignore": true
    }
   },
   "outputs": [],
   "source": [
    "# ipypublish\n",
    "from ipypublish.scripts.ipynb_latex_setup import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# impressão de gráficos inline \n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tópico: Ajuste de Curvas \n",
    "\n",
    "## Descrição \n",
    "\n",
    "Notebook desenvolvido para suporte ao curso de Cálculo Numérico. Solucionário matemático e computacional de exemplo e da Lista de Exercícios 5.\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",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# importação de módulos\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemplo: solução fechada 2D "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fceb8fba610>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# 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:')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resolução da Lista 5"
   ]
  },
  {
   "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"
   ]
  },
  {
   "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 $ax^2 + bx + c$; "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "#### Metodologia matemática"
   ]
  },
  {
   "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",
    "$$f(x) = 0.1749x + 0.2167$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) \n",
    "\n",
    "$$g_1(x) = x²$$$$ g_2(x)=x$$$$ g_3(x)=1$$ \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",
    "$$f(x) = 0.01547 + 0.07738x + 0.4071x^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Metodologia computacional"
   ]
  },
  {
   "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]: 0.21666666666666667\n",
      "Coeficiente de ajuste p[1]: 0.1749999999999997\n"
     ]
    },
    {
     "data": {
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\n",
      "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)"
   ]
  },
  {
   "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]: 0.015476190476190473\n",
      "Coeficiente de ajuste p[1]: 0.07738095238095231\n",
      "Coeficiente de ajuste p[2]: 0.4071428571428572\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": [
    "# grau 2\n",
    "g = 2\n",
    "p = resolve_ajuste(x,y,g)"
   ]
  },
  {
   "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}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "#### Metodologia matemática\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$g_1(x) = 1$$$$ g_2(x)=x$$$$ g_3(x)=x²$$ $$ g_4(x)=x³$$\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",
    "$$f(x) = 0.5813  - 4.3250x + 12.79x^2 - 8.1043x^3$$"
   ]
  },
  {
   "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]: 0.5888082299746916\n",
      "Coeficiente de ajuste p[1]: -4.365386461549383\n",
      "Coeficiente de ajuste p[2]: 12.851592009434105\n",
      "Coeficiente de ajuste p[3]: -8.131256481519875\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.040251260748211545"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# 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)"
   ]
  },
  {
   "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}"
   ]
  },
  {
   "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",
    "$$f(x) = 0.5276x - 20.0832$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Metodologia computacional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fceb95f3450>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "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)"
   ]
  },
  {
   "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]: -20.078037383177602\n"
     ]
    },
    {
     "data": {
      "image/png": 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qglRuf+89TAVbJIrOwDPspqG9ad+mOQaaSisVj/6qfvG+crUuCxRJgQp4hmkqrRQtne4V7gXPRmLDX/AKd0lZcHmJ5BFVlyzIp6m0Fq1Yy8hHZnPHKX3p2alt9ne4tQauibtue6/D4dRJ2d+3SIFptICb2d7AY1Gh7sBo4EE/3g1YDAxzzn2d+RQlW+puOvq8eiPDJ8zglYsGZPcTg4Z5FcmoRrtQnHMLnXN9nHN9gAOB9cBTwOXAFOdcD2CKvyx5JGc3HU0ZW794X75ExVukidLtAx8EfOyc+ww4FpjoxycCx2UyMcmunNx09NWnXuF+8y+R2JDxXuFu2cgNOiLSqHQ/L58E/NN/3sk5txzAObfczDomeoGZjQBGAHTt2nVb85QMa+imo2H9mnjZo3NwdbvYWJtOcMmiprUrIjFSPgM3s+bAMcDj6ezAOTfeOVfhnKvo0KFDuvlJlmTtpqPru9Yv3mOqVbxFsiCdLpSjgNnOuRX+8goz2wXAf1yZ6eQke4b168LAfTrSotR7CzT5pqM5D3vdJZui+rUveE/93CJZlE4BP5lI9wnAM8Dp/vPTgaczlZTkRkZuOtrwtVe4n/5tJHboH73C3U5dZiLZlFIfuJm1Bg4HzokK3wBUmtlZwBLgxMynJ9lUd9NR3XXgaV9CqMsCRQJlziWYmipLKioq3MyZM3O2P8mSiYPh0zdiY6O/gmYlibcXkSYxs1nOuYr4uG6ll9R9MtU7644u3mf/2zvrzlHx1nR1IhEq4NK4ms1e4X7wmEhsv+O9wr3bgTlLQ9PVicTSWCjSsBD1cye6c/SOU/oGkotIGOgMXBJ74bL6xfuKzwMr3pquTqQ+nYFLrFWL4M5+sbFfPgz7HB1MPr6s3jkqkqdUwItZVaU30FT1Mm9y4Oq4s9n2PWHkjGByi3PZkb246pn3Y4q4pquTYqcCXqyqKmHyKNiywVuOL94hu55b09WJ1Kc+8GI1ZWykeEdru2voincdTVcnEksFvBht/Kb+GXedtctzm0saNF2dSCz9BhSbRJcFRivvnJs8tlE+TVcnkm06Ay8Wr1xVv3iXtaq/PGh07nISkSbRGXih+/xdGB93xnrBPGjXpf5VKINGQ+9hweQpImlTAS9UNZvh2rgJNI7+K1QMjyz3HqaCLZLHVMAL0V97w5rPIss7dodRc4LLR0SyQgW8kMy4D567ODZ25WooKQsmHxHJKhXwQvD1Z/C3uGuiz30Ldt4/mHxEJCdUwPNZotnfD7kEBl0ZTD4iklMq4PnqoePh4ymxsZDeQSki2aECnm8WPAePnhIbu3wptNw+mHxEJDAq4Pli/Vdw4x6xsdOegj0HBpOPiAROBTwfxN9Buf+JcMJ9weQiIqGhAh5mz10CM+6NjV21BsyCyUdEQkUFPIyWTof7D4+NXbwQ2u4cTD4iEkoq4GGyZSNc1yk2dtzd0OfkYPIRkVBTAQ+LcXvAhq8iy7scAOe8EVw+IhJ6KuBB++/t8PKfY2NXfgkl+q8RkYapSgRl9Udwx4Gxsd9Nhw57B5OPiOQdFfBcq90KY3eMjQ28EgZcEkw+IpK3VMBz6e9HwpK3I8ulLeHPK4LLR0Tymgp4Lsx7AiadGRu7Yjk0bx1MPiJSEFTAM+3Zi2DWA+C2gpV4j9GGvwC79w8kNREpLCrgmfTsRTDz/shydPHu+2s45vbc5yQiBUuz0mfSrAcSx61ExVtEMk4FPFO+/qx+d0mdZHERkSZQF0pT1WyG+w+D5XOTb2MluctHRIqGzsCb4vVxcG2HSPHe/ZDE2x14Rs5SEpHioTPwbbH4LXjgF5Hl/YbA0AneMK/xV6EceAYcfUtQmYpIAVMBT8e6VXDzXpHlkubeMK+to+6sPPoWFWwRyQkV8FTU1sI/fwkfvhyJnfUqdOkXXE4iUvRSKuBm1g64D/ge4IAzgZ8BZwOr/M2ucM49n40kAzXjPnju4sjy4WPhR78PLh8REV+qZ+B/A150zg01s+ZAa7wCfqtz7uasZRek5VVwT9SXkl37w+mTNcyriIRGo9XIzLYHBgBnADjnNgObrVDnZdz4DfztgNjJFS6aD9vvGlxOIiIJpHIZYXe8bpIJZjbHzO4zs+38dSPNrMrM/m5mOyR6sZmNMLOZZjZz1apViTYJB+fg6d/BDV0ixftXT8CYahVvEQmlVAp4KdAXuMs5933gW+By4C5gT6APsBz4S6IXO+fGO+cqnHMVHTp0yEzWmTbvSbi6Hcz5h7fc/3yvcPc4LNi8REQakEqH7jJgmXNumr88CbjcOffdQNZmdi/wbBbyy64vP4bb+0aWd9wTzvsPlLUKLicRkRQ1WsCdc1+Y2VIz29s5txAYBHxgZrs455b7mw0B5mUz0Yyq2QT3DIBVCyKxkTOhfY/gchIRSVOql1ScDzzsX4HyCTAcuM3M+uBdVrgYOCcrGWbalLHwZlRvzwn3w/5Dg8tHRGQbpVTAnXPvAhVx4dMyn04WffwaPHRcZPmAk+G4u7zb30VE8lDhX9S89gv4S9RM783bwkXvQ8vy4HISEcmAwi3gtVu9M+5P34jEzn4Nduub/DUiInmkMAv4O3fBi5dHlo8cBwefG1w+IiJZUFgF/H+z4N6BkeXuP4VTn4BmmlBBRApPYRTwDWvgln1hy7eR2MWLoG2n4HISEcmy/C7gzsETv4F5kyKxXz8N3Q8NKiMRkZzJ3wI+9zF4akRkecClMPDPweUjIpJj4S/gVZXezTfVy6C8Mxw0Al65MrK+434w4jUobRFcjiIiAQh3Aa+qhMmjYMsGb7l6aWzxHjUHduweTG4iIgEL96z0U8ZGine01jt5owWGtHgvWrGWI26dyqIVa4NORUQKWLgLePWyxPH1XyWOh8D6zTUMnzCdD1euY/iEGazfXBN0SiJSoMJdwMs7pxcPgUsnVbF63Wacg9XrNvGHSVVBpyQiBSrcBXzQ6Ppjc5e18uIhVDljKf+ev5JNNbUAbKqpZcr8lVTOWBpwZiJSiMJdwHsPg8G3QXkXwLzHwbd58RAa9+ICNmzZGhPbsGUr415ckOQVIiLbLtxXoYBXrENasONddmQvrnrm/Zgi3qqshMuP6hVgViJSqMJ9Bp5nhvXrwsB9OtKi1DusLUqbMWifjpxY0SXgzESkEKmAZ9hNQ3vTvk1zDGjfpgU3Du0ddEoiUqBUwDOsdfNSJgw/iB6d2jBheD9aNw9/L5WI5CdVlyzo2aktL1/4k6DTEJECpzNwEZE8pQIuIpKnVMBFRPKUCriISJ5SARcRyVMq4CIieUoFXEQkT6mAi4jkKRVwEZE8lRcFXFOUiYjUF/oCrinKREQSC30B1xRlIiKJhbqAa4oyEZHkQl3ANUWZiEhyoS7glx3Zi1ZlJTExTVEmIuIJdQHXFGUiIsmFuoCDpigTEUkm9AVcU5SJiCSWF9VQU5SJiNSX0hm4mbUzs0lmtsDM5pvZD81sRzN7xcw+9B93yHayIiISkWoXyt+AF51zvYADgPnA5cAU51wPYIq/LCIiOdJoATez7YEBwP0AzrnNzrk1wLHARH+zicBx2UpSRETqS+UMvDuwCphgZnPM7D4z2w7o5JxbDuA/dkz0YjMbYWYzzWzmqlWrMpa4iEixM+dcwxuYVQDvAD9yzk0zs78B3wDnO+faRW33tXOuwX5wM1sFfNb0tJukPbA64BxSlU+5Qn7lq1yzJ5/yzZdcd3fOdYgPpnIVyjJgmXNumr88Ca+/e4WZ7eKcW25muwArG2soUQK5ZmYznXMVQeeRinzKFfIrX+WaPfmUbz7lmkijXSjOuS+ApWa2tx8aBHwAPAOc7sdOB57OSoYiIpJQqteBnw88bGbNgU+A4XjFv9LMzgKWACdmJ0UREUkkpQLunHsXSPQxY1Bm08mJ8UEnkIZ8yhXyK1/lmj35lG8+5VpPo19iiohIOIV+LBQREUlMBVxEJE8VVAE3s7+b2UozmxcXP9/MFprZ+2Z2Y1T8j2b2kb/uZ2HO18y6mdkGM3vX/7k76FzN7LGofBab2btR60J3bJPlG9Jj28fM3vHzmWlmB/lxM7Pb/GNbZWZ9c5nrNuR7qJlVRx3b0SHI9QAze9vM3jOzyf7d5nXrAn3fps05VzA/eLf89wXmRcV+CrwKtPCXO/qP+wJzgRbAHsDHQEmI8+0WvV0Yjm3c+r8Ao8N8bBvIN3THFngZOMp//nPg9ajnLwAGHAxMC3m+hwLPhuzYzgB+4j8/E7jGfx74+zbdn4I6A3fOvQF8FRc+D7jBObfJ36buhqNjgUedc5ucc58CHwEH5SxZ0s43UElyBbyzQmAY8E8/FNZjCyTMN1BJcnVA3ZlhOfC5//xY4EHneQdo599IlzNp5huoJLnuDbzhP38FOMF/Hvj7Nl0FVcCT6AkcYmbTzGyqmfXz47sB0dPbL/NjQUuWL8Ae/ng0U83skKASTOAQYIVz7kN/OazHtk58vhC+Y3sBcJOZLQVuBv7ox8N6bJPlC/BDM5trZi+Y2X7BpBdjHnCM//xEoG6OxrAe26SKoYCXAjvgfdy8FO/mI8P7CBovDNdUJst3OdDVOfd94CLgkei+u4CdTOzZbFiPbZ34fMN4bM8DLnTOdQEuxB8NlPAe22T5zsYbx+MA4HbgXwHlF+1M4HdmNgtoC2z242E9tkkVQwFfBjzpf+ScDtTiDWCzjMhfXoDOhONjX8J8/Y91XwI452bh9c/1DDBPAMysFDgeeCwqHNZjmzDfkB7b04En/eePE/koH9ZjmzBf59w3zrl1/vPngTIzax9Mih7n3ALn3BHOuQPx/pB/7K8K67FNqhgK+L+AgQBm1hNojjf62DPASWbWwsz2AHoA0wPLMiJhvmbWwcxK/Hh3vHw/CSzLiMOABc65ZVGxsB5bSJBvSI/t50DdPIIDgbrunmeAX/tXoxwMVDt/WOeAJczXzHb2P0HiX5nSDPgykAx9ZtbRf2wG/Bmou+oozO/bxIL+FjWTP3h/TZcDW/D+mp6FVwD/gdfvNRsYGLX9n/D++i7E/wY9rPnifdHyPt635LOBwUHn6scfAM5NsH3ojm2yfMN4bIEfA7P8nKYBB/rbGnCnf2zfAyrCcGwbyHdk1LF9B+gfglx/Dyzyf27AvyM9DO/bdH90K72ISJ4qhi4UEZGCpAIuIpKnVMBFRPKUCriISJ5SARcRyVMq4CIieUoFPADRw5dGxZINLZtsmM5j/eFE6+I/TrKvZO0mG1r1oKj4XDMbkqTd68xsqZmtS7BumJl9YN5wuI9ExW/0Y/PNGxK13q3LZjbSH87TRd+xZ2bl/tCfc/02hmeo3aTDnZrZhX6788zsn2bWMkG7J/rb1JpZRdy63uYNW/q+eUOXtvTjL0b9O+6uu4ko7rUDzGy2mdWY2dC4deP8nOaZ2S+j4vf77VaZ2SQza5Og3V5+TpvM7JK4de381y3wj+UP/fg1Ue+1l81s1wTt7mRmr5nZOjO7IyreNurYvmtmq83sr/66rv5r5vjt/9yPH+K/f+bF70fiBH0hejH+kGD4UpIMf0ryYTrbEJkSrzfe3YWJ9tXgsKr+NtFDq7YGSv3nuwAr65bjXnOwv35dXLwHMAfYwV+uGw63P/AfoMT/eRs4NEG73/ePz2K8IQTq4lcA4/znHfBGmGuegXYPJcFwp3iDGH0KtPKXK4EzEmy3D97odq8TdVMN3pg2VcAB/vJO+EOTAtv7jwY8AZyU5D3SG3gQGBoV/wXeCHqlwHbAzKj2to/a7hbg8gTtdgT6AdcBl8Stmwj8xn/eHGiXoN1RwN0J2t0O72aec4E7GnivzQIG+M/HA+f5z/cFFjf0O6Kf+j+pzkovWeace8PMuiVaRYJhOp0/voRvO5IMutNAu0DM0KoD/e3XR61u2UC77/ivj191NnCnc+5rf7u64XCd315zvMJVBqxI0O6cJO06oK2fbxu8Al6TgXYbUgq0MrMteH/Y6o2L4Zybn6TdI4Aq59xcf7svo17zTVT7zUlwjJ1zi/12a+NW7QtMdc7VADVmNhc4Eqisa9c/Rq2StLsSWGlmv4iOmzd41wDgDH+7zfiDPEXlC0nea865b4G3zGyv+HVR++iB9wfkzbqXEcIhaPOJulDCL+kwnWY2xMwWAHBgCWcAAAQSSURBVM/hjbC2LeoNrWpmPzCz9/Fu1T7XLxap6gn0NLP/mNf1cySAc+5t4DW825qXAy/VFb8U3YF3tvu5n9fvnXO1GWgXEgx36pz7H97xXuK3W+2cezmNNnsCzsxe8rtC/hC90sxewvt0sxaYlEa7c4GjzKy13xX0U6IGYDKzCcAXQC+80f9S1R1YBUzwuzTuM7Ptotq9zn8P/grY1ll1TgYec/4pNjAGONXMlgHPA+dvY7tFSwU8/JIN04lz7innXC/gOOCabWw/fmhVnHPTnHP74X3U/mOivt8GlOJ1oxzqt32f37e6F14B7ozXPTHQzAak0e7PgHeBXYE+wB1mtn0G2k043KmZ7YA3wP8e/j63M7NT02i3FK9L4Vf+4xAzG1S30jn3M7wuqBb4n35S4f8ReR74L97/29t4n0Tq1g/3850P/DJRGw3k2xe4y3nD6n4LXB7V7p/89+DDeOObbIuTiH2vnQw84JzrjNc9+JB5A0xJinSwwi/ZsKLfcd6sI3tamsN0WuKhYKPbnY/3i/y9NJpdBjztnNvivFlNFuIV9CHAO865dX73zwt4/eipGk5kmN2P8PqnezW1XZd8uNPDgE+dc6ucc1vw/g/6p5HvMryujtV+t9TzeAUyet8b8UbAOzaNdnHOXeec6+OcOxyv2+jDuPVb8f5PT0j0+gbyXeacm+YvT4rP1/dImu0C3jyUeN+lzIoKn4X33ULdJ7SWeEM9S4pUwMMv2TCde/l9nZg3sW1z0h+mM9HQqnv4hR0z2x3vC7rFabT5L7yP9fiFsCfe0KxLgJ+YWamZlfn/pnS6OpYAg/x2O/l5NbldSz7c6RLgYL+rwvx9p5PvS0Bv//Wlfl4fmFkb86dA8+M/BxakkW+Jme3kP++N90Xny+bZy48bMDiddp1zXwBLzWxvPzQI+MBvr0fUpsek026Uep/0iP0/3QevgK/ahraLV9DfohbjD4mvQkk2/GmyYTovwxum8128j9E/TrKvhO366x6g/tCqp0W1Oxs4Lkm7N/rt1fqPY/y44V0B8QFeX/VJfrwEuAevCH4A3JKk3VF+ezV4f7zu8+O74l2R8x7eULunZqjdpMOdAlfjFat5wEP4E03HtTvEb3cT3penL0WtO9Vvex5wox/rhDepbpW/7nYSX+XTz2/3W7w/KO/78Zb+v/MDP98+frwZ3tU4dcfnYaKuHolqd2e/3W+ANf7zuqtY+uBd1VKF94e47kqiJ/w2q4DJwG5JjvFivC+X1/nt7hu17hOgV9z2+/o5z/Xfb0c09Duin/o/Gk42AP5VIc8659LpmhApGvodSY26UIKxFSi3qBt5RMRj3qTSk/FmzpIG6AxcRCRP6QxcRCRPqYCLiOQpFXARkTylAi4ikqf+P8CMjsbxC9f6AAAAAElFTkSuQmCC\n",
      "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q4-c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.24672897196261\n",
      "189.69619131975202\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"
   ]
  },
  {
   "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]: 1.5856741573033695\n",
      "Coeficiente de ajuste p[1]: 60.294943820224766\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": [
    "p2 = resolve_ajuste(peso,altura,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q4-e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.33835252435786\n",
      "0.091623552395248\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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### solucao-L5-Q4-f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fceb9923290>,\n",
       " <matplotlib.lines.Line2D at 0x7fceb9970a50>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# comparação das retas de ajuste\n",
    "# influência do resíduo => inclinações diferentes\n",
    "\n",
    "plt.plot(altura,p(altura),altura,(altura - p2[0])/p2[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## solucao-L5-Q5-a"
   ]
  },
  {
   "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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\n",
      "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 0x7fceb9b63490>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# 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)"
   ]
  },
  {
   "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]: 0.014183494308426046\n",
      "Coeficiente de ajuste p[1]: -53.81354030388454\n",
      "Coeficiente de ajuste p[2]: 51061.177900276765\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "249.95013340013247"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "\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]: 0.014183494308426046\n",
      "Coeficiente de ajuste p[1]: -53.81354030388454\n",
      "Coeficiente de ajuste p[2]: 51061.177900276765\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7fceb9b04450>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Integração Numérica"
   ]
  },
  {
   "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"
   ]
  },
  {
   "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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\n",
      "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();"
   ]
  },
  {
   "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')"
   ]
  },
  {
   "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"
   ]
  },
  {
   "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_"
   ]
  },
  {
   "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"
   ]
  },
  {
   "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]))"
   ]
  },
  {
   "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]))"
   ]
  },
  {
   "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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lKukVYwy3zszn7W/M4aZpeTzyzh4W/GIVSzeX6yCnSATzdRbKPwPPGGM2A1OA//a9JOmrjKQ4fvbpSfz1SxeRkRTL/c9u5I7HPmRXVX2oSxORADDB7KFNnz7drlu3Lmj7G8jc7ZZnP9zPz5eV0NTm5nMXj+DL80aTGh8T6tJEpJeMMeuttdO7Pq8zMSOUI8pw56wC3v7mXG6cOpQ/vLuHOT9fweNr9tLq0t1/RCKBAjzCDU6K44FPT2bpP8+mKDeFH766jSv+9x3e2Fqp8XGRMKcAHyCKclN5+u4LePyfZhAdZbj36fV89vcfsOmgzr0SCVcK8AHEGMO8wixe/+ol/PjGCeypqWfhb9Zw/7Mb2FOtA50i4UYHMQew+hYXv1u5m8dW76XF5eamaXl8Zf4Yhg1KCHVpItJJdwcxFeBCdV0Lv125m6c/3I+1ls/OGMb988aQneoMdWkiggJceqDieBMPvb2L59ce9MxiuXA4984dxeCkuFCXJjKgKcClxw4eaeRXy3eyZEMZzhgHi2cVcPfsEWQmK8hFQkEBLr22u7qe//3HTpZuLifWEcUtM4Zxz5xRDE2LD3VpIgOKAlz6bE91Pb9duZuXNh7CGLhx6lC+NHc0IwafdvVgEQkABbj47NCxJh5ZtZvn1h6kzd3ONZNy+fK8URRmp4S6NJGIpgAXv6mua+Gx1Xt5+oP91Le4WDAuiy9eMpKZIwZhjAl1eSIRRwEufne8sY0n3t/H42v2crSxjYlDU/nCJSO4emIOMQ6dIybiLwpwCZjmNjdLNhzi0dV72FPdQE6qk3+6qIBbZubr6ocifqAAl4Brb7esLK3i0Xf38t7uWhJiHXxm+jDunj1CZ3eK+EABLkFVXH6cx1bv5dWPy3G3Wy4fn81dFxVw4UiNk4v0lgJcQqLyeDNPvr+PZz86wLHGNsZkJXHnrOHcOHUoyU4Nr4j0hAJcQqq5zc2rH5fz1Af72Vx2nMRYBzdOG8riWQWcNyQ51OWJ9GsKcOk3Pj54jCff38+rm8tpdbVzwYhB3DlrOFcUZWv2isgZKMCl3znS0MoL6w7y9If7OXikiazkOG6ZMYybpw/TQU+RThTg0m+52y2rSqt48v39rCqtBmD26MF8dsYwPjV+CHHRjhBXKBJaCnAJC4eONfHCuoO8sK6MQ8eaSE+IYdG0PD47Y5jGymXAUoBLWHG3W1bvquEvaw/y5rZK2tyWaflp3DIjn2sm5ZAYFx3qEkWCRgEuYau2voWXNh7iubUH2VVVT2Ksg+sm53LT+XlMH56ueeUS8RTgEvastWw4cJTnPjrI0s0VNLW5yR+UwI1Th7Jo2lCGZ+jythKZFOASURpaXCwrrmTJhkOs2V2DtTB9eDo3ThvKtRNzSU3QSUISORTgErEqjjfxt43lLNlQxs6qemIdUSwYn8WiqXnMGZupueUS9hTgEvGstWw9dIIlG8t4ZVM5tQ2tDEqM5frJuVw/JZepw9I0Xi5hSQEuA0qbu513SqtZsuEQb20/TKurnbz0eK6bnMv1k3MpzE5WmEvYUIDLgHWiuY03iw/z6sflrN5Vg7vdMjoriesn53Ld5Fzd21P6PQW4CJ4pia9vreSVj8v5aO8RACYOTeW6yTlcOymX3LT4EFcocrqABbgxxgGsAw5Za68927oKcOlPKo438drmCl75uJzNZccBmFkwiGsn53BlUTZZKc4QVyjiEcgA/xdgOpCiAJdwta+mgVc/LueVj8vZWVWPMTBj+CCumpjNlROyyUlVz1xCJyABbozJA54Afgz8iwJcIsHOw3X8fUslr2+tYEdlHQDT8tO4emIOV07IJi9dV0qU4ApUgL8I/ARIBr55pgA3xtwD3AOQn59//v79+/u8P5Fg211dzxtbK/n7lgqKy08AMDkvlasm5nDVhGyd/SlB4fcAN8ZcC1xtrb3PGDOXbgK8M/XAJZztr23g9a2VvL61ko8PHgOgKDeFqyZkc0VRNqOzkjQ1UQIiEAH+E+BOwAU4gRRgibX2ju62UYBLpCg72sgb3jBfv/8oACMGJ3L5+CFcXjSEqcPSiYpSmIt/BHQaoXrgMpAdPtHMW9sO8+a2w7y/u4Y2t2VwUhyf8ob5RaMydFMK8Ul3Aa6LKov4aEiKkzsuHM4dFw7nRHMbK0uqWVZcySubDvHnjw6QGOtgbmEWl48fwrzCLFKcutCW+IdO5BEJkBaXm/d21/Jm8WHe2naYmvoWYhyGC0dmcHlRNvMLs3TikPSIzsQUCaH2dsvGg8d4s7iSZcWV7KttBGB8TgoLxmUxf9wQJg5N1bi5nJECXKSfsNayu7qef2yvYvn2w6zff5R2C5nJccwv9IT5xaMzSIjVCKd4KMBF+qmjDa2sKKli+Y4q3imppq7FRVx0FBeNymD+uCHMH5elM0EHOAW4SBhodbWzdt8R/rH9MMu3V3HgiGeopSg3xRPmhVkaahmAFOAiYcZay66qT4ZaNhzwDLUMToplznlZzCvM5JIxmaTGa1ZLpFOAi4S5Iw2tvFNazYqSKlaVVnOssQ1HlOH84elcVpjFvLFZnDdEZ4NGIgW4SARxudvZdPAYK0qqeHtHNdsrPNdpGZoWz9yxmVxWmMWsUToQGikU4CIRrPJ4MytKqlixo4rVu2pobHUTGx3FrJEZzBubydyxWRTozkNhSwEuMkC0uNys3XuUt3dUsbKkij01DQAUZCQwd2wWc8ZmMmtkBs4Ynd4fLhTgIgPUvpoGVpZUsbK0mvd319LiaicuOooLR2Yw19s7131B+zcFuIjQ3Obmgz21rCypZlVpNXu9vfPhGQnMPc8T5heOzCA+Vr3z/kQBLiKn2V/bwKrSalaWVPPe7hqa2zy98wtGZngDPZMRgxM1syXEwv9qhI9fc/pzRQth5hehtRGeufmT5/evhuGzYcptsGclVG6B6u2nbjt8Nsz4PBS/5Gk/uu/09ovuh7WPetrrD5/efuk34Z3/8bS3HO++/eCH0N7Wffv+1af/bMNnw5xvwaqf9729u9ePioFhF3TfHpcK2RO7b08a4mmf8QV476HT29MLPO1FN8LaP57enjnO0z5yLmx69vT23Gme9uyJUPy309uHz/a0peRC6bIztw+bATEJsGfVmdtHzoG2Rji49szt510BJ8o9/7Znai9a6Gmr3ALlG05vD5PP3vD9q1kMLAZweL72JU3l/6pvZPy+PzPyH11qP7m9Pnu9++yNnAuLXz79vfJRlN9fUUTCWkFGIr+4eTJThqWdsX1bxQmWbi6nsc0V5MqkKw2hiMg5tbjcrN93lJWl1awqqabksOdmz7mpTuaMzWTOeZlcPHowybrWeUBoDFxE/Kb8WBPvlHoOhK7eWUNdi4voKMO04enM8Y6dj89J0di5nyjARSQg2tztbDxwjJXeU/yLyz1nhWYlx3nDPIvZYwbrmi0+UICLSFBU1TWzqqSalaXVvFtazYlmF44ow7T8NOaOzVLvvA8U4CISdCev2bKypJqVpVVsPaTeeV8owEUk5KrqmnmntIYVJVXqnfeCAlxE+pXueufZKU7mFWYxvzCLi0cP1lmhKMBFpJ87OXb+9o4q3imtpqHVTVx0FLNGZTC/MIt5hVnkpSeEusyQUICLSNg4eWu55dureHvHYfbVem4tN3ZIMpeNy+KywiymDksj2jEwzkVUgItI2NpTXc/bO6pYvr2KtfuO4Gq3pCXEMOc8z80r5o7NiugDoQpwEYkIJ5rbeLe0huU7DrOypJojDa1ERxlmjcrgiqJsLh8/hKwUZ6jL9CsFuIhEHHe7ZdPBY7y5rZI3iw+zt6YBY2DqsDSuKMrmiqLsiLgTkQJcRCKatZadVfUs21rJsm2VHbNaxg5J5oqiIVxelE1RbnhOUVSAi8iAUna0kTeLD7OsuJK1+47QbiEvPZ7Lx2dz5YRspg9PJyoqPMJcAS4iA1ZtfQvLt1fxRnElq3fW0OpuJzfVyfVThrJwai6F2SmhLvGsFOAiIkB9i4vl2w/z8qZyVpVW4263FGYnc+PUoVw/JZec1PhQl3gavwe4MWYY8CSQDbQDj1hrf3W2bRTgItKf1Na38NqWCl7aeIiNB45hDFw4IoMbpw7lyonZpPST65sHIsBzgBxr7QZjTDKwHlhord3W3TYKcBHpr/bVNPC3TYd4eVM5e2saiI2OYsG4LBZOGcq8wixiQnjSUMCHUIwxLwMPWWvf6m4dBbiI9HfWWj4uO87fNh7i1Y/LqW1oJTvFyV0XFXDbzHxSE4LfKw9ogBtjCoB3gAnW2hNd2u4B7gHIz88/f//+/T7vT0QkGNrc7awqqebx9/ayZlct8TEOPjM9j89dPCKo88sDFuDGmCRgFfBja+2Ss62rHriIhKtt5Sf445q9vLzpEK52y4JxQ/jC7BHMHDEo4HPLAxLgxpgYYCmwzFr74LnWV4CLSLirOtHMUx/s5+kP9nO0sY2JQ1O5e/YIrpmUE7Bx8kAcxDTAE8ARa+3XerKNAlxEIkVTq5uXNh7isdV72F3dwLicFB78zGTG5fh/Tnl3Ae7LfxcXA3cClxljNnm/rvbh9UREwkZ8rIPbLsjnra/P4be3T6O6roXrH1rNb1bswuVuD0oN0X3d0Fq7GgiP81BFRAIkKspw1cQcLhyZwb+/vJWfLyvhzW2H+cXNkxmdlRTYfQf01UVEBoj0xFgeum0a/3frVPbXNnDNr9/l0Xf30N4euLPdFeAiIn503eRc3vz6pVwyJpMfvbadh1bsCti+FOAiIn6WlezkD4vPZ97YTJ76YD9tARoTV4CLiASAMYY7Zw2nuq6Ft7YdDsg+FOAiIgEy57wshqbF88yHgTkDXQEuIhIgUQYmD0tlza5aautb/P/6fn9FERHBWssDy0r4+5ZKbpqWx6DEWL/vo8/zwEVE5MystfzX0u38cc1ebrsgnx/dMCEg10tRgIuI+FF7u+XfX97KMx8e4HMXF/D/rh0fsItdKcBFRPxgV1U9SzeXs3RzBbuq6rl3zii+feXYgF6pUAEuItJH+2oaOkJ7R2UdxsCMgkH84ubJLJo2NOCXmVWAi4j0wsEjjby2pYKlm8vZeshz/5rzh6fzg+vGc/XEHIakOINWiwJcROQcKo438drmCpZurmDTwWMATM5L5XtXj+PqSTkMTQvNnewV4CIiXu3tlrKjTWyrOMF279eOyjoOHGkEoCg3hW9fWci1k3IYNighxNUqwEVkgGpsdbGjsq4jqLdX1FFSWUd9iwsAY2DE4EQmDk3l1pn5XFE0hJGZgb08bG8pwEUkollrOXSsie0VncP6BPuPNHLyhmTJcdGMy0lh0bShjMtJYVxOCmOHJBMf6wht8eegABeRiNHc5qakS696e+UJ6ppdHesUZCRQmJ3CjVPzGJeTzLicFPLS4wM+YyQQFOAiEhastdTUt1JxvInyY83e702UH2+m4lgTFcebOXyimZP3T0iMdVCYk8L1k3M7etWF2ckkxkVO7EXOTyIiYctay4lmFxXHm6g41ky5N5xPLlccb6biWDOtXa6rHRcdRW5aPDmpTi4aNZi89PiOXvWw9ASiosKvV90bCnARCbjmNrcnkI83c8gbzBXHP+k9lx9roqHVfco2jihDdoqTnFQnk/LSuLLIs5ybFt8R2oMSY8Ny6MNfFOAi4pM2dzuHTzRTcbzZM6TRMbzxyTDH0ca207YbnBRLblo8IzMTuXj0YHLTnN5gjic3zUlWshNHhPegfaUAF5EOJ4cyjjW2cqShlaONrRxtaONox+M2jja0cqSx1btOG0caWuh6395kZzS53iCePCyN3FSnN5g9zw1JceKM6d8zPMKBAlwkQp0M46Mng9gbuF3D+Uhjq3cdT5urm7uoO6IM6QkxpCfEkp4Yy4jBiZw/PJbMpDhyvEMaQ9PiyUmLJymCDhT2Z3qXRcJA5zDu3Ps9NZw/6SEfbWzlWGPbOcI41hPIibGMykwiPdETzoMSY0lLiGWQ9/HJwE5xRg/o8eb+SAEuEmTt7Za6ZpcndDv1fk8N50+GLjxfbbi7CePoKHNK4HrC+NQA9oRyDIMSPWGcHKcwjgQKcJEestbS2OqmocVFXYuL+mYX9S0u6ppdNLR4lk8+rm9po6HF3bFc712/rq6t+DMAAAfVSURBVNnFsaazh3F6YiyDEjyBOzor6bTe8MkQPtl7VhgPXApwiXitrvaOgK1rPhm0bdS3uL0h3OYJ1xbX6et5w/lkWze5e4oYhyHZGUNSXHTHV1ayk5GDo0lyRneE8ydB7Ans9ETPNgpj6SkFuPRL7e2WxrZPAtbTy3V3LJ8M1/rWT3rCXUP45ONWV/s592cMJMV6AjbRG7rJzmiyU5wkxXmeS3Z6A9kZfUo4JzmjSY6L8W7rIC5asyskOBTg4lctLvcngdppmKHrUMMpPdzWUx/Xt3iesz3o7cZGR5HcJVSzU5yfPHZGkxx3aignecO2cwAnxDgi/qw9iTwK8AHE3W5pbnPT1OamqdV9ynJTW+fH7Z889rY1tblp7rR8yvZtbk/vuNl12qnOZ2IMnjCN+6THm+yMJjfN6Q3VGJLiHN6QjekmhD2PY6OjgvDOifRPCvB+wFpLi6v9lLDsNmBb3TS19TJgW900u9p7NJTQVZSB+BgH8bEOnDGOU5bTEmLJiXHgjInqCNvkTj3brsMOJ0M4IdahcV4RP/ApwI0xVwK/AhzAo9ban/qlqn7CWkub2/YyLE8N12bXmXq4bpq9IXyyrS+cMVGeQI1x4Ix1dCwnxUUzOCmu4/Gp4evZxul9vuv2HevFOHDGRhHriFLYivRTfQ5wY4wD+A3wKaAMWGuMecVau81fxZ2Nu91221NtanPT4sNwQFNre8fj7qZ7nU2sI8oTrp1D0buc4ow5JWw7h2tHIHfp7Z4pcOOiozRmKzLA+dIDnwnsstbuATDGPAfcAPg9wL/30hbW7Ko5pffak7HWrqIMJMRGe8OwU++103BAb3qrZwpYZ3QU0Q6Ny4pI4PkS4EOBg50elwEXdF3JGHMPcA9Afn5+n3aUmxbPpLy0Xg8HdF0/xmE0HCAiEcOXAD9TEp423mCtfQR4BGD69Om9H48AvjxvdF82ExGJaL78rV8GDOv0OA8o960cERHpKV8CfC0wxhgzwhgTC9wCvOKfskRE5Fz6PIRirXUZY+4HluGZRvhHa22x3yoTEZGz8mkeuLX278Df/VSLiIj0gua7iYiEKQW4iEiYUoCLiIQpBbiISJgyticXXfbXzoypBvb3cfPBQI0fywmmcK4dwrt+1R4a4Vw79L/6h1trM7s+GdQA94UxZp21dnqo6+iLcK4dwrt+1R4a4Vw7hE/9GkIREQlTCnARkTAVTgH+SKgL8EE41w7hXb9qD41wrh3CpP6wGQMXEZFThVMPXEREOlGAi4iEqX4R4MaYK40xJcaYXcaY75yhPc4Y87y3/UNjTEGntu96ny8xxlwRzLq9++9T7caYTxlj1htjtni/XxYutXdqzzfG1Btjvhmsmjvt25fPzCRjzPvGmGLv++8MZu3eGvr6uYkxxjzhrXu7Mea7/bD2S40xG4wxLmPMp7u03WWM2en9uit4VXfsv0+1G2OmdPrMbDbGfDa4lXfDWhvSLzyXot0NjARigY+B8V3WuQ/4nXf5FuB57/J47/pxwAjv6zjCpPapQK53eQJwKFze907tfwVeAL4ZLrXjuQLnZmCy93FGMD8zfqj/NuA573ICsA8o6Ge1FwCTgCeBT3d6fhCwx/s93bucHia1nweM8S7nAhVAWjA/N2f66g898I6bI1trW4GTN0fu7AbgCe/yi8B847m55Q14Pswt1tq9wC7v6wVLn2u31m601p68g1Ex4DTGxAWlag9f3neMMQvx/AKG4hrwvtR+ObDZWvsxgLW21lrrDlLdJ/lSvwUSjTHRQDzQCpwITtlAD2q31u6z1m4Gut55/ArgLWvtEWvtUeAt4MpgFO3V59qttaXW2p3e5XKgCjjtzMhg6w8BfqabIw/tbh1rrQs4jqfn1JNtA8mX2ju7CdhorW0JUJ1n0ufajTGJwLeBHwahzjPx5X0/D7DGmGXeP5X/NQj1duVL/S8CDXh6gAeA/7HWHgl0wWeqy6s3v3Ph8Pt6TsaYmXh68Lv9VFef+XRDBz/pyc2Ru1unRzdWDiBfavc0GlME/AxPzzCYfKn9h8AvrbX13g55sPlSezQwG5gBNALLjTHrrbXL/VviWflS/0zAjefP+HTgXWPMP6y1e/xbYrd8+Z0Lh9/Xs7+AMTnAU8Bd1tquf2EEXX/ogffk5sgd63j/dEwFjvRw20DypXaMMXnAS8Bia22w/zf3pfYLgAeMMfuArwH/Zjy31wsWXz8zq6y1NdbaRjx3lJoW8Iq7qc2rN/XfBrxhrW2z1lYBa4BgXrPDl9+5cPh97ZYxJgV4Dfi+tfYDP9fWN6EehMfTI9qD5yDkyQMLRV3W+TKnHtD5i3e5iFMPYu4huAcxfak9zbv+TeH2vndZ5z8I/kFMX973dGADngOA0cA/gGvCqP5vA4/j6U0mAtuASf2p9k7r/onTD2Lu9f4bpHuXB4VJ7bHAcuBrwfysnPNnCnUB3jfnaqAUz5jS97zP/SdwvXfZiWe2wy7gI2Bkp22/592uBLgqXGoHvo9nLHNTp6+scKi9y2v8B0EOcD98Zu7Ac/B1K/BAsGv38XOT5H2+GE94f6sf1j4DT2+3AagFijtt+3nvz7QL+Fy41O79zLR1+X2dEorPTucvnUovIhKm+sMYuIiI9IECXEQkTCnARUTClAJcRCRMKcBFRMKUAlxEJEwpwEVEwtT/B9nWRD4AIlFCAAAAAElFTkSuQmCC\n",
      "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();"
   ]
  },
  {
   "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",
    "```"
   ]
  },
  {
   "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)"
   ]
  },
  {
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exemplos de integrandos com singularidades \n",
    "\n",
    "Esses casos não são bem manipulados pelo submódulo `integrate`."
   ]
  },
  {
   "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",
    "# integração\n",
    "f = lambda x: ((1-x**2)**(-1/2))*x**2*x**2\n",
    "quadrature(f, -1, 1) "
   ]
  },
  {
   "cell_type": "markdown",
   "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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