DSA-Python-Cap08-04-SciPy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font color='blue'>Data Science Academy - Python Fundamentos - Capítulo 8</font>\n",
    "\n",
    "## Download: http://github.com/dsacademybr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Versão da Linguagem Python Usada Neste Jupyter Notebook: 3.8.8\n"
     ]
    }
   ],
   "source": [
    "# Versão da Linguagem Python\n",
    "from platform import python_version\n",
    "print('Versão da Linguagem Python Usada Neste Jupyter Notebook:', python_version())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SciPy\n",
    "\n",
    "Para compreender o SciPy é necessário compreender conceitos avançados de Matemática e Estatística, o que está fora do escopo deste treinamento. Caso queira aprender aplicações práticas do pacote em Machine Learning e IA, consulte estes dois cursos aqui na DSA:\n",
    "\n",
    "<a href=\"https://www.datascienceacademy.com.br/course/machine-learning-engineer\">Machine Learning</a>\n",
    "\n",
    "<a href=\"https://www.datascienceacademy.com.br/course/programao-paralela-em-gpu\">Programação Paralela em GPU</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### O SciPy possui um conjunto de pacotes para operações matemáticas e científicas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table class=\"ArticleTableNoBorder\">\n",
    "\t<tbody>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><strong>Pacote</strong></td>\n",
    "\t\t\t<td><strong>Descrição</strong></td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>cluster</code></td>\n",
    "\t\t\t<td>Clustering algorithms</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>constants</code></td>\n",
    "\t\t\t<td>Mathematical and physical constants</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>fftpack</code></td>\n",
    "\t\t\t<td>Fourier transforms</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>integrate</code></td>\n",
    "\t\t\t<td>Numerical integration</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>interpolate</code></td>\n",
    "\t\t\t<td>Interpolation</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>io</code></td>\n",
    "\t\t\t<td>Input and output</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>linalg</code></td>\n",
    "\t\t\t<td>Linear algebra</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>maxentropy</code></td>\n",
    "\t\t\t<td>Maximum entropy models</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>misc</code></td>\n",
    "\t\t\t<td>Miscellaneous</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>ndimage</code></td>\n",
    "\t\t\t<td>Multi-dimensional image processing</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>odr</code></td>\n",
    "\t\t\t<td>Orthogonal distance regression</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>optimize</code></td>\n",
    "\t\t\t<td>Optimization</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>signal</code></td>\n",
    "\t\t\t<td>Signal processing</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>sparse</code></td>\n",
    "\t\t\t<td>Sparse matrices</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>spatial</code></td>\n",
    "\t\t\t<td>Spatial algorithms and data structures</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>special</code></td>\n",
    "\t\t\t<td>Special functions</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>stats</code></td>\n",
    "\t\t\t<td>Statistical functions</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>stsci</code></td>\n",
    "\t\t\t<td>Image processing</td>\n",
    "\t\t</tr>\n",
    "\t\t<tr>\n",
    "\t\t\t<td><code>weave</code></td>\n",
    "\t\t\t<td>C/C++ integration</td>\n",
    "\t\t</tr>\n",
    "\t</tbody>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Processamento de Imagens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.7.0'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy\n",
    "scipy.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.4.2'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib\n",
    "matplotlib.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        ...,\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]],\n",
       "\n",
       "       [[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        ...,\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]],\n",
       "\n",
       "       [[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        ...,\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        ...,\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]],\n",
       "\n",
       "       [[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        ...,\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]],\n",
       "\n",
       "       [[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        ...,\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]]], dtype=float32)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Função imread foi descontinuada no Scipy\n",
    "# from scipy import misc\n",
    "# misc.imread('Matplotlib-Mapa.png')   \n",
    "\n",
    "# Usamos agora a função do pacote imageio\n",
    "from imageio import imread\n",
    "imread('Matplotlib-Mapa.png')  \n",
    "\n",
    "# Matplotlib tem uma função similar\n",
    "import matplotlib.pyplot as plt\n",
    "plt.imread('Matplotlib-Mapa.png') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integração Numérica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.21.0'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "from scipy.integrate import quad, dblquad, tplquad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.0)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Integração\n",
    "val, abserr = quad(lambda x: exp(-x ** 2),  Inf, Inf)\n",
    "val, abserr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint, ode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import *\n",
    "%matplotlib inline"
   ]
  },
  {
   "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": [
    "def dy(y, t, zeta, w0):\n",
    "    x, p = y[0], y[1]\n",
    "    \n",
    "    dx = p\n",
    "    dp = -2 * zeta * w0 * p - w0**2 * x\n",
    "\n",
    "    return [dx, dp]\n",
    "\n",
    "\n",
    "y0 = [1.0, 0.0]\n",
    "\n",
    "t = linspace(0, 10, 1000)\n",
    "w0 = 2*pi*1.0\n",
    "\n",
    "\n",
    "y1 = odeint(dy, y0, t, args=(0.0, w0)) \n",
    "y2 = odeint(dy, y0, t, args=(0.2, w0)) \n",
    "y3 = odeint(dy, y0, t, args=(1.0, w0)) \n",
    "y4 = odeint(dy, y0, t, args=(5.0, w0)) \n",
    "\n",
    "fig, ax = subplots()\n",
    "ax.plot(t, y1[:,0], 'k', label=\"Não Abafado\", linewidth=0.25)\n",
    "ax.plot(t, y2[:,0], 'r', label=\"Pouco Abafado\")\n",
    "ax.plot(t, y3[:,0], 'b', label=\"Criticamente Abafado\")\n",
    "ax.plot(t, y4[:,0], 'g', label=\"Perigosamente Abafado\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fourier Transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fftpack import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fourier transformation\n",
    "N = len(t)\n",
    "dt = t[1]-t[0]\n",
    "\n",
    "F = fft(y2[:,0]) \n",
    "\n",
    "w = fftfreq(N, dt)\n",
    "\n",
    "fig, ax = subplots(figsize=(9,3))\n",
    "ax.plot(w, abs(F));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Álgebra Linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[3, 2, 0], [1, -1, 0], [0, 5, 1]])\n",
    "b = np.array([2, 4, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2., -2.,  9.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Resolvendo um sistema de equações lineares\n",
    "x = solve(A, b)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.20316645+0.33302516j, 0.20316645-0.33302516j,\n",
       "       1.8163585 +0.j        ])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = rand(3,3)\n",
    "B = rand(3,3)\n",
    "\n",
    "evals, evecs = eig(A)\n",
    "\n",
    "evals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.11019898-0.47311607j, -0.11019898+0.47311607j,\n",
       "        -0.58476521+0.j        ],\n",
       "       [ 0.42220712+0.25208019j,  0.42220712-0.25208019j,\n",
       "        -0.45048226+0.j        ],\n",
       "       [-0.72264382+0.j        , -0.72264382-0.j        ,\n",
       "        -0.6746224 +0.j        ]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evecs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-0.62167662,  0.23169968, -0.74822018],\n",
       "        [-0.46296535, -0.87922094,  0.11239943],\n",
       "        [-0.63180793,  0.41627611,  0.65386003]]),\n",
       " array([2.00408772, 0.59006022, 0.23375065]),\n",
       " array([[-0.55387118, -0.75089749, -0.35969386],\n",
       "        [ 0.82914148, -0.45809332, -0.32042927],\n",
       "        [ 0.07583618, -0.47571364,  0.87632494]]))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svd(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Otimização"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": [
    "def f(x):\n",
    "    return 4*x**3 + (x-2)**2 + x**4\n",
    "\n",
    "fig, ax  = subplots()\n",
    "x = linspace(-5, 3, 100)\n",
    "ax.plot(x, f(x));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 2.804988\n",
      "         Iterations: 4\n",
      "         Function evaluations: 12\n",
      "         Gradient evaluations: 6\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.46961743])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_min = optimize.fmin_bfgs(f, -0.5)\n",
    "x_min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estatística"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y = stats.norm()\n",
    "\n",
    "x = linspace(-5,5,100)\n",
    "\n",
    "fig, axes = subplots(3,1, sharex=True)\n",
    "\n",
    "axes[0].plot(x, Y.pdf(x))\n",
    "\n",
    "axes[1].plot(x, Y.cdf(x));\n",
    "\n",
    "axes[2].hist(Y.rvs(size=1000), bins=50);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 1.0, 1.0)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.mean(), Y.std(), Y.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0513371546702971, 0.9590619936636546)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# T-test\n",
    "t_statistic, p_value = stats.ttest_ind(Y.rvs(size=1000), Y.rvs(size=1000))\n",
    "t_statistic, p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Obrigado\n",
    "\n",
    "### Visite o Blog da Data Science Academy - <a href=\"http://blog.dsacademy.com.br\">Blog DSA</a>\n"
   ]
  }
 ],
 "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}