CalculoNumerico3 - quase final.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TRABALHO 3 DE CÁLCULO NUMÉRICO\n",
    "\n",
    "# Alunos: Pedro Machado, João Centenaro e Alex Lima"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 1:\n",
    "x = {0,15 |0,17 |0,19 |0,21 |0,23 |0,25 |0,27 |0,29 |0,31}\n",
    "\n",
    "f(x) = {0,1761 |0,2304 |0,2788 |0,3222 |0,3617 |0,3979 |0,4314 |0,4624 |0,4914}\n",
    "\n",
    "a) Utilizando a Forma de Lagrange para interpolar todos os pontos tabelados e fazer uma estimativa para f(0,20) e f(0,22)\n",
    "b) Plotar o gráfico do polinômio obtido\n",
    "\n",
    "Pela Forma de Lagrange, temos que $P(x) = y_0 l_0(x) + y_1 l_1(x) + y_2 l_2(x) + y_3 l_3(x) + y_4 l_4(x) + y_5 l_5(x) + y_6 l_6(x) + y_7 l_7(x) + y_8 l_8(x)$\n",
    "\n",
    "Assim, montamos um programa em Python para calcular nosso polinômio e achar os pontos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P( 0.2 ) 0.30103611755371096\n",
      "P( 0.22 ) 0.34239778747558597\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb3ab0c550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "X = [0.15, 0.17, 0.19, 0.21, 0.23, 0.25, 0.27, 0.29, 0.31]\n",
    "Y = [0.1761, 0.2304, 0.2788, 0.3222, 0.3617, 0.3979, 0.4314, 0.4624, 0.4914]\n",
    "\n",
    "\n",
    "def calcP(x):\n",
    "    valor = 0\n",
    "    for k in range(len(Y)):\n",
    "        lk = 1.0\n",
    "        for i in range(len(X)):\n",
    "            if k != i:\n",
    "                lk = lk*(x - X[i])/(X[k]-X[i])\n",
    "        valor = valor +Y[k]*lk \n",
    "    return valor\n",
    "\n",
    "print (\"P(\",0.20,\")\", calcP(0.20))\n",
    "print (\"P(\",0.22,\")\", calcP(0.22))\n",
    "\n",
    "\n",
    "Xplot = []\n",
    "Yplot = []\n",
    "n = 20              \n",
    "dx = (X[-1]-X[0])/n \n",
    " \n",
    "for i in range(n+1):\n",
    "    x = X[0] + i*dx\n",
    "    y = calcP(x)\n",
    "    Xplot.append(x)\n",
    "    Yplot.append(y)\n",
    "\n",
    "\n",
    "plt.plot(X, Y, \"ro\")  \n",
    "plt.plot(Xplot, Yplot, \"-\") \n",
    "plt.grid(True) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) A questão pede um polinômio de grau 3, logo temos que usar n+1 termos, que é 4. Assim, podemos repetir o código anterior para 4 termos equidistantes, ao invés dos 9 dados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P( 0.2 ) 0.30095078124999997\n",
      "P( 0.22 ) 0.34244296875\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb3d2fa748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "X = [0.17, 0.21, 0.25, 0.29]\n",
    "Y = [0.2304, 0.3222, 0.3979, 0.4624]\n",
    "\n",
    "\n",
    "def calcP(x):\n",
    "    valor = 0\n",
    "    for k in range(len(Y)):\n",
    "        lk = 1.0\n",
    "        for i in range(len(X)):\n",
    "            if k != i:\n",
    "                lk = lk*(x - X[i])/(X[k]-X[i])\n",
    "        valor = valor +Y[k]*lk \n",
    "    return valor\n",
    "\n",
    "print (\"P(\",0.20,\")\", calcP(0.20))\n",
    "print (\"P(\",0.22,\")\", calcP(0.22))\n",
    "\n",
    "\n",
    "Xplot = []\n",
    "Yplot = []\n",
    "n = 20              \n",
    "dx = (X[-1]-X[0])/n \n",
    " \n",
    "for i in range(n+1):\n",
    "    x = X[0] + i*dx\n",
    "    y = calcP(x)\n",
    "    Xplot.append(x)\n",
    "    Yplot.append(y)\n",
    "\n",
    "\n",
    "plt.plot(X, Y, \"ro\")  \n",
    "plt.plot(Xplot, Yplot, \"-\") \n",
    "plt.grid(True) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assim, pelo gráfico, podemos notar que a curva é semelhante a da letra b), porém os valores dos pontos são menos aproximados, devido ao menor número de ponto avaliados para a interpolação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) Para a Fórmula de Newton, usaremos as diferenças divididas, dadas pela forma:\n",
    "$$f[x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8]= \\frac{f[x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8] - f[x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7]}{x_8 - x_0} $$\n",
    "\n",
    "Assim, montamos o programa:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P( 0.2 ) 0.30103611755371096\n",
      "P( 0.22 ) 0.342397787475586\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb3ba78400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Definindo a lista de pontos a serem interpolados\n",
    "X  = [0.15, 0.17, 0.19, 0.21, 0.23, 0.25, 0.27, 0.29, 0.31]\n",
    "Y  = [0.1761, 0.2304, 0.2788, 0.3222, 0.3617, 0.3979, 0.4314, 0.4624, 0.4914]    \n",
    "dd = []  #dd sendo as diferenças divididas  \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "dd.append(Y) \n",
    "     \n",
    "\n",
    "\n",
    "for ordem in range(1, len(X), 1):\n",
    "    dd.append([])   \n",
    "    \n",
    "    \n",
    "    for k in range(0, len(X)-ordem, 1): \n",
    "         \n",
    "        valor = (dd[ordem-1][k+1]-dd[ordem-1][k])/(X[k+ordem]-X[k])    \n",
    "               \n",
    "        dd[ordem].append(valor)\n",
    "    \n",
    "\n",
    "\n",
    "def produtorio(x,n):\n",
    "    prod = 1.\n",
    "    for i in range(n):\n",
    "        prod = prod * (x-X[i])\n",
    "    return prod\n",
    "\n",
    "\n",
    "def calculaP(x):\n",
    "    soma = dd[0][0]\n",
    "    for i in range(1,len(X)):\n",
    "        soma = soma + produtorio(x,i)*dd[i][0]\n",
    "    return soma\n",
    "\n",
    "print (\"P(\",0.20,\")\", calculaP(0.20))\n",
    "print (\"P(\",0.22,\")\", calculaP(0.22))\n",
    "\n",
    "Xp = np.linspace(X[0], X[-1], num=10) \n",
    "Yp = []\n",
    "for x in Xp:\n",
    "    y = calculaP(x)\n",
    "    Yp.append(y)\n",
    "\n",
    "    \n",
    "plt.plot(X, Y, 'ro', Xp, Yp,'-', )\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 2\n",
    "\n",
    "θ = {50 |52 |54 |56 |58 |60}\n",
    "f(θ) = {2,75 |1,45 |0,50 |0,15 |0,20 |0,85}\n",
    "\n",
    "Como a questão pede para encontrar um polinômio de grau 2, temos que escolher três pontos e aplicar o minimos quadrados:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F(X) = 6.13839286(10^-2))x^2 -6.94651786x + 1.96639286(10^2)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb3d2e0208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy as np\n",
    "from scipy.linalg import solve\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X= np.array([50.0, 52.0 ,54.0 ,56.0 ,58.0 ,60.0])\n",
    "Y= np.array([2.75 ,1.45 ,0.50 ,0.15 ,0.20, 0.85])\n",
    "\n",
    "\n",
    "# Calcula os elementos das marizes\n",
    "A11 = np.sum(X**4)\n",
    "A12 = np.sum(X**3)\n",
    "A13 = np.sum(X**2)\n",
    "A21 = A12\n",
    "A22 = np.sum(X**2)\n",
    "A23 = np.sum(X**1)\n",
    "A31 = A13\n",
    "A32 = A23\n",
    "A33 = 6\n",
    "B1 = np.sum(X**2*Y)\n",
    "B2 = np.sum(X*Y)\n",
    "B3 = np.sum(Y)\n",
    "\n",
    "# Monta e resolve o sistema\n",
    "A = np.array([[A11,A12,A13],[A21, A22, A23],[A31,A32,A33]])\n",
    "B = np.array([[B1],[B2],[B3]])\n",
    "a = solve(A, B)\n",
    "\n",
    "# define a funcao g(x) para plotar \n",
    "g = lambda x: 6.13839286*(10**(-2))*x**2 -6.94651786*x + 1.96639286*(10**(2))\n",
    "\n",
    "# cria pontos (x, y) da reta \n",
    "Xr = np.arange(X[0], X[-1]+1, 0.2)\n",
    "Yr = []\n",
    "for x in Xr:\n",
    "    Yr.append(g(x))    \n",
    "print(\"F(X) = 6.13839286(10^-2))x^2 -6.94651786x + 1.96639286(10^2)\")\n",
    "# Plota os pontos e a reta\n",
    "plt.plot(X, Y, \".\", Xr, Yr, \"-\") \n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora, para determinar o mínimo, derivamos o polinômio e igualamos a 0:\n",
    "P(x) = 12.28*10(-2)x - 6,9465 = 0\n",
    "x = 56,57"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "O valor de Fb é: 0.11346438962613092\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.linalg import solve\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = 56.57\n",
    "\n",
    "g = lambda x: 6.13839286*(10**(-2))*x**2 -6.94651786*x + 1.96639286*(10**(2))\n",
    "print(\"O valor de Fb é:\",g(x))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " y(x) = 1.63135153(10^3))x^2 + 1.39944577(10^2)x + 6.10226320(10^-4)\n"
     ]
    }
   ],
   "source": [
    "% matplotlib inline\n",
    "import numpy as np\n",
    "from scipy.linalg import solve\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = np.array([0.002 ,0.006 ,0.012 ,0.018 ,0.024])\n",
    "Y = np.array([0.287 ,0.899 ,1.915 ,3.048 ,4.299])\n",
    "\n",
    "A11 = np.sum(X**4)\n",
    "A12 = np.sum(X**3)\n",
    "A13 = np.sum(X**2)\n",
    "A21 = A12\n",
    "A22 = np.sum(X**2)\n",
    "A23 = np.sum(X**1)\n",
    "A31 = A13\n",
    "A32 = A23\n",
    "A33 = 5\n",
    "B1 = np.sum(X**2*Y)\n",
    "B2 = np.sum(X*Y)\n",
    "B3 = np.sum(Y)\n",
    "A = np.array([[A11,A12,A13],[A21, A22, A23],[A31,A32,A33]])\n",
    "B = np.array([[B1],[B2],[B3]])\n",
    "a= solve(A, B)\n",
    "\n",
    "g = lambda x: 1.63135153*(10**(3))*x**2 + 1.39944577*(10**(2))*x + 6.10226320*(10**(-4))\n",
    "\n",
    "print(\" y(x) = 1.63135153(10^3))x^2 + 1.39944577(10^2)x + 6.10226320(10^-4)\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "dx/dy = 3.26270306(10^3)x + 1.39944577(10^2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 4\n",
    "a) Plotar os pontos\n",
    "b) Determinar T = 7,5°C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb3a1b2fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P( 7.5 ) 1.4068632289341518\n"
     ]
    }
   ],
   "source": [
    "% matplotlib inline\n",
    "import numpy as np\n",
    "from scipy.linalg import solve\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = [0.0, 5, 10, 20, 30, 40]\n",
    "\n",
    "Y = [1.787, 1.519, 1.307, 1.002, 0.7975, 0.6529]\n",
    "\n",
    "\n",
    "## Plota os pontos \n",
    "\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(X, Y, \".\") \n",
    "\n",
    "plt.show()\n",
    "\n",
    "def calcP(x):\n",
    "    valor = 0\n",
    "    for k in range(len(Y)):\n",
    "        lk = 1.0\n",
    "        for i in range(len(X)):\n",
    "            if k != i:\n",
    "                lk = lk*(x - X[i])/(X[k]-X[i])\n",
    "        valor = valor +Y[k]*lk \n",
    "    return valor\n",
    "\n",
    "print (\"P(\",7.5,\")\", calcP(7.5))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Calculando por regressão polinomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-4.40476190e-10]\n",
      " [ 1.85297619e-07]\n",
      " [-2.24333333e-05]\n",
      " [ 1.42489881e-03]\n",
      " [-6.01865476e-02]\n",
      " [ 1.78700000e+00]]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Crash\\Anaconda\\lib\\site-packages\\scipy\\linalg\\basic.py:40: RuntimeWarning: scipy.linalg.solve\n",
      "Ill-conditioned matrix detected. Result is not guaranteed to be accurate.\n",
      "Reciprocal condition number/precision: 5.929554525557527e-17 / 1.1102230246251565e-16\n",
      "  RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb3ba876d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% matplotlib inline\n",
    "import numpy as np\n",
    "from scipy.linalg import solve\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = np.array([0.0, 5.0, 10.0, 20.0, 30.0, 40.0])\n",
    "Y = np.array([1.787, 1.519, 1.307, 1.002, 0.7975, 0.6529])\n",
    "\n",
    "g10 = X**10\n",
    "g9 = X**9\n",
    "g8 = X**8\n",
    "g7 = X**7\n",
    "g6 = X**6\n",
    "g5 = X**5\n",
    "g4 = X**4\n",
    "g3 = X**3\n",
    "g2 = X**2\n",
    "g1 = X**1\n",
    "g0 = X**0\n",
    "h5 = (X**5)*Y\n",
    "h4 = (X**4)*Y\n",
    "h3 = (X**3)*Y\n",
    "h2 = (X**2)*Y\n",
    "h1 = (X**1)*Y\n",
    "h0 = (X**0)*Y\n",
    "\n",
    "a11 = np.sum(g10)\n",
    "a12 = np.sum(g9)\n",
    "a13 = np.sum(g8)\n",
    "a14 = np.sum(g7)\n",
    "a15 = np.sum(g6)\n",
    "a16 = np.sum(g5)\n",
    "a21 = a12\n",
    "a22 = np.sum(g8)\n",
    "a23 = np.sum(g7)\n",
    "a24 = np.sum(g6)\n",
    "a25 = np.sum(g5)\n",
    "a26 = np.sum(g4)\n",
    "a31 = a13\n",
    "a32 = a23\n",
    "a33 = np.sum(g6)\n",
    "a34 = np.sum(g5)\n",
    "a35 = np.sum(g4)\n",
    "a36 = np.sum(g3)\n",
    "a41 = a14\n",
    "a42 = a24\n",
    "a43 = a34\n",
    "a44 = np.sum(g4)\n",
    "a45 = np.sum(g3)\n",
    "a46 = np.sum(g2)\n",
    "a51 = a15\n",
    "a52 = a25\n",
    "a53 = a35\n",
    "a54 = a45\n",
    "a55 = np.sum(g2)\n",
    "a56 = np.sum(g1)\n",
    "a61 = a16\n",
    "a62 = a26\n",
    "a63 = a36\n",
    "a64 = a46\n",
    "a65 = a56\n",
    "a66 = np.sum(g0)\n",
    "\n",
    "b1 = np.sum(h5)\n",
    "b2 = np.sum(h4)\n",
    "b3 = np.sum(h3)\n",
    "b4 = np.sum(h2)\n",
    "b5 = np.sum(h1)\n",
    "b6 = np.sum(h0)\n",
    "\n",
    "A = np.array([[a11,a12, a13, a14, a15, a16],[a21, a22, a23, a24, a25, a26], [a31, a32, a33, a34, a35, a36], [a41, a42, a43, a44, a45, a46], [a51, a52, a53, a54, a55, a56], [a61, a62, a63, a64, a65, a66]])\n",
    "B = np.array([[b1] , [b2],  [b3],  [b4],  [b5],  [b6]])\n",
    " \n",
    "\n",
    "\n",
    "a = solve(A, B)\n",
    "\n",
    "print(a)\n",
    "\n",
    "\n",
    "i = lambda x: 1.85297619*(10**(-7))*(x**4) - 4.40476190*(10**(-10))*(x**5) - 2.24333333*(10**(-5))*(x**3) + 0.00142489881*(x**2) - 0.0601865476*x + 1.787\n",
    "Xp = np.linspace(X[0], X[-1], num=10) \n",
    "Yp = []\n",
    "for x in Xp:\n",
    "    y = i(x)\n",
    "    Yp.append(y)\n",
    "\n",
    "    \n",
    "plt.plot(X, Y, 'ro', Xp, Yp,'-', )\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 5\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "O valor de m é [4.72446756]\n",
      "O valor de B é 1.4611221255378586\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb3d415f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb3ba87f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% matplotlib inline\n",
    "import numpy as np\n",
    "from scipy.linalg import solve\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import quad\n",
    "import math\n",
    "from numpy import exp\n",
    "\n",
    "X = np.array([0.0004, 0.0011, 0.0021, 0.0031])\n",
    "Y = np.array([5.775, 8.577, 10.874, 12.555])\n",
    "\n",
    "L = np.log(X)\n",
    "K = np.log(Y)\n",
    "\n",
    "A11 = np.sum(L**2)\n",
    "A12 = np.sum(L**1)\n",
    "A21 = A12\n",
    "A22 = np.sum(L**0)\n",
    "\n",
    "B1 = np.sum(L*K) \n",
    "B2 = np.sum(K)\n",
    "\n",
    "A = np.array([[A11, A12],[A21, A22]])\n",
    "C = np.array([[B1],[B2]])\n",
    "\n",
    "a = solve(A, C)\n",
    "\n",
    "\n",
    "m = a[1]\n",
    "B = math.exp(a[0])\n",
    "\n",
    "print(\"O valor de m é\", m)\n",
    "print(\"O valor de B é\", B)\n",
    "\n",
    "i= lambda x: 0.379*x + 4.72\n",
    "Xp = np.linspace(X[0], X[-1], num=10) \n",
    "Yp = []\n",
    "for x in Xp:\n",
    "    y = i(x)\n",
    "    Yp.append(y)\n",
    "\n",
    "    \n",
    "plt.plot(L, K, '.', Xp, Yp,'-', )\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "p= lambda x: 1.46*x**(4.724)\n",
    "Xp = np.linspace(X[0], X[-1], num=10) \n",
    "Yp = []\n",
    "for x in Xp:\n",
    "    y = p(x)\n",
    "    Yp.append(y)\n",
    "\n",
    "    \n",
    "plt.plot(X, Y, '.', Xp, Yp,'-', )\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}