standard normal.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Standard Normal N(0,1)\n",
    "\n",
    "Generate a total of 2000 i.i.d. standard normals N(0,1) using each method. Test the normality of the standard normals obtained from each method, using the Anderson-Darling test. Which data set is closer to the normal distribution? (Consult the paper by Stephens - filename 2008 Stephens.pdf on Canvas - to find the appropriate critical points for the Anderson-Darling statistic. Clearly identify those percentiles in your soultion.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.036412Z",
     "start_time": "2019-05-23T15:54:36.995643Z"
    }
   },
   "outputs": [],
   "source": [
    "# imports\n",
    "import random\n",
    "import math\n",
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import anderson\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "%matplotlib notebook\n",
    "\n",
    "# project imports\n",
    "import rand\n",
    "import halton\n",
    "import bfs\n",
    "import box_muller\n",
    "import beasley_springer_moro"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate a total of 2000 i.i.d. standard normals N (0, 1) using Box Muller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.053097Z",
     "start_time": "2019-05-23T15:54:37.042500Z"
    }
   },
   "outputs": [],
   "source": [
    "# generate 1000 2-dim vectors, then flatten to create 2000 standard normals\n",
    "N = 1000\n",
    "s = 2\n",
    "seq = rand.rand_seq\n",
    "seq = halton.halton_seq\n",
    "#seq = bfs.bfs_seq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.093406Z",
     "start_time": "2019-05-23T15:54:37.059566Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0.7443300850272079, -0.6113446172758047), (0.22750250323107185, 1.3746076837154961), (-0.2494802853218258, -0.44280186764434915), (1.6558473350849008, 0.01741370677972137), (-0.3827115346426496, 0.647064691400064), (0.21543958611815975, -1.1509103496429351), (2.532576610273044, 2.170874557206201), (-1.7154082878285117, 0.6040055310970016), (-0.712862863490848, -0.4796718958687281), (1.1489490697564084, -0.5619728901777015)]\n",
      "[0.7443300850272079, -0.6113446172758047, 0.22750250323107185, 1.3746076837154961, -0.2494802853218258, -0.44280186764434915, 1.6558473350849008, 0.01741370677972137, -0.3827115346426496, 0.647064691400064, 0.21543958611815975, -1.1509103496429351, 2.532576610273044, 2.170874557206201, -1.7154082878285117, 0.6040055310970016, -0.712862863490848, -0.4796718958687281, 1.1489490697564084, -0.5619728901777015]\n"
     ]
    }
   ],
   "source": [
    "l = box_muller.box_muller_seq(s, N, seq=seq)\n",
    "# print the first 20\n",
    "print(l[:10])\n",
    "# flatten the sequence into 1 dimension\n",
    "flattened = [item for sublist in l for item in sublist]\n",
    "nums = flattened\n",
    "print(nums[:20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-23T20:27:44.696352Z",
     "start_time": "2019-03-23T20:27:44.681703Z"
    }
   },
   "source": [
    "### Sort the sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.109399Z",
     "start_time": "2019-05-23T15:54:37.097758Z"
    }
   },
   "outputs": [],
   "source": [
    "nums = numpy.array(nums)\n",
    "nums = sorted(nums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.127443Z",
     "start_time": "2019-05-23T15:54:37.115697Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.5409431816696766, -3.1398610496653436, -2.9805243083534694, -2.9368656765203136, -2.9183735528681174, -2.749374931759913, -2.696584045082842, -2.673434038789564, -2.6637133132283606, -2.602326318987692, -2.590178545528447, -2.5814016358470764, -2.515685310747461, -2.453941617556857, -2.452827867160038, -2.4113719915033367, -2.3938365329485434, -2.3420632093356692, -2.3329943092852723, -2.276147668551989]\n"
     ]
    }
   ],
   "source": [
    "print(nums[:20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the sample mean and standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.151342Z",
     "start_time": "2019-05-23T15:54:37.129406Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 0.0014995686420993478\n",
      "variance = 0.9935254197054167\n",
      "standard deviation = 0.996757452796525\n"
     ]
    }
   ],
   "source": [
    "nums = numpy.array(nums)\n",
    "mean = numpy.mean(nums)\n",
    "var = numpy.var(nums)\n",
    "std = numpy.std(nums)\n",
    "\n",
    "print('mean = {}'.format(mean))\n",
    "print('variance = {}'.format(var))\n",
    "print('standard deviation = {}'.format(std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.359384Z",
     "start_time": "2019-05-23T15:54:37.159576Z"
    },
    "scrolled": false
   },
   "outputs": [
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       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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Sed8dHd3Kzs7Ww0NDQn3T5s2TRUVFef8/pMnT2rjxo0aMGCANmzYIElqbW1VIBBQU1NTwmMnTpyou+++O6nrYoAAZ5guRn4J4Bfs7zQXwGuvvTapTJo06byO297erkAgoC1btiTcP3/+fEUikTN+X0dHhwYOHKi+ffsqFArppz/9afxrmzdvViAQ0JtvvpnwPbfddpumTp3a6/G6urrU2dkZT1tbm+8HCEiW6XJDKIBADwqgS34FnGoBjMVi2rt3r5qamrRkyRLl5eVp06ZNklIrgLW1tQoEAqfFzwMEJMt0uSEUQKAHBdAlBdDqr4B73Hnnnbr++uslpfYrYH4CCKTOdLkhFECgBwXQxgLY86veM+V8RSIRzZ49O347FoupqKjovN4E8s1vflNlZWWSTr0JZMmSJfGvd3Z28iYQwCamyw2hAAI92N82FsDvfve7CamurtaECROUl5eX9Jss/n/19fUKhUKqq6tTS0uLZsyYoXA4rMOHD0uSKisrVVNTE3/8ww8/rA0bNqi1tVUtLS1asmSJ+vbtq5/85CfxxyxevFjhcFiNjY3asWOHpkyZwsfAADYxXW4IBRDowf428Cvg2tpazZ07N6XvXbZsmYqLixUMBhWJRLRt27b418rKyhSNRuO3Fy5cqFGjRiknJ0eDBw/W+PHjVV9fn3C8ng+CHjZsmEKhkMrLy7V79+6kr4cBApJnutwQCiDQg/1toADu3btXgwcPdvq0tmCAgOSZLjeEAgj0YH8bKIBr1qzR8OHDnT6tLRggIHmmyw2hAAI92N82FsBbbrklITfffLOuueYaZWdn64EHHrDrtI5igIDkmS43hAII9GB/21gA77jjjoRMnz5d99xzj37961/bdUrHMUBA8kyXG0IBBHqwv13yOYCZigECkme63BAKINCD/U0BtIQBApJnutwQCiDQg/1tQwEsLS1NKl7AAAHJM11uCAUQ6MH+tqEAZmVlacSIEVqwYIGeeOKJM8YLGCAgeabLDaEAAj3Y3zYUwHXr1mny5MnKycnRLbfcohdffFGxWCzdp8kIDBCQPNPlhlAAgR7sbxv/DOChQ4f00EMPadSoUSosLNQ999yjPXv22HU6IxggIHmmyw2hAAI92N8OvQnklVde0bXXXqs+ffrovffec+KUjmCAgOSZLjeEAgj0YH/bXACPHz+un//855o0aZL69++v22+/XV1dXXae0lEMEJA80+WGUACBHuxvmwrgtm3bVFVVpby8PI0bN07Lli3z1E/+ejBAQPJMlxtCAQR6sL9tKIB/93d/pyFDhujuu+/Wa6+9lu7DZxQGCEie6XJDKIBAD/a3TR8Dk5ubq3A4rMGDB58xXsAAAckzXW4I5RHowf62oQDW1dUlFS9ggIDkmS4ohAII9GB/81fBWcIAAckzXVAIBRDowf6mAFrCAAHJM11QCAUQ6MH+pgBawgAByTNdUAgFEOjB/qYAWsIAAckzXVAIBRDowf6mAFrCAAHJM11QCAUQ6MH+trEAHj9+/Ixfe/PNN+06raMYICB5pgsKoQACPdjfNhbAsWPHqqmp6bT7n3vuOQ0ZMsSu0zqKAQKSZ7qgEAog0IP9bWMBvOuuuxQKhbR48WJJ0rFjxxSNRtW/f3899thjdp3WUQwQkDzTBYVQAIEe7G+b/wzgr371KxUUFOhLX/qSRo4cqcsvv1yvv/66nad0FAMEJM90QSEUQKAH+9vmAhiLxfStb31LWVlZ6tevn15++WU7T+c4BghInumCQiiAQA/2t40FcN++fYpEIiouLtaGDRu0cOFCBYNBzZ8/Xx999JFdp3UUAwQkz3RBIRRAoAf728YCmJubq9tvv13vv/9+/L7Nmzdr5MiRuuKKK+w6raMYICB5pgsKoQACPdjfNhbANWvW9Hr/Bx98oOnTp9t1WkcxQEDyTBcUQgEEerC/Hfog6La2NrW1tTlxKkcxQEDyTBcUQgEEerC/bSyAsVhMDz74oC644AL16dNHffr0UV5env7lX/5FsVjMrtM6igECkme6oBAKINCD/W1jAaypqVF+fr6efPJJNTc3q7m5WStWrFB+fr4WLFhg12kdxQAByTNdUAgFEOjB/raxAA4fPlyNjY2n3f/CCy+osLDQrtM6igECkme6oBAKINCD/W1jAQyFQtq9e/dp9//pT39STk6OXad1FAMEJM90QSEUQKAH+9vGAhiJRPTtb3/7tPtnz56ta665xq7TOooBApJnuqAQCiDQg/1tYwF85ZVXNHDgQI0dO1bTp0/X9OnTNXbsWOXm5uq3v/1tSsdcvny5SkpKFAqFFIlEtH379jM+dtWqVfrSl76kcDiscDis8vLy0x4fjUYVCAQScsMNNyR9PQwQkDzTBYVQAIEe7G+bPwamvb1dCxYs0K233qpbb71VCxcuVHt7e0rHqq+vVzAY1OrVq7Vz505VVVUpHA7ryJEjvT7+G9/4hlasWKGmpibt2rVLd9xxh/Ly8nTo0KH4Y6LRqCZPnqy33nornvfeey/pa2KAgOSZLiiEAgj0YH879DmA6RCJRFRdXR2/HYvFVFhYqEWLFiX1/SdOnNCgQYP0s5/9LH5fNBrVlClTUr4mBghInumCQiiAQA/2t0MF8NixY/rpT3+q5cuXa8+ePef9/d3d3crOzlZDQ0PC/dOmTVNFRUVSx/jggw+Uk5OjF198MX5fNBpVXl6e8vPzNWbMGM2aNUvvvPPOGY/R1dWlzs7OeNra2nw/QECyTBcUQgEEelAAbSiABw8e1MSJE5Wbm6vrrrtOBw8e1JgxY5SVlaWsrCwNGDBAr7766nkds729XYFAQFu2bEm4f/78+YpEIkkd46677tLFF1+s48ePx+9bu3atGhsbtWPHDjU0NGjs2LG6+uqrdeLEiV6PUVtbe9qfGfT7AAHJMl1QCAUQ6EEBtKEA3nbbbfrCF76gX/ziF6qoqNCll16qG2+8UYcPH9Zf//pX/f3f/70mTZp0Xse0WgAXLVqkwYMHq7m5+ayPa21tVSAQ0MaNG3v9Oj8BBFJnuqAQCiDQgwJoQwEcNmxY/N227777rrKyshKK22uvvaZPfepT53VMK78CfvTRR5WXl6c//OEPSZ1ryJAhWrlyZVKPZYCA5JkuKIQCCPRgf9tQALOysnT48OH47YEDB6q1tTV++/Dhw+rTp895HzcSiWj27Nnx27FYTEVFRWd9E8gjjzyiCy64QFu3bk3qHG1tbcrKyur1bzDpDQMEJM90QSEUQKAH+9umAvj/fzRLbm5uWgpgfX29QqGQ6urq1NLSohkzZigcDsfLZmVlpWpqauKPX7x4sYLBoJ577rmEj3k5evSoJOno0aOaN2+etm7dqv3792vjxo268sorNXr0aHV1dSV1TQwQkDzTBYVQAIEe7G+bCuDMmTM1Z84czZkzR8FgUNOnT4/fnjlzZkoFUJKWLVum4uJiBYNBRSIRbdu2Lf61srIyRaPR+O2SkpJe37BRW1srSfrwww91/fXXKz8/X/369VNJSYmqqqoSfnp5LgwQkDzTBYVQAIEe7G8bCmBZWZmuvfbac8YLGCD4jemSQTI3gJuwv130QdCZiAGC35guGSRzA7gJ+5sCaAkDBL8xXTJI5gZwE/Y3BdASBgh+Y7pkkMwN4CbsbwqgJQwQ/MZ0ySCZG8BN2N8UQEsYIPiN6ZJBMjeAm7C/KYCWMEDwG9Mlg2RuADdhfztUAC+77DL95S9/ceJUjmKA4DemSwbJ3ABuwv52qAB+8m8D8QoGCH5jumSQzA3gJuxvCqAlDBD8xnTJIJkbwE3Y3w4VwK9+9at68803nTiVoxgg+I3pkkG8GcBp7G/eBGIJAwS/MV0UiDcDOI39TQG0hAGC35guCsSbAZzG/qYAWsIAwW9MFwXizQBOY39TAC1hgOA3posC8WYAp7G/KYCWMEDwG9NFgXgzgNPY3xRASxgg+I3pokC8GcBp7O80F8BwOKzBgwcnFS9ggOA3posC8WYAp7G/01wA6+rqko4XMEDwG9NFgXgzgNPY3/wK2BIGCH5juigQbwZwGvvboQJ4/PhxdXZ2JsQLGCD4jemiQLwZwGnsbxsL4LFjx1RdXa38/Hz16dPntHgBAwS/MV0UiDcDOI39bWMB/Na3vqWxY8fqueeeU//+/bV69Wp9//vf16c//Wn94he/sOu0jmKA4DemiwLxZgCnsb9tLIAXXXSRNm3aJEkaNGiQ9u7dK0las2aNvvrVr9p1WkcxQPAb00WBeDOA09jfNhbAgQMH6uDBg5KkoqIibd++XZL05z//WQMHDrTrtI5igOA3posC8WYAp7G/bSyAn/3sZ/XKK69IksrLyzV37lxJ0tKlS1VUVGTXaR3FAMFvTBcF4s0ATmN/21gAH3vsMS1dulSS9Jvf/EY5OTkKhULq06ePnnjiCbtO6ygGCH5juigQbwZwGvvbwc8BPHDggH75y1+qubnZqVPajgGC35guCsSbAZzG/uaDoC1hgOA3posC8WYAp7G/bS6Av//97/XII49o7ty5mjNnTkK8gAGC35guCsSbAZzG/raxAP7gBz9QVlaWLr30UpWVlenaa6+NZ9KkSXad1lEMEPzGdFEg3gzgNPa3jQVw6NCheuaZZ+w6fEZggOA3posC8WYAp7G/bSyABQUF2rNnj12HzwgMEPzGdFEg3gzgNPa3jQXwkUce0Xe+8x27Dp8RGCD4jemiQLwZwGnsbxsLYCwW0+TJk3XxxRfrpptu0i233JKQVCxfvlwlJSUKhUKKRCLxv12kN6tWrdKXvvQlhcNhhcNhlZeXn/b4kydP6r777lNBQYFycnJUXl5+Xj+1ZIDgN6aLAvFmAKexv20sgNXV1QqFQpo8ebKi0ajuuOOOhJyv+vp6BYNBrV69Wjt37lRVVZXC4bCOHDnS6+O/8Y1vaMWKFWpqatKuXbt0xx13KC8vT4cOHYo/ZvHixcrLy9MLL7yg5uZmVVRUqLS0VMePH0/qmhgg+I3pokC8GcBp7G8bC2Bubq5+9av0/YMdiURUXV0dvx2LxVRYWKhFixYl9f0nTpzQoEGD9LOf/UzSxz/9Kygo0KOPPhp/TEdHh0KhkNauXZvUMRkg+I3pokC8GcBp7G8bC2BxcbF27dqVlmN1d3crOztbDQ0NCfdPmzZNFRUVSR3jgw8+UE5Ojl588UVJUmtrqwKBgJqamhIeN3HiRN199929HqOrq0udnZ3xtLW1+X6A4C+miwLxZgCnUQBtLICrV6/W1KlT9X//93+Wj9Xe3q5AIKAtW7Yk3D9//nxFIpGkjnHXXXfp4osvjv96d/PmzQoEAnrzzTcTHnfbbbdp6tSpvR6jtrZWgUDgtPh5gOAvposC8WYAp1EAbSyAV1xxhQYNGqTc3FxddtllGjduXELOh9UCuGjRIg0ePDjh7yFOpQDyE0D4nemiQLwZwGkUQBsL4AMPPHDWnA8rvwJ+9NFHlZeXpz/84Q8J96fyK+BPYoDgRqaXPSHpDJAK9rdNBfBvf/ubHnzwQbW1taXtmJFIRLNnz47fjsViKioqOuubQB555BFdcMEF2rp162lf63kTyJIlS+L3dXZ28iYQeJ7phU1IOgOkgv1t87uA9+/fn7bj1dfXKxQKqa6uTi0tLZoxY4bC4bAOHz4sSaqsrFRNTU388YsXL1YwGNRzzz2nt956K56jR48mPCYcDquxsVE7duzQlClT+BgYeJ7phU1IOgOkgv1tYwGsqKhQXV1dWo+5bNkyFRcXKxgMKhKJaNu2bfGvlZWVKRqNxm+XlJT0+oaN2tra+GN6Pgh62LBhCoVCKi8v1+7du5O+HgYIbmR6YROSzgCpYH/bWACfeuopFRQUaO7cuXr22WfV2NiYEC9ggOBGphc2IekMkAr2t40FMCsr64zp06ePXad1FAMENzK9sAlJZ4BUsL9tLIB+wADBjUwvbELSGSAV7G8KoCUMENzI9MImJJ0BUsH+trkAvvLKK7rppps0cuRIjRw5Ul//+tf122WU0O4AAB8TSURBVN/+1s5TOooBghuZXtiEpDNAKtjfNhbAn//85+rbt6+mTp2qpUuXaunSpZo6dar69eunf/u3f7PrtI5igOBGphc2IekMkAr2t40F8NJLL9Vjjz122v0/+tGPdOmll9p1WkcxQHAj0wubkHQGSAX728YCGAwGtXfv3tPu37t3r0KhkF2ndRQDBDcyvbAJSWeAVLC/bSyAI0eO1MqVK0+7/6mnntKoUaPsOq2jGCC4kemFTUg6A6SC/W1jAXzyyScVDAY1a9YsrVmzRmvWrNHMmTMVCoV6LYZuxADBjUwvbELSGSAV7G+b3wX8/PPPa8KECbrwwgt14YUXasKECXrhhRfsPKWjGCC4kemFTUg6A6SC/c3nAFrCAMGNTC9sQtIZIBXsbwqgJQwQ3Mj0wiYknQFSwf62oQCOGDFCpaWlZ83FF1+c7tMawQDBjUwvbELSGSAV7G8bCuATTzxxxnz3u99V//791adPn3Sf1ggGCG5kemETks4AqWB/O/Qr4HfffVff/e53FQqFNHHiRG3dutWJ09qOAYIbmV7YhKQzQCrY3zYXwA8//FAPPfSQwuGwLr/8cq1fv97O0zmOAYIbmV7YhKQzQCrY3zYVwBMnTuipp55SQUGBRowYoTVr1ujkyZN2nMooBghuZHphE5LOAKlgf9tQAP/93/9do0ePVn5+vp544gl1d3en+xQZgwGCG5le2ISkM0Aq2N82FMCsrCwNGDBAd955p+bMmXPGeAEDBDcyvbAJSWeAVLC/bSiAZWVluvbaa8+aSZMmpfu0RjBAcCPTC5uQdAZIBfubD4K2hAGCG5le2ISkM0Aq2N8UQEsYILiR6YVNSDoDpIL9TQG0hAGCG5le2ISkM0Aq2N8UQEsYILiR6YVNSDoDpIL9TQG0hAGCG5le2ISkM0Aq2N8UQEsYILiR6YVNSDoDpIL9neYC2NzcnHS8gAGCG5le2ISkM0Aq2N9pLoBZWVnq06dP/D/PFi9ggOBGphc2IekMkAr2d5oL4IEDB+JpaGjQyJEjtXLlyvhP/VauXKnRo0eroaEhnac1hgGCG5le2ISkM0Aq2N82/hnAq6++WuvXrz/t/vXr1+vKK6+067SOYoDgRqYXNiHpDJAK9reNBTAnJ0ctLS2n3d/S0qKcnBy7TusoBghuZHphE5LOAKlgf9tYAMeNG6fKykp1d3fH7+vu7lZlZaXGjRtn12kdxQDBjUwvbELSGSAV7G8bC+D27ds1dOhQ5efnq7y8XOXl5crPz9fQoUO1fft2u07rKAYIbmR6YROSzgCpYH/b/DmAx44d049//GPNmTNHc+bM0apVq3Ts2LGUjrV8+XKVlJQoFAopEomctUS+8cYbuvXWW1VSUqJAIKDHH3/8tMfU1tYqEAgk5JJLLjmva2KA4EamFzYh6QyQCva3TQXwo48+0sUXX9zrnwFMRX19vYLBoFavXq2dO3eqqqpK4XBYR44c6fXxv//97zVv3jytXbtWBQUFZyyAn/nMZ/TWW2/F8/bbb5/XdTFAcCPTC5uQdAZIBfvbxp8AFhYWpq0ARiIRVVdXx2/HYjEVFhZq0aJF5/zekpKSMxbAyy+/3NJ1MUAwxfTSJSRTAqSC/W1jAfzBD36gaDSqv/3tb5aO093drezs7NM+O3DatGmqqKg45/efrQAOGDBAw4cPV2lpqb7xjW/o4MGD53VtDBBMMb10CcmUAKlgf9tYAG+++WYNGjRIw4cP1/XXX69bbrklIclqb29XIBDQli1bEu6fP3++IpHIOb//TAXwpZde0rp169Tc3KyXX35Z48ePV3FxsT744IMzHqurq0udnZ3xtLW1+X6AYIbppUtIpgRIBQXQxgJ4xx13nDXJsqsAftL777+vCy64QE8//fQZH9PbG0f8PkAww/TSJSRTAqSCAmjzu4DTwa5fAffm85//vGpqas74dX4CiExheukSkikBUkEBdEEBlD5+E8js2bPjt2OxmIqKiiy9CeSTjh49qsGDB2vp0qVJXxcDBFNML11CMiVAKtjfNhfA//iP/9Btt92ma665RuPGjUvI+aivr1coFFJdXZ1aWlo0Y8YMhcNhHT58WJJUWVmZ8JO77u5uNTU1qampScOHD9e8efPU1NSkvXv3xh8zd+5cvfLKK9q/f782b96s6667TkOGDNFf//rXpK+LAYIpppcuIZkSIBXsbxsL4NKlS5Wbm6vZs2crGAxq5syZuu6665SXl6cFCxac9/GWLVum4uJiBYNBRSIRbdu2Lf61srIyRaPR+O39+/f3+mf1ysrK4o+5/fbbNXz4cAWDQRUVFen222/Xvn37zuuaGCCYYnrpEpIpAVLB/raxAF5yySV69tlnJUm5ublqbW2VJN13330Jn+nnZgwQTDG9dAnJlACpYH/bWAD79++vAwcOSJLy8/P12muvSZL27NmjCy+80K7TOooBgimmly4hmRIgFexvGwtgaWmp/vjHP0qSrrrqKq1cuVKS9Otf/1qDBw+267SOYoBgiumlS0imBEgF+9vGAnjnnXfqgQcekCQtX75c/fv313XXXadwOKzp06fbdVpHMUAwxfTSJSRTAqSC/W1jAYzFYgl/DdzatWv17W9/W//6r/+q7u5uu07rKAYIppheuoRkSoBUsL9d8jmAmYoBgimmly4hmRIgFezvNBfA5ubmpOMFDBBMMb10CcmUAKlgf6e5AGZlZalPnz7x/zxbvIABgimmly4hmRIgFezvNBfAAwcOxNPQ0KCRI0dq5cqV8Z/6rVy5UqNHjz7t7/V1KwYIppheuoRkSoBUsL9t/DOAV199tdavX3/a/evXr9eVV15p12kdxQDBFNNLl5BMCZAK9reNBTAnJ0ctLS2n3d/S0qKcnBy7TusoBgimmF66hGRKgFSwv20sgOPGjVNlZWXCR750d3ersrJS48aNs+u0jmKAYIrppUtIpgRIBfvbxgK4fft2DR06VPn5+SovL1d5ebny8/M1dOhQbd++3a7TOooBgimmly4hmRIgFexvmz8H8NixY/rxj3+sOXPmaM6cOVq1apWOHTtm5ykdxQDBFNNLl5BMCZAK9jcfBG0JAwRTTC9dQrwQ+Bf72+YCuGfPHv34xz/W97//fT344IMJ8QIGCKaYXpyEeCHwL/a3jQVw1apVys7O1rBhw3T55ZfriiuuiIc3gQDWmF6chHgh8C/2t40FsLi4WIsXL7br8BmBAYIpphcnIV4I/Iv9bWMBHDRokFpbW+06fEZggGCK6cVJiBcC/2J/21gAp0+frqeeesquw2cEBgimmF6chHgh8C/2t40F8OGHH9aQIUMUjUa1ZMkSLV26NCFewADBFNOLkxAvBP7F/raxAI4YMeKMKS0tteu0jmKAYIrpxUmIFwL/Yn/zOYCWMEAwxfTiJMQLgX+xvymAljBAMMX04iTEC4F/sb9tLoBtbW1asWKF7rnnnvhfB9cTL2CAYIrpxUmIFwL/Yn/bWAA3btyoAQMG6LLLLlPfvn11xRVXKBwOKy8vT5MmTbLrtI5igGCK6cVJiBcC/2J/21gAr776at1///2SpNzcXLW2turo0aOqqKjQk08+addpHcUAwRTTi5MQLwT+xf62sQDm5uZq3759kqRwOKw33nhDkvTaa6+ppKTErtM6igGCKaYXJyFeCPyL/W1jARw2bJhaWlokSWPHjlVjY6OkjwvgwIED7TqtoxggmGJ6cRLihcC/2N82FsApU6Zo1apVkqS5c+dq1KhReuihh3TllVeqvLzcrtM6igGCKaYXJyFeCPyL/W1jAWxtbVVzc7Mk6dixY5o5c6Y++9nP6tZbb9WBAwfsOq2jGCCYYnpxEuKFwL/Y33wOoCUMEEwxvTgJ8ULgX+xvGwtgaWmp3nnnndPuf//99/mr4ACLTC9OQrwQ+Bf728YCmJWVpSNHjpx2/+HDhxUMBu06raMYIJhienES4oXAv9jfNhTAxsZGNTY2KisrS2vWrInfbmxs1PPPP6/q6mqNGTPmvI+7fPlylZSUKBQKKRKJaPv27Wd87BtvvKFbb71VJSUlCgQCevzxxy0fszcMEEwxvTgJ8ULgX+xvGwpgVlaWsrKy1KdPn/h/70kwGNSYMWP04osvntcx6+vrFQwGtXr1au3cuVNVVVUKh8O9/oRRkn7/+99r3rx5Wrt2rQoKCnotgOd7zN4wQDDF9OIkxAuBf7G/bfwV8IgRI/T222+n5ViRSETV1dXx27FYTIWFhVq0aNE5v7ekpKTXAmjlmD0YIJhienES4vfA3djfLngXcHd3t7Kzs9XQ0JBw/7Rp01RRUXHO7++tAFo9Zg8GCKaYXn6E+D1wN/a3DQVwy5Ytp/2K92c/+5lGjBih/Px8VVVVqaurK+njtbe3KxAIaMuWLQn3z58/X5FI5Jzf31sBTPWYXV1d6uzsjKetrc33AwQzTC8/QvweuBsF0IYCOHnyZC1evDh+e8eOHerbt6/+6Z/+ST/60Y9UUFCg2trapI+XSQWwtrZWgUDgtPh5gGCG6eVHiN8Dd6MA2lAACwoK9Ic//CF+e8GCBZowYUL89rp16zR27Nikj5dJvwLmJ4DIFKaXHyF+D9yNAmhDAQyFQvrLX/4Svz1hwgQ99NBD8dv79+9Xbm7ueR0zEolo9uzZ8duxWExFRUWW3wSS6jF7MEAwxfTyI8Tvgbuxv20ogMXFxXr11VclffyTtv79+2vjxo3xr+/YsUODBw8+r2PW19crFAqprq5OLS0tmjFjhsLhsA4fPixJqqysVE1NTfzx3d3dampqUlNTk4YPH6558+apqalJe/fuTfqYyWCAYIrp5UeI3wN3Y3/bUABnzZql8ePH67e//a2+973v6VOf+pS6u7vjX//FL36hz3/+8+d93GXLlqm4uFjBYFCRSETbtm2Lf62srEzRaDR+e//+/b3+Wb2ysrKkj5kMBgimmF5+hPg9cDf2tw0F8O2339aXv/xlZWVladCgQXr++ecTvv6Vr3xFCxYsSPdpjWCAYIrp5UeI3wN3Y3/b+DmAHR0dOnHixGn3v/vuuwk/EXQzBgimmF5+hPg9cDf2tws+CDqTMUCwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMECwwvQCI4SkHrgb+5sCaAkDBCtMLzBCSOqBu7G/KYCWMEAwvYQIIe4LzGN/UwAtYYBgepEQQtwXmMf+pgBawgDB9CIhhLgvMI/9TQG0hAGC6UVCCHFfYB77mwJoCQME04uEEOK+wDz2NwXQEgYIphcJIcR9gXnsbwqgJQwQTC8SQoj7AvPY3xRASxggmF4khBD3Beaxv11WAJcvX66SkhKFQiFFIhFt3779rI9ft26dLrnkEoVCIV122WVav359wtej0agCgUBCbrjhhqSvhwGC6UVCCHFfYB7720UFsL6+XsFgUKtXr9bOnTtVVVWlcDisI0eO9Pr4zZs3Kzs7Wz/84Q/V0tKie++9V/369dPrr78ef0w0GtXkyZP11ltvxfPee+8lfU0MEEwvEkKI+wLz2N8uKoCRSETV1dXx27FYTIWFhVq0aFGvj586dapuvPHGhPuuueYazZw5M347Go1qypQpKV8TAwTTi4QQ4r7APPa3Swpgd3e3srOz1dDQkHD/tGnTVFFR0ev3XHTRRXr88ccT7rv//vv1uc99Ln47Go0qLy9P+fn5GjNmjGbNmqV33nkn6etigLzB9DIghPgrMI/97ZIC2N7erkAgoC1btiTcP3/+fEUikV6/p1+/fnr22WcT7luxYoWGDh0av7127Vo1NjZqx44damho0NixY3X11VfrxIkTvR6zq6tLnZ2d8bS1tfl+gLzA9DIghPgrMI8C6PMC+Emtra0KBALauHFjr1+vra097U0jfh8gLzC9DAghJNkgPSiALimAdv0KuDdDhgzRypUre/0aPwH0JtMv6IQQkmyQHhRAlxRA6eM3gcyePTt+OxaLqaio6KxvArnpppsS7hs/fnzCm0A+qa2tTVlZWWpsbEzqmhggbzD9gk4IIckG6cH+dlEBrK+vVygUUl1dnVpaWjRjxgyFw2EdPnxYklRZWamampr44zdv3qy+fftqyZIl2rVrl2praxM+Bubo0aOaN2+etm7dqv3792vjxo268sorNXr0aHV1dSV1TQyQN5h+QSeEkGSD9GB/u6gAStKyZctUXFysYDCoSCSibdu2xb9WVlamaDSa8Ph169ZpzJgxCgaD+sxnPpPwQdAffvihrr/+euXn56tfv34qKSlRVVVVvFAmgwHyBtMv6IQQkmyQHuxvlxXATMMAeYPpF3RCCEk2SA/2NwXQEgbIG0y/oBNCSLJBerC/KYCWMEDeYPoFnRBCkg3Sg/1NAbSEAfIG0y/ohBCSbJAe7G8KoCUMkDeYfkEnhJBkg/Rgf1MALWGAvMH0CzohhCQbpAf7mwJoCQPkDaZf0AkhJNkgPdjfFEBLGCBvMP2CTgghyQbpwf6mAFrCAHmD6Rd0QghJNkgP9jcF0BIGyBtMv6ATQkiyQXqwvymAljBA3mD6BZ0QQpIN0oP9TQG0hAHyBtMv6IQQkmyQHuxvCqAlDJA3mH5BJ4SQZIP0YH9TAC1hgLzB9As6IYQkG6QH+5sCaAkD5A2mX9AJISTZID3Y3xRASxggbzD9gk4IIckG6cH+pgBawgB5g+kXdEIISTZID/Y3BdASBsgbTL+gE0KIE8Ep7G8KoCUMkDeYflEmhBAnglPY3xRASxggbzD9okwIIU4Ep7C/KYCWMEDeYPpFmRBCnAhOYX9TAC1hgDKH6RdWQgjJ9OAU9jcF0BIGKHOYfmElhJBMD05hf1MALWGAMofpF1ZCCMn04BT2NwXQEgYoc5h+YSWEkEwPTmF/UwAtYYAyh+kXVkIIyfTgFPY3BdASBihzmH5hJYSQTA9OYX9TAC1hgNLL9IsjIYSQ3uM17G8KoCUMUHqZfoEjhBDSe7yG/U0BtIQBSi/TL3CEEELSn0zE/qYAWsIApZfpFylCCCHpTyZif1MALWGATmf6hYYQQkhmJROxvymAljBApzP9QkMIISSzkonY3xRAS7w6QKZfLAghhHgnmcir+/t8UAAt8OoAmX6xIIQQ4p1kIq/u7/PhqgK4fPlylZSUKBQKKRKJaPv27Wd9/Lp163TJJZcoFArpsssu0/r16xO+fvLkSd13330qKChQTk6OysvLtWfPnqSvx6sDZPrFghBCCCm5x77y6NX9fT5cUwDr6+sVDAa1evVq7dy5U1VVVQqHwzpy5Eivj9+8ebOys7P1wx/+UC0tLbr33nvVr18/vf766/HHLF68WHl5eXrhhRfU3NysiooKlZaW6vjx40ldk1cHyPQ/8IQQQkjJPRRAO7mmAEYiEVVXV8dvx2IxFRYWatGiRb0+furUqbrxxhsT7rvmmms0c+ZMSR//9K+goECPPvpo/OsdHR0KhUJau3ZtUtdk9wCZ/gePEEIIMRm7UABdUgC7u7uVnZ2thoaGhPunTZumioqKXr/noosu0uOPP55w3/3336/Pfe5zkqTW1lYFAgE1NTUlPGbixIm6++67ez1mV1eXOjs74/nLX/6iQCCgtra2hPvTlYu+u44QQgjxbezYrZ2dnWpra1MgEFBHR0eq1cT1XFEA29vbFQgEtGXLloT758+fr0gk0uv39OvXT88++2zCfStWrNDQoUMlffwr4kAgoDfffDPhMbfddpumTp3a6zFra2sVCAQIIYQQ4oG0tbWlWk1cjwJ4HgXwkz8BfP/999Xa2qqOjg7b/i0lU9Lzb0t2/bTTbeH54Lng+eD54Llw7/PR0dGhtrY2xWKxVKuJ67miAGbKr4D9rLOTPy/x/+P5OIXnIhHPRyKej1N4LhLxfJjligIoffwmkNmzZ8dvx2IxFRUVnfVNIDfddFPCfePHjz/tTSBLliyJf72zs/O83gTiJ/yDmojn4xSei0Q8H4l4Pk7huUjE82GWawpgfX29QqGQ6urq1NLSohkzZigcDuvw4cOSpMrKStXU1MQfv3nzZvXt21dLlizRrl27VFtb2+vHwITDYTU2NmrHjh2aMmXKeX0MjJ/wD2oino9TeC4S8Xwk4vk4heciEc+HWa4pgJK0bNkyFRcXKxgMKhKJaNu2bfGvlZWVKRqNJjx+3bp1GjNmjILBoD7zmc+c8YOghw0bplAopPLycu3evduJ/ymu09XVpdraWnV1dZm+lIzA83EKz0Uino9EPB+n8Fwk4vkwy1UFEAAAANZRAAEAAHyGAggAAOAzFEAAAACfoQACAAD4DAUQ5+3rX/+6LrroIoVCIRUUFOgf//Ef1d7ebvqyjNi/f7+mT5+uESNGKCcnRxdffLHuv/9+dXd3m740Yx566CGNHz9e/fv3V15enunLcdTy5ctVUlKiUCikSCSi7du3m74kY1599VXddNNNGj58uAKBwGkf5O8nDz/8sD7/+c8rNzdX+fn5mjJliv70pz+ZviwjnnzySX32s5/VoEGDNGjQIH3hC1/QSy+9ZPqyfIkCiPP22GOPaevWrTpw4IA2b96s8ePHa/z48aYvy4j/+q//0h133KFf//rXam1tVWNjo4YOHaq5c+eavjRj7r//fj322GP63ve+56sCWF9fr2AwqNWrV2vnzp2qqqpSOBzWkSNHTF+aES+99JIWLlyo559/3vcF8IYbbtAzzzyjN954Q6+99pq+9rWvqbi4WMeOHTN9aY77z//8T61fv1579uzR7t27tWDBAvXr109vvPGG6UvzHQogLGtsbFRWVpY++ugj05eSEX74wx+qtLTU9GUY98wzz/iqAEYiEVVXV8dvx2IxFRYWnvFvK/ITvxfAT/rrX/+qQCCgV1991fSlZITBgwfr6aefNn0ZvkMBhCXvvvuupk6dqgkTJpi+lIyxcOFCXXXVVaYvwzg/FcBU/r5yP6EAJtq7d68CgUDC30zlRydOnNDatWsVDAa1c+dO05fjOxRApOSf//mfNWDAAAUCAX3hC1/QO++8Y/qSMsLevXt1wQUXaNWqVaYvxTg/FcD29nYFAgFt2bIl4f758+crEokYuqrMQQE8JRaL6cYbb/T1vzTv2LFDAwcOVHZ2tvLy8k77W7rgDAogJEn33HOPAoHAWbNr1674499++23t3r1bGzZs0IQJE/S1r31NJ0+eNPi/IL3O9/mQpEOHDmnkyJG68847DV21fVJ5PiiAFMAeFMBTZs2apZKSErW1tZm+FGO6u7u1d+9e/c///I9qamo0ZMgQfgJoAAUQkj7+Mym7du06a870zta2trZel5+bne/z0d7ertGjR6uyslKxWMzgldsjlfnwUwHkV8BnRwH8WHV1tT796U/rz3/+s+lLySjl5eWaMWOG6cvwHQogLDt48KACgYA2bdpk+lKMOHTokEaPHq1/+Id/0IkTJ0xfTsbwUwGUPn4TyOzZs+O3Y7GYioqKeBOIKIAnT55UdXW1CgsLtWfPHtOXk3EmTZqkaDRq+jJ8hwKI87Jt2zYtW7ZMTU1NOnDggP77v/9bX/ziFzVy5Eh1dXWZvjzHHTp0SKNGjVJ5ebkOHTqkt956Kx6/OnjwoJqamvTggw8qNzdXTU1Nampq0tGjR01fmq3q6+sVCoVUV1enlpYWzZgxQ+FwWIcPHzZ9aUYcPXo0/v99IBDQY489pqamJh08eND0pTnurrvuUl5enl555ZWE14gPP/zQ9KU5rqamRq+++qr279+vHTt2qKamRllZWdqwYYPpS/MdCiDOy44dOzRp0iRdeOGFCoVCGjFihGbNmqVDhw6ZvjQjnnnmmTP+mTi/ikajvT4ffvgJ8bJly1RcXKxgMKhIJKJt27aZviRjNm3a1Osc+PEnPWd6jXjmmWdMX5rjpk+frpKSEgWDQeXn56u8vJzyZ4h/txQAAIBPUQABAAB8hgIIAADgMxRAAAAAn6EAAgAA+AwFEAAAwGcogAAAAD5DAQQAAPAZCiAAAIDPUAABAAB8hgIIAADgMxRAAAAAn6EAAgAA+AwFEAAAwGcogAAAAD5DAQQAAPAZCiAAAIDPUAABAAB8hgIIAADgMxRAAAAAn6EAAgAA+AwFEAAAwGcogAAAAD5DAQQAAPAZCiAAAIDPUAABAAB8hgIIAADgMxRAAAAAn6EAAgAA+AwFEAAAwGcogAAAAD5DAQQAAPCZ/we+ZDz5l8lR5QAAAABJRU5ErkJggg==\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the histogram\n",
    "plt.hist(nums, density=True, bins=30)\n",
    "plt.ylabel('Standard Normal - Box Muller');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-24T10:55:32.879344Z",
     "start_time": "2019-03-24T10:55:32.830382Z"
    }
   },
   "source": [
    "### Anderson Darling Test\n",
    "\n",
    "reference:\n",
    "https://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test#Test_for_normality\n",
    "\n",
    "reference:\n",
    "2008 Stephens.pdf pg. 4, \"1.3 Modificatons for a test for normality, u, and sigma^2 unknown\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.386393Z",
     "start_time": "2019-05-23T15:54:37.363743Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistic: 0.041\n",
      "15.000: 0.575, data looks normal (fail to reject H0)\n",
      "10.000: 0.655, data looks normal (fail to reject H0)\n",
      "5.000: 0.785, data looks normal (fail to reject H0)\n",
      "2.500: 0.916, data looks normal (fail to reject H0)\n",
      "1.000: 1.090, data looks normal (fail to reject H0)\n"
     ]
    }
   ],
   "source": [
    "# normality test using scipy.stats\n",
    "result = anderson(nums)\n",
    "print('Statistic: %.3f' % result.statistic)\n",
    "p = 0\n",
    "for i in range(len(result.critical_values)):\n",
    "    sl, cv = result.significance_level[i], result.critical_values[i]\n",
    "    if result.statistic < result.critical_values[i]:\n",
    "        print('%.3f: %.3f, data looks normal (fail to reject H0)' % (sl, cv))\n",
    "    else:\n",
    "        print('%.3f: %.3f, data does not look normal (reject H0)' % (sl, cv))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate a total of 2000 i.i.d. standard normals N (0, 1) using Beasley-Springer-Moro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.425422Z",
     "start_time": "2019-05-23T15:54:37.389979Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(-0.45354220491354497,), (-1.4389723392670315,), (0.18932048542646718,), (1.6456218388230586,), (-0.1254613002624064,), (-0.841338444465769,), (0.5246282553188133,), (1.2137540974782643,), (-0.2856341307724526,), (-1.0912603031903014,), (0.35199549745081987,), (-2.238962442870265,), (0.031536554447300705,), (-0.6354141211428904,), (0.714623629180169,), (1.0639714340786743,), (-0.3682881880881213,), (-1.2462888763124396,), (0.2697642345248874,), (2.0820090832222746,)]\n",
      "[-0.45354220491354497, -1.4389723392670315, 0.18932048542646718, 1.6456218388230586, -0.1254613002624064, -0.841338444465769, 0.5246282553188133, 1.2137540974782643, -0.2856341307724526, -1.0912603031903014, 0.35199549745081987, -2.238962442870265, 0.031536554447300705, -0.6354141211428904, 0.714623629180169, 1.0639714340786743, -0.3682881880881213, -1.2462888763124396, 0.2697642345248874, 2.0820090832222746]\n"
     ]
    }
   ],
   "source": [
    "N=2000\n",
    "s=1\n",
    "\n",
    "l = beasley_springer_moro.beasley_springer_moro_seq(s=s, N=N, seq=seq)\n",
    "# print the first 20\n",
    "print(l[:20])\n",
    "# flatten the sequence into 1 dimension\n",
    "flattened = [item for sublist in l for item in sublist]\n",
    "nums = flattened\n",
    "print(nums[:20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sort the sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.438396Z",
     "start_time": "2019-05-23T15:54:37.428881Z"
    }
   },
   "outputs": [],
   "source": [
    "nums = numpy.array(nums)\n",
    "nums = sorted(nums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.455407Z",
     "start_time": "2019-05-23T15:54:37.441637Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.3727194621923373, -3.1346044221532785, -3.000267898341195, -2.90487610870623, -2.830292443600595, -2.7687540302075453, -2.7161964314970097, -2.6702165174341346, -2.6292716619518317, -2.5923108117998117, -2.5585846646267565, -2.5275396610714904, -2.498754904793903, -2.4719026739584775, -2.446722653047625, -2.42300452486657, -2.4005758596607176, -2.3792934740686174, -2.3590371290895824, -2.339704844677499]\n"
     ]
    }
   ],
   "source": [
    "print(nums[:20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the sample mean and standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.475442Z",
     "start_time": "2019-05-23T15:54:37.456944Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 0.00017262607399879925\n",
      "variance = 0.9995629114486932\n",
      "standard deviation = 0.999781431838326\n"
     ]
    }
   ],
   "source": [
    "nums = numpy.array(nums)\n",
    "mean = numpy.mean(nums)\n",
    "var = numpy.var(nums)\n",
    "std = numpy.std(nums)\n",
    "\n",
    "print('mean = {}'.format(mean))\n",
    "print('variance = {}'.format(var))\n",
    "print('standard deviation = {}'.format(std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.591400Z",
     "start_time": "2019-05-23T15:54:37.484865Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the histogram\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.hist(nums, density=True, bins=30)\n",
    "ax.set_ylabel('Standard Normal - Beasley-Springer-Moro');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-05-23T15:54:37.619559Z",
     "start_time": "2019-05-23T15:54:37.595021Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistic: 0.002\n",
      "15.000: 0.575, data looks normal (fail to reject H0)\n",
      "10.000: 0.655, data looks normal (fail to reject H0)\n",
      "5.000: 0.785, data looks normal (fail to reject H0)\n",
      "2.500: 0.916, data looks normal (fail to reject H0)\n",
      "1.000: 1.090, data looks normal (fail to reject H0)\n"
     ]
    }
   ],
   "source": [
    "# normality test using scipy.stats\n",
    "result = anderson(nums)\n",
    "print('Statistic: %.3f' % result.statistic)\n",
    "p = 0\n",
    "for i in range(len(result.critical_values)):\n",
    "    sl, cv = result.significance_level[i], result.critical_values[i]\n",
    "    if result.statistic < result.critical_values[i]:\n",
    "        print('%.3f: %.3f, data looks normal (fail to reject H0)' % (sl, cv))\n",
    "    else:\n",
    "        print('%.3f: %.3f, data does not look normal (reject H0)' % (sl, cv))"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}