notebooks_adicionales/Scipy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SciPy - Biblioteca de algorítmos científicos para Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Traducido y adaptado por P. Gzlez. Rodelas (prodelas at gmail.com) a partir de otro notebook original de J.R. Johansson (jrjohansson at gmail.com).\n",
    "\n",
    "La última versión en inglés de este [IPython notebook](http://ipython.org/notebook.html) está disponible en [http://github.com/jrjohansson/scientific-python-lectures](http://github.com/jrjohansson/scientific-python-lectures)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#    Aquí cargamos el módulo 'pyplot' dentro del paquete 'matplotlib' \n",
    "# con el pseudónimo 'plt', así como el módulo 'Image' dentro del paquete\n",
    "# 'display' de IPython, indicando que los gráficos los muestre en línea\n",
    "# dentro del mismo notebook de IPython.\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introducción"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Toda la infraestructura de SciPy está construida a partir de la que proporciona NumPy para el manejo de arrays multidimensionales, y proporciona un gran número de algoritmos científicos de alto nivel. Alguno de los temas que cubre SciPy son:\n",
    "\n",
    "* Funciones especiales ([scipy.special](http://docs.scipy.org/doc/scipy/reference/special.html))\n",
    "* Integración ([scipy.integrate](http://docs.scipy.org/doc/scipy/reference/integrate.html))\n",
    "* Optimización ([scipy.optimize](http://docs.scipy.org/doc/scipy/reference/optimize.html))\n",
    "* Interpolación ([scipy.interpolate](http://docs.scipy.org/doc/scipy/reference/interpolate.html))\n",
    "* Transformadas de Fourier ([scipy.fftpack](http://docs.scipy.org/doc/scipy/reference/fftpack.html))\n",
    "* Procesamiento de Señales ([scipy.signal](http://docs.scipy.org/doc/scipy/reference/signal.html))\n",
    "* Álgebra Lineal ([scipy.linalg](http://docs.scipy.org/doc/scipy/reference/linalg.html))\n",
    "* Problemas de Valores Propios de matrices huecas ([scipy.sparse](http://docs.scipy.org/doc/scipy/reference/sparse.html))\n",
    "* Estadística ([scipy.stats](http://docs.scipy.org/doc/scipy/reference/stats.html))\n",
    "* Procesamiento de Imágenes Multi-dimensional ([scipy.ndimage](http://docs.scipy.org/doc/scipy/reference/ndimage.html))\n",
    "* Entrada/Salida de ficheros ([scipy.io](http://docs.scipy.org/doc/scipy/reference/io.html))\n",
    "\n",
    "Cada uno de estos submódulos proporciona un determinado número de funciones y clases que pueden ser usadas para resolver problemas relacionados con sus respectivos temas.\n",
    "\n",
    "En este notebook se explorará y expondrá cómo usar alguno de estos paquetes o submódulos.\n",
    "\n",
    "Para acceder al paquete SciPy en un programa de Python, empezaremos importándolo todo desde el módulo `scipy`, tal y cómo sigue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pero si lo que necesitamos es sólo una parte concreta de la extensa infraestructura de SciPy podremos selectivamente incluir sólo aquellos módulos en los que estemos interesados. Por ejemplo, para incluir tan sólo el paquete de álgebra lineal bajo el pseudónimo `la`, podemos simplemente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.linalg as la"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Funciones especiales"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un gran número de funciones matemáticas especiales resultan importantes para numerosos problemas computacionales en Física e Ingeniería. SciPy proporciona implementaciones de una extensa colección de funciones especiales. Para más detalles, consultar la lista completa de estas funciones en la documención de referencia en http://docs.scipy.org/doc/scipy/reference/special.html#module-scipy.special. \n",
    "\n",
    "Para mostrar el uso típico de estas funciones especiales veremos con más detalle el caso de las funciones de Bessel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#\n",
    "# El módulo scipy.special incluye un gran número de funciones de Bessel.\n",
    "# Aquí de momento usaremos las funciones jn e yn, que corresponden con las\n",
    "# funciones de Bessel de primera y segunda especie con valores reales. \n",
    "# También incluiremos los procedimientos jn_zeros e yn_zeros que nos \n",
    "# proporcionan los ceros de estas funciones, jn e yn, respectivamente.\n",
    "#\n",
    "\n",
    "from scipy.special import jn, yn, jn_zeros, yn_zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J_0(0.000000) = 1.000000\n",
      "Y_0(1.000000) = 0.088257\n"
     ]
    }
   ],
   "source": [
    "n = 0    # orden\n",
    "x = 0.0\n",
    "\n",
    "# función de Bessel de primera especie\n",
    "print(\"J_%d(%f) = %f\" % (n, x, jn(n, x)))\n",
    "\n",
    "x = 1.0\n",
    "# función de Bessel de segunda especie\n",
    "print(\"Y_%d(%f) = %f\" % (n, x, yn(n, x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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GDRpg69atea8vX778hWWEhYVh9erVBsUhN+7+UEipUqIbJDoamDZN7WgYY4wZ07p163D4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\nKIqiKIouVFKhKIqiKIou/g+odcdrbbDfqgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x873dfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(0, 10, 100)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "for n in range(4):\n",
    "    ax.plot(x, jn(n, x), label=r\"$J_%d(x)$\" % n)\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.40482556,   5.52007811,   8.65372791,  11.79153444])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ceros de las funciones de Bessel\n",
    "n = 0 # orden\n",
    "m = 4 # número de raíces a calcular\n",
    "jn_zeros(n, m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integración"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integración numérica: cuadratura (\"quadrature\" en inglés)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se trata de calcular numéricamente la integral definida de una cierta función\n",
    "\n",
    "$\\displaystyle \\int_a^b f(x) dx$\n",
    "\n",
    "que también se suele denominar *cuadratura numérica*, o simplemente *cuadratura*. SciPy proporciona ciertos procedimientos para diferentes tipos de cuadratura, por ejemplo: `quad`, `dblquad` y `tplquad` para integrales simples, dobles o triples, respectivamente.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import quad, dblquad, tplquad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La función o procedimiento `quad` también puede tener un gran número de argumentos opcionales que nos permitirán afinar bastante el comportamiento de dicho procedimiento (pruebe con `help(quad)` para obtener más detalles).\n",
    "\n",
    "El uso básico sería el siguiente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# primero debemos disponer de una cierta función para el integrando\n",
    "def f(x):\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "valor de la integral = 0.5 , error en valor absoluto = 5.551115123125783e-15\n"
     ]
    }
   ],
   "source": [
    "x_min = 0 # el límite inferior de integración en x\n",
    "x_max = 1 # el límite superior de integración en x\n",
    "\n",
    "val, abserr = quad(f, x_min, x_max)\n",
    "\n",
    "print( \"valor de la integral =\", val, \", error en valor absoluto =\", abserr )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si necesitamos pasar argumentos extra a la función integrando, podemos usar la palabra clave `args` como argumento:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004995343578232489 5.545945456467126e-17\n"
     ]
    }
   ],
   "source": [
    "def integrando(x, n):\n",
    "    \"\"\"\n",
    "    Función de Bessel de primera especie y orden n. \n",
    "    \"\"\"\n",
    "    return jn(n, x)\n",
    "\n",
    "\n",
    "x_min = 0 # el límite inferior de integración en x\n",
    "x_max = 1 # el límite superior de integración en x\n",
    "\n",
    "val, abserr = quad(integrando, x_min, x_max, args=(3,))\n",
    "\n",
    "print( val, abserr )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para funciones relativamente simples podríamos usar una función de tipo lambda (también llamadas funciones sin nombre) en vez de definir explícitamente una función para el integrando:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "integral numérica  = 1.7724538509055159 1.4202636781830878e-08\n",
      "integral analítica = 1.77245385091\n"
     ]
    }
   ],
   "source": [
    "val, abserr = quad(lambda x: exp(-x ** 2), -Inf, Inf)\n",
    "\n",
    "print (\"integral numérica  =\", val, abserr)\n",
    "\n",
    "analitica = sqrt(pi)\n",
    "print( \"integral analítica =\", analitica)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como se ha mostrado en el ejemplo anterior, también podemos calcular y aproximar el valor de integrales impropias, introduciendo '-Inf' o 'Inf' como alguno de los límites de integración.\n",
    "\n",
    "Cuando se trate de integrales multi-dimensionales se procederá de la misma manera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7853981633974476 1.375309851021853e-08\n"
     ]
    }
   ],
   "source": [
    "def integrando(x, y):\n",
    "    return exp(-x**2-y**2)\n",
    "\n",
    "x_min =  0  \n",
    "x_max = 10\n",
    "y_min =  0\n",
    "y_max = 10\n",
    "\n",
    "val, abserr = dblquad(integrando, x_min, x_max, lambda x : y_min, lambda x: y_max)\n",
    "\n",
    "print( val, abserr )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nótese cómo se han pasado funciones lambda como límites para la integración en y, ya que en general éstos pueden ser funciones de x."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ecuaciones diferenciales ordinarias  (EDOs, u ODEs en inglés)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy proporciona dos maneras diferentes de resolver EDOs: Una API basada en la función o procedimiento `odeint`, y otra API orientada a objetos basada en la clase `ode`. Usualmente `odeint` es más fácil para empezar, pero la clase `ode` ofrece un nivel de control mucho más fino.\n",
    "\n",
    "Aquí, de momento usaremos el procedimiento `odeint`. Para más información acerca de la clase `ode`, pruebe con `help(ode)`. Esta última realiza más o menos las mismas cosas que `odeint`, pero de una visión más orientada a objetos.\n",
    "\n",
    "Para usar `odeint`, primero debemos importarla desde el módulo `scipy.integrate`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint, ode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un sistema de EDOs usualmente deberá estar formulado de una forma estándard antes de poder ser atacado numéricamente. Esta forma estándard es la siguiente:\n",
    "\n",
    "$y' = f(y, t)$\n",
    "\n",
    "donde \n",
    "\n",
    "$y = [y_1(t), y_2(t), ..., y_n(t)]$ \n",
    "\n",
    "y $f$ es cierta función que nos proporciona las derivadas de las componentes $y_i(t)$. Para resolver una EDO necesitamos conocer esta función $f$ y una condición inicial, $y(0)$.\n",
    "\n",
    "Nótese que EDOs de mayor orden siempre pueden ser escritas en esta forma estándard introduciendo nuevas variables virtuales para las derivadas intermedias.\n",
    "\n",
    "Una vez que tenemos definidos en Python la función `f` y el array `y_0` (correspondientes a $f$ e $y(0)$ en su formulación matemática), podremos usar el procedimiento `odeint` de la siguiente manera:\n",
    "\n",
    "    y_t = odeint(f, y_0, t)\n",
    "\n",
    "donde `t` es un array con coordenadas temporales donde resolver el problema. `y_t` es otro array con una fila por cada nodo temporal en `t`, donde cada columna corresponde a la solución `y_i(t)` en ese instante de tiempo. \n",
    "\n",
    "Veremos cómo podemos implementar `f` e `y_0` en Python en los siguientes ejemplos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejemplo: doble péndulo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consideremos un ejemplo físico: El doble péndulo compuesto, descrito con cierto detalle en el siguiente link: http://en.wikipedia.org/wiki/Double_pendulum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://upload.wikimedia.org/wikipedia/commons/c/c9/Double-compound-pendulum-dimensioned.svg\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(url='http://upload.wikimedia.org/wikipedia/commons/c/c9/Double-compound-pendulum-dimensioned.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Las ecuaciones del movimiento de este péndulo también se proporcionan en esta misma página de wikipedia:\n",
    "\n",
    "${\\dot \\theta_1} = \\frac{6}{m\\ell^2} \\frac{ 2 p_{\\theta_1} - 3 \\cos(\\theta_1-\\theta_2) p_{\\theta_2}}{16 - 9 \\cos^2(\\theta_1-\\theta_2)}$\n",
    "\n",
    "${\\dot \\theta_2} = \\frac{6}{m\\ell^2} \\frac{ 8 p_{\\theta_2} - 3 \\cos(\\theta_1-\\theta_2) p_{\\theta_1}}{16 - 9 \\cos^2(\\theta_1-\\theta_2)}.$\n",
    "\n",
    "${\\dot p_{\\theta_1}} = -\\frac{1}{2} m \\ell^2 \\left [ {\\dot \\theta_1} {\\dot \\theta_2} \\sin (\\theta_1-\\theta_2) + 3 \\frac{g}{\\ell} \\sin \\theta_1 \\right ]$\n",
    "\n",
    "${\\dot p_{\\theta_2}} = -\\frac{1}{2} m \\ell^2 \\left [ -{\\dot \\theta_1} {\\dot \\theta_2} \\sin (\\theta_1-\\theta_2) +  \\frac{g}{\\ell} \\sin \\theta_2 \\right]$\n",
    "\n",
    "Para hacer el código Python más simple y fácil de seguir, introduzcamos los nuevos nombres de variable y una notación vectorial: $x = [\\theta_1, \\theta_2, p_{\\theta_1}, p_{\\theta_2}]$\n",
    "\n",
    "${\\dot x_1} = \\frac{6}{m\\ell^2} \\frac{ 2 x_3 - 3 \\cos(x_1-x_2) x_4}{16 - 9 \\cos^2(x_1-x_2)}$\n",
    "\n",
    "${\\dot x_2} = \\frac{6}{m\\ell^2} \\frac{ 8 x_4 - 3 \\cos(x_1-x_2) x_3}{16 - 9 \\cos^2(x_1-x_2)}$\n",
    "\n",
    "${\\dot x_3} = -\\frac{1}{2} m \\ell^2 \\left [ {\\dot x_1} {\\dot x_2} \\sin (x_1-x_2) + 3 \\frac{g}{\\ell} \\sin x_1 \\right ]$\n",
    "\n",
    "${\\dot x_4} = -\\frac{1}{2} m \\ell^2 \\left [ -{\\dot x_1} {\\dot x_2} \\sin (x_1-x_2) +  \\frac{g}{\\ell} \\sin x_2 \\right]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "g = 9.82\n",
    "L = 0.5\n",
    "m = 0.1\n",
    "\n",
    "def dx(x, t):\n",
    "    \"\"\"\n",
    "    El segundo término de la EDO del péndulo\n",
    "    \"\"\"\n",
    "    x1, x2, x3, x4 = x[0], x[1], x[2], x[3]\n",
    "    \n",
    "    dx1 = 6.0/(m*L**2) * (2 * x3 - 3 * cos(x1-x2) * x4)/(16 - 9 * cos(x1-x2)**2)\n",
    "    dx2 = 6.0/(m*L**2) * (8 * x4 - 3 * cos(x1-x2) * x3)/(16 - 9 * cos(x1-x2)**2)\n",
    "    dx3 = -0.5 * m * L**2 * ( dx1 * dx2 * sin(x1-x2) + 3 * (g/L) * sin(x1))\n",
    "    dx4 = -0.5 * m * L**2 * (-dx1 * dx2 * sin(x1-x2) + (g/L) * sin(x2))\n",
    "    \n",
    "    return [dx1, dx2, dx3, dx4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# elegimos una condición inicial\n",
    "x0 = [pi/4, pi/2, 0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# el conjunto de instantes temporales en los que aproximaremos la solución\n",
    "# de la EDO: de 0 a 10 segundos\n",
    "t = linspace(0, 10, 250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# resolución del problema del péndulo\n",
    "x = odeint(dx, x0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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llBOklD+E+7mnnw7s2AGUlpr51zBupqyMRLvRImLZ2bRU+eBuwizh7sZQedUKzohwB1i4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Y8emhIv8MgjTMJ9+qn5z42OZiD89dccF3r2rO+2Mj178nY8bx4VrdJS7blbb6W6lpkpR8NJSFQ0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\nu6IoiqIoiqIoiqJkYv4PiwvvPjg3jS0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa338ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# dibujemos ahora los ángulos en función del tiempo\n",
    "\n",
    "fig, axes = plt.subplots(1,2, figsize=(12,4))\n",
    "axes[0].plot(t, x[:, 0], 'r', label=\"theta1\")\n",
    "axes[0].plot(t, x[:, 1], 'b', label=\"theta2\")\n",
    "\n",
    "x1 = + L * sin(x[:, 0])\n",
    "y1 = - L * cos(x[:, 0])\n",
    "\n",
    "x2 = x1 + L * sin(x[:, 1])\n",
    "y2 = y1 - L * cos(x[:, 1])\n",
    "    \n",
    "axes[1].plot(x1, y1, 'r', label= u\"péndulo1\")\n",
    "axes[1].plot(x2, y2, 'b', label= u\"péndulo2\")\n",
    "axes[1].set_ylim([-1, 0])\n",
    "axes[1].set_xlim([1, -1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SUoKBAwciOjoaixYt8kl7OobxBLoV7kJQuDznuTOOKCgAmjcH6tRxbrumTU3F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TYQBQku+XbUKNpRH37YXYcbTkiS4qG4t29vnRq0EZrGJJDfObkhzHJfuZKL42WXeT7epg0/D49c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\nibuZmZmZmZlZA/t/zG9MQ1WEWukAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaafcd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# dibujemos ahora los ángulos en función del tiempo\n",
    "\n",
    "fig, axes = plt.subplots(1,2, figsize=(12,4))\n",
    "axes[0].plot(t, x[:, 0], 'r', label=r\"$\\theta_1$\")\n",
    "axes[0].plot(t, x[:, 1], 'b', label=r\"$\\theta_2$\")\n",
    "axes[0].legend(loc=0);\n",
    "\n",
    "\n",
    "x1 = + L * sin(x[:, 0])\n",
    "y1 = - L * cos(x[:, 0])\n",
    "\n",
    "x2 = x1 + L * sin(x[:, 1])\n",
    "y2 = y1 - L * cos(x[:, 1])\n",
    "    \n",
    "axes[1].plot(x1, y1, 'r', label= \"péndulo1\")\n",
    "axes[1].plot(x2, y2, 'b', label= \"péndulo2\")\n",
    "axes[1].set_ylim([-1, 0])\n",
    "axes[1].set_xlim([1, -1])\n",
    "axes[1].legend(loc=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una animación simple del movimiento pendular, aunque hay posibilidades mejores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.display import display, clear_output\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "00280\n"
     ]
    }
   ],
   "source": [
    "t_idx = 280; print(\"%05d\" % t_idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'00280'"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(\"%05d\" % t_idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\Pedro\\\\Dropbox\\\\Cursos\\\\TallerPythonUGR\\\\TallerPythonUGR-master\\\\notebooks_adicionales\\\\Animacion'"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%pwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%mkdir Animacion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Pedro\\Dropbox\\Cursos\\TallerPythonUGR\\TallerPythonUGR-master\\notebooks_adicionales\\Animacion\\Animacion\n"
     ]
    }
   ],
   "source": [
    "%cd Animacion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " El volumen de la unidad C no tiene etiqueta.\n",
      " El número de serie del volumen es: 84A6-5A60\n",
      "\n",
      " Directorio de C:\\Users\\Pedro\\Dropbox\\Cursos\\TallerPythonUGR\\TallerPythonUGR-master\\notebooks_adicionales\\Animacion\\Animacion\n",
      "\n",
      "19/09/2018  14:31    <DIR>          .\n",
      "19/09/2018  14:31    <DIR>          ..\n",
      "               0 archivos              0 bytes\n",
      "               2 dirs   3.476.897.792 bytes libres\n"
     ]
    }
   ],
   "source": [
    "%ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa46a5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa46a5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(4,4))\n",
    "\n",
    "for t_idx, tt in enumerate(t[:200]):\n",
    "    # print(t_idx, tt)\n",
    "    x1 = + L * sin(x[t_idx, 0])\n",
    "    y1 = - L * cos(x[t_idx, 0])\n",
    "\n",
    "    x2 = x1 + L * sin(x[t_idx, 1])\n",
    "    y2 = y1 - L * cos(x[t_idx, 1])\n",
    "    \n",
    "    ax.cla()    \n",
    "    ax.plot([0, x1], [0, y1], 'r.-')\n",
    "    ax.plot([x1, x2], [y1, y2], 'b.-')\n",
    "    ax.set_ylim([-1.5, 0.5])\n",
    "    ax.set_xlim([1, -1])\n",
    "\n",
    "    clear_output() \n",
    "    display(fig)\n",
    "\n",
    "    time.sleep(0.1)\n",
    "    fig.savefig(\"doble-pendulo-\" + str(\"%05d\" % t_idx) + \".png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
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    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " El volumen de la unidad C no tiene etiqueta.\n",
      " El número de serie del volumen es: 84A6-5A60\n",
      "\n",
      " Directorio de C:\\Users\\Pedro\\Dropbox\\Cursos\\TallerPythonUGR\\TallerPythonUGR-master\\notebooks_adicionales\\Animacion\\Animacion\n",
      "\n",
      "19/09/2018  14:31             6.669 doble-pendulo-00000.png\n",
      "19/09/2018  14:31             7.446 doble-pendulo-00001.png\n",
      "19/09/2018  14:31             7.582 doble-pendulo-00002.png\n",
      "19/09/2018  14:31             7.753 doble-pendulo-00003.png\n",
      "19/09/2018  14:31             7.941 doble-pendulo-00004.png\n",
      "19/09/2018  14:31             8.113 doble-pendulo-00005.png\n",
      "19/09/2018  14:31             8.154 doble-pendulo-00006.png\n",
      "19/09/2018  14:31             8.048 doble-pendulo-00007.png\n",
      "19/09/2018  14:31             8.269 doble-pendulo-00008.png\n",
      "19/09/2018  14:31             7.826 doble-pendulo-00009.png\n",
      "19/09/2018  14:31             7.579 doble-pendulo-00010.png\n",
      "19/09/2018  14:31             7.676 doble-pendulo-00011.png\n",
      "19/09/2018  14:31             7.516 doble-pendulo-00012.png\n",
      "19/09/2018  14:31             7.918 doble-pendulo-00013.png\n",
      "19/09/2018  14:31             8.125 doble-pendulo-00014.png\n",
      "19/09/2018  14:31             8.217 doble-pendulo-00015.png\n",
      "19/09/2018  14:31             8.198 doble-pendulo-00016.png\n",
      "19/09/2018  14:31             7.918 doble-pendulo-00017.png\n",
      "19/09/2018  14:31             8.324 doble-pendulo-00018.png\n",
      "19/09/2018  14:31             8.275 doble-pendulo-00019.png\n",
      "19/09/2018  14:31             8.229 doble-pendulo-00020.png\n",
      "19/09/2018  14:31             8.109 doble-pendulo-00021.png\n",
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      "19/09/2018  14:32             7.768 doble-pendulo-00198.png\n",
      "19/09/2018  14:32             7.536 doble-pendulo-00199.png\n",
      "             200 archivos      1.574.026 bytes\n",
      "               0 dirs   3.590.348.800 bytes libres\n"
     ]
    }
   ],
   "source": [
    "ls *.png"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ffmpeg version N-82314-g863ebe6 Copyright (c) 2000-2016 the FFmpeg developers\n",
      "  built with gcc 5.4.0 (GCC)\n",
      "  configuration: --enable-gpl --enable-version3 --disable-w32threads --enable-dxva2 --enable-libmfx --enable-nvenc --enable-avisynth --enable-bzlib --enable-libebur128 --enable-fontconfig --enable-frei0r --enable-gnutls --enable-iconv --enable-libass --enable-libbluray --enable-libbs2b --enable-libcaca --enable-libfreetype --enable-libgme --enable-libgsm --enable-libilbc --enable-libmodplug --enable-libmp3lame --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libopenh264 --enable-libopenjpeg --enable-libopus --enable-librtmp --enable-libschroedinger --enable-libsnappy --enable-libsoxr --enable-libspeex --enable-libtheora --enable-libtwolame --enable-libvidstab --enable-libvo-amrwbenc --enable-libvorbis --enable-libvpx --enable-libwavpack --enable-libwebp --enable-libx264 --enable-libx265 --enable-libxavs --enable-libxvid --enable-libzimg --enable-lzma --enable-decklink --enable-zlib\n",
      "  libavutil      55. 36.100 / 55. 36.100\n",
      "  libavcodec     57. 66.101 / 57. 66.101\n",
      "  libavformat    57. 57.100 / 57. 57.100\n",
      "  libavdevice    57.  2.100 / 57.  2.100\n",
      "  libavfilter     6. 66.100 /  6. 66.100\n",
      "  libswscale      4.  3.100 /  4.  3.100\n",
      "  libswresample   2.  4.100 /  2.  4.100\n",
      "  libpostproc    54.  2.100 / 54.  2.100\n",
      "Input #0, image2, from 'doble-pendulo-%05d.png':\n",
      "  Duration: 00:00:08.00, start: 0.000000, bitrate: N/A\n",
      "    Stream #0:0: Video: png, rgba(pc), 400x400 [SAR 3937:3937 DAR 1:1], 25 fps, 25 tbr, 25 tbn, 25 tbc\n",
      "Output #0, avi, to 'doble-pendulo.avi':\n",
      "  Metadata:\n",
      "    ISFT            : Lavf57.57.100\n",
      "    Stream #0:0: Video: mpeg4 (FMP4 / 0x34504D46), yuv420p, 400x400 [SAR 1:1 DAR 1:1], q=2-31, 200 kb/s, 25 fps, 25 tbn, 25 tbc\n",
      "    Metadata:\n",
      "      encoder         : Lavc57.66.101 mpeg4\n",
      "    Side data:\n",
      "      cpb: bitrate max/min/avg: 0/0/200000 buffer size: 0 vbv_delay: -1\n",
      "Stream mapping:\n",
      "  Stream #0:0 -> #0:0 (png (native) -> mpeg4 (native))\n",
      "Press [q] to stop, [?] for help\n",
      "frame=  200 fps=0.0 q=6.8 Lsize=     344kB time=00:00:08.00 bitrate= 352.1kbits/s speed=16.6x    \n",
      "video:333kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: 3.122858%\n"
     ]
    }
   ],
   "source": [
    "!ffmpeg -r 25 -i doble-pendulo-%05d.png doble-pendulo.avi\n",
    "# esta utilidad de generación de video debe estar correctamente instalada"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " El volumen de la unidad C no tiene etiqueta.\n",
      " El número de serie del volumen es: 84A6-5A60\n",
      "\n",
      " Directorio de C:\\Users\\Pedro\\Dropbox\\Cursos\\TallerPythonUGR\\TallerPythonUGR-master\\notebooks_adicionales\\Animacion\\Animacion\n",
      "\n",
      "19/09/2018  14:33           352.080 doble-pendulo.avi\n",
      "               1 archivos        352.080 bytes\n",
      "               0 dirs   3.590.119.424 bytes libres\n"
     ]
    }
   ],
   "source": [
    "ls doble-pendulo.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Pedro\\Dropbox\\Cursos\\TallerPythonUGR\\TallerPythonUGR-master\\notebooks_adicionales\n"
     ]
    }
   ],
   "source": [
    "%cd .."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejemplo: oscilador armónico amortiguado "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los problemas de EDOs son importantes en  Física Computacional, por lo que mostraremos otro ejemplo significativo: el oscilador armónico amortiguado. Este problema está bien descrito en la página de Wikipedia: http://en.wikipedia.org/wiki/Damping\n",
    "\n",
    "La ecuación del movimiento para el oscilador amortiguado es:\n",
    "\n",
    "$\\displaystyle \\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2} + 2\\zeta\\omega_0\\frac{\\mathrm{d}x}{\\mathrm{d}t} + \\omega^2_0 x = 0$\n",
    "\n",
    "donde $x$ es la posición del oscilador, $\\omega_0$ ees la frecuencia, y $\\zeta$ es la ratio de amortiguación. Para escribir está EDO de segundo orden en forma estándard introducimos $p = \\frac{\\mathrm{d}x}{\\mathrm{d}t}$:\n",
    "\n",
    "$\\displaystyle \\frac{\\mathrm{d}p}{\\mathrm{d}t} = - 2\\zeta\\omega_0 p - \\omega^2_0 x$\n",
    "\n",
    "$\\displaystyle \\frac{\\mathrm{d}x}{\\mathrm{d}t} = p$\n",
    "\n",
    "En la implementación de este ejemplo añadiremos argumentos extra a la función de la parte derecha (RHS de \"right hand side\" en inglés) de la EDO, en vez de usar variables globales como hicimos en el ejemplo anterior.\n",
    "Como consecuencia de estos argumentos extra en el RHS, necesitaremos pasar una palabra clave (\"keyword\" en inglés) como argumento `args` de la procedimiento `odeint`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def dy(y, t, zeta, w0):\n",
    "    \"\"\"\n",
    "    La función RHS de la EDO del oscilador amortiguado\n",
    "    \"\"\"\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]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# estado inicial: \n",
    "y0 = [1.0, 0.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# partición en tiempo donde resolver la EDO\n",
    "t = linspace(0, 10, 1000)\n",
    "w0 = 2*pi*1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# resolvemos la EDO para tres valores diferentes \n",
    "# del coeficiente de amortiguamiento\n",
    "\n",
    "y1 = odeint(dy, y0, t, args=(0.0, w0)) # caso no amortiguado\n",
    "y2 = odeint(dy, y0, t, args=(0.2, w0)) # amortiguación atenuada\n",
    "y3 = odeint(dy, y0, t, args=(1.0, w0)) # amortiguamiento crítico\n",
    "y4 = odeint(dy, y0, t, args=(5.0, w0)) # sobre amortiguado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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C+B7Az4SQT5QXIsMwjOpJW2I5LCwMAoEA3bt3V0NEDFN7Sh1TQSk9DuA4ABD5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j+kFx+g4UafHR0dngvSjAcv2ny4NfxeDIyNFSGEJ20+XK4KU8+tZ7ikY8bm1jNcxt6Ojg7PBYBH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\n/gXfB52lYo8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x872d208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(t, y1[:,0], 'k', label=u\"sin amortiguación\", linewidth=0.25)\n",
    "ax.plot(t, y2[:,0], 'r', label=u\"amortiguación atenuada\")\n",
    "ax.plot(t, y3[:,0], 'b', label=u\"amortiguación crítica\")\n",
    "ax.plot(t, y4[:,0], 'g', label=u\"sobre amortiguación\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Transformada de Fourier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Las transformadas de Fourier son una de las herramientas universales en  Física Computacional, que aparecen una y otra vez en diferentes contextos. SciPy proporciona funciones para acceder a la biblioteca clasica [FFTPACK](http://www.netlib.org/fftpack/) de NetLib, que es una muy eficiente y bien testeada biblioteca escrita en FORTRAN. La API de SciPy tiene algunos procedimientos o funciones adicionales, pero en conjunto la API está estrechamente relacionada con la biblioteca original en FORTRAN.\n",
    "\n",
    "Para usar el módulo `fftpack` en un programa de python, incluirlo usando:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from numpy.fft import fftfreq\n",
    "from scipy.fftpack import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para demostrar cómo realizar una transformada rápida de Fourier (FFT) con SciPy, echemos un vistazo a la FFT de la solución del oscilador amortiguado de la sección anterior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = len(t)\n",
    "dt = t[1]-t[0]\n",
    "\n",
    "# calcula la transformada rápida de Fourier \n",
    "# y2 es la solución del oscilador atenuado de la sección anterior\n",
    "F = fft(y2[:,0]) \n",
    "\n",
    "# calcula las frecuencias de las componentes en F\n",
    "w = fftfreq(N, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nP+luPyRpdzJTlfafA0uApZXlt2bofSRpt3DBBTAwAP/9v3e7J/A7v5Mr7hde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\nLkmSJBWcoV2SJEkquP8NGO6RwK2SpusAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa035080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(9,3))\n",
    "ax.plot(w, abs(F));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ya que la señal es real, el espectro es simétrico y nosotros sólo tenemos que representar la parte que corresponda a las frecuencias postivas. Para extraer dicha parte de `w` y `F` podemos usar alguno de los trucos de indexado disponibles para arrays de NumPy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "indices = where(w > 0) \n",
    "# selecciona sólo aquellos índices de los elementos que correspondan\n",
    "# a frecuencias positivas\n",
    "w_pos = w[indices]\n",
    "F_pos = F[indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UTk0pXQ/Eak5bmlKal1J6vWlr7FyZai0lOOEEeO01+O1vYfDgoitST7LddjB9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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa12dfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(9,3))\n",
    "ax.plot(w_pos, abs(F_pos))\n",
    "ax.set_xlim(0, 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como se esperaba, vemos ahora que el pico (\"peak\" en inglés) en el espectro está centrada alrededor del valor 1, que es precisamente la frecuencia usada en el ejemplo del oscilador amortiguado."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Álgebra lineal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El módulo de álgebra lineal contiene numerosas funciones y procedimientos relacionados, incluyendo la resolución de sistemas lineales, cálculo de valores y vectores propios (\"eigenvalue\" y \"eigenvectors\" en inglés), diferentes operaciones matriciales (como por ejemplo la exponenciación matricial), cierto número de diferentes descomposctiones matriciales (SVD, LU, Cholesky), etc. \n",
    "\n",
    "Una documetación detallada está disponible en: http://docs.scipy.org/doc/scipy/reference/linalg.html\n",
    "\n",
    "Aquí veremos como usar algunas de estas funciones y procedimientos:\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Resolución de sistemas de ecuaciones lineales "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los sistemas de ecuaciones lineales pueden escribirse de forma matricial\n",
    "\n",
    "$A x = b$\n",
    "\n",
    "donde $A$ es una matriz y $x, b$ son vectores, y pueden resolverse de la siguiente manera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.linalg import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "A = array([[1,2,3], [4,5,6], [7,8,9]])\n",
    "b = array([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.33333333,  0.66666667,  0.        ])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = solve(A, b)\n",
    "\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.00000000e+00,  -2.22044605e-16,   0.00000000e+00])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check\n",
    "dot(A, x) - b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "También podemoss hacer lo mismo con\n",
    "\n",
    "$A X = B$\n",
    "\n",
    "donde $A, B, X$ son matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "A = rand(3,3)\n",
    "B = rand(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = solve(A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.03105302,  2.07281952, -1.29603642],\n",
       "       [ 0.28724883,  0.05776324,  1.14359303],\n",
       "       [-1.24467928, -1.73984133,  0.52050302]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.992586547019258e-16"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# comprobémoslo\n",
    "norm(dot(A, X) - B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Valores y vectores propios (\"eigenvalues\" y \"eigenvectors\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El problema de valores y vectores propios para una matriz $A$:\n",
    "\n",
    "$\\displaystyle A v_n = \\lambda_n v_n$\n",
    "\n",
    "donde $v_n$ es el $n$-ésimo vector propio (\"eigenvector\") y $\\lambda_n$ es el valor propio (\"eigenvalue\") correspondiente.\n",
    "\n",
    "Para calcular los valores propios de una matriz, usar `eigvals` y para calcular tanto los valores como los vectores propios, usar la función `eig`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "evals = eigvals(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.3336193+0.j,  0.1822869+0.j, -0.5514125+0.j])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "evals, evecs = eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.3336193+0.j,  0.1822869+0.j, -0.5514125+0.j])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.58314384, -0.77883189,  0.27763935],\n",
       "       [-0.7358319 ,  0.27007247, -0.69350967],\n",
       "       [-0.34423057,  0.56611108,  0.66480127]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evecs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los vectores propios correspondientes al valor propio $n$-ésimo (almacenado en `evals[n]`) es la $n$-ésima *columna* en `evecs`, es decir `evecs[:,n]`. Para verificar esto, probemos a multiplicar estos posibles vectores propios por la matriz y comparemos a su vez con el producto del correspondiente valora propio por este mismo vector propio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.752780664831301e-16"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 1\n",
    "\n",
    "norm(dot(A, evecs[:,n]) - evals[n] * evecs[:,n])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hay también otros procedimientos más especializados, como `eigh` para matrices Hermitianas. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operaciones matriciales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.22825502, -0.6580032 , -2.79200423],\n",
       "       [-0.35923073,  0.05330675,  2.09747197],\n",
       "       [-2.52730045,  1.82006806,  1.14061089]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# matriz inversa\n",
    "inv(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.13404910716621246"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# determinante\n",
    "det(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.3589419322045251, 1.8811715566148621)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# distintos tipos de normas\n",
    "norm(A, ord=2), norm(A, ord=Inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrices huecas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrices huecas (\"sparse\" en inglés) suelen ser útiles en las simulaciones numéricas que dan lugar a sistemas lineales de gran tamaño en las que la mayoría de los elementos de la matriz asociada son nulos. Scipy tiene buen soporte para este tipo de matrices, con operaciones básicas de álgebra lineal (como la resolución de los correspondientes sistemas de ecuaciones lineales, cálculo de valores y vectores propios, etc). Hay diversas  estrategias posibles para el almacenamiento de estas matrices huecas de manera eficiente. Alguna de las más comunes son las denominadas en forma coordinada (COO), en forma de listas de listas (LIL), y en forma de columna hueca comprimida CSC (o fila hueca comprimida, CSR). Cada formato posee sus ventajas y desventajas. La mayoría de los algorítmos computacionales (resolución de sistemas de ecuaciones lineales, multiplicación de matrices, etc) pueden ser implementados eficientemente usando los formatos CSR o CSC, pero no son tan intuitivos y fáciles de inicializar. Muy a menudo una matriz hueca se crea inicialmente en formato COO o LIL (con el que podemos eficientemente añadir elementos a la matriz), y convertirla posteriormente al formato CSC o CSR justo antes de ser usadas para los cálculos definitivos.\n",
    "\n",
    "Para más información acerca de estos formatos para matrices huecas, consultar por ejemplo http://en.wikipedia.org/wiki/Sparse_matrix\n",
    "\n",
    "Cuando creamos una matriz hueca debemos elegir con que formato deberá ser almacenada. Por ejemplo, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.sparse import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0],\n",
       "       [0, 3, 0, 0],\n",
       "       [0, 1, 1, 0],\n",
       "       [1, 0, 0, 1]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# matriz densa\n",
    "M = array([[1,0,0,0], [0,3,0,0], [0,1,1,0], [1,0,0,1]]); M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.int32'>'\n",
       "\twith 6 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ahora la convertimos de densa a hueca con formato CSR\n",
    "A = csr_matrix(M); A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 0, 0, 0],\n",
       "        [0, 3, 0, 0],\n",
       "        [0, 1, 1, 0],\n",
       "        [1, 0, 0, 1]], dtype=int32)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y la volvemos a convertir de hueca a densa\n",
    "A.todense()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una manera más eficiente de crear matrices huecas: crear una matriz vacía en un formato comprimido determinado y a continuación rellenar sólo los valores no nulos de la matriz a partir de los índices apropiados (evitar crear una matriz densa potencialmente grande)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 6 stored elements in LInked List format>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = lil_matrix((4,4)) # matriz hueca 4x4 con formato LIL\n",
    "A[0,0] = 1\n",
    "A[1,1] = 3\n",
    "A[2,2] = A[2,1] = 1\n",
    "A[3,3] = A[3,0] = 1\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  3.,  0.,  0.],\n",
       "        [ 0.,  1.,  1.,  0.],\n",
       "        [ 1.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.todense()   # conversión a una matriz densa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convirtiendo entre diferentes formatos de matrices huecas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 6 stored elements in LInked List format>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 6 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = csr_matrix(A); A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 6 stored elements in Compressed Sparse Column format>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = csc_matrix(A); A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nosotros podemos realizar cálculos con matrices huecas como con las matrices densas: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  3.,  0.,  0.],\n",
       "        [ 0.,  1.,  1.,  0.],\n",
       "        [ 1.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  9.,  0.,  0.],\n",
       "        [ 0.,  4.,  1.,  0.],\n",
       "        [ 2.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(A * A).todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  3.,  0.,  0.],\n",
       "        [ 0.,  1.,  1.,  0.],\n",
       "        [ 1.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  9.,  0.,  0.],\n",
       "        [ 0.,  4.,  1.,  0.],\n",
       "        [ 2.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dot(A).todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = array([1,2,3,4])[:,newaxis]; v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.],\n",
       "       [ 6.],\n",
       "       [ 5.],\n",
       "       [ 5.]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# multiplicación de una matriz hueca por un vector\n",
    "A * v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.],\n",
       "        [ 6.],\n",
       "        [ 5.],\n",
       "        [ 5.]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# el mismo resultado con una matriz densa\n",
    "A.todense() * v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimización"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimización (encontrar mínimos o máximos de una función) es un vasto campo de las matemáticas, y la optimización de funciones complicadas o de muchas variables puede resultar una tarea compleja. Aquí sólo veremos algunos ejemplos simples. Para una introducción más detallada del paquete de optimización de SciPy consultar: http://scipy-lectures.github.com/advanced/mathematical_optimization/index.html\n",
    "\n",
    "Para usar el módulo de optimización en Scipy habrá que empezar con importar el módulo `optimize`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Buscando un mínimo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Veamos primero cómo encontrar el mínimo de una función sencilla de una sóla variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 4*x**3 + (x-2)**2 + x**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GRCT7lJXB8cfDvvv6BlMat5B+Cgw54ic/gaOPhrPPhiVLYlcjIpI9Kipg5Egf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\nH82WDuiI2M3oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa13d710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax  = plt.subplots()\n",
    "x = linspace(-5, 3, 100)\n",
    "ax.plot(x, f(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos usar la función o procedimiento `fmin_bfgs` para buscar el mínimo de la función:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: -3.506641\n",
      "         Iterations: 5\n",
      "         Function evaluations: 24\n",
      "         Gradient evaluations: 8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-2.67298151])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_min = optimize.fmin_bfgs(f, -2)\n",
    "x_min "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SJEmf9vDDeTK3jTfOryA3a2yWKka5Xk+eRZ475UxgWeAN4A7g7JTSnCbl1gda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\nkiRVLBMVSZJUsf4/gGRnjQVWmykAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9f89eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax  = plt.subplots()\n",
    "x = linspace(-2.7, -2.6, 100)\n",
    "ax.plot(x, f(x));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 2.804988\n",
      "         Iterations: 3\n",
      "         Function evaluations: 15\n",
      "         Gradient evaluations: 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.46961745])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fmin_bfgs(f, 0.5) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Mgz3Lo0qGiIhIgkpKwmDPww+HXr2ijiZ1qZIhIiKSoOuvD4tvTZ2qwZ4VUSVDREQkAR99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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa1e0208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax  = plt.subplots()\n",
    "x = linspace(0.4, 0.6, 100)\n",
    "ax.plot(x, f(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "También podemos usar los procedimientos `brent` o `fminbound`, que tienen una sintaxis algo diferente y usan diferentes algoritmos. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.46961743402759754"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.brent(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.6729822917513886"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fminbound(f, -4, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Encontrando la solución  de una ecuación o cero de una función "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para buscar la raíz de una ecuación de la forma $f(x) = 0$ podemos usar el procedimiento `fsolve`, que requiere un valor o estimación inicial: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "omega_c = 3.0\n",
    "def f(omega):\n",
    "    # una ecuación transcendental: frecuencias de resonancia\n",
    "    # de un resonador de microondas de tipo low-Q SQUID\n",
    "    return tan(2*pi*omega) - omega_c/omega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:5: RuntimeWarning: divide by zero encountered in true_divide\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZK0C2MQGybfFiYN99ueYLgx0T+Y97789f/z87524EsApAVwATEvnayYQVIHsqKtj+ZtWa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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa1e6a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax  = plt.subplots(figsize=(10,4))\n",
    "x = linspace(0, 3, 1000)\n",
    "y = f(x)\n",
    "mask = where(abs(y) > 50)\n",
    "x[mask] = y[mask] = NaN \n",
    "# nos deshacemos de la línea vertical cuando la función cambie de signo\n",
    "ax.plot(x, y)\n",
    "ax.plot([0, 3], [0, 0], 'k')\n",
    "ax.set_ylim(-5,5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.23743014])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fsolve(f, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.71286972])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fsolve(f, 0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.18990285])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fsolve(f, 1.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolación"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La interpolación resulta una tarea simple y asequible en Scipy: gracias al procedimiento `interp1d`, con adecuados arrays describiendo los datos X e Y, devolverá un objeto que se comporta como una función que podrá evaluarse posteriormente para un valor arbitrario de x (en el rango cubierto por X), devolviendo el correspondiente valor interpolado de y:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.interpolate import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = arange(0, 10)  \n",
    "x = linspace(0, 9, 100)\n",
    "\n",
    "y_sim = f(n) + 0.1 * randn(len(n)) # medidas simuladas con ruido\n",
    "y_real = f(x)\n",
    "\n",
    "linear_interpolation = interp1d(n, y_sim)\n",
    "y_interp1 = linear_interpolation(x)\n",
    "\n",
    "cubic_interpolation = interp1d(n, y_sim, kind='cubic')\n",
    "y_interp3 = cubic_interpolation(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EQkJC0nw/BQoUQMmSJVG6dGnUrVsXdevWRbZs2dJ8Px+79evXY/369QavhYeHv/P2FPKN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\n4Z2uObQ6Lfbf3o8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wBWVjY8Opm6fSzMOMP9cH+fPPpg5RmMilS5eYM2dO/blRvnz5pMnR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uaQUuboB+ACyNDQUJmR0NBQ+ao6OVVgYKDUaDQyIiJCV2Zvby81Go3cv3+/ruzu3bvSxMREDho0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\nVDyDkSRJkqTiGYwkSZIkFe8TJiypN1ubXVIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x49df710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,4))\n",
    "ax.plot(n, y_sim, 'bs', label='datos con ruido')\n",
    "ax.plot(x, y_real, 'k', lw=2, label=u'función real')\n",
    "ax.plot(x, y_interp1, 'r', label=u'interpolación lineal')\n",
    "ax.plot(x, y_interp3, 'g', label=u'interpolación cubica')\n",
    "ax.legend(loc=3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estadística"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El módulo `scipy.stats` contiene un gran número de distribuciones y tests estadísticos. Para una documentación completa de todas sus características, consultar http://docs.scipy.org/doc/scipy/reference/stats.html.\n",
    "\n",
    "Hay otro paquete de Python muy completo y poderoso para modelado estadístico denominado 'statsmodels'. Consultar http://statsmodels.sourceforge.net para más detalles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Ahora creamos una variable aleatoria (discreta) \n",
    "# con distribución de Poisson\n",
    "\n",
    "X = stats.poisson(3.5) \n",
    "# distribución de fotones para un estado coherente con n=3.5 fotones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IWAt0AqskHRUR/UPUPwz4JmkBq7OAdwM3SXoyIr6b1fl94DbgE8C3SFuJf03SsRHxaI6f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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9fb0978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = arange(0,15)\n",
    "\n",
    "fig, axes = plt.subplots(3,1, sharex=True)\n",
    "\n",
    "# dibujamos la función de probabilidad (FDP)\n",
    "# (PMF, de \"probability mass function\" en inglés)\n",
    "axes[0].step(n, X.pmf(n))\n",
    "\n",
    "# así como la función de distribución acumulada \n",
    "# (\"commulative distribution function\" (CDF) en inglés)\n",
    "axes[1].step(n, X.cdf(n))\n",
    "\n",
    "# Finalmente mostramos el histograma de 1000 realizaciones\n",
    "# aleatorias de la variable estocástica X\n",
    "axes[2].hist(X.rvs(size=1000));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Ahora crearemos una variable aleatoria (contínua) \n",
    "# con distribución normal\n",
    "Y = stats.norm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Burr78dHxmwDvAXcA9xGSg5uAAxuqQppZD+AV4E+EipBVwMVAhbt/kFGAIiIi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\nYGZmZkUcGszMzKzIT/vwKs+bnFcPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x885c358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-5,5,100)\n",
    "\n",
    "fig, axes = plt.subplots(3,1, sharex=True)\n",
    "\n",
    "# representamos la función de densidad de probabilidad (PDF)\n",
    "axes[0].plot(x, Y.pdf(x))\n",
    "\n",
    "# y la función de distribución acumulada (CDF)\n",
    "axes[1].plot(x, Y.cdf(x));\n",
    "\n",
    "# así como el histograma con 1000 realizaciones aleatorias\n",
    "# de la variable estocástica  Y\n",
    "axes[2].hist(Y.rvs(size=1000), bins=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estadísticos obtenidos a partir de las distribuciones anteriores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.5, 1.8708286933869707, 3.5)"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.mean(), X.std(), X.var() #  distribución de Poission"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 1.0, 1.0)"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.mean(), Y.std(), Y.var() #  distribución normal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tests estadísticos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verifiquemos por ejemplo si dos conjuntos de datos aleatorios (en principio independientes) provienen o no de la misma distribución:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-estadistico = -0.0121726151942\n",
      "p-valor = 0.990289113389\n"
     ]
    }
   ],
   "source": [
    "t_estadistico, p_valor = stats.ttest_ind(X.rvs(size=1000), X.rvs(size=1000))\n",
    "\n",
    "print (\"t-estadistico =\", t_estadistico)\n",
    "print (\"p-valor =\", p_valor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ya que el p-valor es bastante grande no podemos rechazar la hipótesis de que ambos conjuntos de datos aleatorios tengan medias *diferentes*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para chequear si la media de una de las muestras de datos tiene media 0.1 (aunque la verdadera media es 0.0):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-4.6132645327539148, pvalue=4.4788111184570531e-06)"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Y.rvs(size=1000), 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Este p-valor tan bajo significa que ahora sí que podemos rechazar esta hipótesis de que la media de la variable aleatoria Y es 0.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Veámos qué pasa ahora cuando pasamos este mismo test con los valores correctos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=0.075961111136128717, pvalue=0.9394652464599621)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Y.rvs(size=1000), Y.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lecturas adicionales"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* http://www.scipy.org - La página web oficial del proyecto SciPy.\n",
    "* http://docs.scipy.org/doc/scipy/reference/tutorial/index.html - Un tutorial sobre cómo empezar a usar SciPy. \n",
    "* https://github.com/scipy/scipy/ - El código fuente de SciPy. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Versiones de los paquetes de Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.5.2 64bit [MSC v.1900 64 bit (AMD64)]"
        },
        {
         "module": "IPython",
         "version": "5.1.0"
        },
        {
         "module": "OS",
         "version": "Windows 7 6.1.7601 SP1"
        },
        {
         "module": "numpy",
         "version": "1.11.1"
        },
        {
         "module": "matplotlib",
         "version": "1.5.3"
        },
        {
         "module": "scipy",
         "version": "0.18.1"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.5.2 64bit [MSC v.1900 64 bit (AMD64)]</td></tr><tr><td>IPython</td><td>5.1.0</td></tr><tr><td>OS</td><td>Windows 7 6.1.7601 SP1</td></tr><tr><td>numpy</td><td>1.11.1</td></tr><tr><td>matplotlib</td><td>1.5.3</td></tr><tr><td>scipy</td><td>0.18.1</td></tr><tr><td colspan='2'>Wed Sep 19 14:36:49 2018 Hora de verano romance</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.5.2 64bit [MSC v.1900 64 bit (AMD64)] \\\\ \\hline\n",
       "IPython & 5.1.0 \\\\ \\hline\n",
       "OS & Windows 7 6.1.7601 SP1 \\\\ \\hline\n",
       "numpy & 1.11.1 \\\\ \\hline\n",
       "matplotlib & 1.5.3 \\\\ \\hline\n",
       "scipy & 0.18.1 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Wed Sep 19 14:36:49 2018 Hora de verano romance} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.5.2 64bit [MSC v.1900 64 bit (AMD64)]\n",
       "IPython 5.1.0\n",
       "OS Windows 7 6.1.7601 SP1\n",
       "numpy 1.11.1\n",
       "matplotlib 1.5.3\n",
       "scipy 0.18.1\n",
       "Wed Sep 19 14:36:49 2018 Hora de verano romance"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%load_ext version_information\n",
    "\n",
    "%version_information numpy, matplotlib, scipy"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}