nb01-empezando-python-cientifico.ipynb

{
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  {
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   "source": [
    "# Comenzando con python para computo cientifico: el entorno notebook, numpy y matplotlib\n",
    "En este notebook, empezaremos por explorar las herramientas que contiene el ecosistema de python cientifico (SciPy)."
   ]
  },
  {
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   "source": []
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   "metadata": {
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     "id": "8feae209-830c-4f75-be7f-8220417846f2"
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   "source": [
    "## El Ipython notebook\n",
    "Este mismo documento es un ipython notebook, es un documento computacionalmente interactivo que puede ser modificado y ejecutado ahora con la herramienta jupyter. Aqui incluimos codigo en python, codigo markdown, html, imagenes y multimedia.\n",
    "\n",
    "Cada celda tiene propiedades que le permiten mostrar los elementos anteriores."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "4b942b3f-f83c-47b1-a3f1-6be7231ef4fe"
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   },
   "source": [
    "## Numpy desde arriba\n",
    "Empezemos por visualizar algunos datos"
   ]
  },
  {
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     "id": "925a95fe-d944-4b8f-98a3-5b1a88146e92"
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   "source": [
    "# importamos la funcionalidad numpy usando la convencion.\n",
    "import numpy as np \n",
    "import os\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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     "id": "c8b26eab-e26b-44ea-9c76-8cbe12f7ec0d"
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   "outputs": [],
   "source": [
    "x = np.arange( -2*np.pi , 2*np.pi , 0.1 )"
   ]
  },
  {
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   "execution_count": 9,
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    {
     "data": {
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       "array([-6.28318531, -6.18318531, -6.08318531, -5.98318531, -5.88318531,\n",
       "       -5.78318531, -5.68318531, -5.58318531, -5.48318531, -5.38318531,\n",
       "       -5.28318531, -5.18318531, -5.08318531, -4.98318531, -4.88318531,\n",
       "       -4.78318531, -4.68318531, -4.58318531, -4.48318531, -4.38318531,\n",
       "       -4.28318531, -4.18318531, -4.08318531, -3.98318531, -3.88318531,\n",
       "       -3.78318531, -3.68318531, -3.58318531, -3.48318531, -3.38318531,\n",
       "       -3.28318531, -3.18318531, -3.08318531, -2.98318531, -2.88318531,\n",
       "       -2.78318531, -2.68318531, -2.58318531, -2.48318531, -2.38318531,\n",
       "       -2.28318531, -2.18318531, -2.08318531, -1.98318531, -1.88318531,\n",
       "       -1.78318531, -1.68318531, -1.58318531, -1.48318531, -1.38318531,\n",
       "       -1.28318531, -1.18318531, -1.08318531, -0.98318531, -0.88318531,\n",
       "       -0.78318531, -0.68318531, -0.58318531, -0.48318531, -0.38318531,\n",
       "       -0.28318531, -0.18318531, -0.08318531,  0.01681469,  0.11681469,\n",
       "        0.21681469,  0.31681469,  0.41681469,  0.51681469,  0.61681469,\n",
       "        0.71681469,  0.81681469,  0.91681469,  1.01681469,  1.11681469,\n",
       "        1.21681469,  1.31681469,  1.41681469,  1.51681469,  1.61681469,\n",
       "        1.71681469,  1.81681469,  1.91681469,  2.01681469,  2.11681469,\n",
       "        2.21681469,  2.31681469,  2.41681469,  2.51681469,  2.61681469,\n",
       "        2.71681469,  2.81681469,  2.91681469,  3.01681469,  3.11681469,\n",
       "        3.21681469,  3.31681469,  3.41681469,  3.51681469,  3.61681469,\n",
       "        3.71681469,  3.81681469,  3.91681469,  4.01681469,  4.11681469,\n",
       "        4.21681469,  4.31681469,  4.41681469,  4.51681469,  4.61681469,\n",
       "        4.71681469,  4.81681469,  4.91681469,  5.01681469,  5.11681469,\n",
       "        5.21681469,  5.31681469,  5.41681469,  5.51681469,  5.61681469,\n",
       "        5.71681469,  5.81681469,  5.91681469,  6.01681469,  6.11681469,\n",
       "        6.21681469])"
      ]
     },
     "execution_count": 9,
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     "output_type": "execute_result"
    }
   ],
   "source": [
    "x\n"
   ]
  },
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    "nbpresent": {
     "id": "f3b436da-3a6b-4ea2-b99d-3d13617f4f07"
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   },
   "source": [
    "Que tipo de objeto es: x "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "b0b5f8a1-4158-4276-9c40-fb82e4def479"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(x)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x.dot?"
   ]
  },
  {
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   "metadata": {
    "nbpresent": {
     "id": "0433d528-4717-49e2-880e-1105c48790db"
    }
   },
   "source": [
    "El corazon de la libreria numpy es el objeto ndarray, un arreglo de *n*-dimensiones, este objeto tiene propiedades que describen los datos y metodos, este entorno nos permite explorar que es lo que contiene, presionando **TAB** despues de escribir **x.**"
   ]
  },
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   "execution_count": 12,
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     "id": "3addacc0-c734-44dd-b21d-45a76bb4dc22"
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    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dtype"
   ]
  },
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   "cell_type": "code",
   "execution_count": 13,
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     "id": "40aed528-1d6f-472d-9c59-13fa7b3ccbd3"
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    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
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    }
   ],
   "source": [
    "x.ndim"
   ]
  },
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   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
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    "nbpresent": {
     "id": "4bf3b57e-b097-42b3-b110-21d024a72a04"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "126"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.size"
   ]
  },
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   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
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     "id": "12bf985a-7f38-4fcc-9691-b698b61cdba6"
    }
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(126,)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "6db97975-0ceb-4aab-8cd9-d1f5e995b5bb"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.1813487046306523"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
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     "id": "c2c0d875-6f19-4f16-9dc5-25dc487204ed"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.14159265, -2.93215314, -2.72271363, -2.51327412, -2.30383461,\n",
       "       -2.0943951 , -1.88495559, -1.67551608, -1.46607657, -1.25663706,\n",
       "       -1.04719755, -0.83775804, -0.62831853, -0.41887902, -0.20943951,\n",
       "        0.        ,  0.20943951,  0.41887902,  0.62831853,  0.83775804,\n",
       "        1.04719755,  1.25663706,  1.46607657,  1.67551608,  1.88495559,\n",
       "        2.0943951 ,  2.30383461,  2.51327412,  2.72271363,  2.93215314,\n",
       "        3.14159265])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(-1*np.pi , 1*np.pi , 31)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "392f5814-5800-4864-8ab3-193b13946261"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "8bd52533-fab3-4188-a45a-17d247ca1e8b"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.14159265, -2.93215314, -2.72271363, -2.51327412, -2.30383461,\n",
       "       -2.0943951 , -1.88495559, -1.67551608, -1.46607657, -1.25663706,\n",
       "       -1.04719755, -0.83775804, -0.62831853, -0.41887902, -0.20943951,\n",
       "        0.        ,  0.20943951,  0.41887902,  0.62831853,  0.83775804,\n",
       "        1.04719755,  1.25663706,  1.46607657,  1.67551608,  1.88495559,\n",
       "        2.0943951 ,  2.30383461,  2.51327412,  2.72271363,  2.93215314,\n",
       "        3.14159265])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "2357aaa7-515c-4d8c-b3a9-52a0fa9a5865"
    }
   },
   "source": [
    "**Ejemplo:** Evaluaremos el cada elemento del arreglo x con la funcion seno. La forma funcional, o al \"estilo python\" de hacerlo es la siguiente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "6512381c-5bf3-4df5-949e-33dc2ae940d0"
    }
   },
   "outputs": [],
   "source": [
    "from math import sin \n",
    "\n",
    "sin1 = [sin(i) for i in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "d5befe13-b5f9-491f-b2f5-0583b406f28c"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1.2246467991473532e-16,\n",
       " -0.20791169081775931,\n",
       " -0.40673664307580043,\n",
       " -0.5877852522924732,\n",
       " -0.7431448254773942,\n",
       " -0.8660254037844385,\n",
       " -0.9510565162951536,\n",
       " -0.9945218953682733,\n",
       " -0.9945218953682733,\n",
       " -0.9510565162951535,\n",
       " -0.8660254037844387,\n",
       " -0.7431448254773945,\n",
       " -0.5877852522924731,\n",
       " -0.4067366430758003,\n",
       " -0.20791169081775962,\n",
       " 0.0,\n",
       " 0.20791169081775918,\n",
       " 0.40673664307579993,\n",
       " 0.5877852522924731,\n",
       " 0.7431448254773941,\n",
       " 0.8660254037844385,\n",
       " 0.9510565162951535,\n",
       " 0.9945218953682733,\n",
       " 0.9945218953682734,\n",
       " 0.9510565162951536,\n",
       " 0.8660254037844389,\n",
       " 0.7431448254773945,\n",
       " 0.5877852522924732,\n",
       " 0.4067366430758008,\n",
       " 0.20791169081775973,\n",
       " 1.2246467991473532e-16]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "b4cd7cc2-42f6-4434-9497-351df91385d1"
    }
   },
   "source": [
    "Podemos convertir una lista a un objeto mas eficiente ndarray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "480b73f3-1f5e-44cf-b185-6c94cd33d26c"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin2 = np.array(sin1)\n",
    "type(sin2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "2b3dd24f-f690-4d60-9277-40fbfc57821b"
    }
   },
   "source": [
    "Lo anterior no es lo mas eficiente que podemos hacer, en su lugar el paquete numpy contiene versiones de funciones math en metodos vectorizados y optimizados para el objeto ndarray, llamados *\"ufunc\"* corto para *\"universal functions\"*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "2ac5d98b-9338-4347-9cd5-8d775b2765d2"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -1.22464680e-16,  -2.07911691e-01,  -4.06736643e-01,\n",
       "        -5.87785252e-01,  -7.43144825e-01,  -8.66025404e-01,\n",
       "        -9.51056516e-01,  -9.94521895e-01,  -9.94521895e-01,\n",
       "        -9.51056516e-01,  -8.66025404e-01,  -7.43144825e-01,\n",
       "        -5.87785252e-01,  -4.06736643e-01,  -2.07911691e-01,\n",
       "         0.00000000e+00,   2.07911691e-01,   4.06736643e-01,\n",
       "         5.87785252e-01,   7.43144825e-01,   8.66025404e-01,\n",
       "         9.51056516e-01,   9.94521895e-01,   9.94521895e-01,\n",
       "         9.51056516e-01,   8.66025404e-01,   7.43144825e-01,\n",
       "         5.87785252e-01,   4.06736643e-01,   2.07911691e-01,\n",
       "         1.22464680e-16])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin3 = np.sin(x)\n",
    "sin3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "6f8ba47c-eca0-48a5-9512-99040c6d5cd2"
    }
   },
   "source": [
    "Que tan optimizado?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "13c57300-0fcb-4579-a4d3-afc1f2c9ab55"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 5.49 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "100000 loops, best of 3: 7.6 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit sin2 = np.array([sin(i) for i in x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "096e86e8-5df7-4bd3-a388-44b18a527f7c"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 14.01 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "1000000 loops, best of 3: 1.44 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit sin3 = np.sin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "fd51bf62-60e2-4a6e-bacd-9bc5a0f879dd"
    }
   },
   "source": [
    "**np.sin()** es una funcion universal que evalua elemento por elemento. Numpy promueve que pensemos de forma vectorizada, que hagamos operaciones sobre los arreglos como si fuera una unidad.  De esta forma dejamos que el nucleo de estas librerias se encargen de realizar la parte complicada e incluso encargarse de optimizaciones, en multiples CPUs, o GPU's."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ejercicio** Ejecutar funciones artimeticas y matematicas sobre arreglos numpy.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Que es numpy?\n",
    "Pensemos en el como el objeto que nos provee con metodos optimizados la siguiente funcionalidad\n",
    "- arreglo de datos numericos, adecuado para datos cientificos (vectores, matrices)\n",
    "- operaciones vectorizadas para sus arreglos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Por ejemplo operaciones aritmeticas sobre arreglos\n",
    "x = np.array([1.,2.,3.,4.,5.])\n",
    "y = np.array([6,7,8,9,10]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-37-3830e41c773f>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-37-3830e41c773f>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    x .* y\u001b[0m\n\u001b[1;37m       ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "x * y "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -2.9,  -5.8,  -8.7, -11.6, -14.5])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x\n",
    "x * -2.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('complex128')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = x + 2j\n",
    "z.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizando los datos: matplotlib\n",
    "Ahora que ya tenemos datos, realizamos operaciones sobre ellos y representan un posible resultado de algun experimento, lo que sigue es visualizarlos.\n",
    "El paquete estandar para hacer esto es matplotlib, que es parte del paquete de scipy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "e75f55d2-a3d7-42d0-8ae5-210894d13a79"
    }
   },
   "outputs": [],
   "source": [
    "# importando matplotlib siguiendo la convencion\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recordemos como obtuvimos datos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "c7a47147-2486-41bf-ae03-30e55887beee"
    }
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2*np.pi, 2*np.pi, 100)\n",
    "y = np.sin(x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hagamos un grafico"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "7ad0977b-8708-4ad5-8aeb-549af1fbabaa"
    }
   },
   "outputs": [],
   "source": [
    "myplt = plt.plot(x,y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Muestrame mi grafico!\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f74edc05908>]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ToooKmDjRdxX7vPmmbujVuLHvSrJn0CDdSG3nTt+V7DNlSrYu2IIFvgnR2WdD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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74edcb7b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Incluyelo en mi notebook\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f74edc14208>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ew684U0FkWCSxfWO1aSgqgmnTVFkFOxg7aCxHzx/lZP1JexrwAHdKx+lF9cyA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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74edc14400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, np.sin(x))\n",
    "plt.plt.plot(x, np.cos(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.plot?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f74edb12e48>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8+M03sMceNWeCfWLRIjjxRGiYyMg0R0IE6XhdvDj2itGp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\nHI6k4ZyMw+FwOJKGczIOh8PhSBr/D7iP7thhLVY1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74edc3a7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, np.sin(x), \"--\"  , label=\"$\\sin(x)$\" )\n",
    "plt.plot(x, np.cos(x), \"ro--\", label=\"$\\cos(x)$\")  # red points and dashed lines\n",
    "plt.xlabel(\"$x$\", size=20)\n",
    "plt.ylabel(\"$\\sin(x), \\cos(x)$\", size=20)\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74ed3e1d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Salvamos nuestro grafico asi. \n",
    "plt.savefig(\"sincos.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.plot?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ejercicio** Que tal si hacemos un grafico de la funcion logaritmica y el exponencial en un mismo grafico mas una linea punteada, mostrando la leyenda $y=x$ para denotar la simetria.\n",
    "\n",
    "Para ajustar nuestros limites visibles del grafico podemos usar `plt.ylim([ymin, ymax])` para ajustar en el eje Y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5, 5)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nmmgU7rwT8vJg3DgFuUia0DBLqtm3D2rVcqs70+TmEiKiYRYRDbNIqGnRkIhI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\nEBaKSBMp5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74ecb4b5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[x>0], np.log(x[x>0]), \"-\")\n",
    "plt.plot(x, np.exp(x), \"-\")\n",
    "plt.plot(x,x,\"--\",label=\"$y=x$\")\n",
    "plt.legend()\n",
    "\n",
    "\n",
    "plt.axhline(y=0)\n",
    "plt.axvline(x=0)\n",
    "plt.ylim([-5,5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cargando datos en numpy\n",
    "Generalmente las aplicaciones cientificas no generan datos a partir de funciones, o travez de simulaciones numericas, si no de datos ya existentes.\n",
    "\n",
    "Numpy cuenta con funcionalidad para cargar y salvar datos a sus arreglos, aun mas funcionalidad esta disponible en la libreria `pandas`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.5474918 ,  0.78878503,  0.16325052,  0.40631857,  0.2774425 ,\n",
       "        0.52468145,  0.52052233,  0.61937627,  0.55938531,  0.90868494])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generemos datos aleatorios\n",
    "np.random.rand(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 28.24702562,  26.47248378,  23.85184173,  23.75468923,\n",
       "        19.94246103,  16.03053163,  18.94884992,  15.22097288,\n",
       "        16.29456242,  11.57554023,  10.89748651,  11.76946391,\n",
       "         7.63200879,   5.5685312 ,   8.53069983,   5.26402443,\n",
       "         6.05148689,   6.19798044,   3.86075681,   5.58545446,\n",
       "         1.11093367,   2.33371577,   2.86832031,   2.39863092,\n",
       "         4.33513072,   2.31218201,   2.44547957,   4.2519523 ,\n",
       "         0.8576819 ,   4.47914683,   3.96820588,   6.42379984,\n",
       "         5.61448753,   5.63050068,   5.73330696,   7.96045853,\n",
       "         8.29888478,   8.99704858,   9.27120565,  11.1755766 ,\n",
       "        10.3908207 ,  12.47633002,  17.63901878,  18.26512429,\n",
       "        16.04881155,  18.74257505,  20.99108876,  23.8788008 ,\n",
       "        23.58272932,  26.92471953])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Vectores con datos , \"simulando datos cientificos\"\n",
    "x = np.linspace(-5, 5, 50)\n",
    "y = x**2 + 5*np.random.rand(x.size)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f74ec8e2390>]"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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czBNH7aS2+GbYqk9gXDNZ7GN7p6RPKOvR3xERN/XZhxBH46X2hwf1N/XFPrY3SPonSZdI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\nASBh/w/1KYoYt5mjowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74ec98e470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizamos nuestros datos.\n",
    "plt.plot(x,y,'.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para exportar nuestros datos, de preferencia los salvaremos en forma tabulada, creando una matriz en numpy a partir de los dos vectores x,y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5],\n",
       "       [ 6,  7,  8,  9, 10, 11]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ar = np.arange(12).reshape(2,6)\n",
    "ar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.        , -4.79591837, -4.59183673, -4.3877551 , -4.18367347,\n",
       "       -3.97959184, -3.7755102 , -3.57142857, -3.36734694, -3.16326531,\n",
       "       -2.95918367, -2.75510204, -2.55102041, -2.34693878, -2.14285714,\n",
       "       -1.93877551, -1.73469388, -1.53061224, -1.32653061, -1.12244898,\n",
       "       -0.91836735, -0.71428571, -0.51020408, -0.30612245, -0.10204082,\n",
       "        0.10204082,  0.30612245,  0.51020408,  0.71428571,  0.91836735,\n",
       "        1.12244898,  1.32653061,  1.53061224,  1.73469388,  1.93877551,\n",
       "        2.14285714,  2.34693878,  2.55102041,  2.75510204,  2.95918367,\n",
       "        3.16326531,  3.36734694,  3.57142857,  3.7755102 ,  3.97959184,\n",
       "        4.18367347,  4.3877551 ,  4.59183673,  4.79591837,  5.        ])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -5.        ,  28.24702562],\n",
       "       [ -4.79591837,  26.47248378],\n",
       "       [ -4.59183673,  23.85184173],\n",
       "       [ -4.3877551 ,  23.75468923],\n",
       "       [ -4.18367347,  19.94246103],\n",
       "       [ -3.97959184,  16.03053163],\n",
       "       [ -3.7755102 ,  18.94884992],\n",
       "       [ -3.57142857,  15.22097288],\n",
       "       [ -3.36734694,  16.29456242],\n",
       "       [ -3.16326531,  11.57554023],\n",
       "       [ -2.95918367,  10.89748651],\n",
       "       [ -2.75510204,  11.76946391],\n",
       "       [ -2.55102041,   7.63200879],\n",
       "       [ -2.34693878,   5.5685312 ],\n",
       "       [ -2.14285714,   8.53069983],\n",
       "       [ -1.93877551,   5.26402443],\n",
       "       [ -1.73469388,   6.05148689],\n",
       "       [ -1.53061224,   6.19798044],\n",
       "       [ -1.32653061,   3.86075681],\n",
       "       [ -1.12244898,   5.58545446],\n",
       "       [ -0.91836735,   1.11093367],\n",
       "       [ -0.71428571,   2.33371577],\n",
       "       [ -0.51020408,   2.86832031],\n",
       "       [ -0.30612245,   2.39863092],\n",
       "       [ -0.10204082,   4.33513072],\n",
       "       [  0.10204082,   2.31218201],\n",
       "       [  0.30612245,   2.44547957],\n",
       "       [  0.51020408,   4.2519523 ],\n",
       "       [  0.71428571,   0.8576819 ],\n",
       "       [  0.91836735,   4.47914683],\n",
       "       [  1.12244898,   3.96820588],\n",
       "       [  1.32653061,   6.42379984],\n",
       "       [  1.53061224,   5.61448753],\n",
       "       [  1.73469388,   5.63050068],\n",
       "       [  1.93877551,   5.73330696],\n",
       "       [  2.14285714,   7.96045853],\n",
       "       [  2.34693878,   8.29888478],\n",
       "       [  2.55102041,   8.99704858],\n",
       "       [  2.75510204,   9.27120565],\n",
       "       [  2.95918367,  11.1755766 ],\n",
       "       [  3.16326531,  10.3908207 ],\n",
       "       [  3.36734694,  12.47633002],\n",
       "       [  3.57142857,  17.63901878],\n",
       "       [  3.7755102 ,  18.26512429],\n",
       "       [  3.97959184,  16.04881155],\n",
       "       [  4.18367347,  18.74257505],\n",
       "       [  4.3877551 ,  20.99108876],\n",
       "       [  4.59183673,  23.8788008 ],\n",
       "       [  4.79591837,  23.58272932],\n",
       "       [  5.        ,  26.92471953]])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.stack((x,y), axis=1) \n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -5.        ,  26.80810656],\n",
       "       [ -4.79591837,  25.68854708],\n",
       "       [ -4.59183673,  21.63241622],\n",
       "       [ -4.3877551 ,  22.01193531],\n",
       "       [ -4.18367347,  20.31405965],\n",
       "       [ -3.97959184,  17.74539758],\n",
       "       [ -3.7755102 ,  18.31746474],\n",
       "       [ -3.57142857,  14.68420575],\n",
       "       [ -3.36734694,  12.82156494],\n",
       "       [ -3.16326531,  13.13858941],\n",
       "       [ -2.95918367,  11.34653309],\n",
       "       [ -2.75510204,   8.71416151],\n",
       "       [ -2.55102041,   9.1729447 ],\n",
       "       [ -2.34693878,  10.48949056],\n",
       "       [ -2.14285714,   7.63499573],\n",
       "       [ -1.93877551,   5.66674393],\n",
       "       [ -1.73469388,   6.72204856],\n",
       "       [ -1.53061224,   2.7723582 ],\n",
       "       [ -1.32653061,   5.81837737],\n",
       "       [ -1.12244898,   1.68596217],\n",
       "       [ -0.91836735,   4.31226995],\n",
       "       [ -0.71428571,   5.10051562],\n",
       "       [ -0.51020408,   2.4750284 ],\n",
       "       [ -0.30612245,   1.81966239],\n",
       "       [ -0.10204082,   2.53211706],\n",
       "       [  0.10204082,   3.93226453],\n",
       "       [  0.30612245,   3.193222  ],\n",
       "       [  0.51020408,   2.59530423],\n",
       "       [  0.71428571,   5.39494173],\n",
       "       [  0.91836735,   1.0350096 ],\n",
       "       [  1.12244898,   2.23112323],\n",
       "       [  1.32653061,   3.06057034],\n",
       "       [  1.53061224,   7.18481253],\n",
       "       [  1.73469388,   6.63700191],\n",
       "       [  1.93877551,   5.15074918],\n",
       "       [  2.14285714,   6.21848522],\n",
       "       [  2.34693878,   9.06963243],\n",
       "       [  2.55102041,  10.81902185],\n",
       "       [  2.75510204,   8.27235318],\n",
       "       [  2.95918367,  10.59692223],\n",
       "       [  3.16326531,  11.14789286],\n",
       "       [  3.36734694,  11.75430795],\n",
       "       [  3.57142857,  16.24325894],\n",
       "       [  3.7755102 ,  15.49173372],\n",
       "       [  3.97959184,  16.21432112],\n",
       "       [  4.18367347,  20.74267413],\n",
       "       [  4.3877551 ,  19.37442967],\n",
       "       [  4.59183673,  26.00958112],\n",
       "       [  4.79591837,  25.20495124],\n",
       "       [  5.        ,  28.09227586]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.hstack((x[:,np.newaxis],y[:,np.newaxis]))\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.savetxt(\"cuadratica-ruido.txt\", z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5.000000000000000000e+00 2.824702562420766583e+01\r\n",
      "-4.795918367346938993e+00 2.647248378150305115e+01\r\n",
      "-4.591836734693877986e+00 2.385184173119323248e+01\r\n",
      "-4.387755102040816091e+00 2.375468923151409228e+01\r\n",
      "-4.183673469387755084e+00 1.994246103445604490e+01\r\n",
      "-3.979591836734694077e+00 1.603053162724983238e+01\r\n",
      "-3.775510204081632626e+00 1.894884991956936915e+01\r\n",
      "-3.571428571428571175e+00 1.522097287953479139e+01\r\n",
      "-3.367346938775510168e+00 1.629456241638368397e+01\r\n",
      "-3.163265306122449161e+00 1.157554023382974506e+01\r\n",
      "-2.959183673469387710e+00 1.089748651161886706e+01\r\n",
      "-2.755102040816326259e+00 1.176946390905610684e+01\r\n",
      "-2.551020408163265252e+00 7.632008793374686739e+00\r\n",
      "-2.346938775510204245e+00 5.568531201749807202e+00\r\n",
      "-2.142857142857142794e+00 8.530699829161520142e+00\r\n",
      "-1.938775510204081343e+00 5.264024433670237535e+00\r\n",
      "-1.734693877551020336e+00 6.051486889151954429e+00\r\n",
      "-1.530612244897959329e+00 6.197980440787007161e+00\r\n",
      "-1.326530612244897878e+00 3.860756806616196801e+00\r\n",
      "-1.122448979591836427e+00 5.585454460204204885e+00\r\n",
      "-9.183673469387754196e-01 1.110933667200340924e+00\r\n",
      "-7.142857142857144126e-01 2.333715771550480156e+00\r\n",
      "-5.102040816326525174e-01 2.868320306634464689e+00\r\n",
      "-3.061224489795915105e-01 2.398630915603418234e+00\r\n",
      "-1.020408163265305035e-01 4.335130720253237868e+00\r\n",
      "1.020408163265305035e-01 2.312182009856941889e+00\r\n",
      "3.061224489795915105e-01 2.445479571020570120e+00\r\n",
      "5.102040816326534056e-01 4.251952295242000801e+00\r\n",
      "7.142857142857144126e-01 8.576818989232950496e-01\r\n",
      "9.183673469387754196e-01 4.479146831473111767e+00\r\n",
      "1.122448979591837315e+00 3.968205881682113745e+00\r\n",
      "1.326530612244898322e+00 6.423799835472181918e+00\r\n",
      "1.530612244897959329e+00 5.614487529912880248e+00\r\n",
      "1.734693877551020336e+00 5.630500681861990486e+00\r\n",
      "1.938775510204081343e+00 5.733306962408925678e+00\r\n",
      "2.142857142857143238e+00 7.960458525412763109e+00\r\n",
      "2.346938775510204245e+00 8.298884777030480109e+00\r\n",
      "2.551020408163265252e+00 8.997048583115015319e+00\r\n",
      "2.755102040816327147e+00 9.271205646681103474e+00\r\n",
      "2.959183673469388154e+00 1.117557660184447244e+01\r\n",
      "3.163265306122449161e+00 1.039082069834641331e+01\r\n",
      "3.367346938775510168e+00 1.247633002061017393e+01\r\n",
      "3.571428571428571175e+00 1.763901878040118376e+01\r\n",
      "3.775510204081632182e+00 1.826512429422394845e+01\r\n",
      "3.979591836734694965e+00 1.604881155333788811e+01\r\n",
      "4.183673469387755972e+00 1.874257504581618505e+01\r\n",
      "4.387755102040816979e+00 2.099108875662204099e+01\r\n",
      "4.591836734693877986e+00 2.387880080401864547e+01\r\n",
      "4.795918367346938993e+00 2.358272932452515036e+01\r\n",
      "5.000000000000000000e+00 2.692471953440272969e+01\r\n"
     ]
    }
   ],
   "source": [
    "# Comando magico cat - funciona en windows?\n",
    "%cat cuadratica-ruido.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.savetxt(\"cuadratica-ruido.txt\", z, fmt=\"%10.5f\", delimiter=\",\", header=\"X, Y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "binario.dat\r\n",
      "cuadratica-ruido.txt\r\n",
      "data\r\n",
      "ejercicios-numpy.txt\r\n",
      "Extra-dask-futures.ipynb\r\n",
      "extra-tabla-equivalencias-matlab-numpy_files\r\n",
      "extra-tabla-equivalencias-matlab-numpy.html\r\n",
      "extra-tabla-equivalencias-matlab-numpy.ipynb\r\n",
      "images\r\n",
      "LICENSE\r\n",
      "log\r\n",
      "nb00-python-basics.ipynb\r\n",
      "nb01-empezando-python-cientifico.ipynb\r\n",
      "nb02-numpy-basics.ipynb\r\n",
      "nb03-timeseries-numpy.ipynb\r\n",
      "nb04-timeseries-pandas.ipynb\r\n",
      "nb05-pandas-demo-ejercicios.ipynb\r\n",
      "nb05-pandas-demo-ejercicios-SOLUCIONES.ipynb\r\n",
      "nb06-pandas-demo-ejercicios.ipynb\r\n",
      "nb06-pandas-demo-ejercicios-SOLUCIONES.ipynb\r\n",
      "nb07-pandas-demo-ejercicios.ipynb\r\n",
      "nb07-pandas-demo-ejercicios-SOLUCIONES.ipynb\r\n",
      "pandas-imdb.notas\r\n",
      "README.md\r\n",
      "sincos.pdf\r\n",
      "sincos.png\r\n",
      "texto.txt\r\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.savetxt?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -5.     ,  28.24703],\n",
       "       [ -4.79592,  26.47248],\n",
       "       [ -4.59184,  23.85184],\n",
       "       [ -4.38776,  23.75469],\n",
       "       [ -4.18367,  19.94246],\n",
       "       [ -3.97959,  16.03053],\n",
       "       [ -3.77551,  18.94885],\n",
       "       [ -3.57143,  15.22097],\n",
       "       [ -3.36735,  16.29456],\n",
       "       [ -3.16327,  11.57554],\n",
       "       [ -2.95918,  10.89749],\n",
       "       [ -2.7551 ,  11.76946],\n",
       "       [ -2.55102,   7.63201],\n",
       "       [ -2.34694,   5.56853],\n",
       "       [ -2.14286,   8.5307 ],\n",
       "       [ -1.93878,   5.26402],\n",
       "       [ -1.73469,   6.05149],\n",
       "       [ -1.53061,   6.19798],\n",
       "       [ -1.32653,   3.86076],\n",
       "       [ -1.12245,   5.58545],\n",
       "       [ -0.91837,   1.11093],\n",
       "       [ -0.71429,   2.33372],\n",
       "       [ -0.5102 ,   2.86832],\n",
       "       [ -0.30612,   2.39863],\n",
       "       [ -0.10204,   4.33513],\n",
       "       [  0.10204,   2.31218],\n",
       "       [  0.30612,   2.44548],\n",
       "       [  0.5102 ,   4.25195],\n",
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       "       [  1.12245,   3.96821],\n",
       "       [  1.32653,   6.4238 ],\n",
       "       [  1.53061,   5.61449],\n",
       "       [  1.73469,   5.6305 ],\n",
       "       [  1.93878,   5.73331],\n",
       "       [  2.14286,   7.96046],\n",
       "       [  2.34694,   8.29888],\n",
       "       [  2.55102,   8.99705],\n",
       "       [  2.7551 ,   9.27121],\n",
       "       [  2.95918,  11.17558],\n",
       "       [  3.16327,  10.39082],\n",
       "       [  3.36735,  12.47633],\n",
       "       [  3.57143,  17.63902],\n",
       "       [  3.77551,  18.26512],\n",
       "       [  3.97959,  16.04881],\n",
       "       [  4.18367,  18.74258],\n",
       "       [  4.38776,  20.99109],\n",
       "       [  4.59184,  23.8788 ],\n",
       "       [  4.79592,  23.58273],\n",
       "       [  5.     ,  26.92472]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zz = np.loadtxt(\"cuadratica-ruido.txt\", delimiter=\",\")\n",
    "zz "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -5.     ,  28.24703])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zz[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Titulo\n",
    "## subtitulo\n",
    "\n",
    "- lista\n",
    "- lista2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esta es una celda markdown\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ejercicio** Como podemos extraer ahora los elementos de cada columna de la matriz que salvamos.\n",
    "\n",
    "-----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Documentando nuestro codigo en el entorno Notebook \"Literate programming\"\n",
    "Podemos agregar informacion complementaria utilizando un lenguaje ligero para hacer anotaciones llamado **markdown**.\n",
    "\n",
    "Markdown nos permite escribir en *italicas*, poner texto en **negritas**, \n",
    "- hacer listas, \n",
    "- definir titulos, \n",
    "- tablas, resaltar algun texto:.\n",
    "\n",
    "> Alguna frase\n",
    "\n",
    "Resulta util para el computo cientifico poder incluir en celdas con Markup formulas escritas con LaTeX, encasillando las ecuaciones entre `$`, y `$$` para parrafos.\n",
    "\n",
    "Por ejemplo $y=x^2$ , Una mas complicada seria:\n",
    "$$\n",
    "\\mathcal{N}(x)=Ce^{-x^2}\n",
    "$$delimiter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resumen\n",
    "Hemos revisado de manera general los componentes fundamentales del paquete SciPy\n",
    "\n",
    "- El IPython Notebook\n",
    "    - Un entorno que facilita los flujos de trabajo de computo\n",
    "    - Soporte para visualizacion interactiva\n",
    "    - Posibilidad de exportar en distintos formatos\n",
    "- numpy\n",
    "    - Manejo de vectores, matrices y arreglos de n-dimensiones\n",
    "    - Provee de funciones vectorizadas optimizadas para arreglos    \n",
    "\n",
    "- matplotlib\n",
    "    - Flexibilidad\n",
    "    - Calidad para publicaciones\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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