aula-17-ajusteNaoLinear.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ajuste de curvas: caso não-linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivação: comportamento de fluidos lei de potência"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gamma = np.linspace(0,1,20,True)\n",
    "n1 = 1.5 # dilatante\n",
    "n2 = 0.7 # pseudoplastico\n",
    "k = 0.1\n",
    "tau1 = k*gamma**n1\n",
    "tau2 = k*gamma**n2\n",
    "tau3 = k*gamma\n",
    "\n",
    "plt.plot(gamma,tau1,'o',label='dilatante')\n",
    "plt.plot(gamma,tau2,'o',label='pseudoplástico')\n",
    "plt.plot(gamma,tau3,'-o',label='newtoniano')\n",
    "plt.legend()\n",
    "plt.xlabel('$\\dot{\\gamma}$')\n",
    "plt.ylabel('$\\sigma}$')\n",
    "plt.grid(axis='x')\n",
    "plt.title('Dispersão: fluidos lei de potência')\n",
    "plt.tick_params(axis='both',which='both',labelbottom=False,labelleft=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemplo \n",
    "\n",
    "Determine os parâmetros $a$ e $b$ de modo que $y = f(x) = ae^{bx}$ ajuste os seguintes dados no sentido de mínimos quadrados: \n",
    "\n",
    "x|y\n",
    "---|---\n",
    "1.2|7.5\n",
    "2.8|16.1\n",
    "4.3|38.9\n",
    "5.4|67.0\n",
    "6.8|146.6\n",
    "7.9|266.2\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotando o gráfico de dispersão:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "x = np.array([1.2,2.8,4.3,5.4,6.8,7.9])\n",
    "y = np.array([7.5,16.1,38.9,67.0,146.6,266.2])\n",
    "plt.plot(x,y,'o');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Teste de alinhamento:** façamos a linearização \n",
    "\n",
    "$$Y = Z + bx,$$\n",
    "\n",
    "onde $Y = \\log(y)$ e $Z = \\log(a)$.\n",
    "\n",
    "Plotemos a dispersão $(x,Y)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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": [
    "Y = np.log(y)\n",
    "plt.plot(x,Y,'d');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O teste do alinhamento nos diz que a função de ajuste é adequada para a regressão linear. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Regressão linear:** façamos a regressão linear para buscar os parâmetros $b$ e $Z$ do modelo linearizado."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inclinação = 0.537; offset = 1.332; R2 = 0.999.\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import linregress\n",
    "\n",
    "b,Z,R,p,e = linregress(x,Y)\n",
    "print(f'Inclinação = {b:.3f}; offset = {Z:.3f}; R2 = {R*R:.3f}.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De fato, o coeficiente $R^2 \\approx 1.0$ mostra correlação quase máxima no modelo linearizado."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comparação entre dados experimentais e ajustados:** plotaremos agora a dispersão e o modelo ajustado."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LiARI5S4iEiCVu4hIgFTuIiIBUrmLiARI5S4iEiCVu4hIgFTuIiIBUrmLiARI5S4iEiCVu4hIgFTuIiIBUrmLiARI5S4iEiCVu4hIgFTuIiIBUrmLiASoy3I3sxVm1mRm77cbyzWz183sw+h6aLv7HjWzOjPbbWaz0xVcREQ6l8w792eBOReNPQKsc/dxwLpoGTObAMwHCqNtnjazfj2WVkREktJlubv7m8DRi4bnAs9Ft58D5rUbf8ndT7v7XqAOmNIzUUVEJFndnXO/zt0PAUTXw6PxkcD+dus1RmOXMLP7zazazKqbm5u7GUNERDrS0x+oWgdj3tGK7r7c3UvdvTQvL6+HY4iI9G3dLfePzWwEQHTdFI03AqParZcPHOx+PBER6Y7ulvsa4O7o9t3A6nbj881sgJmNBsYBm1OLKCIiV6p/VyuY2YvANGCYmTUC/wQ8AbxsZt8B9gFfA3D3HWb2MrATOAsscPeWNGUXEZFOdFnu7v6NTu6a0cn6i4BFqYQSEZHU6BuqIiIBUrmLiARI5S4iEiCVu4hIgFTuIiIBUrmLiARI5S4iEiCVu4hIgFTuIiIBUrmLiARI5S4iEiCVu4hIgFTuIiIBUrmLiARI5S4iEiCVu0g2SSTA7NJLIhF3MskwXZ6sQ0QySEMDq99tZOn6OuqaTjJ2+GAWTB/L3En5cSeTDKNyF8kyi1/bTVVFMWWJXLbUH6Vy5Xbmxh1KMo6mZUSyTFVFMeVjhpHT7yrKxwyjqqI47kiSgVTuIlmmLJF72WURULmLZJ0t9UcvuywCmnMXySqfjMinfGzeBWPl0figeCJJhlK5i2SRQQf3s7rmwKV7y5SMjDuaZBiVu0iWmVsyUmUuXdKcu4hIgFTuIiIBUrmLiARI5S4iEiCVu4hIgFLaW8bM6oETQAtw1t1LzSwX+CWQAOqBr7v7H1OLKSIiV6In3rlPd/cSdy+Nlh8B1rn7OGBdtCwiIr0oHdMyc4HnotvPAfPS8BwiInIZqZa7A6+Z2VYzuz8au87dDwFE18M72tDM7jezajOrbm5uTjGGiIi0l+o3VKe6+0EzGw68bma7kt3Q3ZcDywFKS0s9xRwiItJOSu/c3f1gdN0ErAKmAB+b2QiA6Lop1ZAiInJlul3uZnaNmQ05fxuYBbwPrAHujla7G1idakgREbkyqUzLXAesMrPzj/Ov7v7vZrYFeNnMvgPsA76WekwREbkS3S53d/8I+EIH40eAGamEEhGR1OgbqtI3JBJgduklkYg7mUhaqNylb2ho4KaqdWyqa+bM2RY21TVzU9U6aGiIO5lIWqjcpc+oqiimfMwwcvpdRfmYYVRVFMcdSSRtVO7SZ5Qlci+7LBISlbv0GVvqj152WSQkKnfpMypXbmfTnsOcaTnHpj2HqVy5Pe5IImmjE2RL31BQwMbKGVDZulgObIzGRUKkcpe+ob4+7gQivUrTMiIiAVK5i4gESOUuIhIglbuISIBU7iIiAVK5i4gESOUuIhIglbuISIBU7qHS8ctF+jR9QzVUDQ2sfreRpevrqGs6ydjhg1kwfSxzJ+XHnUxEeoHKPWCLX9tNVUUxZYlcttQfpXLldubGHUpEeoWmZQKmk1OI9F0q94Dp5BQifZfKPWA6OYVI36U590B9MiKf8rF5F4yVR+OD4okkIr1I5R6oQQf3s7rmwKV7y5SMjDuaiPSC7C33RAIaGi4dLyjQiRkic0tGqsxF+qjsnXNvaOCmqnVsqmvmzNkWNtU1c1PVuo4LX0Skj8necke7+omIdCary127+omIdCyry127+omIdCxt5W5mc8xst5nVmdkj6XiOypXb2bTnMGdazrFpz2EqV25Px9OIiGSdtOwtY2b9gKXATKAR2GJma9x9Z489SUEBGytnQGXrYjmwMRoXEenr0rUr5BSgzt0/AjCzl4C5QM+Vu3Z3FBHpVLqmZUYC+9stN0ZjbczsfjOrNrPq5ubmNMUQEemb0lXu1sGYX7DgvtzdS929NC8vr4PVRUSku9JV7o3AqHbL+cDBND2XiIhcJF3lvgUYZ2ajzewzwHxgTZqeS0RELpKWD1Td/ayZPQj8X6AfsMLdd6TjuURE5FLm7l2vle4QZs1ARweFGQYc7uU4PSEbc2djZsjO3NmYGbIzd+iZC9y9ww8tM6LcO2Nm1e5eGneOK5WNubMxM2Rn7mzMDNmZuy9nzurDD4iISMdU7iIiAcr0cl8ed4Buysbc2ZgZsjN3NmaG7MzdZzNn9Jy7iIh0T6a/cxcRkW5QuYuIBCgjy93MVphZk5m9H3eWZJnZKDNbb2a1ZrbDzL4fd6ZkmNlAM9tsZu9Fuf9r3JmSZWb9zOxdM3sl7izJMrN6M/u9mdWYWXXceZJhZtea2a/MbFf07/tLcWfqipmNj37G5y/HzewHcefqipk9HP0/fN/MXjSzgd1+rEycczezm4GTwP9y94lx50mGmY0ARrj7NjMbAmwF5vXoMezTwMwMuMbdT5pZDvAW8H13/23M0bpkZv8ZKAX+yt3viDtPMsysHih196z5Yo2ZPQdsdPdfRIcTGeTux2KOlbTo/BIHgC+6e0dflswIZjaS1v9/E9z9UzN7GVjr7s925/Ey8p27u78JZNU589z9kLtvi26fAGq56DDHmchbnYwWc6JL5v3Gv4iZ5QO3A7+IO0vIzOyvgJuBZwDc/c/ZVOyRGcCeTC72dvoDV5tZf2AQKRxwMSPLPduZWQKYBPwu5ihJiaY3aoAm4HV3z4bc/wP4L8C5mHNcKQdeM7OtZnZ/3GGScD3QDPzPaArsF2Z2TdyhrtB84MW4Q3TF3Q8Ai4F9wCHgT+7+WncfT+Xew8xsMLAS+IG7H487TzLcvcXdS2g9NPMUM8voqTAzuwNocvetcWfphqnu/rfArcCCaAoyk/UH/hb4ubtPAv4fkJZzIqdDNI10J/C/487SFTMbSusZ60YDfw1cY2bf6u7jqdx7UDRnvRJ4wd1/HXeeKxX9ub0BmBNvki5NBe6M5q9fAv6TmT0fb6TkuPvB6LoJWEXrKSkzWSPQ2O6vuV/RWvbZ4lZgm7t/HHeQJNwC7HX3Znc/A/ya1tNDd4vKvYdEH0w+A9S6+5Nx50mWmeWZ2bXR7atp/Qe2K9ZQXXD3R909390TtP7J/Rt37/Y7nN5iZtdEH7YTTW3MAjJ6jzB3/wOw38zGR0Mz6MlzIaffN8iCKZnIPuBGMxsU9ckMWj+765aMLHczexF4BxhvZo1m9p24MyVhKvBtWt9Fnt/96ra4QyVhBLDezLbTepKV1909a3YtzDLXAW+Z2XvAZuBVd//3mDMl4yHghejfSAnw3+ONkxwzGwTMpPUdcMaL/jr6FbAN+D2t/dztQxFk5K6QIiKSmox85y4iIqlRuYuIBEjlLiISIJW7iEiAVO4iIgFSuYuIBEjlLiISoP8PQMaonAWHpx4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.exp(Z) # recupera o valor de a \n",
    "modelo = lambda x: a*np.exp(b*x)\n",
    "\n",
    "plt.plot(x,y,'o',mfc='None')\n",
    "plt.plot(x,modelo(x),'rs',mfc='None');\n",
    "plt.legend(('amostras','ajuste'));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Estimando valores não tabelados:** visto que o modelo exponencial se acomoda bem aos dados experimentais, agora podemos estimar valores que são desconhecidos, tais como $x = 3.2$ ou $x = 7.5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Em x = 3.2, a estimativa é f(x) = 21.097\n",
      "Em x = 7.5, a estimativa é f(x) = 211.969\n"
     ]
    }
   ],
   "source": [
    "xp = np.array([3.2,7.5]) # valores procurados\n",
    "\n",
    "for p in xp:\n",
    "    print(f'Em x = {p:g}, a estimativa é f(x) = {modelo(p):g}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercício\n",
    "\n",
    "A seguinte tabela mostra a variação de condutividade térmica relativa $k$ de sódio com a temperatura $T$ em graus Celsius. Busque um modelo não-linear que ajusta os dados no sentido de mínimos quadrados.\n",
    "\n",
    "k|T\n",
    "---|---\n",
    "1.00|79\n",
    "0.932|190\n",
    "0.839|357\n",
    "0.759|524\n",
    "0.693|690\n"
   ]
  }
 ],
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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