Notebooks/Clase6a_Interpolacion-ajuste.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src=\"../static/aeropython_name_mini.png\" alt=\"AeroPython\" style=\"width: 300px;\"/>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Clase 6a: Interpolaci\u00f3n y ajuste"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "_La \u00faltimas tareas importantes que vamos a ver c\u00f3mo hacer con SciPy van a ser **interpolar** y **ajustar** una serie de puntos. Son tareas diferentes que aprovecharemos en circunstancias distintas, pero ambas muy \u00fatiles. Esta clase est\u00e1 basada en el art\u00edculo http://pybonacci.org/2013/08/15/ajuste-e-interpolacion-unidimensionales-basicos-en-python-con-scipy/ _"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Dos problemas diferentes\n",
      "\n",
      "Supongamos que tenemos una serie de puntos que representan los datos de un cierto experimento. Como ejemplo, vamos a cargar los datos de la polar de un avi\u00f3n que est\u00e1n en el archivo `polar.dat`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#!cat polar.dat  Linux / Mac OS X\n",
      "!type ../static/polar.dat"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "# Polar data for a certain airplane\r\n",
        "# 1st line: C_L\r\n",
        "# 2rd line: C_D\r\n",
        "\r\n",
        "-0.9100  -0.7200  -0.4800  -0.2700  -0.0600   0.1600   0.3100   0.4700   0.6000   0.8200   1.0200   1.2000   1.2400   1.1500   1.0000   0.8000\r\n",
        " 0.0538   0.0438   0.0316   0.0245   0.0228   0.0232   0.0262   0.0301   0.0348   0.0461   0.0608   0.0771   0.0814   0.0900   0.0950   0.1000\r\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La primera l\u00ednea son los datos de $C_L$ y la segunda los datos de $C_D$. Recordamos que hab\u00eda que usar la funci\u00f3n `np.loadtxt`, y en este caso no hay que especificar ning\u00fan argumento extra m\u00e1s porque ya por defecto detecta que los comentarios empiezan por `#`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "datos = np.loadtxt(\"../static/polar.dat\")\n",
      "C_L = datos[0]\n",
      "C_D = datos[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vamos a representar esos datos con cruces azules (pista: usar `mew=2`, \"marker edge width 2\", para que las cruces se vean mejor):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(C_D, C_L, 'x', mew=2, label=\"Datos reales\")\n",
      "plt.xlabel(\"$C_D$\")\n",
      "plt.ylabel(\"$C_L$\")\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.legend.Legend at 0x7f187af94240>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QMbO/NLPKEMUkEZ2GASB3pxQqZvaJ9G13/y9JNwerKGHoNAwAuTulORUz+7+SHpL0H+7+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\nBQAQDKECAAjm/wNfzqv/EOh++QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f187af94278>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vemos la forma cl\u00e1sica de la polar de un avi\u00f3n. Hallando *el \u00edndice* del m\u00e1ximo valor de $C_L$ podemos descartar los datos fuera de la regi\u00f3n de entrada en p\u00e9rdida, y para eso necesitamos la funci\u00f3n `np.argmax`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "idx_stall = np.argmax(C_L)\n",
      "idx_stall"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "12"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C_L[idx_stall]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "1.24"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(C_D[:idx_stall + 1], C_L[:idx_stall + 1], 'x', mew=2, label=\"Datos reales\")\n",
      "plt.plot(C_D[idx_stall + 1:], C_L[idx_stall + 1:], 'o', mfc='none', label=\"Fuera del modelo\")\n",
      "plt.xlabel(\"$C_D$\")\n",
      "plt.ylabel(\"$C_L$\")\n",
      "plt.legend(loc=4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.legend.Legend at 0x7f187ab84978>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nFNf1Rb0DHG1mRUA58HOgpOZKjf1QRETk4IRmTMXMfmpma4D+wCwzmx1d3s3M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\nkcAoVEREJDAKFRERCcz/B9N+gw+btBcSAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f187abf0be0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Hay dos cosas que nos pueden interesar:\n",
      "\n",
      "* Como *solo tenemos puntos intermedios*, no tenemos posibilidad de evaluar, por ejemplo, $C_L$ para un $C_D$ que no est\u00e9 en los datos. Si **interpolamos** la curva ya podemos hacerlo.\n",
      "* Sabemos que, fuera de la regi\u00f3n de entrada en p\u00e9rdida, la polar tiene *forma parab\u00f3lica*. Si **ajustamos** la curva podemos hallar el $C_{D0}$ y el $k$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Interpolaci\u00f3n\n",
      "\n",
      "Para interpolar utilizaremos el paquete `interpolate` de SciPy:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import interpolate"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vamos a generar unos puntos de ejemplo para explicar c\u00f3mo funciona. Para eso, vamos a usar simplemente la funci\u00f3n $\\sin{x}$ en un dominio con pocos puntos:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_i = [0.0, 0.9, 1.8, 2.7, 3.6, 4.4, 5.3, 6.2, 7.1, 8.0]\n",
      "y_i = [0.0, 0.8, 1.0, 0.5, -0.4, -1.0, -0.8, -0.1, 0.7, 1.0]\n",
      "plt.plot(x_i, y_i, 'x', mew=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f1877820b00>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ny+WXJR2TdEG9VXUXEa+Wi2dL2iZp4ALK9kWSrpb0t+p9wcEgGdgabf+opPdExB1SGr8b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\nD+JqYRWtEDO0AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f18785bfb38>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Para crear una **funci\u00f3n interpolante** utilizaremos el objeto `InterpolatedUnivariateSpline` del paquete `interpolate`. A este objeto solo hay que pasarle los puntos de interpolaci\u00f3n y el grado, y generar\u00e1 un *spline*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f_interp = interpolate.InterpolatedUnivariateSpline(x_i, y_i, k=1)\n",
      "f_interp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<scipy.interpolate.fitpack2.InterpolatedUnivariateSpline at 0x7f1877833dd8>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u00bfC\u00f3mo obtengo los puntos desde aqu\u00ed? El resultado que hemos obtenido es una *funci\u00f3n* y admite como argumento la $x$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f_interp(np.pi / 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "array(0.949065850398866)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vamos a representar esta funci\u00f3n junto con los puntos de interpolaci\u00f3n. F\u00edjate en que, ahora que tenemos una funci\u00f3n interpolante, podemos representarla en un dominio:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(0, 8)\n",
      "y_interp = f_interp(x)\n",
      "\n",
      "plt.plot(x_i, y_i, 'x', mew=2)\n",
      "plt.plot(x, y_interp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f187782f6a0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LsbLSArgX2CIiF4vzGWPMFxYzZeVaYLZjVUMQ8J4xZoXlTDnx5mnG\nssCnjpuGhwBzjTFf2o2UpWHAXMeg7kegv+U8WXK8WLYDvPFaBwDGmM2O3zATybyG9D0wNbvj9Q1T\nSinl52xP3SillHIzLXqllPJzWvRKKeXntOiVUsrPadErpZSf06JXSik/p0WvlFJ+ToteKaX83P8D\nSf4fEwW8FisAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f187782f6d8>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Retrocede ahora y comprueba lo que pasa si cambias el grado del *spline*."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Ejercicio**: Crear una funci\u00f3n interpolante $C_D = f(C_L)$ usando splines de grado 2 y representarla. Utiliza solo los datos que resultan de haber eliminado la regi\u00f3n de entrada en p\u00e9rdida. y ten en cuenta que la $x$ y la $y$ para este caso est\u00e1n cambiadas de sitio.\n",
      "\n",
      "1. Crea un polinomio interpolante usando los valores que encajan en el modelo parab\u00f3lico.\n",
      "2. Crea un dominio de $C_L$ entre `C_L.min()` y `C_L.max()`.\n",
      "3. Halla los valores interpolados de $C_D$ en ese dominio.\n",
      "4. Representa la funci\u00f3n y los puntos."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f_C_D = interpolate.InterpolatedUnivariateSpline(C_L[:idx_stall + 1], C_D[:idx_stall + 1], k=2)\n",
      "\n",
      "C_L_domain = np.linspace(C_L.min(), C_L.max())\n",
      "C_D_interp = f_C_D(C_L_domain)\n",
      "\n",
      "plt.plot(C_D_interp, C_L_domain)\n",
      "plt.plot(C_D, C_L, 'x', mew=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f187ab7f0b8>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Hu+5KRCQlklEsztozgsZdRP+9NcrJ3y1k+HC4/fYAAxMRSTNZmQhqu4jWXhH83odRBs3M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\nEnJKBCIiIadEICISckoEIiIh9/8BCnMAEzD1DB8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1877815080>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Ajuste\n",
      "\n",
      "El ajuste funciona de manera totalmente distinta: obtendremos una curva que no pasar\u00e1 por ninguno de los puntos originales, pero que a cambio tendr\u00e1 una expresi\u00f3n anal\u00edtica simple. Para realizar ajustes polin\u00f3micos vamos a utilizar el paquete `np.polynomial.polynomial` (s\u00ed, est\u00e1 dos veces)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.polynomial import polynomial"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vamos otra vez a generar unos datos para ver c\u00f3mo funcionar\u00eda, del tipo:\n",
      "\n",
      "$$y(x) = x^2 - x + 1 + \\text{Ruido}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_i = np.linspace(-2, 3, num=10)\n",
      "y_i = x_i ** 2 - x_i + 1 + 0.5 * np.random.randn(10)\n",
      "plt.plot(x_i, y_i, 'x', mew=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f1877751a58>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3l2xfZPukpLOS1iOis915u47i2PKDj0i6aptDvxsRD/bO+T1J/xcR919AzY1R5VrMMXqd\nsSPbl0t6QNKdvSfpudRrcbi+11/3sO0sIvKt51UO6Ii4dbfjtm+X9GaVY6Zn2rBrMeeelHTNps/X\nqHyKxpyz/TJJn5L0VxHxN9OuJwUR8Yztz0p6vaR86/G6RnEclvReSW/vNYCjtOssoRn1mKSftn3Q\n9gFJvyLpb6dcE6bMtiV9VFInIu6Zdj3TZPvltq/sbV8i6VZJJ7Y7t6426D+VdLmkR2yfsH2spt9t\nHNvvsH1GZU/1Z20/NO2aJikiXpDUn9zUkfTX8zq5yfYnJH1F0qttn7H9rmnXNEVvlPRrKkcsnOj9\nzesIl1dI+odeG/RxSQ9GxBe3O5GJKgCQKF55BQCJIqABIFEENAAkioAGgEQR0ACQKAIaABJFQANA\noghoAEjU/wM4nvvkdAo1gwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f18777832b0>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vamos a utilizar la funci\u00f3n `polynomial.polyfit`, que recibe los puntos de interpolaci\u00f3n y el grado del polinomio. El resultado ser\u00e1n los coeficientes del mismo, **en orden de potencias crecientes**."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a, b, c = polynomial.polyfit(x_i, y_i, deg=2)\n",
      "a, b, c"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "(0.88761170078475216, -1.1492479540254799, 1.0412654720539836)"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u00a1Muy similares a lo que esper\u00e1bamos! Para evaluar un polinomio con estos coeficientes, o bien construimos la funci\u00f3n nosotros mismos o usamos la funci\u00f3n `polynomial.polyval`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(-2, 3)\n",
      "#y_fit = a + b * x + c * x ** 2\n",
      "y_fit = polynomial.polyval(x, (a, b, c))\n",
      "\n",
      "l, = plt.plot(x, y_fit)\n",
      "plt.plot(x_i, y_i, 'x', mew=2, c=l.get_color())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f187772e080>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cnLJZxXFiCGHTEELLEEL7EMKwfAQmhadDB//oPW2a73Tr2tU/jqtGXSMEX4lx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\nStAiIgn1//8h+Nm9ATHsAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f187772e390>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Ejercicio**: Si modelizamos la polar como:\n",
      "\n",
      "$$C_D = C_{D0} + k C_L^2$$\n",
      "\n",
      "hallar los coeficientes $C_{D0}$ y $k$.\n",
      "\n",
      "<p></p>\n",
      "\n",
      "<div class=\"alert alert-warning\">**\u00a1Importante!** Estamos tentados de hacer un ajuste parab\u00f3lico pero ese no es el camino, porque nos dar\u00e1 un t\u00e9rmino lineal que ya sabemos que es cero. Es mejor hacer un cambio de variable y hacer un ajuste lineal:</div>\n",
      "\n",
      "$$y \\leftarrow C_D \\\\ x \\leftarrow C_L^2 \\\\ y = C_{D0} + k x$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_i = C_D[:idx_stall + 1]\n",
      "x_i = C_L[:idx_stall + 1] ** 2\n",
      "\n",
      "C_D0, k = polynomial.polyfit(x_i, y_i, deg=1)\n",
      "C_D0, k"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "(0.022155579233867944, 0.038058791717716381)"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#C_D_fit = polynomial.polyval(C_L_domain ** 2, (C_D0, k))\n",
      "C_D_fit = C_D0 + k * C_L_domain ** 2\n",
      "\n",
      "l, = plt.plot(C_D_fit, C_L_domain)\n",
      "plt.plot(C_D, C_L, 'x', mew=2, c=l.get_color())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7f187765c5f8>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qeXsqcGmNn2GHqGOqcUwL4D2gW5QxJZ/zFtA6efsR4KKof35AL3wh677J13kO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\niIjE3P8YFUA0AAAABUlEQVQBAmZT7diSnzIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f187765c6a0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Si te ha gustado esta clase:\n",
      "\n",
      "<a href=\"https://twitter.com/share\" class=\"twitter-share-button\" data-url=\"https://github.com/AeroPython/Curso_AeroPython\" data-text=\"Aprendiendo Python con\" data-via=\"pybonacci\" data-size=\"large\" data-hashtags=\"AeroPython\">Tweet</a>\n",
      "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n",
      "\n",
      "---"
     ]
    },
    {
     "cell_type": "heading",
     "level": 6,
     "metadata": {},
     "source": [
      "<img src=\"../static/linkedin.png\" alt=\"AeroPython\" style=\"width: 25px\" align=\"right\";/> Curso impartido por: [Juan Luis Cano](http://es.linkedin.com/in/juanluiscanor)  & [\u00c1lex S\u00e1ez](http://es.linkedin.com/pub/alejandro-saez-mollejo/55/22/473)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 6,
     "metadata": {},
     "source": [
      "En colaboraci\u00f3n: Alberto Lorenzo"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "<h4 align=\"right\">\u00a1S\u00edguenos en Twitter!"
     ]
    },
    {
     "cell_type": "heading",
     "level": 6,
     "metadata": {},
     "source": [
      "<a href=\"https://twitter.com/Pybonacci\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Pybonacci</a>\n",
      "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n",
      "\n",
      "<a href=\"https://twitter.com/Alex__S12\" class=\"twitter-follow-button\" data-show-count=\"false\" align=\"right\";>Follow @Alex__S12</a>\n",
      "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>\n",
      "\n",
      "<a href=\"https://twitter.com/newlawrence\" class=\"twitter-follow-button\" data-show-count=\"false\" align=\"right\";>Follow @newlawrence</a>\n",
      "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/deed.es\"><img alt=\"Licencia Creative Commons\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\">Curso AeroPython</span> por <span xmlns:cc=\"http://creativecommons.org/ns#\" property=\"cc:attributionName\">Juan Luis Cano Rodriguez y Alejandro S\u00e1ez Mollejo</span> se distribuye bajo una <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/deed.es\">Licencia Creative Commons Atribuci\u00f3n 4.0 Internacional</a>."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "<script src=\"//platform.linkedin.com/in.js\" type=\"text/javascript\"></script>\n",
      "<script type=\"IN/MemberProfile\" data-id=\"http://es.linkedin.com/in/juanluiscanor\" data-format=\"inline\" data-related=\"false\"></script>\n",
      "<script src=\"//platform.linkedin.com/in.js\" type=\"text/javascript\"></script>\n",
      "<script type=\"IN/MemberProfile\" data-id=\"http://es.linkedin.com/in/alejandrosaezm\" data-format=\"inline\" data-related=\"false\"></script>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "_Las siguientes celdas contienen configuraci\u00f3n del Notebook_\n",
      "\n",
      "_Para visualizar y utlizar los enlaces a Twitter el notebook debe ejecutarse como [seguro](http://ipython.org/ipython-doc/dev/notebook/security.html)_\n",
      "\n",
      "    File > Trusted Notebook"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%html\n",
      "<a href=\"https://twitter.com/Pybonacci\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Pybonacci</a>\n",
      "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<a href=\"https://twitter.com/Pybonacci\" class=\"twitter-follow-button\" data-show-count=\"false\">Follow @Pybonacci</a>\n",
        "<script>!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0],p=/^http:/.test(d.location)?'http':'https';if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src=p+'://platform.twitter.com/widgets.js';fjs.parentNode.insertBefore(js,fjs);}}(document, 'script', 'twitter-wjs');</script>"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.HTML at 0x430e208>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Esta celda da el estilo al notebook\n",
      "from IPython.core.display import HTML\n",
      "css_file = '../static/styles/style.css'\n",
      "HTML(open(css_file, \"r\").read())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<link href='http://fonts.googleapis.com/css?family=Source+Sans+Pro|Josefin+Sans:400,700,400italic|Ubuntu+Condensed' rel='stylesheet' type='text/css'>\n",
        "\n",
        "El estilo se ha aplicado =)\n",
        "\n",
        "<style>\n",
        "\n",
        "\n",
        "\n",
        "#notebook_panel { /* main background */\n",
        "    background: #f7f7f7;\n",
        "}\n",
        "\n",
        "div.cell { /* set cell width */\n",
        "    width: 900px;\n",
        "}\n",
        "\n",
        "div #notebook { /* centre the content */\n",
        "    background: #fff; /* white background for content */\n",
        "    width: 950px;\n",
        "    margin: auto;\n",
        "    padding-left: 0em;\n",
        "}\n",
        "\n",
        "#notebook li { /* More space between bullet points */\n",
        "    margin-top:0.7em;\n",
        "}\n",
        "\n",
        "/* draw border around running cells */\n",
        "div.cell.border-box-sizing.code_cell.running { \n",
        "    border: 1px solid #111;\n",
        "}\n",
        "\n",
        "/* Put a solid color box around each cell and its output, visually linking them*/\n",
        "div.cell.code_cell {\n",
        "    font-family: 'Source Sans Pro', sans-serif;\n",
        "    background-color: rgb(256,256,256);\n",
        "    font-size: 110%;\n",
        "    border-radius: 0px; \n",
        "    padding: 0.5em;\n",
        "    margin-left:1em;\n",
        "    margin-top: 1em;\n",
        "}\n",
        "\n",
        "div.text_cell_render{\n",
        "    font-family: 'Josefin Sans', serif;\n",
        "    line-height: 145%;\n",
        "    font-size: 125%;\n",
        "    font-weight: 500;\n",
        "    width:750px;\n",
        "    margin-left:auto;\n",
        "    margin-right:auto;\n",
        "}\n",
        "\n",
        "\n",
        "/* Formatting for header cells */\n",
        ".text_cell_render h1, .text_cell_render h2, .text_cell_render h3,\n",
        ".text_cell_render h4, .text_cell_render h5 {\n",
        "    font-family: 'Ubuntu Condensed', sans-serif;\n",
        "}\n",
        "/*\n",
        ".text_cell_render h1 {\n",
        "    font-family: Flux, 'Ubuntu Condensed', serif;\n",
        "    font-style:regular;\n",
        "    font-weight: 400;    \n",
        "    font-size: 30pt;\n",
        "    text-align: center;\n",
        "    line-height: 100%;\n",
        "    color: #335082;\n",
        "    margin-bottom: 0.5em;\n",
        "    margin-top: 0.5em;\n",
        "    display: block;\n",
        "}\n",
        "*/\n",
        ".text_cell_render h1 {\n",
        "    font-weight: 600;\n",
        "    font-size: 35pt;\n",
        "    line-height: 100%;\n",
        "    color: #234765;\n",
        "    margin-bottom: 0.1em;\n",
        "    margin-top: 0.3em;\n",
        "    display: block;\n",
        "}\n",
        "\n",
        ".text_cell_render h2 {\n",
        "    margin-top:16px;\n",
        "    font-size: 27pt;\n",
        "    font-weight: 550;\n",
        "    margin-bottom: 0.1em;\n",
        "    margin-top: 0.3em;\n",
        "    font-style: regular;\n",
        "    color: #234765;\n",
        "}\t\n",
        "\n",
        ".text_cell_render h3 {\n",
        "    font-size: 20pt;\n",
        "    font-weight: 550\n",
        "    text-align: left;\n",
        "    margin-bottom: 0.1em;\n",
        "    margin-top: 0.3em;\n",
        "    font-style: regular;\n",
        "    color:  #376f9e;\n",
        "}\n",
        "\n",
        ".text_cell_render h4 {    /*Use this for captions*/\n",
        "    font-size: 18pt;\n",
        "    font-weight: 450\n",
        "    text-align: left;\n",
        "    margin-bottom: 0.1em;\n",
        "    margin-top: 0.3em;\n",
        "    font-style: regular;\n",
        "    color:  #376f9e;\n",
        "}\n",
        "\n",
        ".text_cell_render h5 {  /*Use this for small titles*/\n",
        "    font-size: 18pt;\n",
        "    font-weight: 550;\n",
        "    color: rgb(163,0,0);\n",
        "    font-style: italic;\n",
        "    margin-bottom: .1em;\n",
        "    margin-top: 0.8em;\n",
        "    display: block;\n",
        "    color:  #b21c0d;\n",
        "}\n",
        "\n",
        ".text_cell_render h6 { /*use this for copyright note*/\n",
        "    font-family: 'Ubuntu Condensed', sans-serif;\n",
        "    font-weight: 300;\n",
        "    font-size: 14pt;\n",
        "    line-height: 100%;\n",
        "    color: #252525;\n",
        "    text-align: right;\n",
        "    margin-bottom: 1px;\n",
        "    margin-top: 1px;\n",
        "}\n",
        "\n",
        ".CodeMirror{\n",
        "        font-family: 'Duru Sans', sans-serif;\n",
        "        font-size: 100%;\n",
        "}\n",
        "\n",
        "</style>\n",
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
        "                           extensions: [\"AMSmath.js\"],\n",
        "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
        "                }\n",
        "        });\n",
        "</script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.HTML at 0x430e358>"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
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