gistfile1.txt

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "def diff_flux(energy, gamma):\n",
      "    return energy ** (- gamma)\n",
      "\n",
      "def int_flux(energy_min, energy_max, gamma):\n",
      "    return (energy_max ** (1 - gamma) - energy_min ** (1 - gamma)) / (1 - gamma)\n",
      "\n",
      "def energy_lafferty_power_law(energy_min, energy_max, spectral_index):\n",
      "    term0 = 1 - spectral_index\n",
      "    term1 = energy_max - energy_min\n",
      "    term2 = 1. / term0\n",
      "    flux_lw = term2 / term1 * (energy_max ** term0 - energy_min ** term0)\n",
      "    energy_lw = np.exp(- np.log(flux_lw) / spectral_index)\n",
      "    return energy_lw, flux_lw\n",
      "\n",
      "for spectral_index in [1.1, 2, 3, 4]:\n",
      "    energy_min, energy_max = 1, 2\n",
      "    #energy_min, energy_max = 10, 11\n",
      "    flux_min, flux_max = diff_flux(energy_min, spectral_index), diff_flux(energy_max, spectral_index)\n",
      "    energy_lw, flux_lw = energy_lafferty_power_law(energy_min, energy_max, spectral_index)\n",
      "    print('spectral_index = {0}'.format(spectral_index))\n",
      "    print('energy:', energy_min, energy_max, energy_lw)\n",
      "    print('flux:', flux_min, flux_max, flux_lw)\n",
      "    print(flux_lw * (energy_max - energy_min), int_flux(energy_min, energy_max, spectral_index))\n",
      "    x_lw = np.log(energy_lw / energy_min) / np.log(energy_max / energy_min)\n",
      "    print('x:', x_lw)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "spectral_index = 1.1\n",
        "('energy:', 1, 2, 1.4398202389003543)\n",
        "('flux:', 1.0, 0.4665164957684037, 0.6696700846319253)\n",
        "(0.6696700846319253, 0.6696700846319253)\n",
        "('x:', 0.52588870289285417)\n",
        "spectral_index = 2\n",
        "('energy:', 1, 2, 1.4142135623730949)\n",
        "('flux:', 1.0, 0.25, 0.5)\n",
        "(0.5, 0.5)\n",
        "('x:', 0.49999999999999994)\n",
        "spectral_index = 3\n",
        "('energy:', 1, 2, 1.3867225487012693)\n",
        "('flux:', 1.0, 0.125, 0.375)\n",
        "(0.375, 0.375)\n",
        "('x:', 0.47167916642628116)\n",
        "spectral_index = 4\n",
        "('energy:', 1, 2, 1.3607498666342404)\n",
        "('flux:', 1.0, 0.0625, 0.29166666666666663)\n",
        "(0.29166666666666663, 0.2916666666666667)\n",
        "('x:', 0.44440189466588803)\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "2 ** (1. / 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "1.2599210498948732"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
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  }
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}