{
 "metadata": {
  "name": "SciPyAnswers_1"
 },
 "nbformat": 2,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "input": [
      "import scipy as sp"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "source": [
      "**I. Integration and interpolation**"
     ]
    },
    {
     "cell_type": "code",
     "input": [
      "zz = np.loadtxt('wiggleZ_DR1_z.dat',dtype='float'); # Load WiggleZ redshifts"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "input": [
      "np.min(zz)"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "1.0000000000000001e-05"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "input": [
      "np.max(zz)"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "1.9903999999999999"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "input": [
      "nbins = 50;"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "input": [
      "n, bins, patches = hist(zz,nbins)"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD9CAYAAAC1DKAUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSgEgImJR/w+CRGLiOkZxQAAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "input": [
      "x = bins[0:nbins] + (bins[2]-bins[1])/2; # Adjust bin edges to centre"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "input": [
      "from scipy.interpolate import interp1d"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "input": [
      "zdist = interp1d(x,n, kind='cubic', bounds_error = False, fill_value=0)"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "input": [
      "z = linspace(0,2,100)"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "input": [
      "plot(z,zdist(z))"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1056bfb10>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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esjsKkfChJ4AOXH01TJxo1puVyLdvn1m4p6oKDvRbEIl4mgwuCLZuhbffhhtu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\ngIhIjFICEBGJUf8fltGBnSG4oF4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "input": [
      "from scipy import integrate"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "input": [
      "cumz = lambda z0: integrate.quad(zdist,0,z0)[0]"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "input": [
      "total = cumz(5)"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/local/Cellar/python/2.7.3/lib/python2.7/site-packages/scipy/integrate/quadpack.py:288: UserWarning: The maximum number of subdivisions (50) has been achieved.\n",
        "  If increasing the limit yields no improvement it is advised to analyze \n",
        "  the integrand in order to determine the difficulties.  If the position of a \n",
        "  local difficulty can be determined (singularity, discontinuity) one will \n",
        "  probably gain from splitting up the interval and calling the integrator \n",
        "  on the subranges.  Perhaps a special-purpose integrator should be used.\n",
        "  warnings.warn(msg)\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "input": [
      "total"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "3232.7938146343804"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "input": [
      "Pz = 0 * z;\n",
      "for i in range(len(z)):\n",
      "    Pz[i] = cumz(z[i]) / total"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "input": [
      "plot(z,Pz,Pz,z)"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10589a810>,\n",
        " <matplotlib.lines.Line2D at 0x10589aa10>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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eVEtEbZjFUvZm1U0k5Sdhus90Sx3SJHQ64NtvgYEDgcOHgZQUce317t2lroyI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\n"
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "input": [
      "zvar = interp1d(Pz,z,kind='cubic')"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "input": [
      "from numpy import random"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "input": [
      "rand()"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "0.6928841274449873"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "input": [
      "output = zvar(rand(100000,1))"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "input": [
      "hist(output,100)"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "(array([  53,   28,   14,   11,   15,   10,    9,   10,   13,    6,   14,\n",
        "          5,  194,  129,  114,  419,  955,  922,  944, 1097, 1253, 1376,\n",
        "       1414, 1726, 1866, 2003, 2384, 2661, 2687, 2960, 3473, 3684, 3535,\n",
        "       3703, 4113, 4146, 4151, 4325, 4348, 4017, 3586, 3273, 2906, 2747,\n",
        "       2686, 2376, 2136, 1935, 1711, 1646, 1497, 1233,  924,  786,  787,\n",
        "        730,  607,  452,  363,  371,  277,  268,  248,  184,  173,  145,\n",
        "         66,   69,   93,   89,   66,   29,   16,   25,   35,   42,   27,\n",
        "         28,   33,   42,   55,   27,   35,   35,   58,   33,   30,   12,\n",
        "         23,   21,   22,   42,   18,   20,   32,   17,   12,   11,    2,\n",
        "          1]),\n",
        " array([-0.23761697, -0.21519182, -0.19276667, -0.17034152, -0.14791637,\n",
        "       -0.12549122, -0.10306607, -0.08064092, -0.05821577, -0.03579063,\n",
        "       -0.01336548,  0.00905967,  0.03148482,  0.05390997,  0.07633512,\n",
        "        0.09876027,  0.12118542,  0.14361057,  0.16603572,  0.18846087,\n",
        "        0.21088601,  0.23331116,  0.25573631,  0.27816146,  0.30058661,\n",
        "        0.32301176,  0.34543691,  0.36786206,  0.39028721,  0.41271236,\n",
        "        0.43513751,  0.45756265,  0.4799878 ,  0.50241295,  0.5248381 ,\n",
        "        0.54726325,  0.5696884 ,  0.59211355,  0.6145387 ,  0.63696385,\n",
        "        0.659389  ,  0.68181415,  0.70423929,  0.72666444,  0.74908959,\n",
        "        0.77151474,  0.79393989,  0.81636504,  0.83879019,  0.86121534,\n",
        "        0.88364049,  0.90606564,  0.92849079,  0.95091593,  0.97334108,\n",
        "        0.99576623,  1.01819138,  1.04061653,  1.06304168,  1.08546683,\n",
        "        1.10789198,  1.13031713,  1.15274228,  1.17516743,  1.19759257,\n",
        "        1.22001772,  1.24244287,  1.26486802,  1.28729317,  1.30971832,\n",
        "        1.33214347,  1.35456862,  1.37699377,  1.39941892,  1.42184407,\n",
        "        1.44426921,  1.46669436,  1.48911951,  1.51154466,  1.53396981,\n",
        "        1.55639496,  1.57882011,  1.60124526,  1.62367041,  1.64609556,\n",
        "        1.66852071,  1.69094585,  1.713371  ,  1.73579615,  1.7582213 ,\n",
        "        1.78064645,  1.8030716 ,  1.82549675,  1.8479219 ,  1.87034705,\n",
        "        1.8927722 ,  1.91519735,  1.93762249,  1.96004764,  1.98247279,\n",
        "        2.00489794]),\n",
        " <a list of 100 Patch objects>)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 23
    }
   ]
  }
 ]
}