Vectors.ipynb

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     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
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   "source": [
    "%pylab notebook"
   ]
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  {
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   "source": [
    "# Vectors #\n",
    "\n",
    "Vectors are algebraic objects that have a *magnitude* and a *direction*.\n",
    "\n",
    "They are typically represented as an array of coordinates"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Representations ##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vectors as algebraic objects are usually represented by a variable with an arrow overhead\n",
    "\n",
    "$\\vec{a}$\n",
    "\n",
    "The contents of a vector can be represented in various ways\n",
    "\n",
    "A simple representation only defining the values in each dimension can be represented as an array.\n",
    "\n",
    "$\\vec{a} = <a_{1}, a_{2}, a_{3}, ...> = (a_{1}, a_{2}, a_{3}, ...)$\n",
    "\n",
    "Sometimes vectors are represented as a *linear combination* of unit vectors (which we'll come to later)\n",
    "\n",
    "$\\vec{a} = a_{1} \\hat{i} + a_{2} \\hat{j} + a_{3} \\hat{k} + ...$\n",
    "\n",
    "$\\vec{a} =  a_{1} \\hat{x} + a_{2} \\hat{y} + a_{3} \\hat{z} + ...$\n",
    "\n",
    "$\\vec{a} = a_{1} \\vec{e}_{1} + a_{2} \\vec{e}_{2} + a_{3} \\vec{e}_{3} + ...$\n",
    "\n",
    "We can also represent vectors in other coordinate systems, such as polar coordinates.\n",
    "In this representation, the magnitude of the vector is determined by the $\\hat{r}$ component and the direction is represented by the angle components ($\\hat{\\theta}, \\hat{\\phi}, ...$)\n",
    "\n",
    "$\\vec{a} = a_{1} \\hat{r} + a_{2} \\hat{\\theta} + a_{3} \\hat{\\phi} + ...$\n",
    "\n",
    "### Creating a vector in Python\n",
    "\n",
    "We can represent a vector in python an an array.  Vectors are typically draw as an arrow starting at the origin.\n"
   ]
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     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
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       " * http://stackoverflow.com/a/24161582/3208463\n",
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       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-1, 1)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%pylab notebook\n",
    "\n",
    "a = np.array([0.5, 0.9]) # this is a vector\n",
    "\n",
    "\n",
    "plt.arrow(0, 0, *a, head_width=0.02)\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Getting the magnitude of the vector ###\n",
    "\n",
    "We can determine the magnitude of a vector from our knowledge of geometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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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width=\"640\">"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-1, 1)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%pylab notebook\n",
    "\n",
    "a = np.array([0.5, 0.9])\n",
    "\n",
    "plt.arrow(a[0],0,0,a[1], color='r', ls='--')\n",
    "plt.arrow(0,0,a[0],0, color='r', ls='--')\n",
    "plt.arrow(0, 0, *a, head_width=0.02)\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The magnitude of a vector can be determined by the *Pathagorean Theorem*\n",
    "\n",
    "$\\boxed{||\\vec{a}|| = \\sqrt{a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + ...}}$\n",
    "\n",
    "The angle of a vector in each dimension can be figured out from geometry as well.  Here's an example for a 2D vector, since in higher dimensions this becomes a bit more messy since we have more angles.\n",
    "\n",
    "$\\boxed{cos(\\theta) = \\frac{a_{1}}{||\\vec{a}||}}$\n",
    "\n",
    "$\\boxed{sin(\\theta) = \\frac{a_{2}}{||\\vec{a}||}}$\n",
    "\n",
    "$\\boxed{tan(\\theta) = \\frac{a_{2}}{a_{1}}}$\n",
    "\n",
    "so\n",
    "\n",
    "$\\theta = cos^{-1}\\left(\\frac{a_{1}}{||\\vec{a}||}\\right) = sin^{-1}\\left(\\frac{a_{2}}{||\\vec{a}||}\\right) = tan^{-1}\\left(\\frac{a_{2}}{a_{1}}\\right)$\n",
    "\n",
    "### Getting the magnitude of a vector in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.103277807866851\n"
     ]
    }
   ],
   "source": [
    "def mag(vec):\n",
    "    \n",
    "    # first, square all of the elements\n",
    "    squares = vec*vec\n",
    "    # this is an array where each element \n",
    "    # is the square of the elements in our vector\n",
    "    # Note: this is not the same as vector multiplication\n",
    "    # which will be described later.\n",
    "    # This is just element-wise multiplication\n",
    "    \n",
    "    # next we add up all the elements\n",
    "    total = np.sum(squares)\n",
    "    \n",
    "    # the magnitude of our vector is the square-root of this sum\n",
    "    magnitude = np.sqrt(total)\n",
    "    \n",
    "    return magnitude\n",
    "\n",
    "a = np.array([5.0, -3.5]) # make a 2D vector\n",
    "\n",
    "print(mag(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Getting the angle of a 2D vector in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.6107259643892086\n"
     ]
    }
   ],
   "source": [
    "def get_angle(vec):\n",
    "    # we use np.arctan2 for inverse tangent\n",
    "    # because np.arctan2 can work with angles all the\n",
    "    # way around a circle\n",
    "    # What I mean by this is that if both elements\n",
    "    # of the vector are negative, the ratio between\n",
    "    # them is the same as if they were positive\n",
    "    # even though the vector lies within a different\n",
    "    # quadrant\n",
    "    \n",
    "    x, y = vec # get the x and y components of our vector\n",
    "    angle = np.arctan2(y, x)\n",
    "    return angle\n",
    "\n",
    "print(get_angle(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Operations ##"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Addition and subtraction ###\n",
    "\n",
    "You can't add a scalar to a vector as this operation doesn't really mean anything, but you can add and subtract vectors from eachother.\n",
    "\n",
    "Vectors work with addition and subtraction element-wise.\n",
    "\n",
    "$\\boxed{\\vec{a} + \\vec{b} = <a_{1} + b_{1}, a_{2} + b_{2}, a_{3} + b_{3}>}$\n",
    "\n",
    "adding two vectors can be represented as placing the second vector such that the first vector is its origin.\n",
    "\n",
    "### Addition and subtraction in Python\n",
    "\n",
    "Adding and subtracting vectors in Python is easy since array operations are already element-wise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 14.8 -26.8   5.9]\n",
      "[-3.6 12.4  0.9]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([5.6, -7.2, 3.4])\n",
    "b = np.array([9.2, -19.6, 2.5])\n",
    "\n",
    "print(a+b)\n",
    "print(a-b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing Addition and Subtraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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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3wRAS2ggAAj06adm7jhxwu5qXG7vXvNgbN5sdzVhhflNALSEBgIAU22tmTf+8he7q4EkacsW86B88ond1YQN5jcB0BIaCABMt97qyxkPPmh3JQjw6qtmCDx+3O5qwgLzmwBoCQ0EAD6LF3PeX1h77jnzAJ07Z3c1tmN+EwAtoYEAQDpwwMwWX3xhdzUI6rHHzANVX293NbZifhMALaGBALhdXZ2ZKfLz7a4GVzRokO9gXX21q28UzfwmAFpCAwFwu+HDfXni3nvtrgQhaWw0E/vdd9tdjW2Y3wRAS2ggAG6Wm2tmiYYGu6tByJp+TcuTT9pdjS2Y3wRAS2ggAG51+LCZIY4csbsatFpFhXkAf/1ru6vpdMxvAqAlNBAAN2r6dbN5eXZXgzYrKzMP5Jtv2l1Np2J+OygALlq0SP3791dsbKxSUlK0+TJ3Nd+wYYMMw2i2lJaWBmy3atUqJScnKyYmRsnJycpv5RnMNBAANxo50vWnkEWOoiIzBO7aZXc1nYb57ZAAmJeXJ4/HoyVLlqikpEQZGRnq3r27Dh061OL2FwPgJ598oqNHj/qXhiYnqRQUFCgqKkrZ2dkqLS1Vdna2oqOjtW3btpDrooEAuM3KlZz3F3HWrjUP6uHDdlfTKZjfDgmAw4cP17Rp0wLWJSUlac6cOS1ufzEAnjlzJuhzPvzww0pLSwtYN3bsWD366KMh10UDAXCT8nIzJ5SV2V0N2tWiRebBraiwu5oOx/x2QACsra1VVFRUs49nZ86cqZEjR7b4mIsBsH///rruuus0atQovffeewHb3HjjjVq4cGHAuoULF6pv375Ba6mpqVFlZaV/KSsrc30DAXCHhgYzH7zyit3VoEPMnGke5Joau6vpUARABwTA8vJyGYahrVu3BqzPysrSwIEDW3zMnj17tHjxYn344YcqKCjQ9OnT1aVLF23atMm/jcfj0YoVKwIet2LFCsXExAStJTMzs8VzC93cQADcYcwYXy648067K0GHuvtuV3ynHwHQQQGwoKAgYP28efOUmJgY8vOMGzdO999/v/9nj8ejlStXBmyzfPlyxcbGBn0O3gEE4Eavv843iLmG1yv16uU72MnJEfttIQRABwTAtnwE3JJ58+YpKSnJ/3NbPgK+FA0EINIdO2aGv4MH7a4GnaLpfX5acV68kzC/HRAAJd9FINOnTw9Yl5ycHPQikJY89NBDurvJPQsefvhh3XvJdxelpaVxEQgA/FPTbw37/e/trgad6vx58+D//Od2V9PumN8OCYAXbwOzdOlSlZSUaNasWerevbsO/vOfo3PmzNGkSZP827/wwgtas2aN9u7dq48++khz5syRYRhavXq1f5utW7cqKipKOTk5Ki0tVU5ODreBAYAmHnjAN/+/9jW7K4Etjh83Q+Al58w7HfPbIQFQ8t0Iul+/foqJiVFKSkrABR3p6elKTU31/zx//nzdfPPN6tq1q66++mp9/etf19q1a5s95+uvv67ExER5PB4lJSUFBMRQ0EAAItWf/2zO/ro6u6uBbfbuNRvh/fftrqbdML8dFADDEQ0EIBI1feNn3z67q4Ht3n/fbIhPPrG7mnbB/CYAWkIDAYg0Tc/7W7TI7moQNpp+Bczx43ZXYxnzmwBoCQ0EINI8/LBvxrfiLltwi+eeM0PguXN2V2MJ85sAaAkNBCCS/PWv5nyvrbW7GoSlRx+NiJtCMr8JgJbQQAAixalTEXeaFzrKoEG+RunVy7E3imZ+EwAtoYEARAKv1wx/L7xgdzUIe01PFB01yu5q2oT5TQC0hAYCEAm++13fLO/f3+5K4Bg1NWYInDnT7mpajflNALSEBgLgdO+8Y87x6mq7q4GjVFSYzfPrX9tdTaswvwmAltBAAJzs9Glzfn/8sd3VwJHKyswmauELF8IV85sAaAkNBMCpmp739/zzdlcDRysqMpupqMjuakLC/CYAWkIDAXCqqVN98/p//S+7K0FEWLvWDIFlZXZXc0XMbwKgJTQQACfatMmc1Rcu2F0NIsaiRWZjVVTYXc1lMb8JgJbQQACcprLSnNF//7vd1SDizJxpNlhNjd3VBMX8JgBaQgMBcJKm5/3NnWt3NYhYd99tNlpjo93VtIj5TQC0hAYC4CRPPumbyT172l0JIprX6/uWEMPwfWtIGGJ+EwAtoYEAOEVBgfmmzPnzdleDiFdfbzbcY4/ZXU0zzG8CoCU0EAAnOHvWnMUffmh3NXCNc+fMxnvuOburCcD8JgBaQgMBCHdNz/t7+mm7q4HrHD9uNuDKlXZX48f8JgBaQgMBCHc//rFv9no8vjAIdLq9e80Q+P77dlcjifktEQAtoYEAhLMdO8y5W1VldzVwtfffN5tx7167q2F+iwBoCQ0EIFw1Pf1q+3a7qwHk+wj4YlMeP25rKcxvAqAlNBCAcNW1q2/OPvWU3ZUATTz3nBkCz52zrQzmNwHQEhoIQDj62c/MGct5fwg7jz5qNmh9vS0lML8JgJbQQADCza5d5mw9e9buaoAgBg3yNWmvXrb8K4X5TQC0hAYCEE7OnzfD35YtdlcDXEZjo9mso0Z1+sszvwmAltBAAMLJ1Vf75un/+T92VwKEoKbGDIEzZ3bqSzO/CYCW0EAAwkXTc+s57w+OUVFhNu6iRZ32ssxvAqAlNBCAcFBcbM7Qigq7qwFaqazMbOC1azvlJZnfBEBLaCAAdquuNmfnxo12VwO0UVGRv5HfyPu5fr4x+FJyvMTyyzG/CYCW0EAA7PaVr/jm5r//u92VABatXesPgckzuujpe67S06OvkmdutK6ae5WMZw0Zzxqau3Gu5ZdifhMALaGBANhpwQLO+0NkaPQ2alvZNr3y/w32N7X3n/+9faqhq+Zepfjn4/Wrbb9SXUOd5ddjfhMALaGBANiltNQMf6dP210N0DoNjQ0qOFygb+d92//OXr8MQ2diDbOxDUN1Vxn69fAueupvT+lM9Zl2e33mNwHQEhoIgB2a3j3j7bftrga4sobGBm05tEX3r7zfH/guXab+8puq/1I3eaOiAkJgQ88eUm1tu9bD/CYAWkIDAbDDV7/qm40TJthdCdCy+sZ6bTq4Sfcuvzdo4Hsw70EVlhWqobHBfODJk9IPfiDvVVcFBsE//7ld62N+EwAtoYEAdLb/+R/O+0P4qW+s14YDGzTmlTFBA9+//fHftOPzHWr0Nl75CYuLpdRUs9kffLBd62V+EwAtoYEAdKa9e815ePKk3dXAzeoa6vTOvnf0zT98M2jge3TVo/qg/IPQAl9LvF5pzRrpxhule+5p1/qZ3w4KgIsWLVL//v0VGxurlJQUbd68Oei2q1ev1ujRo3XNNdeoR48euvPOO7Vu3bqAbXJzc2UYRrOluro65JpoIACdpba20++VC/jVNtTqb5/9Tam5qUED34TVE1R0tKjtgS+Y6mqpvr5dn5L57ZAAmJeXJ4/HoyVLlqikpEQZGRnq3r27Dh061OL2GRkZmj9/vnbs2KG9e/fq6aeflsfj0a5du/zb5ObmqmfPnjp69GjA0ho0EIDOcsstvvD30EN2VwI3qG2o1V8//au+vuzrQQNf+pp0/f3Y3+V14LkIzG+HBMDhw4dr2rRpAeuSkpI0Z86ckJ9j0KBBmjvXvHlkbm6u4uPjLdVFAwHoDL/9rfnuX2M7v7kCSFJNfY3e/ORNjfj9iKCB7/t/+r6Kvyh2ZOC7FPPbAQGwtrZWUVFRys/PD1g/c+ZMjRw5MqTnaGxs1I033qgXX3zRvy43N1dRUVHq27ev+vTpo/vuuy/gHcKW1NTUqLKy0r+UlZW5voEAdKz9+83w98UXdleDSFFdX60/7/mz/nXxvwa/LcsbU/Xx8Y8jIvBdigDogABYXl4uwzC0devWgPVZWVkaOHBgSM+xYMEC9erVS180+duzsLBQr7zyinbv3q3NmzfroYceUlxcnPbu3Rv0eTIzM1s8b9DNDQSg49TVmeFvzRq7q4GTVddXK78kXym/Swka+Ka/OV2lJ0ojMvBdigDooABYUFAQsH7evHlKTEy84uNXrlypbt26af369ZfdrrGxUUOHDtWTTz4ZdBveAQTQmW67zRf+7rvP7krgNBfqLmjVx6s09KWhQQPfjLUz9MnJT1wR+C5FAHRAALTyEXBeXp7i4uL05ptvhvRaU6ZMUVpaWsi10UAAOsqyZea7fw0NV94e7na+7rzyivN0y6Jbgga+jL9m6LNTn7ky8F2K+e2AACj5LgKZPn16wLrk5OTLXgSycuVKde3aVWtC/NzE6/Xq9ttv1+TJk0OuiwYC0BEOHTLDXytvTgCXOFd7Tiv+sUJJv04KGvie+ttT2n96v92lhiXmt0MC4MXbwCxdulQlJSWaNWuWunfvroMHD0qS5syZo0mTJvm3X7lypaKjo7Vo0aKAW7xUVFT4t3n22We1bt067du3T0VFRZo8ebKio6O1ffv2kOuigQC0t/p6M/z98Y92V4NwUVVbpVf+/ooSfpUQNPDNfnu2Dpw5YHepjsD8dkgAlHw3gu7Xr59iYmKUkpKiTZs2+f9fenq6UlNT/T+npqa2eLFGenq6f5tZs2apb9++iomJ0bXXXqsxY8Y0O8/wSmggAO3t61/3hb9Ro+yuBHY6W3NWLxe9rJt+eVPQwPf0O0/rUEXL98PF5TG/HRQAwxENBKA9LV/OeX9uVVlTqd9/+Hv1faFv0MD3n+/9p8oqy+wuNSIwvwmAltBAANrL55+b4e/zz+2uBh2torpCiz9YrD6/6NNi2OvybBc9u+FZlZ8tt7vUiMT8JgBaQgMBaA8NDWb4W77c7mrQEc5Un9FvdvxG//Jf/9Ji4Iv+ebSe2/Scjpw9YneprsD8JgBaQgMBaA/f/KYv/P3v/213JWgvpy6c0ovbX9Q1C65pMfDFPher599/XseqjtldqisxvwmAltBAAKz64x/Nd//q6+2uBm118vxJ/bLwl7o65+oWA1/3rO5asGWBvjjH9/mFA+Y3AdASGgiAFUePmuHvEBdzOsqJ8yf0i4JfqEd2jxYDX8/ne+oXBb/QifMn7C4VLWB+EwAtoYEAtFVjoxn+li61uxpcyRfnvtD8LfPVLatbi4Hv6pyr9cvCX+rk+ZN2l4oQML8JgJbQQADaatw4X/hLSbG7ErTkWNUxZW/OVuxzsS0GvmsXXKsXt7+oUxdO2V0q2oD5TQC0hAYC0BZ/+pP57l9dnd3VQJKOVh3Vc5ueU9TcqBYD33X/fZ1e2vmSTl84bXepaAfMbwKgJTQQgNY6ftwMf/v5mlbblJ8tV+aGzKA3Xe7ziz5a/MFiVVRXXPnJ4DjMbwKgJTQQgNZoet7fb39rdzXuUlZZpp+9+7Ogga/fC/20dNdSVdbw97kbML8JgJbQQABa4zvf8YW/W26xu5LId6jikJ5+5+mgge+r//NVvVz0ss7WnLW7VNiA+U0AtIQGAhCqtWvNd/9qa+2uJvIcOHNAP377x0EDX8KvEvTK319RVW2V3aUiDDC/CYCW0EAAQnHypBn+9u61u5rIsO/0Pv1o3Y+CBr7kXydr5T9W6lztObtLRRhifhMALaGBAFyJ12uGv1/+0u5qnMnr9erTU58q468ZQQPf4N8M1msfvabzdeftLhcOwPwmAFpCAwG4kokTfeHvppvsrsQ5vF6vPjn5iX6w9gdBA9/Ql4Zq1cerCHxoE+Y3AdASGgjA5bz9tvnuX02N3dWEL6/Xq9ITpZr2l2lBA99tv7tNa0rX6ELdBbvLRQRgfhMALaGBAARz+rQZ/kpL7a4mvHi9Xn18/GNNfWNq0MA3fMlwvbHnDVXXV9tdLiIQ85sAaAkNBKAlTc/7+6//srsa+3m9XhV/UazJf5ocNPCN+P0Ird27VjX1vFWKjsf8JgBaQgMBaMm//7sv/F1/vd2V2MPr9Wr30d367prvBg18dy27S3/99K+qbeCeOOh8zG8CoCU0EIBLbdxovvtX7ZJPLxu9jdp1ZJcmrJ4QNPB94+Vv6O3P3ibwISwwv1dtYjgAACAASURBVAmAltBAAJqqqDDD3z/+YXc1HafR26gPyj/QI68/EjTwffMP39S7+99VXUOd3eUCzTC/CYCW0EAALmp63t9zz9ldTftq9DZq++fb9Z0/fido4Bv7ylhtOLBB9Y31dpcLXBHzmwBoCQ0E4KIf/MAX/r78Zbsrsa6hsUGFZYV6MO/BoIHvWyu+pU0HNxH44EjMbwKgJTQQAEnassV89++8A+9L3NDYoK2Ht+r+lfcHDXz3r7xfWw5tUUNjg93lApYxvwmAltBAAM6eNcNfUZHd1YSmvrFemw9u1rdWfCto4Hsw70EVlhUS+BCRmN8EQEtoIMDdmp7397Of2V1NcPWN9dpwYIPGvjI2aOD7zh+/o+2fb1ejt9HucoEOx/wmAFpCAwHu9tRTvvAXG2t3JYHqGur07v53Nfr/jQ4a+B55/RF9UP4BgQ+uxPwmAFpCAwHutX27+e5fVZW9tdQ11Gn9vvW6++W7gwa+CasnaNeRXQQ+QMxviQBoCQ0EuFNVlRn+duzo/NevbajVuk/X6a5ldwUNfN9d813tPrpbXq+38wsEwhzzmwBoCQ0EuJPH4wt///f/ds7r1dTXaO3etRrx+xFBA9/kP01W8RfFBD4gBMxvAqAlNBDgPj/9qfnuX0dlrZr6Gr2x5w3dseSOoIFv6htT9fHxjwl8QBswvwmAltBAgLt8+KEZ/s6ebb/nra6v1prSNbrtd7cFDXzT/jJNpSdKCXxAO2B+EwAtoYEA9zh/3gx/BQXWnutC3QWt+niVvvbbrwUNfD9Y+wN9cvITAh/QAZjfBEBLaCDAPeLjfeFvxozWP/Z83Xm99tFrGvybwUEDX8ZfM/TpqU8JfEAnYH4TAC2hgQB3+PnPW3fe37nac1r5j5VK/nVy0MD3o3U/0r7T+zq+eADNML8dFAAXLVqk/v37KzY2VikpKdq8efNlt9+4caNSUlIUGxurm266SS+99FKzbVatWqXk5GTFxMQoOTlZ+fn5raqJBgIi3z/+YYa/ioqWt6mqrdIrf39FA18cGDTw/fjtH+vAmQOdWjuAljG/HRIA8/Ly5PF4tGTJEpWUlCgjI0Pdu3fXoUOHWtx+//796tatmzIyMlRSUqIlS5bI4/Fo1apV/m0KCgoUFRWl7OxslZaWKjs7W9HR0dq2bVvIddFAQGS7cMEMf5s2mevP1pzVy0Uv66v/89Wgge/pd57WoYqW/44CYC/mt0MC4PDhwzVt2rSAdUlJSZozZ06L28+ePVtJSUkB65544gndeeed/p8ffvhhpaWlBWwzduxYPfrooyHXRQMBke1f/sUX/tIfr9TSXUvV74V+QQPfz979mQ5XHLa7ZAAhYH47IADW1tYqKiqq2cezM2fO1MiRI1t8zF133aWZM2cGrMvPz1d0dLTq6uokSTfeeKMWLlwYsM3ChQvVt2/foLXU1NSosrLSv5SVlbm+gYBI9fzPtio247qggS9zQ6Y+r/zc7jIBtAEB0AEBsLy8XIZhaOvWrQHrs7KyNHDgwBYfk5CQoKysrIB1W7dulWEYOnLkiCTJ4/FoxYoVAdusWLFCMTExQWvJzMyUYRjNFjc3EBCpHps4xB/2ouZG6blNz+nI2SN2lwWgHRAAHRQACy658da8efOUmJjY4mMSEhKUnZ0dsG7Lli0yDENHjx6V5AuAK1euDNhm+fLlio2NDVoL7wAC7vHZu3/R0S/98wTAf/zD7nIAtCMCoAMCYDh9BHwpGgiIcH/6k3kVSHm53dUAaCfMbwcEQMl3Ecj06dMD1iUnJ1/2IpDk5OSAddOmTWt2Eci9994bsE1aWhoXgQAI9MILZgjkdx2ICMxvhwTAi7eBWbp0qUpKSjRr1ix1795dBw8elCTNmTNHkyZN8m9/8TYwP/zhD1VSUqKlS5c2uw3M1q1bFRUVpZycHJWWlionJ4fbwABo2RNPmCGwttbuagBYxPx2SACUfDeC7tevn2JiYpSSkqJNTW7KlZ6ertTU1IDtN27cqGHDhikmJkb9+/dv8UbQr7/+uhITE+XxeJSUlKTVq1e3qiYaCHCRESN8AfCqq6TGRrurAWAB89tBATAc0UCAi3i9UlycLwSmpNhdDQALmN8EQEtoIMBl6urMj4K/9z27qwHQRsxvAqAlNBDgQlVVZgicP9/uagC0AfObAGgJDQS41LFjZgh8/XW7qwHQSsxvAqAlNBDgYqWlZggsLLS7GgCtwPwmAFpCAwEu9957Zgjct8/uagCEiPlNALSEBgKgl182Q+DJk3ZXAyAEzG8CoCU0EABJ0s9+ZobACxfsrgbAFTC/CYCW0EAA/B580AyBDQ12VwPgMpjfBEBLaCAAfl6v9NWv+gLgV77i+xlAWGJ+EwAtoYEABGhoMN8FvPdeu6sBEATzmwBoCQ0EoJnqajME/vjHdlcDoAXMbwKgJTQQgBadPm2GwCVL7K4GwCWY3wRAS2ggAEEdPGiGwLfftrsaAE0wvwmAltBAAC5r504zBBYX210NgH9ifhMALaGBAFzRn/5khsDycrurASDmt0QAtIQGAhCShQvNEMjfF4DtmN8EQEtoIAAhe/xxMwTW1tpdDeBqzG8CoCU0EIBWGTHCFwCvukpqbLS7GsC1mN8EQEtoIACt4vVKcXG+EJiSYnc1gGsxvwmAltBAAFqtrs78KPh737O7GsCVmN8EQEtoIABtUlVlhsD58+2uBnAd5jcB0BIaCECbHTtmhsDXX7e7GsBVmN8EQEtoIACWlJSYIbCw0O5qANdgfhMALaGBAFj23ntmCNy3z+5qAFdgfhMALaGBALSL3FwzBJ48aXc1QMRjfhMALaGBALSbn/7UDIEXLthdDRDRmN8EQEtoIADtavx4MwQ2NNhdDRCxmN8EQEtoIADtyuuVbrrJFwC/8hXfzwDaHfObAGgJDQSg3TU0mO8CfutbdlcDRCTmNwHQEhoIQIeorjZD4OzZdlcDRBzmNwHQEhoIQIc5fdoMgUuW2F0NEFGY3wRAS2ggAB3q4EEzBL79tt3VABGD+U0AtIQGAtDhdu40Q2Bxsd3VABGB+U0AtIQGAtAp/vQnMwQeOWJ3NYDjMb8JgJbQQAA6zcKFZgg8e9buagBHY347IACePn1aEydOVM+ePdWzZ09NnDhRZ86cCbp9XV2dZs+ercGDB6tbt266/vrrNWnSJJWXlwdsl5qaKsMwApZHHnmkVbXRQAA61eOPmyGwttbuagDHYn47IACmpaVp8ODBKigoUEFBgQYPHqxx48YF3b6iokKjR4/Wa6+9pj179qiwsFB33HGHbrvttoDtUlNTNXXqVB09etS/VFRUtKo2GghApxsxwhcAo6Kkxka7qwEcifkd5gGwpKREhmFo27Zt/nWFhYUyDEN79uwJ+Xl27NghwzB06NAh/7rU1FRlZGRYqo8GAtDpvF4pLs4XAi/5hy2A0DC/wzwALl26VPHx8c3Wx8fHa9myZSE/z/r169WlS5eAA52amqprrrlGvXv31qBBg/TUU0/pbCvPq6GBANiirs78KHjyZLurARyH+R3mATArK0sJCQnN1ickJCg7Ozuk56iurtZtt92mCRMmBKxfvHix1q9fr+LiYr366qvq37+/Ro8efdnnqqmpUWVlpX8pKytzfQMBsElVlRkC58+3uxrAUQiANgXAzMzMZhdgXLrs3LlTWVlZGjhwYLPHDxgwQM8///wVX6eurk7jx4/XsGHDrniQP/jgAxmGoQ8//LDVdbu5gQDY6NgxMwSuWmV3NYBjEABtCoAnTpxQaWnpZZfq6mpLHwHX1dXp29/+toYMGaKTJ09esSav1yuPx6O8vLyg2/AOIICwU1JihsAm50sDCI4AGOYfAV+8CGT79u3+ddu2bbviRSAXw98tt9yi48ePh/RaxcXFMgxDmzZtCrk+GghAWHjvPTME7t9vdzVA2GN+h3kAlHy3gRkyZIgKCwtVWFioW2+9tdltYBITE5Wfny9Jqq+v1wMPPKAbbrhBu3fvDrjNS+0/75v12Wefae7cudq5c6cOHDigtWvXKikpScOGDVNDQ0PItdFAAMJGbq4ZAkP41ANwM+a3AwLgqVOnNGHCBPXo0UM9evTQhAkTmt0I2jAM5ebmSpIOHDgQ9LzCDRs2SJIOHz6skSNHqlevXoqJidHNN9+smTNn6tSpU62qjQYCEFZ++lMzBF64YHc1QNhifjsgAIYzGghA2Bk/3gyBrfhEA3AT5jcB0BIaCEDY8Xql/v19AfArX/H9DCAA85sAaAkNBCAsNTSY7wJ+61t2VwOEHeY3AdASGghA2KquNkPg7Nl2VwOEFeY3AdASGghAWDt92gyBS5bYXQ0QNpjfBEBLaCAAYe/AATMEvv223dUAYYH5TQC0hAYC4Ag7dpghsLjY7moA2zG/CYCW0EAAHGPNGjMEHjlidzWArZjfBEBLaCAAjrJwoRkCz561uxrANsxvAqAlNBAAx5k61QyB//x6TMBtmN8EQEtoIACOdOedvgAYHS01NtpdDdDpmN8EQEtoIACO5PVKXbv6QuDtt9tdDdDpmN8EQEtoIACOVVdnfhQ8ebLd1QCdivlNALSEBgLgaFVVZghcsMDuaoBOw/wmAFpCAwFwvGPHzBC4apXd1QCdgvlNALSEBgIQEUpKzBC4bZvd1QAdjvlNALSEBgIQMd591wyB+/fbXQ3QoZjfBEBLaCAAESU31wyBp07ZXQ3QYZjfBEBLaCAAEeenPzVD4IULdlcDdAjmNwHQEhoIQEQaP94MgQ0NdlcDtDvmNwHQEhoIQETyeqX+/X0B8IYbfD8DEYT5TQC0hAYCELEaGsx3Ae+7z+5qgHbF/CYAWkIDAYho1dVmCPzJT+yuBmg3zG8CoCU0EICId/q0GQJ//3u7qwHaBfObAGgJDQTAFQ4cMEPg+vV2VwNYxvwmAFpCAwFwjR07zBD40Ud2VwNYwvwmAFpCAwFwlTVrzBB45Ijd1QBtxvwmAFpCAwFwnV/8wgyBZ8/aXQ3QJsxvAqAlNBAAV5oyxQyBtbV2VwO0GvObAGgJDQTAte64wxcAo6Olxka7qwFahflNALSEBgLgWl6vFBvrC4G33253NUCrML8JgJbQQABcra7O/Ch48mS7qwFCxvwmAFpCAwFwvaoqMwQuWGB3NUBImN8EQEtoIACQdOyYGQJXrbK7GuCKmN8EQEtoIAD4p5ISMwRu22Z3NcBlMb8JgJbQQADQxLvvmiFw/367qwGCYn47IACePn1aEydOVM+ePdWzZ09NnDhRZ86cuexj0tPTZRhGwHLHHXcEbFNTU6MZM2aod+/e6tatm+6//36VlZW1qjYaCAAukZtrhsBTp+yuBmgR89sBATAtLU2DBw9WQUGBCgoKNHjwYI0bN+6yj0lPT1daWpqOHj3qX05d8hfRtGnT1KdPH61fv167du3S3XffraFDh6qhoSHk2mggAGjBT39qhsALF+yuBmiG+R3mAbCkpESGYWhbk/NJCgsLZRiG9uzZE/Rx6enpGj9+fND/X1FRIY/Ho7y8PP+68vJyXXXVVVq3bl3I9dFAABDEAw+YIbAV/7AGOgPzO8wD4NKlSxUfH99sfXx8vJYtWxb0cenp6YqPj9e1116rhIQETZkyRV988YX//7/77rsyDEOnT58OeNyQIUP0zDPPhFwfDQQAQXi9Ur9+vgB4ww2+n4EwwfwO8wCYlZWlhISEZusTEhKUnZ0d9HF5eXl68803VVxcrDfeeENDhw7VLbfcopqaGknSihUrFBMT0+xx99xzjx5//PGgz1tTU6PKykr/UlZW5voGAoCgGhrMdwGvcOoO0JkIgDYFwMzMzGYXaVy67Ny5U1lZWRo4cGCzxw8YMEDPP/98yK935MgReTwerV69WlLwADh69Gg98cQTra7bzQ0EAJdVXW2GwJ/8xO5qAEkEQMmmAHjixAmVlpZedqmurm7zR8AtGTBggHJyciS1/SNg3gEEgDY4fdoMgUuX2l0NQABUmH8EfPEikO3bt/vXbdu27YoXgVzq5MmTio2N1R/+8AdJ5kUgr732mn+bI0eOcBEIAHSUAwfMELh+vd3VwOWY32EeACXfbWCGDBmiwsJCFRYW6tZbb212G5jExETl5+dLkqqqqvTUU0+poKBABw4c0IYNGzRixAj16dNHZ8+e9T9m2rRpuuGGG/TOO+9o165dGjVqFLeBAYCOtGOHGQI/+sjuauBizG8HBMBTp05pwoQJ6tGjh3r06KEJEyY0uxG0YRjKzc2VJF24cEFjxozRtddeK4/Ho759+yo9PV2HDx8OeEx1dbVmzJihXr16KS4uTuPGjWu2zZXQQADQSvn5Zgg8csTuauBSzG8HBMBwRgMBQBv893+bIbDJJzNAZ2F+EwAtoYEAoI2mTDFDYG2t3dXAZZjfBEBLaCAAsGD4cF8AjI7mRtHoVMxvAqAlNBAAWOD1SjExvhD4r/9qdzVwEeY3AdASGggALKqrMz8K/v737a4GLsH8JgBaQgMBQDuoqjJD4H/9l93VwAWY3wRAS2ggAGgnR4+aIfCfX9sJdBTmNwHQEhoIANrRxx+bIbDJN0AB7Y35TQC0hAYCgHb27rtmCNy/3+5qEKGY3wRAS2ggAOgAy5aZIfDUKburQQRifhMALaGBAKCDPP20GQIvXLC7GkQY5jcB0BIaCAA60AMPmCGwoUEqLfUtgEXMbwKgJTQQAHQgr1fq188MgV26SFddJX3+ud2VweGY3wRAS2ggAOhAp09L//ZvZgA0DF8AXLDA7srgcMxvAqAlNBAAdKBduwLD38UlMZHvDoYlzG8CoCU0EAB0IK9Xys+XbrzR9/Fv0xC4a5fd1cHBmN8EQEtoIADoBNXVUlaW1LWrFBXlC4A//KHdVcHBmN8EQEtoIADoRJ9/Lk2Y4AuACQl2VwMHY34TAC2hgQDABgUF0mef2V0FHIz5TQC0hAYCAMB5mN8EQEtoIAAAnIf5TQC0hAYCAMB5mN8EQEtoIAAAnIf5TQC0hAYCAMB5mN8EQEtoIAAAnIf5TQC0hAYCAMB5mN8EQEtoIAAAnIf5TQC0hAYCAMB5mN8EQEtoIAAAnIf5TQC0hAYCAMB5mN8EQEtoIAAAnIf5TQC0hAYCAMB5mN8EQEtoIAAAnIf5TQC0hAYCAMB5mN8EQEtoIAAAnIf5TQC0hAYCAMB5mN8OCICnT5/WxIkT1bNnT/Xs2VMTJ07UmTNnLvsYwzBaXBYsWODfJjU1tdn/f+SRR1pVGw0EAIDzML8dEADT0tI0ePBgFRQUqKCgQIMHD9a4ceMu+5ijR48GLMuWLVOXLl20b98+/zapqamaOnVqwHYVFRWtqo0GAgDAeZjfYR4AS0pKZBiGtm3b5l9XWFgowzC0Z8+ekJ9n/PjxGjVqVMC61NRUZWRkWKqPBgIAwHmY32EeAJcuXar4+Phm6+Pj47Vs2bKQnuPYsWOKjo7WihUrAtanpqbqmmuuUe/evTVo0CA99dRTOnv2bKvqo4EAAHAe5neYB8CsrCwlJCQ0W5+QkKDs7OyQnmP+/Pm6+uqrVV1dHbB+8eLFWr9+vYqLi/Xqq6+qf//+Gj169GWfq6amRpWVlf6lrKzM9Q0EAIDTEABtCoCZmZlBL9S4uOzcuVNZWVkaOHBgs8cPGDBAzz//fEivlZiYqBkzZlxxuw8++ECGYejDDz9sdd1ubiAAAJyGAGhTADxx4oRKS0svu1RXV1v+CHjz5s0yDEO7d+++4rZer1cej0d5eXlBt+EdQAAAnI8AGOYfAV+8CGT79u3+ddu2bQv5IpD09HTddtttIb1WcXGxDMPQpk2bQq6PBgIAwHmY32EeACXfbWCGDBmiwsJCFRYW6tZbb212G5jExETl5+cHrKusrFS3bt300ksvNXvOzz77THPnztXOnTt14MABrV27VklJSRo2bJgaGhpCro0GAgDAeZjfDgiAp06d0oQJE9SjRw/16NFDEyZMaHYjaMMwlJubG7Dud7/7neLi4lq8t9/hw4c1cuRI9erVSzExMbr55ps1c+ZMnTp1qlW10UAAADgP89sBATCc0UAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP85sAaAkNBACA8zC/CYCW0EAAADgP89sBAXDevHkaMWKE4uLiFB8fH9JjvF6vMjMzdf3116tr165KTU3VRx99FLBNTU2NZsyYod69e6tbt266//77VVZW1qraaCAAAJyH+e2AAPjMM89o4cKF+tGPfhRyAMzJyVGPHj20evVqFRcX65FHHtH111+vs2fP+reZNm2a+vTpo/Xr12vXrl26++67NXToUDU0NIRcGw0EAIDzML8dEAAvys3NDSkAer1eXXfddcrJyfGvq6mpUXx8vH77299KkioqKuTxeJSXl+ffpry8XFdddZXWrVsXck00EAAAzsP8jsAAuG/fPhmGoV27dgWsf+CBB/Td735XkvTuu+/KMAydPn06YJshQ4bomWeeCfrcNTU1qqys9C+HDx+WYRgqKysLWM/CwsLCwsISvktZWZkMw1BFRUUbEklkiLgAuHXrVhmGofLy8oD1U6dO1ZgxYyRJK1asUExMTLPH3nPPPXr88ceDPndmZqYMw2BhYWFhYWGJgGXfvn2tTCORw5YAGEqQ2rlzZ8BjWhsAjxw5ErB+ypQpGjt2rKTgAXD06NF64okngj73pe8AHjp0SIZh6PDhw7b/a8aOfzm57Z1P9pv9dsPCfrPfblgufoJ35syZUGJLRLIlAJ44cUKlpaWXXaqrqwMeEw4fAV+qstKd5xCw3+y3G7Df7LcbsN/u2u+mIu4j4IsXgcyfP9+/rra2tsWLQF577TX/NkeOHOEikBCx3+y3G7Df7LcbsN/u2u+mwj4AHjp0SEVFRZo7d66+9KUvqaioSEVFRaqqqvJvk5iYqPz8fP/POTk5io+PV35+voqLi/XYY4+1eBuYG264Qe+884527dqlUaNGcRuYELHf7LcbsN/stxuw3+7a76bCPgCmp6e3eI7ghg0b/NsYhqHc3Fz/zxdvBH3dddcpNjZWI0eOVHFxccDzVldXa8aMGerVq5fi4uI0btw4HT58uFW11dTUKDMzUzU1NVZ20XHYb/bbDdhv9tsN2G937XdTYR8AAQAA0L4IgAAAAC5DAAQAAHAZAiAAAIDLEAABAABchgB4GfPmzdOIESMUFxcX0j0IJfMK5Ouvv15du3ZVamqqPvroo4BtampqNGPGDPXu3VvdunXT/fffr7Kyso7YhTY5ffq0Jk6cqJ49e6pnz56aOHHiFe+WHuwbXRYsWODfJjU1tdn/f+SRRzp6d0LWlv1u6Sr1O+64I2CbSDvedXV1mj17tgYPHqxu3brp+uuv16RJk5p9/WK4He9Fixapf//+io2NVUpKijZv3nzZ7Tdu3KiUlBTFxsbqpptu0ksvvdRsm1WrVik5OVkxMTFKTk4OuB1VuGjNfq9evVqjR4/WNddcox49eujOO+9sdm/U3NzcFn/XL715v91as98bNmxocZ9KS0sDtou04x3sLhuDBg3yb+OE471p0yaNGzdO119/vQzD0Jo1a674mEj5/baCAHgZzzzzjBYuXKgf/ehHIQfAnJwc9ejRQ6tXr1ZxcbEeeeSRFu9B2KdPH61fv167du3S3Xff3ep7EHaktLQ0DR48WAUFBSooKNDgwYM1bty4yz7m6NGjAcuyZcvUpUuXgO9ZTE1N1dSpUwO2C6cv4m7LfqenpystLS1gn06dOhWwTaQd74qKCo0ePVqvvfaa9uzZo8LCQt1xxx267bbbArYLp+Odl5cnj8ejJUuWqKSkRBkZGerevbsOHTrU4vb79+9Xt27dlJGRoZKSEi1ZskQej0erVq3yb1NQUKCoqChlZ2ertLRU2dnZio6O1rZt2zprt66otfudkZGh+fPna8eOHdq7d6+efvppeTyegG9Wys3NVc+ePZv9zoeT1u73xQD4ySefBOxT09/RSDzeFRUVAftbVlamXr16KTMz07+NE473W2+9pf/4j//Q6tWrQwqAkfL7bRUBMASt/RaSnJwc/7qampoWv4UkLy/Pv015eXmrv4Wko5SUlMgwjIAmLywslGEY2rNnT8jPM378eI0aNSpgXWpqqjIyMtqt1vbU1v1OT0/X+PHjg/5/txzvHTt2yDCMgEETTsd7+PDhmjZtWsC6pKQkzZkzp8XtZ8+eraSkpIB1TzzxhO68807/zw8//LDS0tICthk7dqweffTRdqrautbud0sGDRqkuXPn+n8O9e9DO7V2vy8GwMu98+2G471mzRp16dJFBw8e9K9zwvFuKpQAGCm/31YRAEMQjt9D3FGWLl3a4r7Gx8dr2bJlIT3HsWPHFB0drRUrVgSsT01N1TXXXKPevXtr0KBBeuqppwLeGbVTW/c7PT1d8fHxuvbaa5WQkKApU6boiy++8P9/NxxvSVq/fr26dOkScFf9cDnetbW1ioqKavbxzcyZMzVy5MgWH3PXXXdp5syZDonC5QAAB4pJREFUAevy8/MVHR2turo6SdKNN96ohQsXBmyzcOFC9e3btx2rb7u27PelGhsbdeONN+rFF1/0r8vNzVVUVJT69u2rPn366L777mv2d56d2rLfFwNg//79dd1112nUqFF67733ArZxw/EeN26c7rnnnoB14X68LxVKAIyE3+/2QAAMQagBcOvWrTIMo9m5UFOnTtWYMWMkSStWrFBMTEyzx95zzz16/PHH26dgC7KyspSQkNBsfUJCgrKzs0N6jvnz5+vqq69udo7I4sWLtX79ehUXF+vVV19V//79NXr06Hap26q27ndeXp7efPNNFRcX64033tDQoUN1yy23+O8u74bjXV1drdtuu00TJkwIWB8ux7u8vFyGYWjr1q0B67OysjRw4MAWH5OQkKCsrKyAdRd/v48cOSJJ8ng8zf6RE+x426Et+32pBQsWqFevXgH/qCksLNQrr7yi3bt3a/PmzXrooYcUFxenvXv3tmv9bdWW/d6zZ48WL16sDz/8UAUFBZo+fbq6dOmiTZs2+beJ9ON95MgRRUVF6bXXXgtYH+7H+1KhBMBI+P1uD64LgJmZmUEvWLi47Ny5M+AxrQ2AFxvooilTpmjs2LGSgjfQ6NGj9cQTT1jYs8sLdb+D/WUxYMAAPf/88yG9VmJiombMmHHF7T744AMZhqEPP/yw1fsTqs7cb8n3l6jH49Hq1aslRf7xrqur0/jx4zVs2LArfqdmZxzvllwcjAUFBQHr582bp8TExBYf01IA3rJliwzD8J//5PF4tHLlyoBtli9frtjY2Hasvu3ast9NrVy5Ut26ddP69esvu11jY6OGDh2qJ5980lK97cXqfl80btw43X///f6fI/14Z2dnq3fv3qqtrb3sduF2vC8VagB0+u93e3BdADxx4oRKS0svu1z6zlUkfAQc6n5b/Uhw8+bNMgxDu3fvvuK2Xq+32flx7a2z9rupAQMG+M8DjeTjXVdXp29/+9saMmSITp48ecWaOuN4t4SPgFv/kWBeXp7i4uL05ptvhvRaU6ZMaXa+lF3a46NQyRecmp4nFsnH2+v1asCAAZo1a1ZIrxVOx/tSfAQcOtcFwLZo7UUg8+fP96+rra1t8SKQpm+zHzlyJOwuCti+fbt/3bZt20K+KCA9Pb3Z1aDBFBcXyzCMgI9Z7GJ1vy86efKkYmNj9Yc//EFS5B7vi+Hvlltu0fHjx0N6LTuP9/DhwzV9+vSAdcnJyZe9CCQ5OTlg3bRp05qdJH7vvfcGbJOWlhZWJ4m3dr8l3zt/Xbt2DelWGpLv773bb79dkydPtlRre2rLfl/qoYce0t133+3/OVKPt2SeA1lcXHzF1wjH491UqBeBRMLvt1UEwMs4dOiQioqKNHfuXH3pS19SUVGRioqKVFVV5d8mMTEx4F9cOTk5io+PV35+voqLi/XYY4+1eBuYG264Qe+884527dqlUaNGhd1tQYYMGaLCwkIVFhbq1ltvbXZbkEv3W5IqKyvVrVu3Fu+n9Nlnn2nu3LnauXOnDhw4oLVr1yopKUnDhg1z7H5XVVXpqaeeUkFBgQ4cOKANGzZoxIgR6tOnT0Qf7/r6ej3wwAO64YYbtHv37oBbQ1z8+CjcjvfF22MsXbpUJSUlmjVrlrp37+6/2nHOnDmaNGmSf/uLt4n44Q9/qJKSEi1durTZbSK2bt2qqKgo5eTkqLS0VDk5OWF3m4jW7vfKlSsVHR2tRYsWBb19z7PPPqt169Zp3759Kioq0uTJkxUdHR3wjwi7tXa/X3jhBa1Zs0Z79+7VRx99pDlz5sgwDP+pHFJkHu+LJk6c2Oz+pRc54XhXVVX557NhGFq4cKGKior8dyWI1N9vqwiAlxHsJpkbNmzwb2MYhnJzc/0/X7wR9HXXXafY2FiNHDmy2b+qqqurNWPGDPXq1UtxcXEaN26cDh8+3El7dWWnTp3ShAkT1KNHD/Xo0UMTJkxodnuES/dbkn73u98pLi6uxXu9HT58WCNHjlSvXr0UExOjm2++WTNnzmx2zzw7tXa/L1y4oDFjxujaa6+Vx+NR3759lZ6e3uxYRtrxPnDgQNDzCi/+boTj8V60aJH69eunmJgYpaSkBLwTmZ6ertTU1IDtN27cqGHDhikmJkb9+/dv8R82r7/+uhITE+XxeJSUlBQQGMJFa/a7pZt3G4ah9PR0/zazZs1S3759FRMTo2uvvVZjxoxpdt5ZOGjNfs+fP18333yzunbtqquvvlpf//rXtXbt2mbPGWnHW/J9ShEXF6fFixe3+HxOON7BbuR9sW8j+ffbCgIgAACAyxAAAQAAXIYACAAA4DIEQAAAAJchAAIAALgMARAAAMBlCIAAAAAuQwAEAABwGQIgAACAyxAAAQAAXIYACAAA4DIEQAAAAJchAAIAALgMARAAAMBlCIAAAAAuQwAEAABwGQIgAACAyxAAAQAAXIYACAAA4DIEQAAAAJchAAIAALgMARAAAMBlCIAAAAAuQwAEAABwGQIgAACAyxAAAQAAXIYACAAA4DIEQAAAAJchAAIAALgMARAAAMBlCIAAAAAuQwAEAABwmf8fBu3QswCELocAAAAASUVORK5CYII=\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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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width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-1, 1)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%pylab notebook\n",
    "\n",
    "# Just show our two vectors\n",
    "a = np.array([0.5, 0.9])\n",
    "b = np.array([0.4, -0.6])\n",
    "plt.arrow(0, 0, *a, head_width=0.02, label=r'$\\vec{a}$', color='b')\n",
    "plt.arrow(0, 0, *b, head_width=0.02, label=r'$\\vec{b}$', color='r')\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "\n",
    "# Move one of our vectors to have it's origin at the end of another vector\n",
    "plt.figure()\n",
    "plt.arrow(0, 0, *a, head_width=0.02, label=r'$\\vec{a}$', color='b')\n",
    "plt.arrow(0, 0, *b, head_width=0.02, label=r'$\\vec{b}$', color='r')\n",
    "plt.arrow(*(*a, *b), head_width=0.02, color='r')\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "\n",
    "# We can see that the final position is the same as the sum of the vectors\n",
    "plt.figure()\n",
    "plt.arrow(0, 0, *a, head_width=0.02, label=r'$\\vec{a}$', color='b')\n",
    "plt.arrow(0, 0, *b, head_width=0.02, label=r'$\\vec{b}$', color='r')\n",
    "plt.arrow(0, 0, *(a+b), head_width=0.02, label=r'$\\vec{a}+\\vec{b}$', color='g')\n",
    "plt.arrow(*(*a, *b), head_width=0.02, color='r')\n",
    "\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "\n",
    "# To verify commutivity, we see that switching the vectors gives the same result\n",
    "plt.figure()\n",
    "plt.arrow(0, 0, *a, head_width=0.02, label=r'$\\vec{a}$', color='b')\n",
    "plt.arrow(0, 0, *b, head_width=0.02, label=r'$\\vec{b}$', color='r')\n",
    "plt.arrow(0, 0, *(a+b), head_width=0.02, label=r'$\\vec{a}+\\vec{b}$', color='g')\n",
    "plt.arrow(*(*a, *b), head_width=0.02, color='r')\n",
    "plt.arrow(*(*b, *a), head_width=0.02, color='b')\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "subtracting vectors can be represented by drawing a vector from the end of the second vector to the end of the first vector and then placing the resulting vector at the origin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
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       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
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       "    } 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",
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       "        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",
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       "\n",
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       "\n",
       "    this.root = $('<div/>');\n",
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       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
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       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
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       "            fig.send_message(\"refresh\", {});\n",
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       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
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       "                // 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",
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       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
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       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-1, 1)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%pylab notebook\n",
    "\n",
    "a = np.array([0.5, 0.2])\n",
    "b = np.array([0.4, -0.6])\n",
    "plt.arrow(0, 0, *a, head_width=0.02, label=r'$\\vec{a}$', color='b')\n",
    "plt.arrow(0, 0, *b, head_width=0.02, label=r'$\\vec{b}$', color='r')\n",
    "plt.arrow(*(*b, *(a-b)), head_width=0.02, label=r'$\\vec{a}+\\vec{b}$', color='g')\n",
    "plt.arrow(0, 0, *(a-b), head_width=0.02, color='g')\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mutplication ###\n",
    "\n",
    "You can multiply a vector by a scalar because multiplication is *distributive*.\n",
    "\n",
    "$c \\vec{a} = <c a_{1}, c a_{2}, c a_{3}, ...>$ \n",
    "\n",
    "You can also multiply vectors by one another, though there are two ways to do this.  \n",
    "\n",
    "### Dot Product\n",
    "\n",
    "There is the *dot product* (also referred to as the scalar product).  This operation gives back a scalar quantity.  The dot product is the sum of all of the elements in each vector multiplied by one another.\n",
    "\n",
    "$\\boxed{\\vec{a} \\cdot \\vec{b} = a_{1}b_{1} + a_{2}b_{2} + a_{3}b_{3} + ...}$\n",
    "\n",
    "We can actually use this to get the magnitude of a vector, as the magnitude of a vector is just the square root of the vector dotted with itself.\n",
    "\n",
    "$\\boxed{||\\vec{a}|| = \\sqrt{\\vec{a} \\cdot \\vec{a}}}$\n",
    "\n",
    "The dot product has a geometric interpretation.  Let's do an example with some *orthogonal unit vectors*.\n",
    "\n",
    "$\\hat{x} \\cdot \\hat{y} = <1, 0, 0, ...> \\cdot <0, 1, 0, ...> = 0\\times1+0\\times1+0\\times0 + ... = 0$\n",
    "\n",
    "The dot product is zero! This is true for the dot product between any two orthogonal vectors.  We're essentially multiplying how much of a vector is along a certain axis by how much another vector is along a certain axis.  What the dot product does is essentially multiply the amount of one vector that is in the direction of the other vector.  Or another way of wording this, it multiplies the *projection* of one vector onto another vector. We can see this visually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        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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AACwD/PbggDY0NCgiIgIFRQU+O1PT0/X5MmTg7qP5uZmDR8+XL/61a98+/Ly8hQREaERI0Zo2LBhmjFjht8rhIHU19ertrbWt1VWVrq+gQAAsA0B0IIAeOLECTmOo8LCQr/9WVlZGj16dFD3sWLFCg0aNEinT5/27SsuLtZbb72l/fv3a8eOHXr88ccVHR2tQ4cOdXo/mZmZAT836OYGAgDANgRAiwJgUVGR3/5ly5YpPj7+mrdfv369+vXrp61bt151XXNzs8aPH6/nnnuu0zW8AggAgP0IgBYEQJO3gPPz8xUdHa33338/qMeaN2+eUlJSgq6NBgIAwD7MbwsCoNR6EsiCBQv89iUmJl71JJD169erb9++2rx5c1CP0dLSonvvvVdz584Nui4aCAAA+zC/LQmAbZeBWbNmjcrKyrRo0SL1799fR48elSQtWbJEc+bM8a1fv369IiMjtXLlSr9LvNTU1PjWvPrqq9qyZYsOHz6skpISzZ07V5GRkdq1a1fQddFAAADYh/ltSQCUWi8EPXLkSHm9XiUlJWn79u2+f0tLS1NycrLv5+Tk5IAna6SlpfnWLFq0SCNGjJDX69WQIUM0ffr0Dp8zvBYaCAAA+zC/LQqA4YgGAoDeoaVFunRJOnNGqqiQDhyQdu2SPv1UuuKLpNALML8JgEZoIACwX2GhdNNNkuN0vh0+HOoq0Z2Y3wRAIzQQANjvvfckx9klx/mvDsEvKkpasUJqbAx1lehOzG8CoBEaCADsdP689OMfS45zWo7j/dtnxV+W40h9+rSGv2nTpCNHQl0pegLzmwBohAYCAHscOCClpl759u4/XXay4DH16SPdcou0fn3r5wLROzG/CYBGaCAACF+NjdK770p/93dXhr535Thf06xZ/67duw+ooqJCkpSdLf2P/yFVV4e2bvQ85jcB0AgNBADh5cwZ6cUXA5/IMXZshd+lwTZt2hTqchEizG8CoBEaCABCq6VF2rtXmjo1cOj7/velI0ca9C//8i++4Of1enXq1KlQl44QYn4TAI3QQABw49XXS//xH9LNN3cMfFFR0tq1rdf0k6TGxkYdPXpUX/va1+Q4jj755JPQFo+wwPwmABqhgQDgxjh5UkpPD/wq3+TJrRdtvvykjdLSUt8rfl988YW++uqr0BWPsMP8JgAaoYEAoGe0tEhFRdKkSYFD3//8n9Lp0x1vd+HCBd11112+8JeUlKQLFy7c+ANAWGN+EwCN0EAA0H0uXZLeeCPwt3K0XZqloaHz2xcXF/ud5LF3794bVzyswvwmABqhgQDAzPHj0rx5gV/le+ghaf/+a1+Pr6qqSvv379d7772nUaNGKTc3Vy1cxA9XwfwmABqhgQCga5qbpU8/lcaNCxz6/tf/Cv46fGfPntUtt9wix3H093//9z1bOHoV5jcB0AgNBADXdvGi9ItfBA58w4ZJmzd37bt2m5qatGDBAr+3ew8dOtRzB4Beh/lNADRCAwFAYIcPS7NmBQ59//2/S+Xl13/f3/72t33B76233uq+ouEazG8CoBEaCABaNTVJ//mf0qhRgUPfa69JNTXXf/+VlZXKyMjQe++9p40bN2rVqlVq7MrLhsBlmN8EQCM0EAA3q6lp/f7cQIEvLq41EDY1mT1GQ0ODHnvsMd8rfqtXr+6e4uFqzG8CoBEaCIDblJe3voUbKPTNmtX61m93+c1vfuP3Ob8PP/yw++4crsb8JgAaoYEA9HaNjVJBgfT1rwcOfb/8ZetJHt2turraF/zS09PVZPpSInAZ5jcB0AgNBKA3qq5uvRxLoMA3blzrZVyam7v/cf/617/qH/7hH/SNb3xDhYWFqqioUF1dXfc/EFyP+U0ANEIDAegNWlpaL7g8fXrg0Pf0060XbO65x2/RihUr/N7uPXXqVM89IFyP+U0ANEIDAbBVQ0PrV6v9t//WMfDddFPrV7L99a89X8cf//hHv+CXnZ3Nt3igxzG/CYBGaCAANjl9WnrhhcCv8k2aJBUVXftr17pLS0uL/vKXv+jtt9+W4ziaMGGC/vKXv9yYB4frMb8JgEZoIADhrKVF2rVLeuCBwKEvI0M6efLG1tTc3Kwf/OAHchxHycnJqqurU3NPfKAQuArmNwHQCA0EINzU1Ulr1kheb8fAd/PN0n/8h1RfH5rafv/73/u93bt+/frQFALXY34TAI3QQADCwYkT0oIFgV/lmzpV2rv3xr2125n09HRf8JsxY4bqQ5VCATG/JQKgERoIQCg0N0s7dkj33BM49C1ZIp05E+oqpcbGRn388cfav3+/srKy9MADD+jYsWOhLgtgfosAaIQGAnCj/OUv0sqVgQPf3/2d9Nvftl60OVy88847vlf8fvazn4W6HMAP85sAaIQGAtCTjh6V0tICh77UVOnAgVBX2NGXX37p9zm/efPm6auvvgp1WYAf5jcB0AgNBKA7NTVJH30kJSYGDn0//rF0/nyoq+xc2/+JjuNowIAB+vOf/xzqkoCAmN8EQCM0EABTtbXST38aOPDFxkr/+39L4fwCWktLi15//XX98Ic/1Oeff67f/va32rNnT6jLAq6K+U0ANEIDAbgehw5J//zPgUPfE0+0/rsNSkpK+Po2WIn5TQA0QgMBCMZXX7W+kjdyZODQ99Oftr4SaIva2lolJib6gl98fDz/D8IqzG8CoBEaCEBnzp2Tli4NHPjGjJG2bm29nIuNfv3rX/vC3/79+0NdDtBlzG8CoBEaCECblhaptFSaMSNw6PvXf5UqKkJd5fXbvn2776ze48eP609/+pNaQn11aeA6Mb8tCoArV65UbGysoqKilJSUpB07dlx1/WeffaakpCRFRUXpjjvu0Ouvv95hzcaNG5WYmCiv16vExEQVFBR0qSYaCHC3hobW6+/demvg0LdyZev1+2x25swZ3Xzzzb5X/F566aVQlwQYY35bEgDz8/Pl8Xi0evVqlZWVKSMjQ/379+/0ivJHjhxRv379lJGRobKyMq1evVoej0cbN270rSkqKlJERISys7NVXl6u7OxsRUZGaufOnUHXRQMB7nPmjPSjHwUOfPfe2/oNHba+tXulX/7yl34neRw+fDjUJQHdgvltSQCcOHGi5s+f77cvISFBS5YsCbh+8eLFSkhI8Nv37LPPatKkSb6fn3jiCaWkpPiteeihh/TUU08FXRcNBPR+LS3SF19IU6YEDn3f/770pz+Fusrudf78eZ0+fVrf+9735DiO8vPzQ10S0K2Y3xYEwIaGBkVERHR4ezY9PV2TJ08OeJtvfetbSk9P99tXUFCgyMhINf7tu5KGDx+u3NxcvzW5ubkaMWJEp7XU19ertrbWt1VWVrq+gYDeqnBrkSaO/lWHwNe3r7R2rXTpUqgr7H7Hjh3zvdr3b//2b3zGD70WAdCCAHjixAk5jqPCwkK//VlZWRo9enTA28TFxSkrK8tvX2FhoRzHUVVVlSTJ4/Fo3bp1fmvWrVsnr9fbaS2ZmZl+b4e0bW5uIKC3euy7Y+S86ijpzmxNnizt2tX6amBvVF9frxkzZvj+T/N6vTp9+nSoywJ6DAHQogBYVFTkt3/ZsmWKj48PeJu4uDhlZ2f77fvDH/4gx3F08uRJSa0BcP369X5r3n77bUVFRXVaC68AAu6xZcObcl515Lzq6P/7fOO1b2Cpc+fO+f1B+9FHH4W6JKDHEQAtCIDh9BbwlWggoHf73Zsv+kLgiUN7Q11Ot/ryyy/1+9//Xp9//rkWLFigl19+Wc295ewV4BqY3xYEQKn1JJAFCxb47UtMTLzqSSCJiYl+++bPn9/hJJCHH37Yb01KSgongQDwk5sz0xcCa/9cGepyjF28eFHf+MY3fK/4nTlzJtQlATcc89uSANh2GZg1a9aorKxMixYtUv/+/XX06FFJ0pIlSzRnzhzf+rbLwDz//PMqKyvTmjVrOlwGprCwUBEREcrJyVF5eblycnK4DAyAgJ75YaIvBDZcuhjqcq5LS0uLfvKTn/i93btnz55QlwWEBPPbkgAotV4IeuTIkfJ6vUpKStL27dt9/5aWlqbk5GS/9Z999pkmTJggr9er2NjYgBeCfvfddxUfHy+Px6OEhARt2rSpSzXRQIB73J9xs5xXHd30iqPmpq9CXU6XvfHGG77gt2LFCs7whasxvy0KgOGIBgLco6W5WdEvt74KmLQoOtTlBKW6ulpPPfWUVqxYoZ07d2rDhg3661//GuqygJBjfhMAjdBAgLs01v3V91bwv74wKtTldKqpqUnPPfec7xW/rny2GXAD5jcB0AgNBLjPxeqTvhC4fNnD177BDfbxxx/7fc7vN7/5TahLAsIO85sAaIQGAtzp1JFSXwh8999/EOpyJLWe5NHU1KQpU6bIcRz90z/9kxoaGkJdFhCWmN8EQCM0EOBeZbve94XA4v9cHbI6Ghoa9O1vf1uO4+jNN99UdXW1vvrKvpNUgBuJ+U0ANEIDAe72acHPfSHw8P5tN/zx33rrLb+3e/ft23fDawBsxPwmABqhgQD85v+d5wuBZysP3ZDHPHfunPr16+cLft///vfV1NR0Qx4b6A2Y3wRAIzQQAEl6+ZX/xxcCL9VW99jjNDU16fTp0/riiy80evRofe1rX9PZs2d77PGA3or5TQA0QgMBaPPY80N9IbCpsXtPvmhpadHPf/5z3yt+x48f79b7B9yG+U0ANEIDAWjT0tysO16IlPOqo6//8Ca1NDd3y/1+8cUXfp/zW7ZsGd/iARhifhMAjdBAAC7X1NjgexXw4UVDjO8vPz/fF/zGjRunixft/B5iINwwvwmARmggAFequ3jeFwJ/+NI3u3z75uZmvffee/rwww/1u9/9Tt/5zndUWlraA5UC7sX8JgAaoYEABHKu6ogvBK7+5XeDvt3l3+Ixbdq0HqwQcDfmNwHQCA0EoDMVpZ/7QuBHv33tqmtPnTolj8fjC38pKSmqq6u7QZUC7sP8JgAaoYEAXM2erW/6QmDpHwo6XXfXXXf5wl9FRcWNKxBwKeY3AdAIDQTgWn735ou+EFj1X+3f1PHb3/5W3/zmN/Xee++pqKhIZWVlIawScBfmNwHQCA0EIBi5r830hcB9u3f4Xdblk08+CXV5gOswvwmARmggAMH61xdGyxnTHvycSEc7D+4MdVmAKzG/CYBGaCAAwThy7oiGZg9tD39pjiKWRuiVT18JdWmAKzG/CYBGaCAAwfg/p/6PIn8cqT6v9pGT6fjeDh6eO5xv9QBCgPlNADRCAwEI1qGzhzRj3Qw5rzq66ZX2EPj5sc9DXRrgOsxvAqARGghAV235ry2K++WdvgA47ycTQ10S4DrMbwKgERoIwPVobGrULz/6iW5+0dGU7zrSu++GuiTAVZjfBEAjNBAAE2dKClUX6UiOIxUXh7ocwDWY3wRAIzQQAGOfftoaAB1HOnw41NUArsD8JgAaoYEAdIu8vPYQePZsqKsBej3mNwHQCA0EoNu89FJ7CLx0KdTVAL0a85sAaIQGAtCtZs5sD4FNTaGuBui1mN8EQCM0EIBu1dIi3XFHawD8+tdbfwbQ7ZjfBEAjNBCAbtfU1P4q4D/+Y6irAXol5jcB0AgNBKBH1NW1h8DFi0NdDdDrML8JgEZoIAA95ty59hC4enWoqwF6FeY3AdAIDQSgRx092h4CP/oo1NUAvQbzmwBohAYC0OP27GkPgaWloa4G6BWY3wRAIzQQgBvid79rD4FVVaGuBrAe85sAaIQGAnDD5Oa2h8ALF0JdDWA15rcFAfDcuXOaPXu2Bg4cqIEDB2r27Nk6f/58p+sbGxu1ePFijR07Vv369dPQoUM1Z84cnThxwm9dcnKyHMfx25588sku1UYDAbihnnmmPQQ2NIS6GsBazG8LAmBKSorGjh2roqIiFRUVaezYsUpNTe10fU1NjaZNm6YNGzbo4MGDKi4u1n333ad77rnHb11ycrKefvppnTx50rfV1NR0qTYaCMANd//9rQEwIkJqbg51NYCVmN9hHqtrTNoAAB2xSURBVADLysrkOI527tzp21dcXCzHcXTw4MGg72f37t1yHEfHjh3z7UtOTlZGRoZRfTQQgBuupUWKjm4NgVf8YQsgOMzvMA+Aa9asUUxMTIf9MTExWrt2bdD3s3XrVvXp08fviU5OTtatt96qwYMHa8yYMXrhhRd0oYufq6GBAIREY2P7W8Fz54a6GsA6zO8wD4BZWVmKi4vrsD8uLk7Z2dlB3UddXZ3uuecezZo1y2//qlWrtHXrVpWWluqdd95RbGyspk2bdtX7qq+vV21trW+rrKx0fQMBCJGLF9tD4PLloa4GsAoBMEQBMDMzs8MJGFdue/bsUVZWlkaPHt3h9qNGjdJrr712zcdpbGzUzJkzNWHChGs+yV988YUcx9HevXu7XLebGwhACJ061R4CN24MdTWANQiAIQqAZ86cUXl5+VW3uro6o7eAGxsb9dhjj2ncuHE6e/bsNWtqaWmRx+NRfn5+p2t4BRBA2Ckraw+Bl31eGkDnCIBh/hZw20kgu3bt8u3buXPnNU8CaQt/d911l/785z8H9VilpaVyHEfbt28Puj4aCEBY+PTT9hB45EioqwHCHvM7zAOg1HoZmHHjxqm4uFjFxcW6++67O1wGJj4+XgUFBZKkr776So8++qhuv/127d+/3+8yLw1/u27Wl19+qaVLl2rPnj2qqKjQBx98oISEBE2YMEFNTU1B10YDAQgbeXntITCIdz0AN2N+WxAAq6urNWvWLA0YMEADBgzQrFmzOlwI2nEc5eXlSZIqKio6/Vzhtm3bJEnHjx/X5MmTNWjQIHm9Xt15551KT09XdXV1l2qjgQCElZdeag+Bly6FuhogbDG/LQiA4YwGAhB2Zs5sD4FdeEcDcBPmNwHQCA0EIOy0tEixsa0B8Otfb/0ZgB/mNwHQCA0EICw1NbW/CviP/xjqaoCww/wmABqhgQCErbq69hC4eHGoqwHCCvObAGiEBgIQ1s6daw+Bq1eHuhogbDC/CYBGaCAAYa+ioj0EfvRRqKsBwgLzmwBohAYCYIXdu9tDYGlpqKsBQo75TQA0QgMBsMbmze0hsKoq1NUAIcX8JgAaoYEAWCU3tz0EXrgQ6mqAkGF+EwCN0EAArPP00+0h8G9fjwm4DfObAGiEBgJgpUmTWgNgZKTU3BzqaoAbjvlNADRCAwGwUkuL1Ldvawi8995QVwPccMxvAqARGgiAtRob298Knjs31NUANxTzmwBohAYCYLWLF9tD4IoVoa4GuGGY3wRAIzQQAOudOtUeAjduDHU1wA3B/CYAGqGBAPQKZWXtIXDnzlBXA/Q45jcB0AgNBKDX+OST9hB45EioqwF6FPObAGiEBgLQq+TltYfA6upQVwP0GOY3AdAIDQSg13nppfYQeOlSqKsBegTzmwBohAYC0CvNnNkeApuaQl0N0O2Y3wRAIzQQgF6ppUWKjW0NgLff3voz0IswvwmARmggAL1WU1P7q4AzZoS6GqBbMb8JgEZoIAC9Wl1dewj80Y9CXQ3QbZjfBEAjNBCAXu/cufYQ+O//HupqgG7B/CYAGqGBALhCRUV7CNy6NdTVAMaY3wRAIzQQANfYvbs9BB44EOpqACPMbwKgERoIgKts3tweAquqQl0NcN2Y3wRAIzQQANf5+c/bQ+CFC6GuBrguzG8CoBEaCIArzZvXHgIbGkJdDdBlzG8CoBEaCIBr3XdfawCMjJSam0NdDdAlzG8CoBEaCIBrtbRIUVGtIfDee0NdDdAlzG8CoBEaCICrNTa2vxU8d26oqwGCxvwmABqhgQC43sWL7SFwxYpQVwMEhflNADRCAwGApFOn2kPgxo2hrga4JuY3AdAIDQQAf1NW1h4Cd+4MdTXAVTG/CYBGaCAAuMwnn7SHwCNHQl0N0CnmtwUB8Ny5c5o9e7YGDhyogQMHavbs2Tp//vxVb5OWlibHcfy2++67z29NfX29Fi5cqMGDB6tfv3565JFHVFlZ2aXaaCAAuEJeXnsIrK4OdTVAQMxvCwJgSkqKxo4dq6KiIhUVFWns2LFKTU296m3S0tKUkpKikydP+rbqK/4jmj9/voYNG6atW7dq3759mjJlisaPH6+mpqaga6OBACCAl15qD4GXLoW6GqAD5neYB8CysjI5jqOdl32epLi4WI7j6ODBg53eLi0tTTNnzuz032tqauTxeJSfn+/bd+LECd10003asmVL0PXRQADQiUcfbQ+BXfjDGrgRmN9hHgDXrFmjmJiYDvtjYmK0du3aTm+XlpammJgYDRkyRHFxcZo3b55Onz7t+/dPPvlEjuPo3LlzfrcbN26cXnnllaDro4EAoBMtLdLIka0B8PbbW38GwgTzO8wDYFZWluLi4jrsj4uLU3Z2dqe3y8/P1/vvv6/S0lK99957Gj9+vO666y7V19dLktatWyev19vhdg8++KCeeeaZTu+3vr5etbW1vq2ystL1DQQAnWpqan8V8Bof3QFuJAJgiAJgZmZmh5M0rtz27NmjrKwsjR49usPtR40apddeey3ox6uqqpLH49GmTZskdR4Ap02bpmeffbbLdbu5gQDgqurq2kPgj34U6moASQRAKUQB8MyZMyovL7/qVldXd91vAQcyatQo5eTkSLr+t4B5BRAArsO5c+0hcM2aUFcDEAAV5m8Bt50EsmvXLt++nTt3XvMkkCudPXtWUVFRevPNNyW1nwSyYcMG35qqqipOAgGAnlJR0R4Ct24NdTVwOeZ3mAdAqfUyMOPGjVNxcbGKi4t19913d7gMTHx8vAoKCiRJFy9e1AsvvKCioiJVVFRo27Ztuv/++zVs2DBduHDBd5v58+fr9ttv18cff6x9+/Zp6tSpXAYGAHrS7t3tIfDAgVBXAxdjflsQAKurqzVr1iwNGDBAAwYM0KxZszpcCNpxHOXl5UmSLl26pOnTp2vIkCHyeDwaMWKE0tLSdPz4cb/b1NXVaeHChRo0aJCio6OVmpraYc210EAA0EUFBe0hsKoq1NXApZjfFgTAcEYDAcB1+NnP2kPgZe/MADcK85sAaIQGAoDrNG9eewhsaAh1NXAZ5jcB0AgNBAAGJk5sDYCRkVwoGjcU85sAaIQGAgADLS2S19saAr/5zVBXAxdhfhMAjdBAAGCosbH9reDvfS/U1cAlmN8EQCM0EAB0g4sX20PgT38a6mrgAsxvAqARGggAusnJk+0h8G9f2wn0FOY3AdAIDQQA3ej//t/2EHjZN0AB3Y35TQA0QgMBQDf75JP2EHjkSKirQS/F/CYAGqGBAKAHrF3bHgKrq0NdDXoh5jcB0AgNBAA95MUX20PgpUuhrga9DPObAGiEBgKAHvToo+0hsKlJKi9v3QBDzG8CoBEaCAB6UEuLNHJkewjs00e66SbpT38KdWWwHPObAGiEBgKAHnTunPTP/9weAB2nNQCuWBHqymA55jcB0AgNBAA9aN8+//DXtsXH893BMML8JgAaoYEAoAe1tEgFBdLw4a1v/14eAvftC3V1sBjzmwBohAYCgBugrk7KypL69pUiIloD4PPPh7oqWIz5TQA0QgMBwA30pz9Js2a1BsC4uFBXA4sxvwmARmggAAiBoiLpyy9DXQUsxvwmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/PbggB47tw5zZ49WwMHDtTAgQM1e/ZsnT9//qq3cRwn4LZixQrfmuTk5A7//uSTT3apNhoIAAD7ML8tCIApKSkaO3asioqKVFRUpLFjxyo1NfWqtzl58qTftnbtWvXp00eHDx/2rUlOTtbTTz/tt66mpqZLtdFAAADYh/kd5gGwrKxMjuNo586dvn3FxcVyHEcHDx4M+n5mzpypqVOn+u1LTk5WRkaGUX00EAAA9mF+h3kAXLNmjWJiYjrsj4mJ0dq1a4O6j1OnTikyMlLr1q3z25+cnKxbb71VgwcP1pgxY/TCCy/owoULXaqPBgIAwD7M7zAPgFlZWYqLi+uwPy4uTtnZ2UHdx/Lly3XLLbeorq7Ob/+qVau0detWlZaW6p133lFsbKymTZt21fuqr69XbW2tb6usrHR9AwEAYBsCYIgCYGZmZqcnarRte/bsUVZWlkaPHt3h9qNGjdJrr70W1GPFx8dr4cKF11z3xRdfyHEc7d27t8t1u7mBAACwDQEwRAHwzJkzKi8vv+pWV1dn/Bbwjh075DiO9u/ff821LS0t8ng8ys/P73QNrwACAGA/AmCYvwXcdhLIrl27fPt27twZ9EkgaWlpuueee4J6rNLSUjmOo+3btwddHw0EAIB9mN9hHgCl1svAjBs3TsXFxSouLtbdd9/d4TIw8fHxKigo8NtXW1urfv366fXXX+9wn19++aWWLl2qPXv2qKKiQh988IESEhI0YcIENTU1BV0bDQQAgH2Y3xYEwOrqas2aNUsDBgzQgAEDNGvWrA4XgnYcR3l5eX773njjDUVHRwe8tt/x48c1efJkDRo0SF6vV3feeafS09NVXV3dpdpoIAAA7MP8tiAAhjMaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/LQiAy5Yt0/3336/o6GjFxMQEdZuWlhZlZmZq6NCh6tu3r5KTk3XgwAG/NfX19Vq4cKEGDx6sfv366ZFHHlFlZWWXaqOBAACwD/PbggD4yiuvKDc3Vz/4wQ+CDoA5OTkaMGCANm3apNLSUj355JMaOnSoLly44Fszf/58DRs2TFu3btW+ffs0ZcoUjR8/Xk1NTUHXRgMBAGAf5rcFAbBNXl5eUAGwpaVFt912m3Jycnz76uvrFRMTo1//+teSpJqaGnk8HuXn5/vWnDhxQjfddJO2bNkSdE00EAAA9mF+98IAePjwYTmOo3379vntf/TRR/Xd735XkvTJJ5/IcRydO3fOb824ceP0yiuvdHrf9fX1qq2t9W3Hjx+X4ziqrKz028/GxsbGxsYWvltlZaUcx1FNTc11JJLeodcFwMLCQjmOoxMnTvjtf/rppzV9+nRJ0rp16+T1ejvc9sEHH9QzzzzT6X1nZmbKcRw2NjY2Nja2XrAdPny4i2mk9whJAAwmSO3Zs8fvNl0NgFVVVX77582bp4ceekhS5wFw2rRpevbZZzu97ytfATx27Jgcx9Hx48dD/tdMKP5yctsrnxw3x+2GjePmuN2wtb2Dd/78+WBiS68UkgB45swZlZeXX3Wrq6vzu004vAV8pdpad36GgOPmuN2A4+a43YDjdtdxX67XvQXcdhLI8uXLffsaGhoCngSyYcMG35qqqipOAgkSx81xuwHHzXG7AcftruO+XNgHwGPHjqmkpERLly7VzTffrJKSEpWUlOjixYu+NfHx8SooKPD9nJOTo5iYGBUUFKi0tFTf+c53Al4G5vbbb9fHH3+sffv2aerUqVwGJkgcN8ftBhw3x+0GHLe7jvtyYR8A09LSAn5GcNu2bb41juMoLy/P93PbhaBvu+02RUVFafLkySotLfW737q6Oi1cuFCDBg1SdHS0UlNTdfz48S7VVl9fr8zMTNXX15sconU4bo7bDThujtsNOG53Hfflwj4AAgAAoHsRAAEAAFyGAAgAAOAyBEAAAACXIQACAAC4DAHwKpYtW6b7779f0dHRQV2DUGo/A3no0KHq27evkpOTdeDAAb819fX1WrhwoQYPHqx+/frpkUceUWVlZU8cwnU5d+6cZs+erYEDB2rgwIGaPXv2Na+W3tk3uqxYscK3Jjk5ucO/P/nkkz19OEG7nuMOdJb6fffd57emtz3fjY2NWrx4scaOHat+/fpp6NChmjNnToevXwy353vlypWKjY1VVFSUkpKStGPHjquu/+yzz5SUlKSoqCjdcccdev311zus2bhxoxITE+X1epWYmOh3Oapw0ZXj3rRpk6ZNm6Zbb71VAwYM0KRJkzpcGzUvLy/g7/qVF+8Pta4c97Zt2wIeU3l5ud+63vZ8d3aVjTFjxvjW2PB8b9++XampqRo6dKgcx9HmzZuveZve8vttggB4Fa+88opyc3P1gx/8IOgAmJOTowEDBmjTpk0qLS3Vk08+GfAahMOGDdPWrVu1b98+TZkypcvXIOxJKSkpGjt2rIqKilRUVKSxY8cqNTX1qrc5efKk37Z27Vr16dPH73sWk5OT9fTTT/utC6cv4r6e405LS1NKSorfMVVXV/ut6W3Pd01NjaZNm6YNGzbo4MGDKi4u1n333ad77rnHb104Pd/5+fnyeDxavXq1ysrKlJGRof79++vYsWMB1x85ckT9+vVTRkaGysrKtHr1ank8Hm3cuNG3pqioSBEREcrOzlZ5ebmys7MVGRmpnTt33qjDuqauHndGRoaWL1+u3bt369ChQ3rxxRfl8Xj8vlkpLy9PAwcO7PA7H066etxtAfCPf/yj3zFd/jvaG5/vmpoav+OtrKzUoEGDlJmZ6Vtjw/P94Ycf6uWXX9amTZuCCoC95ffbFAEwCF39FpKcnBzfvvr6+oDfQpKfn+9bc+LEiS5/C0lPKSsrk+M4fk1eXFwsx3F08ODBoO9n5syZmjp1qt++5ORkZWRkdFut3el6jzstLU0zZ87s9N/d8nzv3r1bjuP4DZpwer4nTpyo+fPn++1LSEjQkiVLAq5fvHixEhIS/PY9++yzmjRpku/nJ554QikpKX5rHnroIT311FPdVLW5rh53IGPGjNHSpUt9Pwf7/2EodfW42wLg1V75dsPzvXnzZvXp00dHjx717bPh+b5cMAGwt/x+myIABiEcv4e4p6xZsybgscbExGjt2rVB3cepU6cUGRmpdevW+e1PTk7WrbfeqsGDB2vMmDF64YUX/F4ZDaXrPe60tDTFxMRoyJAhiouL07x583T69Gnfv7vh+ZakrVu3qk+fPn5X1Q+X57uhoUEREREd3r5JT0/X5MmTA97mW9/6ltLT0/32FRQUKDIyUo2NjZKk4cOHKzc3129Nbm6uRowY0Y3VX7/rOe4rNTc3a/jw4frVr37l25eXl6eIiAiNGDFCw4YN04wZMzr8nxdK13PcbQEwNjZWt912m6ZOnapPP/3Ub40bnu/U1FQ9+OCDfvvC/fm+UjABsDf8fncHAmAQgg2AhYWFchynw2ehnn76aU2fPl2StG7dOnm93g63ffDBB/XMM890T8EGsrKyFBcX12F/XFycsrOzg7qP5cuX65ZbbunwGZFVq1Zp69atKi0t1TvvvKPY2FhNmzatW+o2db3HnZ+fr/fff1+lpaV67733NH78eN11112+q8u74fmuq6vTPffco1mzZvntD5fn+8SJE3IcR4WFhX77s7KyNHr06IC3iYuLU1ZWlt++tt/vqqoqSZLH4+nwR05nz3coXM9xX2nFihUaNGiQ3x81xcXFeuutt7R//37t2LFDjz/+uKKjo3Xo0KFurf96Xc9xHzx4UKtWrdLevXtVVFSkBQsWqE+fPtq+fbtvTW9/vquqqhQREaENGzb47Q/35/tKwQTA3vD73R1cFwAzMzM7PWGhbduzZ4/fbboaANsaqM28efP00EMPSeq8gaZNm6Znn33W4MiuLtjj7uw/i1GjRum1114L6rHi4+O1cOHCa6774osv5DiO9u7d2+XjCdaNPG6p9T9Rj8ejTZs2Ser9z3djY6NmzpypCRMmXPM7NW/E8x1I22AsKiry279s2TLFx8cHvE2gAPyHP/xBjuP4Pv/k8Xi0fv16vzVvv/22oqKiurH663c9x3259evXq1+/ftq6detV1zU3N2v8+PF67rnnjOrtLqbH3SY1NVWPPPKI7+fe/nxnZ2dr8ODBamhouOq6cHu+rxRsALT997s7uC4AnjlzRuXl5Vfdrnzlqje8BRzscZu+Jbhjxw45jqP9+/dfc21LS0uHz8d1txt13JcbNWqU73Ogvfn5bmxs1GOPPaZx48bp7Nmz16zpRjzfgfAWcNffEszPz1d0dLTef//9oB5r3rx5HT4vFSrd8Vao1BqcLv+cWG9+vltaWjRq1CgtWrQoqMcKp+f7SrwFHDzXBcDr0dWTQJYvX+7b19DQEPAkkMtfZq+qqgq7kwJ27drl27dz586gTwpIS0vrcDZoZ0pLS+U4jt/bLKFietxtzp49q6ioKL355puSeu/z3Rb+7rrrLv35z38O6rFC+XxPnDhRCxYs8NuXmJh41ZNAEhMT/fbNnz+/w4fEH374Yb81KSkpYfUh8a4et9T6yl/fvn2DupSG1Pr/3r333qu5c+ca1dqdrue4r/T4449rypQpvp976/MttX8GsrS09JqPEY7P9+WCPQmkN/x+myIAXsWxY8dUUlKipUuX6uabb1ZJSYlKSkp08eJF35r4+Hi/v7hycnIUExOjgoIClZaW6jvf+U7Ay8Dcfvvt+vjjj7Vv3z5NnTo17C4LMm7cOBUXF6u4uFh33313h8uCXHncklRbW6t+/foFvJ7Sl19+qaVLl2rPnj2qqKjQBx98oISEBE2YMMHa47548aJeeOEFFRUVqaKiQtu2bdP999+vYcOG9ern+6uvvtKjjz6q22+/Xfv37/e7NETb20fh9ny3XR5jzZo1Kisr06JFi9S/f3/f2Y5LlizRnDlzfOvbLhPx/PPPq6ysTGvWrOlwmYjCwkJFREQoJydH5eXlysnJCbvLRHT1uNevX6/IyEitXLmy08v3vPrqq9qyZYsOHz6skpISzZ07V5GRkX5/RIRaV4/7F7/4hTZv3qxDhw7pwIEDWrJkiRzH8X2UQ+qdz3eb2bNnd7h+aRsbnu+LFy/65rPjOMrNzVVJSYnvqgS99ffbFAHwKjq7SOa2bdt8axzHUV5enu/ntgtB33bbbYqKitLkyZM7/FVVV1enhQsXatCgQYqOjlZqaqqOHz9+g47q2qqrqzVr1iwNGDBAAwYM0KxZszpcHuHK45akN954Q9HR0QGv9Xb8+HFNnjxZgwYNktfr1Z133qn09PQO18wLpa4e96VLlzR9+nQNGTJEHo9HI0aMUFpaWofnsrc93xUVFZ1+rrDtdyMcn++VK1dq5MiR8nq9SkpK8nslMi0tTcnJyX7rP/vsM02YMEFer1exsbEB/7B59913FR8fL4/Ho4SEBL/AEC66ctyBLt7tOI7S0tJ8axYtWqQRI0bI6/VqyJAhmj59eofPnYWDrhz38uXLdeedd6pv37665ZZb9MADD+iDDz7ocJ+97fmWWt+liI6O1qpVqwLenw3Pd2cX8m7r2978+22CAAgAAOAyBEAAAACXIQACAAC4DAEQAADAZQiAAAAALkMABAAAcBkCIAAAgMsQAAEAAFyGAAgAAOAyBEAAAACXIQACAAC4DAEQAADAZQiAAAAALkMABAAAcBkCIAAAgMsQAAEAAFyGAAgAAOAyBEAAAACXIQACAAC4DAEQAADAZQiAAAAALkMABAAAcBkCIAAAgMsQAAEAAFyGAAgAAOAyBEAAAACXIQACAAC4DAEQAADAZQiAAAAALkMABAAAcBkCIAAAgMsQAAEAAFzm/weA1F87HXdMkgAAAABJRU5ErkJggg==\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-1, 1)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%pylab notebook\n",
    "\n",
    "a = np.array([0.5, 0.2])\n",
    "b = np.array([0.4, -0.6])\n",
    "a_onto_b = np.dot(a, b)/np.sum(b**2)**(3/2)*b\n",
    "plt.arrow(0, 0, *a, head_width=0.02, label=r'$\\vec{a}$', color='b')\n",
    "plt.arrow(0, 0, *b, head_width=0.02, label=r'$\\vec{b}$', color='r')\n",
    "plt.arrow(0, 0, *a_onto_b, head_width=0.02, color='g')\n",
    "plt.arrow(*(*a, *(a_onto_b-a)), color='k', ls='--')\n",
    "\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now since we're multiplying the vectors in the same direction, this is the same as just multiplying their magnitudes and keeping their direction.  Geomtrically, this is just the area of a rectangle with side lengths $||\\vec{b}||$ and $||proj_{\\vec{b}}(\\vec{a})||$ where $proj_{\\vec{b}}(\\vec{a})$ is the projection of $\\vec{a}$ onto $\\vec{b}$.\n",
    "\n",
    "If we look at this picture in terms of a triangle, we can figure out how to project $\\vec{a}$ onto $\\vec{b}$.  From trigonometry, we know that the horizontal component of a right triangle is the hypotenuse times the cosine of the angle it makes with its base.  In this case, the horizontal component is the projection of $\\vec{a}$ onto $\\vec{b}$, and the hypotenuse is the magnitude of $\\vec{a}$.  Let $\\theta$ be the angle between $\\vec{a}$ and $\\vec{b}$.\n",
    "\n",
    "$cos(\\theta) = \\frac{||proj_{\\vec{b}}(\\vec{a})||}{||\\vec{a}||}$\n",
    "\n",
    "or by rearranging terms\n",
    "\n",
    "$||proj_{\\vec{b}}(\\vec{a})|| = ||\\vec{a}||cos(\\theta)$\n",
    "\n",
    "and we know that the dot product of $\\vec{a}$ and $\\vec{b}$ is\n",
    "\n",
    "$\\vec{a} \\cdot \\vec{b} = ||\\vec{b}|| \\ ||proj_{\\vec{b}}(\\vec{a})||$\n",
    "\n",
    "so by subtitution\n",
    "\n",
    "$\\boxed{\\vec{a} \\cdot \\vec{b} = ||\\vec{b}|| \\ ||\\vec{a}|| cos(\\theta)}$\n",
    "\n",
    "dot products are *commutative*, meaning that \n",
    "\n",
    "$\\vec{a} \\cdot \\vec{b} = \\vec{b} \\cdot \\vec{a}$\n",
    "\n",
    "### Dot product in Python\n",
    "\n",
    "The Python module numpy offers a dot product function, but we can also write one ourselves quite easily."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.499999999999998\n"
     ]
    }
   ],
   "source": [
    "def dot_product(a, b):\n",
    "    \n",
    "    # First, multiply the arrays to get the\n",
    "    # element-wise product\n",
    "    elm_prod = a*b\n",
    "    \n",
    "    # next, as with the magnitude, we sum up the elements\n",
    "    prod = np.sum(elm_prod)\n",
    "    \n",
    "    return prod\n",
    "\n",
    "a = np.array([5.6, -1.2, 4.5])\n",
    "b = np.array([3.5, 1.0, -2.2])\n",
    "\n",
    "print(dot_product(a, b))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we can compute the dot product, we can also compute the angle between the two vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.292848474043176\n"
     ]
    }
   ],
   "source": [
    "def angle_between(a, b):\n",
    "    \n",
    "    # get the dot product\n",
    "    prod = dot_product(a, b)\n",
    "    \n",
    "    # get the magnitudes of each vector\n",
    "    mag_a = mag(a)\n",
    "    mag_b = mag(b)\n",
    "    \n",
    "    # now dividing the dot product by the magnitudes\n",
    "    # gives us the cosine of the angle between them\n",
    "    cos_theta = prod/(mag_a*mag_b)\n",
    "    \n",
    "    # finally, we take the inverse cosine\n",
    "    # to get the angle\n",
    "    angle = np.arccos(cos_theta)\n",
    "    \n",
    "    return angle\n",
    "\n",
    "print(angle_between(a, b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5707963267948966\n"
     ]
    }
   ],
   "source": [
    "# Let's try it with some vectors we know to confirm\n",
    "\n",
    "x_hat = np.array([1.0, 0.0, 0.0])\n",
    "y_hat = np.array([0.0, 1.0, 0.0])\n",
    "\n",
    "print(angle_between(x_hat, y_hat)) # should be pi/2 ~ 1.57"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross Product\n",
    "\n",
    "We also have the *cross product*, which is only defined in 3-dimensional space.  This product gives a vector that points perpendicular to the vectors that are crossed.  The magnitude of this vector is the area of the parallelogram made by the sum of the two vectors.\n",
    "\n",
    "$\\boxed{\\vec{a} \\times \\vec{b} = <a_{2} b_{3} - a_{3} b_{2}, b_{1}a_{3} - a_{1}b_{3}, a_{1}b_{2} - a_{2}b_{1}>}$\n",
    "\n",
    "notice that $\\vec{a} \\times \\vec{b} = - (\\vec{b} \\times \\vec{a})$, so the cross product is *non-commutative* unlike the dot product.\n",
    "\n",
    "So let's take a step back for a second.  The area of a parallelogram is the length of the base of the parallelogram multiplied by its height.  For the length of the base, we can chose the magnitude of either one of the vectors, in this example we'll chose $||\\vec{b}||$ to represent our base.  Our height is going to be related to the projection of $\\vec{a}$ onto $\\vec{b}$, but this time, we want the part of the vector $\\vec{a}$ that is *perpendicular* to $\\vec{b}$.  \n",
    "\n",
    "From now on, we'll represent the projection of $\\vec{a}$ onto $\\vec{b}$ as the *parallel* component of $\\vec{a}$ on $\\vec{b}$, writing it as $\\vec{a}_{\\parallel}$.  The perpendicular component will be represented as $\\vec{a}_{\\bot}$. \n",
    "\n",
    "This is eay enough with the Pathagorean Theorem, as we know that\n",
    "\n",
    "$||\\vec{a}||^{2} = ||\\vec{a}_{\\parallel}||^{2} + ||\\vec{a}_{\\bot}||^{2}$\n",
    "\n",
    "So we can solve for $||\\vec{a}_{\\bot}||$ as\n",
    "\n",
    "$||\\vec{a}_{\\bot}||^{2} = ||\\vec{a}||^{2} - ||\\vec{a}_{\\parallel}||^{2}$\n",
    "\n",
    "so the magnitude of our cross product is\n",
    "\n",
    "$||\\vec{a} \\times \\vec{b}|| = ||\\vec{b}|| \\ \\sqrt{||\\vec{a}||^{2} - ||\\vec{a}_{\\parallel}||^{2}}$\n",
    "\n",
    "but we know something about $||\\vec{a}_{\\parallel}||$ from our discussion of the dot product.\n",
    "\n",
    "$||\\vec{a}_{\\parallel} = ||\\vec{a}||cos(\\theta)$\n",
    "\n",
    "where $\\theta$ is the angle between $\\vec{a}$ and $\\vec{b}$.  Substituting this in gives us\n",
    "\n",
    "$||\\vec{a} \\times \\vec{b}|| = ||\\vec{b}|| \\ \\sqrt{||\\vec{a}||^{2} - ||\\vec{a}||^{2} cos^{2}(\\theta)}$\n",
    "\n",
    "and doing some simplifying\n",
    "\n",
    "$||\\vec{a} \\times \\vec{b}|| = ||\\vec{b}|| \\ ||\\vec{a}||\\sqrt{1 - cos(\\theta)^{2}}$\n",
    "\n",
    "from the Pythagorean trigonometric identity, we know that\n",
    "\n",
    "$cos^{2}(\\theta) + sin^{2}(\\theta) = 1$\n",
    "\n",
    "which means\n",
    "\n",
    "$\\sqrt{1-cos^{2}(\\theta)} = sin(\\theta)$\n",
    "\n",
    "subsituting this back into our expression for the magnitude of the cross product yields\n",
    "\n",
    "$\\boxed{||\\vec{a} \\times \\vec{b}|| = ||\\vec{b}|| \\ ||\\vec{a}||sin(\\theta)}$\n",
    "\n",
    "### Task for you:\n",
    "\n",
    "* Impliment cross products in Python\n",
    "* Use the cross product to find the angle between two vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unit vectors ###\n",
    "\n",
    "We can also represent the direction and magnitude of a vector as a pair of its magnitude and its *unit vector*.\n",
    "A *unit vector* is a vector with the same direction as the original vector but with a magnitude of 1.  We know from above that we can write a vector as a scalar times another vector.  \n",
    "\n",
    "Let's look at an example of how we can represent a 2D vector in terms of direction and magnitude.\n",
    "\n",
    "$\\vec{a} = <a_{1}, a_{2}>$\n",
    "\n",
    "Using our expression for the sines and cosines of a vector and substituting in our expression we get\n",
    "\n",
    "$\\vec{a} = <||\\vec{a}||cos(\\theta), ||\\vec{a}||sin(\\theta)>$\n",
    "\n",
    "since $||\\vec{a}||$ is a scalar, and multiplying a vector by a scalar is distributive, this can be rewritten as\n",
    "\n",
    "$\\vec{a} = ||\\vec{a}||<cos(\\theta), sin(\\theta)>$\n",
    "\n",
    "By our angle identities, we know that $cos^{2}(\\theta) + sin^{2}(\\theta) = 1$, which means the vector of sines and cosines describing the direction of our vector is our unit vector.  We'll denote the unit vector with a hat.\n",
    "\n",
    "$\\hat{a} = <cos(\\theta), sin(\\theta)>$\n",
    "\n",
    "Solving for $\\hat{a}$ in terms of $\\vec{a}$ and $||\\vec{a}||$ we find\n",
    "\n",
    "$\\boxed{\\hat{a} = \\frac{\\vec{a}}{||\\vec{a}||}}$\n",
    "\n",
    "Which is a general solution.  Often we will represent a vector in terms of unit vectors\n",
    "\n",
    "$\\vec{a} = ||\\vec{a}|| \\hat{a} $\n",
    "\n",
    "There are some unit vectors that are very commonly seen because they are simple.  For example, the unit vectors of our Cartesian coordinate system.\n",
    "\n",
    "$\\hat{x} = <1, 0, 0, ...>$\n",
    "\n",
    "$\\hat{y} = <0, 1, 0, ...>$\n",
    "\n",
    "$\\hat{z} = <0, 0, 1, ...>$\n",
    "\n",
    "\n",
    "Occaisonally, $\\hat{i}, \\hat{j}, \\hat{k}, ...$ are used in place of $\\hat{x}, \\hat{y}, \\hat{z}, ...$\n",
    "These vectors are *orthogonal* meaning they are all at right angles to one another.  This means that when we take a linear combination of them, combination gives back one of the elements of the vector.\n",
    "\n",
    "$\\vec{a} =  a_{1} \\hat{x} + a_{2} \\hat{y} + a_{3} \\hat{z} + ...$\n",
    "\n",
    "$\\vec{a} =  a_{1} <1, 0, 0, ...> + a_{2} <0, 1, 0, ...> + a_{3} < 0, 0, 1, ...> + ...$\n",
    "\n",
    "$\\vec{a} =   <a_{1}, 0, 0, ...> +  <0, a_{2}, 0, ...> +  < 0, 0, a_{3}, ...> + ...$\n",
    "\n",
    "\n",
    "\n",
    "$\\vec{a} = <a_{1}, a_{2}, a_{3}, ...>$\n",
    "\n",
    "Since we can chose any set of unit vectors independent of our space to represent our vectors, vectors are commonly\n",
    "seen represented as a linear combination of unit vectors.  For example, if we want to rotate our coordinate grid, we can transform the unit vectors in the same way, and multiply by the vector magnitude to get the coordinates of our vector in a new coordinate system.  This allows you to, in a way, generalize coordinate systems and do some neat tricks.  Like rotating your system so one of your vectors lies accross the x-axis making vector operations easier to compute.\n",
    "\n",
    "### Task for you:\n",
    "\n",
    "* Write a function in Python for finding the unit vector of a given vector"
   ]
  }
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