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    "In this demo, we will find how the speed and 1-D velocity distributions predicted by kinetic gas theory can be found without any \"derivation\", using the simulation below.\n",
    "First, we will import a module containing the classes for this simulation, CollidingParticles, along with some modules for plotting:"
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   "source": [
    "#NAME: 1D Velocity Distributions\n",
    "#DESCRIPTION: Finding the 1D velocity distributions predicted by kinetic gas theory through simulation of hard spheres.\n",
    "\n",
    "from pycav.mechanics import *\n",
    "from vpython import *\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will run the simulation itself. First, we create a canvas which the simulation will display in. We then create a 1x1x1 container, then create a system composed of 200 hard sphere particles inside that container. The simulation will take a minute or two to finish. Once it is done, execute the last two cells. If it takes too long, try running the simulation with the visualisation off, by intialising system with visualize = False, or running the simulation for less time, or having less particles."
   ]
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   "execution_count": 2,
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      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-ee98fc628c2a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0msystem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msteps\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mrate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m150\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m     \u001b[0msystem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msimulate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Applications/anaconda/lib/python3.5/site-packages/pycav/mechanics.py\u001b[0m in \u001b[0;36msimulate\u001b[0;34m(self, dt)\u001b[0m\n\u001b[1;32m    854\u001b[0m             \u001b[0;31m# Collision detection between particles using domains if has container.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    855\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcollides\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 856\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_collision_detection_with_domains\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    857\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    858\u001b[0m             \u001b[0;31m# Collision detection with walls of container if has one.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Applications/anaconda/lib/python3.5/site-packages/pycav/mechanics.py\u001b[0m in \u001b[0;36m_collision_detection_with_domains\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1064\u001b[0m         \u001b[0;31m# Should be fine as if particles are moving so quickly, simulation is inacurrate anyway.)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1065\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msteps\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;36m3\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1066\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_assign_particles_to_domains\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1067\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1068\u001b[0m         \u001b[0;31m# The actual collision detection\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Applications/anaconda/lib/python3.5/site-packages/pycav/mechanics.py\u001b[0m in \u001b[0;36m_assign_particles_to_domains\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    923\u001b[0m             \u001b[0mdomain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparticles\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    924\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mparticle\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparticles\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 925\u001b[0;31m                 \u001b[0;32mif\u001b[0m \u001b[0mdomain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcontains\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparticle\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    926\u001b[0m                     \u001b[0mdomain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparticles\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparticle\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    927\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Applications/anaconda/lib/python3.5/site-packages/pycav/mechanics.py\u001b[0m in \u001b[0;36mcontains\u001b[0;34m(self, particle)\u001b[0m\n\u001b[1;32m    378\u001b[0m             \u001b[0mParticle\u001b[0m \u001b[0mwhich\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mbeing\u001b[0m \u001b[0mchecked\u001b[0m \u001b[0mto\u001b[0m \u001b[0msee\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0minside\u001b[0m \u001b[0mcontainer\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;32mnot\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    379\u001b[0m         \"\"\"\n\u001b[0;32m--> 380\u001b[0;31m         \u001b[0mrelative_pos\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mparticle\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpos\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_origin_pos\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    381\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    382\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mrelative_pos\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdimension\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mrelative_pos\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Applications/anaconda/lib/python3.5/site-packages/pycav/mechanics.py\u001b[0m in \u001b[0;36m_origin_pos\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    304\u001b[0m         \"\"\"\n\u001b[1;32m    305\u001b[0m         \u001b[0ml2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdimension\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 306\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpos\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ml2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ml2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ml2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    307\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    308\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
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   "source": [
    "container = Container(1)\n",
    "system = System(collides = True, interacts = False, visualize = True, container = container)\n",
    "avg_speed = 1\n",
    "system.create_particles_in_container(number = 100, speed = avg_speed, radius = 0.03)\n",
    "dt = 1E-2\n",
    "while system.steps <= 1000:\n",
    "    rate(150)\n",
    "    system.simulate(dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expect a 1D velocity distribution centred on 0, with the following form.\n",
    "\n",
    "$$ \\\\f(v_{x}) = \\sqrt{\\frac{m}{2\\pi k_{B}T}} e^{\\frac{-mv_{x}^{2}}{2k_{B}T}}$$\n",
    "\n",
    "Assuming the relation\n",
    "\n",
    "$$ \\\\<v> = \\sqrt{\\frac{8k_{B}T}{m}} $$\n",
    "\n",
    ",where v denotes the speed in this case, we can find the expected distribution for the system's 1D speed distribution, and compare it with the actual measured one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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       "    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 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);\n",
       "        canvas.attr('height', height);\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'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, fig.canvas.height);\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;\n",
       "    var y = canvas_pos.y;\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 overriden (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",
       "    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 + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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"
    },
    {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "#alpha is a constant = 2kT/m\n",
    "alpha = ((avg_speed)**2) * np.pi / (4)\n",
    "\n",
    "@np.vectorize\n",
    "def f(v):\n",
    "    return ((1/(alpha*np.pi))**(0.5)) * np.exp(-(v**2)/alpha)\n",
    "\n",
    "plt.hist(system.one_d_velocities, 20, normed = True, facecolor='green')\n",
    "v = np.linspace(np.amin(system.one_d_velocities),np.amax(system.one_d_velocities),50)\n",
    "l = plt.plot(v, f(v), 'r--', linewidth=1)\n",
    "plt.ylabel('Probability density')\n",
    "plt.xlabel('velocity')\n",
    "plt.title('1D velocity distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We expect a 1D speed distribution centred on 0, with the following form.\n",
    "\n",
    "$$ \\\\f(v_{x}) = \\frac{m}{2\\pi k_{B}T}^{\\frac{3}{2}} e^{\\frac{-mv^{2}}{2k_{B}T}}$$\n",
    "\n",
    "Assuming the relation\n",
    "\n",
    "$$ \\\\<v> = \\sqrt{\\frac{8k_{B}T}{m}} $$\n",
    "\n",
    "again, we can find the expected distribution for the system's speed distribution, and compare it with the actual measured one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\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",
       "            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",
       "        this.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 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);\n",
       "        canvas.attr('height', height);\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'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, fig.canvas.height);\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;\n",
       "    var y = canvas_pos.y;\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 overriden (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",
       "    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 + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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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ox+oBQIIIIAAAgggUDEBEsCKUbMjBBBAAAEEEEAgDAESwDD6gVoggAACCCCAAAIVEyABrBg1O0IAAQQQQAABBMIQIAEMox+oBQIIIIAAAgggUDEBEsCKUbMjBBBAAAEEEEAgDAESwDD6gVoggAACCCCAAAIVEyABrBg1O0IAAQQQQAABBMIQIAEMox+oBQIIIIAAAgggUDEBEsCKUbMjBBBAAAEEEEAgDAESwDD6gVoggAACCCCAAAIVEyABrBg1O0IAAQQQQAABBMIQIAEMox+oBQIIIIAAAgggUDEBEsCKUbMjBBBAAAEEEEAgDAESwDD6gVoggAACCCCAAAIVEyABrBg1O0IAAQQQQAABBMIQIAEMox+oBQIIIIAAAgggUDEBEsCKUbMjBBBAAAEEEEAgDAESwDD6gVoggAACCCCAAAIVEyABrBg1O0IAAQQQQAABBMIQIAEMox+oBQIIIIAAAgggUDEBEsCKUbMjBBBAAAEEEEAgDAESwDD6gVoggAACCCCAAAIVEyABrBg1O0IAAQQQQAABBMIQyEICeJCopyg+VSxUtNXmPpp/peJNRV3uc4w+axQUBBBAAAEEEEAgFQJtJUOpaKAaUasYpzi5iAatoGVeVnxH0VOxi2IvxXkKCgIIIIAAAgggkAqBZVLRirYbcV9u9qC2F2ua+5a+RpM9PxJ4uWKYgoJAyQL19fXW0NBQ8vptrVhTU2M9evRoaxHmxSBQzj5ctGiRde0a///jfG/E0PFsAoGUCmQhAexs1+2mDfy3sxth/ewKeOLQt39fq/3QD0bHX3r36W2zZ84mCYyfdvEWy92HXZbpYo0LGhfvL64BvjfikmQ7CKRPgASw7T4dqdmbK7ZuezHmItC6gB/5a0r+TtEyy7a+XElz5ukahwtrm44uchSwJMGiViprH+pq48bxSv7i/v7ge6OovmUhBLIqQALYes+fo1lHKPzU8TutL8YcBIoU8OSPM7VFYgW6WDn6UIlaUynHtgNlpFoIIFB9ARLAlvvAbxrZVbGjYlbLiyyZOmLECPNrbbwMHTq0KZbMZQgBBBBAAAEEqi0wYcIE8/BSrmuyq93Gjuw/CwmgX1ndXZE/+ebHYPxxMH5FfuFFN9007WrFpoqdFO8r2i1jxoyxnj39pmEKAggggAACCIQoED1AU1dXZ+PG+bGe7Jb4bzsLz/KHqtIXin/lqjZHn3MVnuD1U3ym2EHhxT8PVnxN8ZrCnwXo8/2TggACCCCAAAIIpEIgC0cAr1JPebRWVozMmKJhPwpIQQABBBBAAAEEUiuQhSOAqe08GoYAAggggAACCJQiQAJYihrrIIAAAggggAACCRYgAUxw51F1BBBAAAEEEECgFAESwFLUWAcBBBBAAAEEEEiwAAlggjuPqiOAAAIIIIAAAqUIkACWosY6CCCAAAIIIIBAggVIABPceVQdAQQQQAABBBAoRYAEsBQ11kEAAQQQQAABBBIsQAKY4M6j6ggggAACCCCAQCkCJIClqLEOAggggAACCCCQYAESwAR3HlVHAAEEEEAAAQRKESABLEWNdRBAAAEEEEAAgQQLkAAmuPOoOgIIIIAAAgggUIoACWApaqyDAAIIIIAAAggkWIAEMMGdR9URQAABBBBAAIFSBEgAS1FjHQQQQAABBBBAIMECJIAJ7jyqjgACCCCAAAIIlCJAAliKGusggAACCCCAAAIJFiABTHDnUXUEEEAAAQQQQKAUARLAUtRYBwEEEEAAAQQQSLAACWCCO4+qI4AAAggggAACpQiQAJaixjoIIIAAAggggECCBUgAE9x5VB0BBBBAAAEEEChFgASwFDXWQQABBBBAAAEEEixAApjgzqPqCCCAAAIIIIBAKQIkgKWosQ4CCCCAAAIIIJBgARLABHceVUcAAQQQQAABBEoRIAEsRY11EEAAAQQQQACBBAuQACa486g6AggggAACCCBQigAJYClqrIMAAggggAACCCRYgAQwwZ1H1RFAAAEEEEAAgVIESABLUWMdBBBAAAEEEEAgwQIkgAnuPKqOAAIIIIAAAgiUIkACWIoa6yCAAAIIIIAAAgkWIAFMcOdRdQQQQAABBBBAoBQBEsBS1FgHAQQQQAABBBBIsAAJYII7j6ojgAACCCCAAAKlCJAAlqLGOggggAACCCCAQIIFSAAT3HlUHQEEEEAAAQQQKEWABLAUNdZBAAEEEEAAAQQSLEACmODOo+oIIIAAAggggEApAiSApaixDgIIIIAAAgggkGABEsAEdx5VRwABBBBAAAEEShEgASxFjXUQQAABBBBAAIEEC5AAJrjzqDoCCCCAAAIIIFCKQBYSwIMEM0XxqWKhor0299Iy1yk+UdQqrlGspKAggAACCCCAAAKpEGgvGUpDIz2JG6c4ucjGePLXR7GOYj3F6oqrFBQEEEAAAQQQQCAVAsukohVtN+K+3OxBbS/WNLe/vu6h2FTxcdMUs9P0+YxiLcXbuWl8IIAAAggggAACiRXIwhHAjnTO5lq4XvFCZKXnNNyg8HkUBBBAAAEEEEAg8QIkgEt3YU+N+rWCheUTTfB5FAQQQAABBBBAIPECJIBLd2GdRlu64aOXpvs8CgIIIIAAAgggkHiBLFwD2JFOekYLL6vYWJE/DbyZhrsrfF6LZcSIEVZTU9M0b+jQoeZBQQABBBBAAIFwBCZMmGAeXhoa/MqubJcsJIB+lNMTOE/svPRQ+ONgvPcbFdEyUyP3KC5QHKbokhu+U5+t3gAyZswY69mTM8QyoiCAAAIIIBCkQPQATV1dnY0b5w8IyW7JQgL4Q3XvFYp8sjcnN7yzPt9STFPsrnhY4cWXv1jxhsLX+adiuIKCAAIJEKivr4/9v3v/Y0FBAAEE0iSQhQTQn+HX1nP8VizoUL/h4/CCaYwigEACBDz569u/r9V+WJuA2lJFBBBAoHoCWUgAq6fLnhFAoKICfl1PU/J3inabv+gjjhr4AcDxcWyIbSCAAAJhCJAAhtEP1AIBBOIU8OTPr/aNq8yLa0NsBwEEEAhDgMfAhNEP1AIBBBBAAAEEEKiYAAlgxajZEQIIIIAAAgggEIYACWAY/UAtEEAAAQQQQACBigmQAFaMmh0hgAACCCCAAAJhCJAAhtEP1AIBBBBAAAEEEKiYAAlgxajZEQIIIIAAAgggEIYACWAY/UAtEEAAAQQQQACBigmQAFaMmh0hgAACCCCAAAJhCJAAhtEP1AIBBBBAAAEEEKiYAAlgxajZEQIIIIAAAgggEIYACWAY/UAtEECgNYF5vIetNRqmI4AAAqUK8C7gUuVYDwEEyi+wcKFZ795mq61mtsEGZhtuuOTzm980W2WV8teBPSCAAAIpFCABTGGn0iQEEiPQ2Gj21FNmH35otueeX652V52keP11s5dfNnvppebPW25p/txlF7MrrvjyOj5Fm6UggAACCLQuQALYug1zEECgXAKe0N1wg9n115t98IHZ8OEtJ4BdupitsUZz7Lzz0rXxo4OtlMnXmfVqUM7YR7niqs3xkj5f1QHDL2paWYnJCCCAQIYEQk4AT1I/XKmoy1B/0FQE0i1wzTVmF11k9uKLZnvtZXbeec2J33LLdbzd3bq1us7R2vRGn+ps8UfNMVQHETfU8Os6m7zVj1pdjRkIIIBAZgRCTgCPVS+MUdys+IviCQUFAQSSLOCndP1o33776RBdr7K15I2Vzd7QgcM7o3vQaeEVuZ8kKsIwAghkWCDku4A3Vb8MVfi/+ZMUTytOUKygoCCAQKgCbd21e9hhZkcdVdbkr1UWnU3+rEfLc7suMtvkvZbnMRUBBBBIo0DICaB7P6w4UrGm4krFyYp3FJcoNlBQEEAgBIEFC8z+/W+zI44w66ML7958M4RaFV2HLfVb5bHLzMbfZbby3KJXY0EEEEAgsQKhJ4B52LU14AmfTuqYrh63lRT/VZymoCCAQDUE/A7eRx5pPqW7pv5HO1ZXbXz1q2aTJ5uts041alTyPp9cy2zTE83W/kQ3ivxJTfmPWRcdFaQggAACaRUIOQFcXujHKPzaPz8S2F0xRPFtxcGK7RUjFRQEEKiGwJQpZt/9rlmDbre9WZfqzphhNnas2RZbKHvS+daElTd0h/BeOkN9jJo04iGzR/9mtuXshDWC6iKAAAJFCoR8E8i7akP+dO+VGtb/5kuVZzT23FJTGEEAgcoJDBpk9p4unGvjbtzKVSamPSlvvVPnGu79mtkvp5odOM3sP31j2jabQQABBAISCDkB1G2CNrEdq4HtzGc2AgiUUyBNyV/EqV7nG0bvHJnAIAIIIJAygZBPAbd2fd9ST3ZIWX/QHAQQQAABBBBAoOwCISeAO7XS+h1bmc5kBBAoh4Df7PHCC+XYcmK3udvreg3x54mtPhVHAAEELMRTwH6jhxd//p+fhIleTb6+xj9TUBBAoBIC/ngXf3CzP+LFX9/Wo0cl9hr8Po7UFcjX36qbRb5jdtm3zBaF/K908JpUEAEEqiEQYgJ4fw5Chx3sgQiKj/uNIb+KTGMQAQTKJTBnjtlBBzXf3et3/JL8LZY+7ADdMfyK2R+UFx+nR8b8WK+e80fJUBBAAIGkCISYAOb/l/ZzThsnBZJ6Vk6gvr5eTx7Ro0fKUGpqapTncJSr6e5ef1fvSnrk5tSp1XlzRxn6N85N3q3zEfeva/ZzPaTqwat0RHATs9N308vL+faJk5ltIYBAmQRCTADzTSX5y0vwuVjAk7++/fta7Ye1i6fFOdC7T2+bPXN2tpPAl14y22MPs4G6yf6yy8yUFFNaFpinu4XPGWx2zWbNzw6cn//3teXFmYoAAggEIxBaAvhryZyb0zm7DaVRbcxjVooF/MhfU/J3ihq5bMwNnWdWe2Ft09HFTB8F9KOrxxxj9pvfJPKBzjF/VxS1uekrmx2/b1GLshACCCAQhEBoCeAOEZXW7gL2awEpWRfw5I9TbeX5LthMh7M8KAgggAACqRUILQHcMyLtdwBTEEAAgUQLdFtottCfaUBBAAEEAhJI0hUreuCC8eaPgL55qAoCCLQjoPMVD1xtdqzuFKYggAACIQmEnADeK6jBOayT9HmX4l+Kn+Wm8YEAAp0R8Me8XHttZ7bAuu0J6CmmvxliNla/zc6Y2t7CzEcAAQQqJxByAriFGB7JUeiKdNtd4dcI/iQ3jQ8EEChV4F09UnPQILMrrjCbP7/UrbBeEQJT1zYbcqQeEaPfZmP8KaeNRazEIggggECZBUJOAPWABfOHva2i6KuYrNDz9211BQUBBEoVmDbNbLvtzDbaSMfUdVC9u/+oUcop8PSaZjsdbXbYc2bj79bN1YvKuTe2jQACCLQvEHIC+LaqP0jxA8WUXFNW0qcnhRQEEChFYLL+j9pBB9KPOMLsqqt4xl8phiWu8+qqZjsqCRzyltmBysEpCCCAQDUFQrsLOGpxtkZ05UxTwuenf73sqvCjgBQEEOiowD33KPM40OxPfzI7WpkIpeICs3qZffs4vS0k7mdYVrwl7BABBJIuEHICeLNw/5kD/iL3+ZA+uZQ6h8EHAh0S+Na3zO64w2yXXTq0GgvHK8Cr4uL1ZGsIIFCaQMgJoLcon/h1zTXvw9KayVoIIGCr6/JZDwoCCCCAQOYF8olViBAbqFIPKvSsCvPbFKOhUQoCCCCQIgHuDk5RZ9IUBMIXCPkI4OXim63wm0A+D5+SGiKAAAKlCaym1f5xrdmR+5u94c89oCCAAAJlFgg5AdxYbR+s4K7fMn8TsPkUCvjdvv6ol5qaFDYufU36QE16VA+7mqp/e3f7odnznKlPXyfTIgQCEwj5FPCbstI9cxQEEOiQwJNPmu2p12o//3yHVmPh6gqcsbNu0N7GbNKVZtvOqm5d2DsCCKRfIOQE8Pfi10mRprd/rKvPaHS0Z87SCn46+TPFJIWegNtq2UpzJipqFf6P+a2K/goKAuELfPKJ2UEHmZ15ptmWW4ZfX2q4RKCL3hQy0GzkED3/6hrdrP3GklkMIYAAAnELhJwAXqnG7qLwR7+8lovXc5/6KLqcoSWHKXZV6FGsTa+Xm6DP5RWFRb+CTc/pb3rWoF+Ws45igeIGBQWBsAUadRfBcceZbaD7p04/Pey6UrtWBcZ/2+zEvXRN4E16BdKnrS7GDAQQQKBTAiFfA+jJVxzlRG1krGJabmMj9XmMYj/Fdblp+Q9/04gniVcoPPHzuFpxs4KCQNgCf/6z/r3RC2ef0bPSu4b8v13YjCHU7rrNdD2gzjvM9t9IFAQQQKAMAiEngDNiaG9PbWOAQhdFLS4LNaS/kLaFojAB1PkzG6fQYRT7hcKf1z9M4aeBKQgEK9D15ZfNztDBbn+3b58+wdaTihUvMGPl4pdlSQQQQKCjAqEfJjhEDbpPoVeoN5Wd9PV7ueFiPjwB9OKJXbR8rJH8vOh0H/67wk891yk+UviRyNMUFASCFVi03npmd91lNlAXkVEQQAABBBBoRyDkBPCnqvt5igcVa+fa4Tdm/Dw3XMyHJ3FeejV/LP7q/1vn5y2eqAH9FW1KOP+gT79GcEWFXxP4qGI5BQWBMAWW0cH8nXcOs27UCgEEEEAgOAH91Qi2DFfN9lD4tXs6t9VUdJ7LvpEbLubDk7zpiq0Vjyu8dFP46V+/tq+wbKoJcxWX5Gb420cuUPh1gxsroqeSNdpcRowYocetNT9vbejQoeZBQQABBOIW2GaWrkl5xmz4nmYL/TcZBQEEihaYMGGCeXhpaOARwyEngH4hU/7GDd3euLh0WTxU3MB4Lea3RPqRxDcVoxTzFLcpCstTmuCZ3LGKKxTdFacq/PExrypaLGPGjLGePVs7o9ziKkxEAAEEOiwwQ+cydlASeMstZgcfoD9iIf8G73DrWAGB8gpED9DU1dXZuHHjyrvDwLce8ilgT7gGF/gN0vhLBdPaG/UjeFcq7ld8qNhOsbvCj/T1U3hyt4PCy0zFdxVHK3zZ2Qo/r7aX4lMFBQEEEKiawHu6KGXQMLM19Vvrhr/rZu9FVasKO0YAgYQLhJwAni1bP0p3rsKPyv1GcYPCp3e0jNYKayhWUAxWvKjwov+lm67ze7hprPmLJ4rbK3orVlEMVkxVUBAIRuCsiXrcn/+LQsmcwMe6OnnPw/Q0e/X/Bfdmrvk0GAEEYhLoGtN2yrGZe7TR/RUbK2YqhiiOV/ArTwiU7AocoWvATnxKh6SXza5B1lteqyRwDyWBhz2n6wHzVzdnHYX2I4BAhwRCv4LEr9vzoCCAgAT8qN/F+tfowAPN3vXLTuthyarAWzpHsc+hOq3RkFUB2o0AAp0RCC0B7F9kY/yIIAWBTAn00D3pN9+iBPDbZhO+nqmm09hWBJ5Yq5UZTEYAAQTaEQgtAZyu+ja2U2efzQMQikBikXQJ/EEv+ajTad9RLTzuz+9oK0fxxxv16NGjHJtmmwgggAACVRQILQGMHtfwP3PHKc5RvKVYR/FrxWUKCgKZEljvf2b7vmL2bf1ELIj++7NADBrv189vaI+/9O7T22bPnE0SGD8tW0QAAQSqKhBaAvhGRONODe+qeCc3ze/cfVrhN4H8LTeNDwQyIfC67kf/2s/07CK/Hz5aFmrE4xRF3DeF6GmZtRfWNj0wlaOAUfQEDBdzHiUBzaCKCCBQPoHQEsBoS/3qFn/1W7R8rBGueomKMJwZgS8lf9GWe/LHmdqoSGaH95+mh5nqnUnD9B4l8sDMfhvQcATaFQj5MTBPqvYXK/zZfV78vbz+jl49AIOCAAIIINCSwFTdSrejbpM7Z0pLc5mGAAIINAuEfATQn/n3T4Uf9fNYWfGaYh8FBQEEEECgBYEP9C+zPyj6EV0o4xdPUxBAAIGWBEI+AvimKryJYpBieO7Tx99QUBBItUA3v66PgkCJAq/0Mdtv/+ZTJt3uv7/ErbAaAgikWSDkBNDdFykeUdyc++TPoiAo6Rborjt7p1xhttvr6W4nrSuvwBSdCvbHKCx/1FFmzz5b3p2xdQQQSJxA6Alg4kCpMAKdFThPB2x6KAmcvHZnt8T6WRe4QQD1Z56pO8TjvkU867K0H4HkC4R8DWDydWkBAh0U2Ed3bx7ztNmWugJ2XvcOrsziCLQgMP/YY225nv7eQAoCCCCwRIAjgEssGEKgqgL9PjG78nazH+2tC1313D8KAggggAAC5RIIOQFctVyNZrsIhCawjK5uvfHvZrdsZHaT3+pEQQABBBBAoIwCISeAb6vd1yt2KmP72TQCQQj0+dxsRi+zk3cPojpUAgEEEEAg5QIhJ4A7yn6O4h6Fnm1vJyn0J5KCQPoE3tUlWoceoAv2ue4vfZ0bYot+8xuz664LsWbUCQEEKiQQcgL4lAz8YdBrKv6k0LMMbLZCD8iwbRUUBBBAAIFSBAYO1G9X/XqdPLmUtVkHAQRSIBByApjn/UwDf1acoHhJcaTiQcWjCq6WEgIFAQQQ6JDAbruZ/fGPelr0fvqt6r9WKQggkDWB0BPAFdUhJyr0YAz7t+IRhSd9qysmKW5RUBBAAAEEOipwzDFmP/6x3hu3p9n773d0bZZHAIGEC4ScAF4u23cUxyn8COBaCr8O8EXFpwpdxNI0TR8UBJIlsGK9mb/xg4JAVQXOOcds++31hvV9zD7XnUgUBBDIjEDICaA/pFrnKexbiksVhb+d/LVwXAsoBEryBC7S8ezz70tevalxygS6dDG7XP9r77ijnjw+L2WNozkIINCWQMgJ4L9Ucb/Or7AcHJnwQmSYQQQSIbDNLLODdBz7wu0SUV0qmXYBf03c739v1rt32ltK+xBAICIQcgJ4SaSe0cHx0RGGEUiSQNdFZhfrwUb/t4PZTB5qlKSuo64IIIBAqgRCTgB1buJLxf9F1Z9QCgLJFDhatzP1/sJsrBJACgIIIIAAAtUS8OvsQis6QWaNiuUUMwsq56+Hu6NgGqMIJEJgZSV+v7vf7Jjv8sDnRHQYlUQAAQRSLBBiAuh39/rRP7/zd2TE3o/8vaeYGJnGIAKJEdhBLzec2t/szvUTU2UqmlWBet2mPny42bnnmn31q1lVoN0IpFogxATwqpz46/qcmmp9Gpcpgbu+bnbXxmpySxc3ZEqCxgYv4DeGzJ1rdoDeT/jAA2Y1NcFXmQoigEDHBEK7BnBApPr+DMB1W4nIYgwikCABkr8EdVaGq+qPh7nsMr2NfY7ZKadkGIKmI5BegdCOAD4n6p45bj8C6NcC5v9k5of9s1tuGT4QQAABBMohsPzyZrfdZrbVVnoaqx7H6m8OoSCAQGoEQksAN4rIrhMZZhABBBBAoNICAwaY3Xxz85tCNtKv52159n6lu4D9IVAugdASQL8DOF9m5Af4RAABBBCoksCQIc03g9yiV6+TAFapE9gtAvELhJYAHl1kEy8vcjkWQ6B6Ai+/3Hz05OSTq1cH9oxAHAI/+1kcW2EbCCAQkEBoCWD0sS+tMfk1gCSArekwPQyBRn2bnnSS2YYbhlGfTtSirq6uE2u3vOqiRYusa9f470ErR11bbkHGpvpNIQWlXo+KaWhoKJgaz2iN7jru0aNHPBtjKwgg0KJAaAkg1/212E1MTJzA7bebPfNM8xHAxFU+V+EF+tTtVv369Yu9BV2W6WKNC/x/OUoSBTz569u/r9V+WFuW6vfu09tmz5xNElgWXTaKQLNAaAkg/YJA8gX8+Wn+6IzzzjPrpRf+luEIWkWQFmovHv4UED0WLraiA4qN45X8xb1dr6AfrORt4bF1VWsb8iN/TclfOfpwnlnthbVNRxc5CthaDzAdgc4LhJYAXqomHZ9r1tVtNO+INuYxC4HqCpx/fvPbE4YNq2494tq7J39xno3TH/imEvd2faP5bTfvga9lFPDjwgt1Bvidlcq4EzaNAAJlE4j/IpzOVdWPN+RL/vhDS5/5ZfhEICyB6dPNxo41u/hi00VuYdWN2iAQo4Af/PvHP3RweH6MG2VTCCBQMYHQjgCeGGn5UZFhBhFIhsAaa5j54zK23joZ9aWWCJQo8CutN0n3hvz5brOjv6uRL98nUuKWWQ0BBCohEPohCq/fDoqDc5+h17cSfcY+Qhbwd6juuWfINaRuCMQi4Gfbv7+f2e56Z9NPnohlk2wEAQQqKBDaEcBo09fVyD8V31B8pFhV8ZpiH8UbCgoCCCCAQBUF3lnR7IAfmN17jdnzXzWbMqCKlWHXCCDQIYGQj6hdopY8olhZofNqTZ8P6dNvFKEggAACCAQg8Eh/s1OH6olHuvJhBT8sSEEAgUQIhHwE0C+i8qN99TnJOfr0647fzY3zgQACCCAQgMClW5k9uabZHF0BQUEAgWQIhHwEcLYIexcw+tFAn05BIByBt98Opy7UBIEqCTytBJCCAALJEQgtAfTr/vJxoYb1kAHzK+q/mfvUSQb7fwoKAmEITJlitskmOvThB6gpCCCAAAIIJEMgtFPAup/M8u+Hyj9U4K4Cym00/reCae2NnqUFjlX0VPxH8RPFi4rWyjDNOFXhyaj/Zb9RcbKCgsASgQV6V9rw4Wa/+pUuflphyXSGEEAAAQQQCFwgtARwnTJ4naFtDlPsqvC7h89UTFD43cV6Z9eXymma8mPFDxWPKfyqlvUVFASWFvjzn/XmCV31fjL/GywNwxgCzQJdFuk/+q5oIIBAiAKh/WjOEFIx0RFLf7j0WMU0hd+jNlLRXaEnWH2prKgpoxU/VfgdyPr1ZV8onlFQEFgi8MEHZqNGmf3xj2Y1NUumM4QAAk0CW79tNvVys+X0ujgKAgiEJxBaAlgotKom7KU4SnF0JDRYVPFTvgMUT0aWXqhhT+i2iEzLD26vgeUVGyheVbyn+JdiUwUFgSUCI0aYDRpkNnTokmkMIYDAYoGn1zCb303X69ypSfkLexbPZQABBKotENop4KjHzhq5TeG/OvzI3GcKv9BqlkL/VxZVPAH08knzx+KvH2soP2/xRA14wtlF4S82Gqjw5c5S/Fvhp4G9DpSsC9TryUQvv2x2zTVZl6D9CLQqsEDJ34EH6qLrS81O1/mUC/ydThQEEAhGIOQE8HdS+r3ibIUnYv4ImPMUngAWW+pyC/YqWMG3pRMUXyr55c/VHD/650WHeppOCW+vT7928EtlhI4G1eROAw7VESEPSooFevTQua2pKW4gTUMgHoEP9S/7fgfpncFXmj37VbP71otnu2wFgVIEJkyYYB5eGhoaStlEqtYJOQH0I2475bT9qJyXcxQvKMb5SBHFE7rpiq0Vjyu86P/SptO/VzeNLf3l6aVHm8by+25hVvOkMWPGWM+eLR1QbHUVZiCAAAKZEPhPX91Vpwt5bvy7fhEfb/Zm70w0m0YGKBA9QFNXV2fjxhWbSgTYmBiqFHICOF/tyydfn2rYT8/6Zx9FR8p4LXy64kHFm4pRCr8Z5DZFYXlbE3y6H/Xz6wR9f2cqahUPKygIIIAAAh0UuGZzs/76bdor/16nDq7P4gggEL9AyAngc2quHwF8QOF35F6smKPQxVcdKhdoab928H6FX0v4lGJ3hT8Cpp/C7w728XyCd6SGL1L4fhYq/AYSP6fr+6YggAACCJQgcO6gElZiFQQQKJtAyAngzyKt/rmGL1OsrTghMr3YwdFa0KOw+PWEnhRGiyd6x+YiOp1hBBBAAAEEEEAgFQIhPwbmRQl7ePFEzY/CbafwI3gUBCon0NjY/MaP1/1FNRQEEEAAAQSSLxByAui6fsTv14q/5D4H6JOCQGUFbrpJb6X+h9lqq1V2v+wNAQQQQACBMgmEnADupja/othHsZJib8VLCj8SSEGgMgJzdEXAaXo74NixenIkd3pXBp29ZEJAB9ZPfEI/VtwYkonuppHhCYScAF4gLn8n77aKQxR++tdf6+bTKQhURuBcPRJy3XXNDj20MvtjLwhkRKCrEsB99S/+NTq47u8MpiCAQGUFQk4A1xHFlQUc12h8QME0RhEoj8Bbb+l+cN0Q/qc/6S9U/olE5dkVW0UgawKL9NfnkAPMNvxIr1ualLXW014Eqi8QcgKokwP27QKirTTu0ykIlF9g5Eizgw8221wPMaMggEDsAp8sZ/Y9/Yj97DGz/f2BXBQEEKiYQGiPgTk60vKHNHyH4irFdMUAxRGKvygoCJRf4Od6+lBvXltQfmj2kGWBabq36of7m12rU8GvrqJXPfkV3xQEECi7QGgJoA65LFXmauzAyJQvNOxJ4OjINAYRKI/AppuWZ7tsFQEElhK4cwNd3K23rZ8zUe8O3m+pWYwggECZBEJLANcpUzvZLAJFC/g7IuMscW8vzrqxLQRCEThnoFmPBarNolBqRD0QSLdAaAlga9qraoYuFaYgUEYB/+PTTe8H7OdvCKQggEAlBRp1RfoXNdpjfSX3yr4QyK5AyAmg/yo4T3G8QpcKm5/+/aviF4oGBQWBeAX8zc8epyiWjXHTfkBxfIzbY1MIIIAAAgh0UiDkBPAstc0fBn24wt/BtZ7ibIVP/5WCgkCsAst48qeywJO/Hk2D8XyZF89m2AoCCCCAAAJxCYT8GJgfqJHfVdyueCH36ZcH66EBFATiFzjhObO/x79ZtogAAqUKzNN/T//7X6lrsx4CCLQhEHICuLLqPaOg7jM1zkMCClAY7bzAirruaNTjzdcYdH5rbAEBBGIROP98HQbQcYAGrvqJxZONIBARCDkB9KN+/uq3aPHrAV+MTmAYgTgETn/EbFpvs7vj2BjbQACBeAROP11Xf+vy75/+NJ7tsRUEEFgsEPI1gH6zx32KYYo3FOsq1lf4dYEUBGITWP0zs1MfNdvl+9rkjbFtlg0hgEBnBZbT/X+33Wa21VZmW2xhdsIJnd0i6yOAQE4g5COA+pNsGypuUXyo8MuzNlL4dAoCsQmMmmw2QbcYPb5GbJtkQwggEJdA//5mt95qdtppZg/5C6IoCCAQh0CoRwBr1LiLFKcq/FEwFATKItBLZ5cO1sUG2x5bls2zUQQQiENgp530qpALzL6vw/TPPmu2Bv+txcHKNrItEGoC6Ff8+t2+P85299D6cgv4y+gHnGxW5499+bTce2P7CCBQsoCf/l1NLw72oCCAQKcFQj4FPEGtG9rpFrIBBNoRaEr+2lmG2QggUGWBLl2ajwB20+t6KAgg0GmBUI8AesP81W9+3d+dircU0TdEjtI4BQEEEEAAAQQQQKAEgZATwI3VnqcUa+Yi37zG/ACfCCCAAAIIIIAAAh0XCDkB3LnjzWENBBBAAAEEEEAAgfYEQr0GcKAqfopih/YawHwEOiqw+btmK+gNUxQEEEi4wKxZzW8KmTMn4Q2h+ghUXiDEBPBoMUxSjFDoCW12uIKCQCwCy843u+MGs71ejWVzbAQBBKop4I+D+fxzsyOP1FXi0cvEq1kp9o1AMgRCTAD1UA77oaKP4ijFzxQUBGIRGP6E7i5a3uxmf6Q4BQEEki2wjK5iuukms6efNjv33GS3hdojUGGBEBPA/jK4Pufgn2tX2ITdpVTAH/o8Qi8S+MWuZo0hfuen1J1mIVBWgVVWMbv9drPzz9czI/yhERQEEChGIMQ/g16n/J2+CzUc8o0qxRizTCACv5yq28p1T/n9XwukQlQDAQTiEdh0U7MrrtC5I508eumleLbJVhBIuUCIydWyMj874q53NSw17rN4DmAEiMH2BdbSWz5++rjZjke3vyxLIIBAAgUOOMDsxRebTwdvuGECG0CVEaisQIgJ4KMi0IsfF5fHCsbzRwcXL8AAAu0JbPSBDhBsob8N/lRJCgIIpFPgzDPT2S5ahUAZBEJMAAeXoZ1sMuMCE75u5kFBAAEEEEAAAbMQrwGkXxBAAAEEEEAAAQTKKEACWEZcNo0AAggggAACCIQoQAIYYq9QJwQQQACBeATuvddsypR4tsVWEEiRAAlgijqTpiCAAAIIFAjMmGH2ve+ZvfJKwQxGEci2AAlgtvs/ta3vpidInjWRd/6mtoNpGALFChx3nNkJJ5jtsYfZB3ocAAUBBJoESAD5RkilwDF6M9RBeiRYfYj3uadSnEYhELDAb39rts02ZvvuazZ3bsAVpWoIVE6ABLBy1uypQgLLN5iNnqTXvn3HbEG3Cu2U3SCAQLgCXfWnzt8U0r272eGHmy30l0xREMi2AMdHst3/qWz9yXp0+IyVzP7BywBS2b80qmMCdXV1HVuhiKXLsc3C3ZZjHzU33mg99t/f7LXXzDbYoHCXjCOQKQESwEx1d/obu+rnZr+YarbPoWprl/S3lxYi0KrAAs3REfB+/fq1ukiQM8pY7959etvsGW9bj+WWC7LpVAqBSgqQAFZSm32VXeDXU/TEh7UVA8q+K3aAQNgCfpbT4xSFv2E9zuIHFcfHucHItspV73lmtRfWWsP8+SSAEW4GsytAApjdvk9ly5/oa/bXLVPZNBqFQGkCnvz1KG3VVtdSMlX2Uo56l73S7ACB5AiQACanr6hpEQI3bFrEQiyCAAIIIIBAxgW4Czjj3wA0HwEEEMi8wLXXmn38ceYZAMiWAAlgtvqb1iKAAAIIRAUWLTK7+WYzvzu4Qc+QoiCQEYGsJIBnqT9nKz5TTFJspGivrKgFpiv8kuSsOKmpFAQQQCBDAv6MwBtu0F8H/Xk49lizxsYMNZ6mZlkgC4nNGergYYpdFasqHlFMUCyvaKtcpJkvtbUA8xBAAAEEUiDwla+Y3XWXHh8wRe+Q9OMFFATSL5CFBPBEdeNYxTSF37s2UqHHwdt+itbKPpqxscLXowQscNDzZn+8J+AKUjUEEEiGwOqrm919t9kf/mB25ZXJqDO1RKATAmlPAHvKZoDiyYiRn9J9RrFFZFp0cBWN/EkxTOHLUgIVqNEDY8c8YPbfNQKtINVCAIFkCWy0kdmtt5r9/vdcD5isnqO2JQhkIQF0lk8KbPx2L08OWyr+eNNLFJz+bUknoGk/fdysTs8Ku3qzgCpFVRBAINkCQ4bov8r/mtXUJLsd1B6BdgTS/hzA/EswexU4rKzxtwum+ejBinUVh/iISv5lYvnP5qkFX0eMGKHfFc2/LIYOHWoelPIKrDLX7DdTzL5/kNmitP8bU15Kto4AAoUCy6T9T2Nhg7MxPmHCBPPw0sAd35b273JPAKcrtlboeFFT0dsxm07/Xp0bj3545uZvCH8/N9GvFfTk713FaYprFF8qY8aMsZ49Wzug+KXFmRCDwKiHzab2N5vo6ToFAQQQQACBdgSiB2jq6ups3Lhx7ayR7tlpTwC99/yU7umKBxVvKkYp5iluUxSWkzXh15GJ22v4JsW3FP+LTGewigL9tO/jnlWn/KiKlWDXCCCAAAIIJFggCyfPLlD/XKm4X/GhYjvF7gqdRDTPJT5T7KDw8qninUj48l582hdNQ3ypusAs1WCrI81e7lP1qlABBBDIgsBC3Q94yy08IzALfZ2hNmbhCKB35+hc+HC0eC7hD3xurUzWDD9lTAlMYBrJX2A9QnUQSLHABx+YnXSS2YwZOp/kJ5QoCCRfICsJYPJ7ihYggAACCFRHYI01mh8UPXiw2dprmx14YHXqwV4RiFEgC6eAY+RiUwgggAACmRTYcsvmV8YddZTuQJuaSQIanS4BEsB09SetQQABBBAol8Deezc/JHqvvcwee6xce2G7CFREgFPAFWFmJ50WeO01s/XW6/Rm2AACCCDQKYHjj29+S8jvfmd2xx2d2hQrI1BNAY4AVlOffRcn8N57euaLnsTzjL/Bj4IAAghUWWD48OZXxlW5Guwegc4IkAB2Ro91KyMwSo9u3G03Pb57i8rsj70ggAAC7QnwtpD2hJgfuACngAPvoMxX74UX9P4VvYDl+eczTwEAAggggAACcQlwBDAuSbZTHgF/5tYJJ3D9X3l02SoCCCCAQEYFSAAz2vGJaLa/tPuJJ8xGjkxEdakkAghkWGD+fLODDzabNi3DCDQ9SQIkgEnqrazV1Z+15df/9e6dtZbTXgQQSJpA9+5m669vNmSI3lP5ctJqT30zKMA1gBns9MQ0+ZxzePdmYjqLiiKAgI0ebbZgQXMSOGmS2Te+AQoCwQqQAAbbNVSsSaBLFyAQQACBZAj476vf/rY5Cdx5Z7PJk7l+ORk9l8lakgBmsttpNAIIIIBAWQQ8CTzvPLOFC808CXz8cbM11yzLrtgoAp0RIAHsjB7rIoAAAgggUCjgSeDYsc3PLl1ttcK5jCMQhAAJYBDdkM5K1NfXW0NDQ6yNq6uri3V7bAwBBBCIQ6DF33f77GM2d26nNl9TU2M9evTo1DZYGYGWBEgAW1JhWqcF/Jdh3/59rfbD2qK3tZmW9Li66DVYEAEEEKi+QCm/74qtde8+vW32zNkkgcWCsVzRAiSARVOxYEcE/MhfU/J3itZatog1G80uvEGXy/ilMoPbWN4PAI5vYz6zEEAAgQoLdPj3XbH1m2dWe2Ft05kUjgIWi8ZyxQqQABYrxXKlCXjyV8TZi3302KyNPzL73qHtLK9fiBQEEEAgSIEift+tNsesq/7hfW/FIFtApTIkwIOgM9TZoTZ1Gd0sN/Y+szMHm9UVkSyG2g7qhQACCLQnMFwvN5p4ldlXP2tvSeYjUF4BEsDy+rL1IgR+9JTZIt00d+mWRSzMIggggECCBUYPNntKl7o8cLVZHx0NpCBQLQESwGrJs98mgZW+MBs9yeyMXfXYrG6gIIAAAukWWKS/usO+Z/bsV5uTwFU/T3d7aV24AiSA4fZNZmp29iCzu3ljUmb6m4YikHUBTwKP2M9sWh+z+6/W684796SYrHPS/hIFSABLhGO1eAQ+Xc7sT9tqWzoFTEEAAQSyIuBnPA7f3+y13mY/eDErraadIQlwF3BIvUFdEEAAAQQyI7BASeBBBzZfA52ZRtPQYARIAIPpCiqCAAIIIJA1AT8dTEGgGgJ861VDnX0igAACCCCAAAJVFCABrCJ+VnfdZVFWW067EUAAgeIE+D1ZnBNLlS5AAli6HWuWIFCzwOw/l5pt8l4JKwy+COAAABaeSURBVLMKAgggkAGBVfRomOf+bLbt7Aw0liZWTYAEsGr02dyxPwXfX4P04mrZbD+tRgABBNoT+N9XzP6yldl9N+oO4fYWZj4CJQqQAJYIx2odF/BnXf1mitnpu+muN77zOg7IGgggkBmBcdso+dMDo/+qFteMHWvWqP+cKQjEKMCf4Rgx2VTbAqMmmz26lh58+rW2l2MuAggggIDZv/S7ckdB1Fx5pV4fMsxs3jxYEIhNgAQwNko21JbA1z8yO/4/euWbjv5REEAAAQSKE3hei33+wANmr7xi9sgjxa3EUggUIcBzAItAYpHOC/ziYbOrNtOrj7j2r/OYbAEBBDIl0Lj66s3JX1eO2WSq48vcWBLAMgOz+WaBk/Yw674QDQQQQACBkgRI/kpiY6XWBUgAW7dhTowCc2ti3BibQgABBBBAAIFOCXA8uVN8rIwAAggggEAVBZ55Ro9V4On6VeyBxO6aBDCxXUfFEUAAAQQyLTB/vtkhh5gdeqjZF19kmoLGd1yABLDjZqyBAAIIIIBA9QW6dzebrOdrzZxpNmSI2QcfVL9O1CAxAiSAiemqZFW024MP2jrJqjK1RQABBJInsJoerTBxotmAAWbb6OnR06Ylrw3UuCoCJIBVYU/5Tt9/35Y76ij7VsqbSfMQQACBIAR69DC7/nqzI44w23775oQwiIpRiZAFSABD7p0k1s1fV3TiibZw8GC7NYn1p84IIIBAEgW6dDE76yyziy8269UriS2gzhUW4DEwFQZP/e5uusls6lSrf+wxs9tuS31zaSACCCAQlMDhhwdVHSoTrgAJYLh9k7ya6dSvDR9u9pe/WOOqqyav/tQYAQQQQACBjAhwCjgjHV2RZv74x2bf+Y7ZAQdUZHfsBAEEEEAAAQRKE+AIYGlurNWSwAknmG2+eUtzmIYAAgggUE2Biy4y07XZlfgdXV9fbw0NDWVpbU1NjfXwm14onRbISgKoK2PtWEVPxX8UP1G8qCgsfTRhrGKgws9hfqS4UTFaUZ7vZm04NWXXXVPTFBqCAAIIpEpg7lz9ZdOfNr9beO+9y9Y0T/769u9rtR/WlmUfvfv0ttkzZ5MExqCbhQTwDDkNU3h28obiTMUExTcU+olYqqygsZcVnjC+pVhX4Xcy+L8bpyooCCCAAAIIJE9gxAiz9dYzO/hgsx/9yOzcc/WXLf4jaX7kryn5O0VEy8bMNM+s9sLapqOLHAXsvG0WrgE8UUx+VM+fjqlvHxup0OPTbT9FYfGk7zyFf3p5U3G5YmcfoSCAAAIIIJBYgR/8wOypp8weeshsyy3N/vvf8jXFkz/PL+OMuBPK8rU+EVtOewLop3wHKJ6M9MZCDevt2bZFZFpbg7tpZhl/StraNfMQQAABBBCIUWCDDcweeaT5SOBpp5n5s1spmRTIQgLoHftJQe9+rHFPDtsrfrTQ72rwT0qhwH338cuj0IRxBBBAIHSBZXT110j9Wbv/fjN/gDQlkwJpvwawLtervQp6d2WNv10wrXD0HE04QjFI8U7hzOj4CF1b4XcmeRk6dGhTROencviWW8z8sS+vvGLWu3cqm0ijEEAAgVQLdOuW6uYVNm7ChAnm4aVcdykX7jPk8SwkgNPVAVsrHs91hH/H++nfq3PjLX2M00S/aWRHxayWFohOGzNmjPXsWcwBxehaCR7+4IPm5G+cmEj+EtyRVB0BBBBoQcBPC6fwyGD0AE1dXZ2N879hGS5pPwXsXTtecbpiI8Vyit8q/GaQlt5T5snhdQrdK287KdpN/rRM9oq/7WPwYDO/oJiCAAIIIJAegQULdOhDxz6u1jESrg9MT7+20JK0HwH0Jl+g8Me76GIHW1GhW6Bsd8VcRT/FtNz4w/rcQaF75JsSxNf06cUvkPCrZDN0iM+b3UrxU78TJ0rN2SgIIIAAAqkS8OsDf/UrPTn3WLPbbze75BKzPn1S1UQa0yyQhSOA3tLRijUUnggOVryo8OJH+Dwp9OTPyxSFHwVcXuEJn4fPJ/kTgkVP/a62mk+hIIAAAgikTcAfFP3CC2ZdlSJsvLHZHXekrYW0RwJZSQDp7DgE/EaX0aM59RuHJdtAAAEEQhZYVS/D8jM+v/+92ZFHNj88mlPCIfdYh+tGAthhsgyv0Es3U//kJ6m8ODjDvUrTEUAAgZYF/EaQww4ze/55syFD+N3fslJip5IAJrbrqDgCCCCAAAIVEOiny+UPOqgCO2IXlRQgAaykNvtCAAEEEEAAAQQCECABDKATqAICCCCAAAKJFJg82Wz+/ERWPeuVJgHM+ndAW+3/6CO9A6XNl6C0tTbzEEAAAQTSLOCJ3ymnmG2/vdlLL6W5palsGwlgKrs1pkb5A59/+cuYNsZmEEAAAQRSJdC9u9kjj5jtvLPZVluZXXSR2aJFqWpimhujJz5SEGhB4NZbze67T09MzD8ysYVlmIQAAgggkG2BHj3Mzj/fbJ99mh4Xs/xNN9m2Enks2yqJaD1HABPRTRWupJ/6PfFEs4svNlt99QrvnN0hgAACCCROYCe9PfXZZ23hwIE21ivv78+iBC1AAhh091Spcn7qd4cd9FI8fyseBQEEEEAAgSIEVlzR5v3616ZUsPklqkWswiLVE+AUcPXsw9xz9NSvPwSUggACCCCAAAKpE+AIYOq6tJMN8us5LruMU7+dZGR1BBBAAIGlBbaZZTZqktkK85aezlh1BEgAq+Me7l732stsv/3CrR81QwABBBBIpEBDN7Nd3zB74w9mP9VdIjULEtmM1FSaBDA1XUlDEEAAAQQQCFfg6TXNdjra7Ojvmh33X7OXdZ/h4c+adeXJMVXpNK4BrAo7O0UAAQQQQCCDArq0/O71zf71dbNDnzc7+0GzHWeanaCnyFAqK0ACWFlv9oYAAggggEDmBRbp/OO1m5ndvJHZKnMzz1EVAE4BV4U9oJ0+9VRAlaEqCCCAAAJZEmjQYah3e2apxeG0lQQwnL6ofE0uvdRsyBCzmTMrv2/2iAACCCCAQBsCW802W6e2jQWY1SkBEsBO8SV45csvNzvtNLN77jHr3z/BDaHqCCCAAAJpFNjzNb2NdLzZH/VnarU5aWxhddvENYDV9W93742NjXbSKSfZtFemtbtssQvsNvtd++m0V+3XW25qW8+aaXvX1RW7atHL1ZVhm0XvnAURQACBVgTK8bupHNtspfqxTq6vr7eGhoZYtxmnxdmDzf7+TbPfTmx+dMyFW5uNibW22d4YCWAC+v/iP+heeZ2pNT2jubPlMB1S/4lyyb23NHvw06et+9HDbH79/M5ulvURQACBsAX8mXN6Dl2/fv3CrmeFaufJX9/+fa32w7DPsU5bzWx/vZXUHyJ94uNmPDowvm8QEsD4LMu7pc21+U5eKLvMQrOTnjH73qFK/r6m7T1kNv8VJX+naHjZmKvvBxXHx7xNNocAAgiUKqDff+bB77smQT/y15T8xe1Rpt/9jytvf7yPqv5CU/X5EoMACWAMiEnZxAL997vtsWaNhVd+evIXw9HFpRx41c9SHIwggEAgAvy+W7oj4vbgd//SvgGPFaYCAVeVqsUh8KXkL46Nsg0EEEAAAQQQSJQACWCiuovKIoAAAggggAACnRcgAey8IVtAAAEEEEAAAQQSJUACmKjuKr6yu+v5SX/+Z/HLsyQCCCCAAAIIZEeABDCFfb3r62a33Gz2wLopbBxNQgABBBBAAIFOC5AAdpowrA0MedPsHzeZHbevHqCpl2xTEEAAAQQQQACBQgESwEKRBI8Pfsvs9hvNTtjb7MZNEtwQqo4AAggggAACZRUgASwrb+U2/q13zO68wWz4nmbXbVa5/bInBBBAAAEEEEieAA+CTl6ftVjjl1c1O+T7Znev3+JsJiKAAAIIIIAAAosFOAK4mCLZA3NrSP6S3YPUHgEEEEAAgcoJkABWzpo9IYAAAggggAACQQiQAAbRDVQCAQQQQAABBBConAAJYOWsY9vTNz8wW74hts2xIQQQQAABBBDImAAJYMI6fLN3zaZcYbbvKwmrONVFAAEEEEAAgWAESACD6Yr2K7Lx+2b3X202dnue89e+FksggAACCCCAQGsCPAamNZnApn/zI73a7e9mF21r9n87BVY5qoMAAggggAACiRLgCGACumsD1XGikr/xW5udOygBFaaKCCCAAAIIIBC0AAlg0N3TXLnj9XGpXu121uAEVJYqIoAAAggggEDwApwCDr6LzE5THRt13Z91SUBlqSICCCCAAAIIBC/AEcDgu0jJn9eR5C8BPUUVEUAAAQQQSIYACWAy+olaIoAAAggggAACsQmQAMZGyYYQQAABBBBAAIFkCGQlATxL3TFb8ZlikmIjRWull2Zcp/hEUau4RrGSgoIAAggggAACCKRCIAsJ4BnqqWGKXRWrKh5RTFAsr2ipePLXR7GOYj3F6oqrFBQEzF4HIVMC9Hemupuf72x1d9Zbm4UE8ER18ljFNMU8xUhFd8V+isLSXxP2UJyq+FjhRwD9Jtx9FWspKFkXICHI1ncA/U1/Z0uA1mZIIO0JYE/15QDFk5E+XajhZxRbRKblBzfXQL3ihfwEfT6naFD4PAoCCCCAAAIIIJB4gbQ/B9ATQC9+PV+0+NG9/LzodJ/2aXRCbtjXb2n5ptl1dXUtrBLPpMbGpofA6D1w2p4ft4yzvJvbmFffj43GWfxqSy9xb7tc2/W6FrNt/1egpe8QX7+1Usx2W1u3velJ3HaS6pzv7yTVOf89k8Q6e93LVe9itpvv77xhsZ/FbLvYbUWXy/1enj17tsX9d+azz3KVTtLv6JxHHBZxbCPaVUkc7pLESnegzp60efK2neLxyHoTNPy84vTINB/cV3GjovD6QD8qeIDiLkW09NXI29EJDCOAAAIIIIBAYgT88q7ZialtjBVN+xFA/99mukJv0V2cAHbTsJ/+vVpRWJ7RhGUVGyvyp4E307Afe/N5heUdTfBvnvz/f4XzGUcAAQQQQACBMAVWVLX87zglpQJ+lG+6wh/9spzid4pZisKjfJrUVP6pr/9WrKJYVXGf4jYFBQEEEEAAAQQQQCBBAqNV13cVcxSTFPnnAPbTsB+920GRL700cK3CTx37tYJ+pLDV6/80j4IAAggggAACCCCAAAIIIIAAAggggAACSRY4S5X3C0T9SOEkRf7ooQa/VPzo4XUKP3pYq+AtIkJIWOlIf09S2/y+NL/W1L8//PMEBSUZAgepmlMUfl+3Px6qvcdi8fMtpASXjvb3JLWVn+9kdrhf6vWcwn+2/e/39Qq/Xr+tws93WzoZnOdvEZmh+KZiWcUYhd/129r1g3dr3r2KlRW9FX794O0KSjIEOtrfD6pZnjBSkimwq6rtScFRimISQH6+k9nP+Vp3tL/5+c7LJe/zXFXZb/b0G139Eq7rFE8r2ir8fLelk8F5b6rNwyPt9juI31ccFpmWH/S3iCxS+B3E+bKpBnxae/955Jfns7oCHelvr6n/gTi7ulVm7zEIDNI22ksA+fmOATqQTRTT315Vfr4D6bAYquFP8/Cf8ZVa2VYmf77bO+XRilUmJvt/DQMUvEUkE93d9F9iR/o7r3KiBv6n8FcN+mmHrygo6RPYXE3iLUHp69f2WsTPd3tCyZg/VNX0s3l+Srilksmf77Q/B7Clji52mieAXj5p/lj81e8Mzs9bPDE3raVvLl+/peWj6zJcfYF8HxXb317jXyleVvg6myiuUgxQHKKgpEvAvz/4+U5Xn7bXGn6+2xNKxvxdVM2Riv3bqG4mf75JAFv/jvAL+r30av5Y/HVlDb29eGzJgC/f0uFlXz+/rSVLMxSaQL6Piu1vr/9jkUY8r+GTFfcr/HpRv3ickh4Bfr7T05fFtoSf72Klwl1ub1XNb8b0y7b8mvzWSiZ/vjkF3Nq3Q3PSNl2zt44s4tcAbqF4OjItP/iMBvwPf/QawM003l3h8yhhC/gvgOmKYvu7rdZ0aWsm8xIpwM93IrutLJXm57ssrLFv1JM+T/4OVNzZztb5+W4HKIuzeYtItnq9I/29mmj8upL8HeH+eCC/XvQWBSUZAv4PsP/TtpvCLxD3vvTx1v7A/1PzeEuQEBJaOtLf/HwntJNz1fabN2sVO3SgGfx8dwArK4uOVkPfVfAWkWz0eLH97XeNPa7wa0L96OGrit8puAlECAkpR6qeixSe/HnkhwdquJ/Cn+0Y/QPSS+PXKj5ReL9frchfO6pBSuACHelvfr4D78x2quc/y34Zjv9u9vCfZf/M/zzz8y0MCgIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACsQlcoS35mzziKDtqI/6WgdZeIRfHPtgGAgggEKuAvxuRggACCCBQusBUreqvhGvMbeJMfT6UG+YDAQQQCFKABDDIbqFSCCCQcIF8MpjwZlB9BBBIqwAJYFp7lnYhkG6B49S81wqa2F3jHyi+p1hJ8WfFdMWHirsU6yhaK2tqxk2K9xTvKm5UrKHIl24aOFXxosJP985UnKHwMljhL5/336eHKkYotlNEX0A/ReMjFdFygEZ8f8tEJzKMAAIIIIAAAggg0LLACprsidjAyOyDNPyOwpO1BxVXKzwR9MTwdwpP3nyelysUPt+LJ25PK65V+Hb9dK4ng08q8tf1/VbDryq2VHjppdimachskD4XKnw7Xs5UTGkaWvLlEA1OXzLaNHSvvp5bMI1RBBBAAAEEEEAAgTYE/qZ5+STOF/OEyhO9LRT1iuUV+eKJ31zF9rkJ0QTQj9YtUHjily+9NeBJ3bdzEzzZ3C83XPhRTALoSagf7dsjt/LX9NmgGJAb5wMBBBCoqED+P9aK7pSdIYAAAjEIXKZtfF/hidsAxc4KTwq/rvCE621FbS4+0mejop+isKylCb6cJ3n54uMfK/orVlX4kcFXFaWW+VrxcsWPchs4Xp8PKKbnxvlAAAEEKirAtScV5WZnCCAQo8Cj2tabisMVqyseVryuWFMxT9FH4Ufx2iuztMDKCj9d/GluYT8C6NNmKDx5nKP4hsJPI7dXFrWywCWa/rJiHcUwxXEKCgIIIIAAAggggEAHBU7R8n793kyFJ4Je/MzGE4q/KjwJ9OLJ3P6KHj6iEj0F7Mv7Nq5RrKjwRPAGRfQawHM17slb/hpA3962Ci+Fp4A9sZuuWFZRWP6pCU8pPOnkDEyhDuMIIIAAAggggEARAqtomXrF/xTRhMuTuD8o/Ajhp4rpiqsV+WWiCaAmW1/FzYr3FX6tnt8E4kcS88WTtdMVngR+ppiZG9fHlxJAPyU9QeF18lPJ2yvyZU8N+BHCM/MT+EQAAQQQQAABBBBIt8AGap5fD+jXHVIQQAABBBBAAAEEUi5Qo/b5aebrU95OmocAAggggAACCCAgAT/16zeS+HWF0VPLGqUggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggEBoAv8fifWKwM4pFY8AAAAASUVORK5CYII=\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "#alpha is a constant = 2kT/m\n",
    "alpha = ((avg_speed)**2) * np.pi / (4)\n",
    "\n",
    "@np.vectorize\n",
    "def f(v):\n",
    "    return ((1/(alpha*np.pi))**(1.5)) * (4*np.pi*((v)**2)) * np.exp(-(v**2)/alpha)\n",
    "\n",
    "values, bins, __ = plt.hist(system.speeds, 20, normed = True, facecolor='green')\n",
    "v = np.linspace(np.amin(system.speeds),np.amax(system.speeds),20)\n",
    "l = plt.plot(v, f(v), 'r--', linewidth=1)\n",
    "plt.ylabel('Probability density')\n",
    "plt.xlabel('velocity')\n",
    "plt.title('3D speed distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}