gistfile1.txt

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Set up "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab\n",
      "pylab.rcParams['xtick.major.pad']='8'\n",
      "pylab.rcParams['ytick.major.pad']='8'\n",
      "#pylab.rcParams['font.sans-serif']='Arial'\n",
      "\n",
      "from matplotlib import rc\n",
      "rc('font', family='sans-serif')\n",
      "rc('font', size=10.0)\n",
      "rc('text', usetex=False)\n",
      "\n",
      "\n",
      "from matplotlib.font_manager import FontProperties\n",
      "\n",
      "panel_label_font = FontProperties().copy()\n",
      "panel_label_font.set_weight(\"bold\")\n",
      "panel_label_font.set_size(12.0)\n",
      "panel_label_font.set_family(\"sans-serif\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from os import listdir\n",
      "files = listdir('.')\n",
      "if 'blackouts.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/blackouts.txt', 'blackouts.txt')\n",
      "if 'words.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/words.txt', 'words.txt')\n",
      "if 'worm.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/worm.txt', 'worm.txt')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import genfromtxt\n",
      "blackouts = genfromtxt('blackouts.txt')#/10**3\n",
      "words = genfromtxt('words.txt')\n",
      "worm = genfromtxt('worm.txt')\n",
      "worm = worm[worm>0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_basics(data, data_inst, fig, units):\n",
      "    from powerlaw import plot_pdf, Fit, pdf\n",
      "    annotate_coord = (-.4, .95)\n",
      "    ax1 = fig.add_subplot(n_graphs,n_data,data_inst)\n",
      "    x, y = pdf(data, linear_bins=True)\n",
      "    ind = y>0\n",
      "    y = y[ind]\n",
      "    x = x[:-1]\n",
      "    x = x[ind]\n",
      "    ax1.scatter(x, y, color='r', s=.5)\n",
      "    plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)\n",
      "    from pylab import setp\n",
      "    setp( ax1.get_xticklabels(), visible=False)\n",
      "\n",
      "    if data_inst==1:\n",
      "        ax1.annotate(\"A\", annotate_coord, xycoords=\"axes fraction\", fontproperties=panel_label_font)\n",
      "\n",
      "    \n",
      "    from mpl_toolkits.axes_grid.inset_locator import inset_axes\n",
      "    ax1in = inset_axes(ax1, width = \"30%\", height = \"30%\", loc=3)\n",
      "    ax1in.hist(data, normed=True, color='b')\n",
      "    ax1in.set_xticks([])\n",
      "    ax1in.set_yticks([])\n",
      "\n",
      "    \n",
      "    ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)\n",
      "    plot_pdf(data, ax=ax2, color='b', linewidth=2)\n",
      "    fit = Fit(data, xmin=1, discrete=True)\n",
      "    fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')\n",
      "    p = fit.power_law.pdf()\n",
      "\n",
      "    ax2.set_xlim(ax1.get_xlim())\n",
      "    \n",
      "    fit = Fit(data, discrete=True)\n",
      "    fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')\n",
      "    from pylab import setp\n",
      "    setp( ax2.get_xticklabels(), visible=False)\n",
      "\n",
      "    if data_inst==1:\n",
      "       ax2.annotate(\"B\", annotate_coord, xycoords=\"axes fraction\", fontproperties=panel_label_font)        \n",
      "       ax2.set_ylabel(u\"p(X)\")# (10^n)\")\n",
      "        \n",
      "    ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)\n",
      "    fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')\n",
      "    fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')\n",
      "    fit.plot_pdf(ax=ax3, color='b', linewidth=2)\n",
      "    \n",
      "    ax3.set_ylim(ax2.get_ylim())\n",
      "    ax3.set_xlim(ax1.get_xlim())\n",
      "    \n",
      "    if data_inst==1:\n",
      "        ax3.annotate(\"C\", annotate_coord, xycoords=\"axes fraction\", fontproperties=panel_label_font)\n",
      "\n",
      "    ax3.set_xlabel(units)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_data = 3\n",
      "n_graphs = 4\n",
      "f = figure(figsize=(8,11))\n",
      "\n",
      "data = words\n",
      "data_inst = 1\n",
      "units = 'Word Frequency'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "data_inst = 2\n",
      "#data = city\n",
      "#units = 'City Population'\n",
      "data = worm\n",
      "units = 'Neuron Connections'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "data = blackouts\n",
      "data_inst = 3\n",
      "units = 'Population Affected\\nby Blackouts'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "f.subplots_adjust(left=None, bottom=None, right=None, top=None, wspace=.3, hspace=.2)\n",
      "figname = 'FigWorkflow'\n",
      "f.savefig(figname+'.eps', bbox_inches='tight')\n",
      "#f.savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAgcAAAIMCAYAAABhZg/4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ng8FgMBgK/D+XSbfRNl4tsgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2feab50>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blackouts = blackouts/10**3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Introduction"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "import powerlaw\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.sigma\n",
      "fit.distribution_compare('power_law', 'exponential')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(12.754562675882063, 0.1522925560442657)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Basic Methods"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Visualization"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### PDF Linear vs Logarithmic Bins"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "####\n",
      "figPDF = powerlaw.plot_pdf(data, color='b')\n",
      "powerlaw.plot_pdf(data, linear_bins=True, color='r', ax=figPDF)\n",
      "####\n",
      "figPDF.set_ylabel(\"p(X)\")\n",
      "figPDF.set_xlabel(r\"Word Frequency\")\n",
      "figname = 'FigPDF'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEaCAYAAAA7YdFPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIhd/h8J5dkbfUsgOwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6f3f950>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "figCCDF = fit.plot_pdf(color='b', linewidth=2)\n",
      "fit.power_law.plot_pdf(color='b', linestyle='--', ax=figCCDF)\n",
      "fit.plot_ccdf(color='r', linewidth=2, ax=figCCDF)\n",
      "fit.power_law.plot_ccdf(color='r', linestyle='--', ax=figCCDF)\n",
      "####\n",
      "figCCDF.set_ylabel(u\"p(X),  p(X\u2265x)\")\n",
      "figCCDF.set_xlabel(r\"Word Frequency\")\n",
      "\n",
      "figname = 'FigCCDF'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEaCAYAAAA7YdFPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiEiIoP8HyON7OnIzFbfAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xf76ed90>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "###\n",
      "x, y = fit.cdf()\n",
      "bin_edges, probability = fit.pdf()\n",
      "y = fit.lognormal.cdf(data=[300,350])\n",
      "y = fit.lognormal.pdf()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Identifying the Scaling Range"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "import powerlaw\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.xmin\n",
      "fit.fixed_xmin\n",
      "fit.alpha\n",
      "fit.D\n",
      "fit = powerlaw.Fit(data, xmin=1.0)\n",
      "fit.xmin\n",
      "fit.fixed_xmin\n",
      "fit.alpha\n",
      "fit.D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "0.37601504850371759"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmin=(250.0, 300.0))\n",
      "fit.fixed_xmin\n",
      "fit.given_xmin\n",
      "fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "272.0"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmax=10000.0)\n",
      "fit.xmax\n",
      "fit.fixed_xmax"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 3"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "#FigCCDFmax = powerlaw.plot_ccdf(data, linewidth=3)\n",
      "fit = powerlaw.Fit(data, discrete=True, xmax=None)\n",
      "FigCCDFmax = fit.plot_ccdf(color='b', label=r\"Empirical, no $x_{max}$\")\n",
      "fit.power_law.plot_ccdf(color='b', linestyle='--', ax=FigCCDFmax, label=r\"Fit, no $x_{max}$\")\n",
      "fit = powerlaw.Fit(data, discrete=True, xmax=1000)\n",
      "fit.plot_ccdf(color='r', label=r\"Empirical, $x_{max}=1000$\")\n",
      "fit.power_law.plot_ccdf(color='r', linestyle='--', ax=FigCCDFmax, label=r\"Fit, $x_{max}=1000$\")\n",
      "#x, y = powerlaw.ccdf(data, xmax=max(data))\n",
      "#fig1.plot(x,y)\n",
      "####\n",
      "#FigCCDFmax.set_ylabel(r\"$p(X\\geq x)$\")\n",
      "FigCCDFmax.set_ylabel(u\"p(X\u2265x)\")\n",
      "FigCCDFmax.set_xlabel(r\"Word Frequency\")\n",
      "handles, labels = FigCCDFmax.get_legend_handles_labels()\n",
      "leg = FigCCDFmax.legend(handles, labels, loc=3)\n",
      "leg.draw_frame(False)\n",
      "\n",
      "figname = 'FigCCDFmax'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEaCAYAAAA7YdFPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n2To9AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6f6fe50>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Continuous vs. Discrete Data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmin=230.0)\n",
      "fit.discrete\n",
      "fit = powerlaw.Fit(data, xmin=230.0, discrete=True)\n",
      "fit.discrete "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Comparing Candidate Distributions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit.power_law\n",
      "fit.power_law.alpha\n",
      "fit.power_law.parameter1\n",
      "fit.power_law.parameter1_name\n",
      "fit.lognormal.mu\n",
      "fit.lognormal.parameter1_name\n",
      "fit.lognormal.parameter2_name\n",
      "fit.lognormal.parameter3_name == None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data)\n",
      "R, p = fit.distribution_compare('power_law', 'exponential', normalized_ratio=True)\n",
      "print R, p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "1.43148048496"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.152292556044\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Generative Mechanisms"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = worm\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'exponential')\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "(-0.070651754953295454, 0.70698857057710152)"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = worm\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'exponential')\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "(-0.070651754953295454, 0.70698857057710152)"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "print fit.distribution_compare('power_law', 'exponential', normalized_ratio=True)\n",
      "print fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "(9.1359147187770002, 6.4856142413795328e-20)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Assuming nested distributions\n",
        "(-0.91712308337346782, 0.17562683168707593)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Assuming nested distributions\n",
        "(-0.91712308337346782, 0.17562683168707593)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 4"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'lognormal')\n",
      "fig = fit.plot_ccdf(linewidth=3, label='Empirical Data')\n",
      "fit.power_law.plot_ccdf(ax=fig, color='r', linestyle='--', label='Power law fit')\n",
      "fit.lognormal.plot_ccdf(ax=fig, color='g', linestyle='--', label='Lognormal fit')\n",
      "####\n",
      "fig.set_ylabel(u\"p(X\u2265x)\")\n",
      "fig.set_xlabel(\"Word Frequency\")\n",
      "handles, labels = fig.get_legend_handles_labels()\n",
      "fig.legend(handles, labels, loc=3)\n",
      "\n",
      "figname = 'FigLognormal'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEaCAYAAAA7YdFPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvvw/Tqp69rg3T6YAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x63cb450>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Creating Simulated Data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "empirical_data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(empirical_data)\n",
      "simulated_data = fit.power_law.generate_random(10000)\n",
      "\n",
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5])\n",
      "simulated_data = theoretical_distribution.generate_random(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5])\n",
      "simulated_data = theoretical_distribution.generate_random(10000)\n",
      "####\n",
      "fit = powerlaw.Fit(simulated_data)\n",
      "fit.power_law.xmin, fit.power_law.alpha"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "(5.6152059101066776, 2.5169721295788654)"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "powerlaw.plot_pdf(simulated_data,linewidth=3)\n",
      "fit.power_law.plot_pdf(simulated_data,linestyle='--',color='r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "<matplotlib.axes.AxesSubplot at 0x8673a90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAELCAYAAAA7h+qnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCEoGIiKCkoGIiKBkICIiKBmIiAjw/8DoFgtaDbkBAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6f6f450>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Advanced Considerations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Discrete Distribution Calculation and Estimation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, discrete=True, estimate_discrete=True)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.estimate_discrete\n",
      "fit = powerlaw.Fit(data, discrete=True, estimate_discrete=False)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.estimate_discrete"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, discrete=True, xmin=230.0, xmax=9000, discrete_approximation='xmax')\n",
      "fit.lognormal.mu\n",
      "fit = powerlaw.Fit(data, discrete_approximation=100000, xmin=230.0, discrete=True)\n",
      "fit.lognormal.mu\n",
      "fit = powerlaw.Fit(data, discrete_approximation='round', xmin=230.0, discrete=True)\n",
      "fit.lognormal.mu"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "0.39905257607693184"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5], discrete=True)\n",
      "simulated_data = theoretical_distribution.generate_random(10000, estimate_discrete=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "empirical_data = blackouts\n",
      "####\n",
      "theoretical_distributionibution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5], discrete=True, estimate_discrete=False)\n",
      "simulated_data = theoretical_distribution.generate_random(10000)\n",
      "\n",
      "fit = powerlaw.Fit(empirical_data, discrete=True, estimate_discrete=True)\n",
      "simulated_data = fit.power_law.generate_random(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Nested Distributions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')\n",
      "fit.distribution_compare('exponential', 'stretched_exponential')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Assuming nested distributions"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "(-13.018342321459157, 3.3499122220614908e-07)"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Restricted Parameter Range"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin\n",
      "\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.1)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "(1.7831398653341155, 0.063521030949327109, 50.0)"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "parameter_range = {'alpha': [2.3, None], 'sigma': [None, .2]}\n",
      "fit = powerlaw.Fit(data, parameter_range=parameter_range)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "(2.3000107113942141, 0.17069976919260452, 234.0)"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "parameter_range = lambda(self): self.sigma/self.alpha < .05\n",
      "fit = powerlaw.Fit(data, parameter_range=parameter_range)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "(1.8833765811180314, 0.094168259953067143, 124.0)"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Multiple Possible Fits"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 5"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.1)\n",
      "print fit.xmin, fit.D, fit.alpha\n",
      "fit = powerlaw.Fit(data)\n",
      "print fit.xmin, fit.D, fit.alpha\n",
      "####\n",
      "from matplotlib.pylab import plot\n",
      "plot(fit.xmins, fit.Ds, label=r'$D$')\n",
      "plot(fit.xmins, fit.sigmas, label=r'$\\sigma$', linestyle='--')\n",
      "plot(fit.xmins, fit.sigmas/fit.alphas, label=r'$\\sigma /\\alpha$', linestyle='--')\n",
      "####\n",
      "ylim(0, .4)\n",
      "legend(loc=4)\n",
      "xlabel(r'$x_{min}$')\n",
      "ylabel(r'$D,\\sigma,\\alpha$')\n",
      "\n",
      "figname = 'FigD'\n",
      "savefig(figname+'.eps', bbox_inches='tight')\n",
      "#savefig(figname+'.tiff', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "50.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.0998297854528 1.78313986533\n",
        "Calculating best minimal value for power law fit\n",
        "230.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.0606737962944 2.27263721983\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZkAAAEVCAYAAAAy15htAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxGAoyRBCCDEYSjKEEEIMhpIMIYQQg/l/GCZbSPqsQY4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9a6f590>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## No Possible Fits"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.001)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin, fit.noise_flag"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "No valid fits found."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "(2.2726372198302882, 0.16568325372336856, 230.0, True)"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit.lognormal.mu, fit.lognormal.sigma\n",
      "range_dict = {'mu': [10.5, None]}\n",
      "fit.lognormal.parameter_range(range_dict)\n",
      "fit.lognormal.mu, fit.lognormal.sigma, fit.lognormal.noise_flag\n",
      "\n",
      "initial_parameters = (12, .7)\n",
      "fit.lognormal.parameter_range(range_dict, initial_parameters)\n",
      "fit.lognormal.mu, fit.lognormal.sigma, fit.lognormal.noise_flag"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "No valid fits found.\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "(10.500000000422041, 5.1423189016918585, False)"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Selecting x<sub>min</sub> with Other Distance Metrics"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmin_distance='D')\n",
      "print fit.xmin, fit.power_law.alpha, fit.D\n",
      "fit = powerlaw.Fit(data, xmin_distance='V')\n",
      "print fit.xmin, fit.power_law.alpha, fit.V\n",
      "fit = powerlaw.Fit(data, xmin_distance='Asquare')\n",
      "print fit.xmin, fit.power_law.alpha, fit.Asquare"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "230.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 2.27263721983 0.0606737962944\n",
        "Calculating best minimal value for power law fit\n",
        "219.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 2.21822784881 0.0921084614746\n",
        "Calculating best minimal value for power law fit\n",
        "230.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 2.27263721983 0.265613512591\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Supporting Information"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import logspace\n",
      "from scipy.stats import variation\n",
      "import pandas as pd\n",
      "\n",
      "def validate(xmin, alpha, discrete='continuous', n_data=10000, n_trials=1):\n",
      "    \n",
      "    if n_trials>1:\n",
      "        return array([validate(xmin, alpha, discrete=discrete, n_data=n_data, n_trials=1) for trial in arange(n_trials)]).T\n",
      "        \n",
      "    if discrete=='continuous':\n",
      "        discrete = False\n",
      "        estimate_discrete = False\n",
      "    elif discrete == 'discrete':\n",
      "        discrete = True\n",
      "        estimate_discrete = False\n",
      "    elif discrete == 'discrete_estimate':\n",
      "        discrete = True\n",
      "        estimate_discrete = True\n",
      "\n",
      "    theoretical_distribution = powerlaw.Power_Law(xmin=xmin, parameters=[alpha], discrete=discrete)\n",
      "    simulated_data = theoretical_distribution.generate_random(n_data, estimate_discrete=estimate_discrete)\n",
      "    fit = powerlaw.Fit(simulated_data, discrete=discrete, estimate_discrete=estimate_discrete)\n",
      "    return fit.xmin, fit.alpha"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_trials = 10\n",
      "n_data = 10000\n",
      "theoretical_xmins = unique(floor(logspace(0.0,2.0,num=20)))\n",
      "theoretical_alphas = array([1.5,2.0,2.5,3.0,3.5])\n",
      "distribution_types = ['continuous','discrete']\n",
      "\n",
      "filename = 'powerlaw_validation_%itrials_%idata.h5'%(int(n_trials),int(n_data))\n",
      "\n",
      "from os import listdir\n",
      "files = listdir('.')\n",
      "if filename in files:\n",
      "    df = pd.read_hdf(filename,'df')\n",
      "else:\n",
      "    print(\"Calculating validation fits on %i synthetic datasets of %i data points each. \"\n",
      "          \"Could take a long time.\")%(n_trials*len(theoretical_alphas)*len(theoretical_xmins)*len(distribution_types), n_data) \n",
      "\n",
      "    ind = [(d,a,x) for d in distribution_types for a in theoretical_alphas for x in theoretical_xmins]\n",
      "    ind = pd.MultiIndex.from_tuples(ind, names=['type', 'alpha','xmin'])\n",
      "    df = pd.DataFrame(columns=['alpha_mean', 'alpha_sd', 'xmin_mean', 'xmin_sd'], index=ind)\n",
      "    \n",
      "    i = 0\n",
      "    for dt, alpha, xmin in ind:\n",
      "        i += 1\n",
      "        print(i)\n",
      "        data = validate(xmin, alpha, discrete=dt, n_data=n_data, n_trials=n_trials)\n",
      "        df.ix[dt,alpha,xmin] = (mean(data[1]), std(data[1]), mean(data[0]), std(data[0]))\n",
      "\n",
      "    df.to_hdf(filename,'df')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "subplot(2,2,1)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['continuous', a]['alpha_mean'].astype('float')\n",
      "    error = df.ix['continuous', a]['alpha_sd'].astype('float')\n",
      "\n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, y_vals-error, y_vals+error, alpha=.1)\n",
      "\n",
      "xscale('log')\n",
      "#xlabel(r\"$x_{min}$\")\n",
      "ylabel(r\"Fitted $\\alpha$\")\n",
      "yticks(theoretical_alphas)\n",
      "setp(gca().get_xticklabels(), visible=False)\n",
      "title(\"Continuous\")\n",
      "\n",
      "#########\n",
      "subplot(2,2,2)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['discrete', a]['alpha_mean'].astype('float')\n",
      "    error = df.ix['discrete', a]['alpha_sd'].astype('float')\n",
      "\n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, y_vals-error, y_vals+error, alpha=.1)\n",
      "\n",
      "xscale('log')\n",
      "#xlabel(r\"$x_{min}$\")\n",
      "#ylabel(r\"Fitted $\\alpha$\")\n",
      "setp(gca().get_xticklabels(), visible=False)\n",
      "setp(gca().get_yticklabels(), visible=False)\n",
      "title(\"Discrete\")\n",
      "\n",
      "########\n",
      "subplot(2,2,3)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['continuous', a]['xmin_mean'].astype('float')\n",
      "    error = df.ix['continuous', a]['xmin_sd'].astype('float')\n",
      "    up = y_vals+error\n",
      "    down = y_vals-error\n",
      "    ind = down<theoretical_xmins\n",
      "    down[ind] = theoretical_xmins[ind]\n",
      "    \n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, down, up, alpha=.1)\n",
      "\n",
      "xlim(xmin=1)\n",
      "ylim(ymin=1)\n",
      "plot(xlim(),xlim(),linestyle='--', color='k')\n",
      "xscale('log')\n",
      "yscale('log')\n",
      "xlabel(r\"$x_{min}$ of Data\")\n",
      "ylabel(r\"Fitted $x_{min}$\")\n",
      "\n",
      "\n",
      "########\n",
      "legend_refs = []\n",
      "########\n",
      "subplot(2,2,4,sharey=gca())\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['discrete', a]['xmin_mean'].astype('float')\n",
      "    error = df.ix['discrete', a]['xmin_sd'].astype('float')\n",
      "    up = y_vals+error\n",
      "    down = y_vals-error\n",
      "    ind = down<theoretical_xmins\n",
      "    down[ind] = theoretical_xmins[ind]\n",
      "\n",
      "    line = plot(theoretical_xmins, y_vals, label=a)\n",
      "    legend_refs += line\n",
      "    fill_between(theoretical_xmins, down, up, alpha=.1)\n",
      "\n",
      "xlim(xmin=1)\n",
      "ylim(ymin=1)\n",
      "plot(xlim(),xlim(),linestyle='--', color='k')\n",
      "xscale('log')\n",
      "yscale('log')\n",
      "xlabel(r\"$x_{min}$ of Data\")\n",
      "#ylabel(r\"Fitted $x_{min}$\")\n",
      "setp(gca().get_yticklabels(), visible=False)\n",
      "\n",
      "\n",
      "#######\n",
      "#figlegend(legend_refs[::-1], theoretical_alphas[::-1],'center right', title=r'$\\alpha$ of Data')\n",
      "subplots_adjust(wspace=.15, hspace=.1)\n",
      "legend( legend_refs[::-1], theoretical_alphas[::-1], loc = 'center right', bbox_to_anchor = (.1,0,1,1),\n",
      "            bbox_transform = plt.gcf().transFigure, title=r'$\\alpha$ of Data' )\n",
      "savefig('Fig_powerlaw_validation_%itrials_%idata.pdf'%(int(n_trials),int(n_data)), bbox_inches='tight')\n",
      "savefig('Fig_powerlaw_validation_%itrials_%idata.tiff'%(int(n_trials),int(n_data)), bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdsAAAEnCAYAAADhKulWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa3a9350>"
       ]
      }
     ],
     "prompt_number": 41
    }
   ],
   "metadata": {}
  }
 ]
}