codeSession-1-bisect.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Code session 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determinação de raízes\n",
    "\n",
    "`bisect`\n",
    "\n",
    "A função `bisect` localiza a raiz de uma função dentro de um intervalo dado usando o método da bisseção. \n",
    "Os argumentos de entrada obrigatórios desta função são: \n",
    "\n",
    "1. a função-alvo `f` (contínua)\n",
    "2. o limite esquerdo `a`\n",
    "3. o limite direito `b`\n",
    "\n",
    "Parâmetros opcionais relevantes são: \n",
    "\n",
    "- `xtol`: tolerância (padrão: 2e-12)\n",
    "- `maxiter`: número máximo de iterações (padrão: 100)\n",
    "- `disp`: mostra erro se algoritmo não convergir (padrão: True) \n",
    "\n",
    "O argumento de saída é:\n",
    "\n",
    "- `x0`: a estimativa para a raiz de `f`\n",
    "\n",
    "Como importá-la? \n",
    "\n",
    "```python \n",
    "from scipy.optimize import bisect\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import bisect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problema 1\n",
    "\n",
    "Encontre a menor raiz positiva (real) de $x^{3} - 3.23x^{2} - 5.54x + 9.84 = 0$ pelo método da bisseção."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resolução"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# função\n",
    "def f(x): \n",
    "    return x**3 - 3.23*x**2 - 5.54*x + 9.84"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# analise gráfica \n",
    "x = np.linspace(-4,5)\n",
    "plt.plot(x,f(x));\n",
    "plt.axhline(y=0,color='r');\n",
    "plt.axvline(x=0,color='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pelo gráfico, vemos que a menor raiz positiva está localizada no intervalo $(0,2]$. Vamos determiná-la utilizando este intervalo de confinamento. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raiz: x = 1.230000\n"
     ]
    }
   ],
   "source": [
    "# resolução com bisect \n",
    "\n",
    "x = bisect(f,0,2) # raiz \n",
    "\n",
    "print('Raiz: x = %f' % x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problema 2\n",
    "\n",
    "Determine a menor raiz não nula positiva de $\\cosh(x) \\cos(x) - 1 = 0$ dentro do intervalo $(4,5)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resolução\n",
    "\n",
    "Sigamos o procedimento aprendido com `bisect`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# função\n",
    "def f(x): \n",
    "    return np.cosh(x)*np.cos(x) - 1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "# analise gráfica \n",
    "x = np.linspace(4,5)\n",
    "plt.plot(x,f(x));\n",
    "plt.axhline(y=0,color='r');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raiz: x = 4.730041\n"
     ]
    }
   ],
   "source": [
    "# resolução com bisect \n",
    "\n",
    "x = bisect(f,4,5) # raiz \n",
    "\n",
    "print('Raiz: x = %f' % x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problema 3\n",
    "\n",
    "Uma raiz da equação $\\tan(x) - \\tanh(x) = 0$ encontra-se em $(7.0,7.4)$. Determine esta raiz com três casas decimais de precisão pelo método da bisseção."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resolução"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# função\n",
    "def f(x): \n",
    "    return np.tan(x) - np.tanh(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "# analise gráfica \n",
    "x = np.linspace(7,7.4)\n",
    "plt.plot(x,f(x));\n",
    "plt.axhline(y=0,color='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para obter as 3 casas decimas, vamos imprimir o valor final com 3 casas decimais. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raiz: x = 7.069\n"
     ]
    }
   ],
   "source": [
    "x = bisect(f,7,7.4) # raiz \n",
    "\n",
    "print('Raiz: x = %.3f' % x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problema 4\n",
    "\n",
    "Determine as raízes de $\\text{sen}(x) + 3\\cos(x) - 1 = 0$ no intervalo $(-2,2)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resolução"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# função\n",
    "def f(x): \n",
    "    return np.sin(x) + np.cos(x) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [
    "# analise gráfica \n",
    "x = np.linspace(-2,2)\n",
    "plt.plot(x,f(x));\n",
    "plt.axhline(y=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A análise gráfica mostra duas raízes. Vamos encontrar uma de cada vez."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raízes: x1 = -0.000000; x2 = 1.570796\n"
     ]
    }
   ],
   "source": [
    "# resolução com bisect \n",
    "\n",
    "x1 = bisect(f,-2,1) # raiz 1  \n",
    "x2 = bisect(f,1,2) # raiz 2 \n",
    "\n",
    "print('Raízes: x1 = %f; x2 = %f' % (x1,x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problema 5\n",
    "\n",
    "Determine todas as raízes reais de $P(x) = x^4 + 0.9x^3 - 2.3x^2 + 3.6x - 25.2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resolução"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# função \n",
    "def P(x):\n",
    "    return x**4 + 0.9*x**3 - 2.3*x**2 + 3.6*x - 25.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define função para analise gráfica \n",
    "def analise_grafica(xrange,f):\n",
    "    plt.plot(xrange,f(xrange));\n",
    "    plt.axhline(y=0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "# analise gráfica 1\n",
    "xrange = np.linspace(-10,10)\n",
    "analise_grafica(xrange,P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": [
    "# refinamento\n",
    "xrange = np.linspace(-5,5)\n",
    "analise_grafica(xrange,P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raízes: x1 = -3.000000; x2 = 2.100000\n"
     ]
    }
   ],
   "source": [
    "# resolução com bisect \n",
    "\n",
    "x1 = bisect(P,-4,-2) # raiz 1  \n",
    "x2 = bisect(P,1,3) # raiz 2 \n",
    "\n",
    "print('Raízes: x1 = %f; x2 = %f' % (x1,x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problema 6\n",
    "\n",
    "Um jogador de futebol americano está prestes a fazer um lançamento para outro jogador de seu time. O lançador tem uma altura de 1,82 m e o outro jogador está afastado de 18,2 m. A expressão que descreve o movimento da bola é a familiar equação da física que descreve o movimento de um projétil:\n",
    "\n",
    "$$y = x\\tan(\\theta) - \\dfrac{1}{2}\\dfrac{x^2 g}{v_0^2}\\dfrac{1}{\\cos^2(\\theta)} + h,$$\n",
    "\n",
    "onde $x$ e $y$ são as distâncias horizontal e verical, respectivamente, $g=9,8 \\, m/s^2$ é a aceleração da gravidade, $v_0$ é a velocidade inicial da bola quando deixa a mão do lançador e $\\theta$ é o Ângulo que a bola faz com o eixo horizontal nesse mesmo instante. Para $v_0 = 15,2 \\, m/s$, $x = 18,2 \\, m$, $h = 1,82 \\, m$ e $y = 2,1 \\, m$, determine o ângulo $\\theta$ no qual o jogador deve lançar a bola. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resolução"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parâmetros do problema\n",
    "v0 = 15.2\n",
    "x = 18.2\n",
    "h = 1.82\n",
    "y = 2.1\n",
    "g = 9.8\n",
    "\n",
    "# função f(theta) = 0\n",
    "f = lambda theta: x*np.tan(theta) - 0.5*(x**2*g/v0**2)*(1/(np.cos(theta)**2)) + h - 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": [
    "# análise gráfica\n",
    "th = np.linspace(0,0.95*np.pi/2,50)\n",
    "plt.plot(th,f(th));\n",
    "plt.axhline(y=0,color='r');"
   ]
  },
  {
   "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": [
    "# análise gráfica - 2\n",
    "th = np.linspace(0,np.pi/4,50)\n",
    "plt.plot(th,f(th));\n",
    "plt.axhline(y=0,color='r');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ângulo de lançamento: 26.41 graus\n"
     ]
    }
   ],
   "source": [
    "# resolução por bisseção\n",
    "xr = bisect(f,0.1,0.6)\n",
    "print('Ângulo de lançamento: %.2f graus' % np.rad2deg(xr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problema 7\n",
    "\n",
    "A equação de Bernoulli para o escoamento de um fluido em um canal aberto com um pequeno ressalto é \n",
    "\n",
    "$$\\dfrac{Q^2}{2gb^2h_0^2} + h_0 = \\dfrac{Q^2}{2gb^2h^2} + h + H,$$\n",
    "\n",
    "onde $Q = 1.2 \\, m^3/s$ é a vazão volumétrica, $g = 9.81 \\, m/s^2$ é a aceleração gravitacional, $b = 1.8 \\, m$ a largura do canal, $h_0 = 0.6 \\, m$ o nível da água à montante, $H = 0.075 \\, m$ a altura do ressalto e $h$ o nível da água acima do ressalto. Determine $h$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resolução\n",
    "\n",
    "Para este problema, definiremos duas funções, uma auxiliar, que chamaremos `a`, e a função `f(h)` que reescreve a equação de Bernoulli acima em função de $h$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# função para cálculo de parâmetros\n",
    "def a(Q,g,b,H,h0):\n",
    "    return Q,g,b,H,h0\n",
    "\n",
    "# função do nível de água\n",
    "def f(h):\n",
    "    frate,grav,width,bHeight,ups = a(Q,g,b,H,h0)\n",
    "    c = lambda arg: frate**2/(2*grav*width**2*arg**2)\n",
    "    return c(h) - c(h0) + h - h0 + H "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note que a função `a` é apenas uma conveniência para o cálculo do termo comum envolvendo a vazão e para construírmos uma generalização para os dados de entrada. Em seguida, definiremos os parâmetros de entrada do problema. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parâmetros de entrada\n",
    "Q = 1.2 # m3/s \n",
    "g = 9.81 # m/s2\n",
    "b = 1.8 # m\n",
    "h0 = 0.6 # m\n",
    "H = 0.075 # m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A partir daí, podemos realizar a análise gráfica para verificar o comportamento de `f(h)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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": [
    "# análise gráfica\n",
    "h = np.linspace(0.1,6,num=100)\n",
    "plt.plot(h,f(h),h,f(h)*0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ampliemos a localização."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "# análise gráfica\n",
    "h = np.linspace(0.25,0.6,num=100)\n",
    "plt.plot(h,f(h),h,f(h)*0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verificamos que `f(h)` admite duas soluções. Vamos determinar cada uma delas. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raiz: h1 = 0.264755\n",
      "Raiz: h2 = 0.495755\n"
     ]
    }
   ],
   "source": [
    "# solução  \n",
    "h1 = bisect(f,0.25,0.32)\n",
    "print('Raiz: h1 = %f' % h1)\n",
    "\n",
    "h2 = bisect(f,0.4,0.55)\n",
    "print('Raiz: h2 = %f' % h2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Nota:** as duas soluções viáveis dizem respeito ao regime de escoamento no canal aberto. Enquanto $h_1$ é um limite para escoamento supercrítico (rápido), $h_2$ é um limite para escoamento subcrítico (lento)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problema 8\n",
    "\n",
    "A velocidade $v$ de um foguete Saturn V em voo vertical próximo à superfície da Terra pode ser aproximada por\n",
    "\n",
    "$$v = u\\textrm{ln}\\left(\\dfrac{M_0}{M_0 - \\dot{m}t} \\right) - gt,$$\n",
    "\n",
    "onde $u = 2510 \\, m/s$ é a velocidade de escape relativa ao foguete, $M_0 = 2.8 \\times 10^6 \\, kg$ é a massa do foguete no momento do lançamento, $\\dot{m} = 13.3 \\times 10^3 \\, kg/s$ é a taxa de consumo de combustível, $g = 9.81 \\, m/s^2$ a aceleração gravitacional e $t$ o tempo medido a partir do lançamento. \n",
    "\n",
    "Determine o instante de tempo $t^*$ quando o foguete atinge a velocidade do som ($335 \\, m/s$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Resolução\n",
    "\n",
    "Seguiremos a mesma ideia utilizada no Problema 7. Primeiramente, construímos uma função auxiliar para calcular parâmetros e, em seguida, definimos uma função `f(t)`.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# função para cálculo de parâmetros\n",
    "def a(u,M0,m,g,v):\n",
    "    return u,M0,m,g,v\n",
    "\n",
    "# função do tempo\n",
    "def f(t):\n",
    "    escape,mass,fuel,grav,vel = a(u,M0,m,g,v)    \n",
    "    return escape*np.log(mass/(mass - fuel*t)) - g*t - vel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definimos os parâmetros do problema."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parâmetros de entrada\n",
    "u = 2510.0 # m/s \n",
    "M0 = 2.8e6 # kg\n",
    "m = 13.3e3 # kg/s\n",
    "g = 9.81 # m/s2\n",
    "v = 335.0 # m/s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilizaremos a análise gráfica para determinar o intervalo de refinamento da raiz. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# análise gráfica\n",
    "t = np.linspace(0.5,100,num=100)\n",
    "plt.plot(t,f(t),t,f(t)*0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos verificar que a raiz está entre 60 e 80 segundos. Utilizaremos estes limitantes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raiz: tr = 70.88 s = 1.18 min\n"
     ]
    }
   ],
   "source": [
    "# solução  \n",
    "tr = bisect(f,60,80)\n",
    "print('Raiz: tr = %.2f s = %.2f min' % (tr,tr/60) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O foguete rompe a barreira do som em 1 minuto e 18 segundos!"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}