FR_rectangles_reconstruction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do `Kernel -> Restart & Run All` in top menu to run the notebook and enable the interactive widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import pi\n",
    "from scipy.signal import square\n",
    "from ipywidgets import widgets\n",
    "import pdb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def square_wave(x, width, height, period):\n",
    "    return height * (square(2*pi*(1/period)*(x+width/2),width/period)+1)/2\n",
    "\n",
    "def sinc(x):\n",
    "    return np.sinc(x / pi)\n",
    "\n",
    "def spectrum_square_wave(k, width, height, period):\n",
    "    omega = 2*pi / period\n",
    "    return height * (width/period) * sinc(width/2 * k * omega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time-domain signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var 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, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_axis = np.linspace(-8,8,1000)\n",
    "width = 2\n",
    "height = 10\n",
    "period = 6\n",
    "\n",
    "sq = square_wave(x_axis, width, height, period)\n",
    "plt.plot(x_axis,sq)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var 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, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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70deXh5UFR/1rXUsAH7Utw6qiry8PPT3szNoIjdjACSrGACJXO7BgweBUTry8zHaV+dYABzlq0NBQQFUFffv37dzFYjIZgyAZBUDIJHLXblyxbw1O/xQN7yyU8oCXcFcunTJzlUgIpsxAHpHuoi8LyKPROSWiNSIyItxlhkrgS8//PXHw/hcBkAilzM6gZ4zd57jAbByfhVUFceOHbNzFYjIZgyA3rFJRH4kIp8QkT8VkQ0icklE/nOMZcZK4Mt/QQKhz3h9aBifywBI5HJ79+6FqmLZihWOB8AVq1ZDVbF79247V4GIbMYA6F3/VQJf7CsxyowdKPNHFj6HAZDI5TZv3gxVRf3GBscD4MZNgc9qaGiwcxWIyGYMgN71EQl8sZ+MUWbsQJmLInJdRBpF5OU47/thCewsxusZYQAkcrXVqwNX5Xbs2u14ANy5OzDk3MqVK+1cBSKyGQOgN31IROpFZHecci+KyE9F5CUR+YKIzBeRJyLy2RjLqERoN8gASORe8+fPh6ri8JFjjgfAw0dboKqYN2+enatARDZjAPSmmRK4qvc/R7DsDhFZFGM+rwASpZiygSdzz5y74HgAPHv+IlQVU6ZMsXMViMhmDIDeM01ErojIsyNcfoKI7B1GebYBJHIxv9+P/Px8qCqu377jeAC8fvuO2eeg3++3c1WIyEYMgN7xexIIf9dE5HkL79MoImuHUZ4BkMjFHj16ZI7O8bCz2/EA+LCzG6oKVcWjR4/sXBUishEDoHfMEJH7IvKqhHbp8gdBZcaJyMKg/78tIt+UwAMjnxSRMhHpF5EvDuNzGQCJXOzatWtQVUyaNGnEoW64ZSdMmABVRVtbm52rQkQ2YgD0jkgdOkMCfQMaqkVke9D/3xGRVhHpEpE7IvKuiLw2zM9lACRysVOnTkFVMXfu3IQFwNmzZ0NVcfr0aTtXhYhsxABIVjEAErnY/v37oapYsWJFwgLg0qVLoap4//337VwVIrIRAyBZxQBI5GKNjY1QVWzcuDFhAbCurg6qim3bttm5KkRkIwZAsooBkMjF1qxZYw7NlqgAuGPHDqgqampq7FwVIrIRAyBZxQBI5GLV1dVQVRw9ejRhAfDw4cNQVSxatMjOVSEiGzEAklUMgEQuVlFRAVXF+fPnExYAz549C1XFjBkz7FwVIrIRAyBZxQBI5GLFxcVQVdy+fTthAfDmzZtQVZSUlNi5KkRkIwZAsooBkMilenp6zE6Zu7u7ExYAOzs7zc/t7e21c5WIyCYMgGQVAyCRS925ExiWraioCH6/P2EB0O/3o7CwEKqKO3fu2LlKRGQTBkCyigGQyKUuXrwIVUV5eTkAa6FuuGXLy8uhqrh48aI9K0NEtmIAJKsYAIlcqqWlBaqK+fPnA0hsAKyqqoKq4tixY/asDBHZigGQrGIAJHKpvXv3QlWxatUqAIkNgEb/g++99549K0NEtmIAJKsYAIlcasuWLVBVNDQ0AEhsANy8eXPIZxORuzAAklUMgEQutXbtWnMUECCxATD86iMRuQsDIFnFAEjkUgsWLICq4siRIwASGwCN9odVVVW2rAsR2YsBkKxiACRyqWnTpkFVce7cOQCJDYAXLlwIeQKZiNyFAZCsYgAkcqmSkhKoKm7dugUgsQGwvb0dqori4mJ7VoaIbMUASFYxABK5UG9vrzkaR2dnJ4DEBsDu7m7z83t6euxZKSKyDQMgWcUASORCd+/ehaqisLAQfr8fQGIDoN/vR1FREUcDIXIpBkCyigGQyIUuXboEVUVZWZk5LZEBEACmTp0KVcWlS5esrQwR2Y4BkKxiACRyoRMnTkBVUVlZaU5LdACsrKyEquL48ePWVoaIbMcASFYxABK50L59+6CqWLlypTkt0QFw5cqVUFXs27fP2soQke0YAMkqBkAiF2psbISqYuPGjea0RAfAjRs3QlXR1NRkbWWIyHYMgGQVAyCRC61btw6qip07d5rTEh0Ad+7cCVVFTU2NtZUhItsxAJJVDIBELrRo0SKoKpqbm81piQ6Ahw8fhqpi0aJF1laGiGzHAEhWMQASudCMGTOgqmhtbTWnJToAnj17FqqKmTNnWlsZIrIdAyBZxQBI5ELjx4+HquLGjRvmtEQHwOvXr0NVMWHCBGsrQ0S2YwAkqxgAiVzmyZMn5igcHR0d5vREB8BHjx6Z9ejv77e2UkRkKwZAsooBkMhl7t27B1VFQUGBOQoIkPgA2N/fj7y8PKgqHj58aG2liMhWDIBkFQMgkctcuXIFqoopU6aETE90AASAiRMnQlVx7dq1ka0METmCAZCsYgAkcpmTJ09CVTFv3ryQ6ckIgLNnz4aq4vTp0yNbGSJyBAMgWcUASOQyBw4cgKpi+fLlIdOTEQCXLFkCVcWhQ4dGtjJE5AgGQO9IF5H3ReSRiNwSkRoReXEIy40VkcMi0iMirSLyo2F+LgMgkcts27YNqor6+vqQ6ckIgOvXr4eqYvv27SNbGSJyBAOgd2ySQHj7hIj8qYhsEJFLIvKfYyzzrIh0iMgkEfmYiPxSRPpE5MvD+FwGQCKXqa2thari3XffDZmejAC4devWiGGUiJKLAdC7/qsEvthXYpQZLyLHw6Ytl0CYHCoGQCKXWbZsGVQV77//fsj0ZATAaLejiSi5GAC96yMS+GI/GaPMThEpC5v2log8GMbnMAASuczcuXOhqjh16lTI9GQEwGgPpBBRcjEAetOHRKReRHbHKXdGAm0Hg70hgR3iD6Is82EJ7CzG6xlhACRylSlTpkBVceXKlZDpyQiAly9fhqqirKxsZCtDRI5gAPSmmSJyUUT+Z5xyIwmAOjA/5MUASOQOfr8fhYWFUFXcvXs3ZF4yAuDdu3cjdkpNRMnFAOg900TkigQe8IhnJLeAeQWQyMW6u7vN4dd6e3tD5iUjAAYPS9fZ2TmylSIi2zEAesfvSSD8XROR54e4zHgRaQmbtlT4EAhRympvb4eqori4eNC8ZARAACgpKYGq4tatW8NbGSJyDAOgd8wQkfsi8qqI/HHQK/hW7jgRWRj0f6MbmFIR+aiI/ELYDQxRSrt48SJUFeXl5YPmJSsATps2DaqK8+fPD29liMgxDIDeMahd3sDrR0FlqkVke9hyY0WkWQIdQZ8TdgRNlNKOHz8OVcX8+fMHzUtWAKyuroaq4tixY8NbGSJyDAMgWcUASOQi+/fvh6pixYoVg+YlKwCuXr0aqoo9e/YMb2WIyDEMgGQVAyCRi8QaeSNZAbChoQGqisbGxuGtDBE5hgGQrGIAJHKRWGPvJisA7ty5E6qKdevWDW9liMgxDIBkFQMgkYssXboUqoqDBw8OmpesAHj48GGoKhYvXjy8lSEixzAAklUMgEQuMmfOHKgqPvjgg0HzkhUAz5w5A1XFrFmzhrcyROQYBkCyigGQyEWiDQMHJC8AXrt2DaqKSZMmDW9liMgxDIBkFQMgkUv4/X4UFBRAVXHv3r1B85MVAB88eABVRX5+PoeDI3IJBkCyigGQyCW6urqiDgMHJC8A9vX1mfXq6OgY3koRkSMYAMkqBkAil7h9+zZUFePGjYs4P1kBEHg6HNzNmzeHtjJE5CgGQLKKAZDIJS5cuABVRUVFRcT5yQyAHA6OyF0YAMkqBkAil4g1DByQ3ADI4eCI3IUBkKxiACRyiX379kFVsXLlyojzkxkAV61aBVXF3r17h7YyROQoBkCyigGQyCWampqgqtiwYUPE+ckMgBs3buRwcEQuwgBIVjEAErmEMQzcjh07Is5PZgA0hoOrqakZ2soQkaMYAMkqBkAil1iyZAlUFYcOHYo4P5kB8NChQxwOjshFGADJKgZAIpeINQwckNwAePr0aagqZs+ePbSVISJHMQCSVQyARC4xefJkqCquXr0acX4yAyCHgyNyFwZAsooBkMgF/H4/8vPzoaq4f/9+xDLJDID379/ncHBELsIASFYxABK5QGdnpznc2pMnkUNYMgPgkydPzPp1dnYObaWIyDEMgGQVAyCRC9y6dQuqipKSkqhlkhkAgafDwd26dSv2yhCR4xgAySoGQCIXiDcMHJD8AMjh4IjcgwGQrGIAJHKBlpYWqCqqqqqilkl2AKyqqoKqoqWlJeb7EZHzGADJKgZAIhfYu3cvVBWrVq2KWibZAZDDwRG5BwMgWcUASOQCjY2NUFVs3LgxaplkB0BjOLimpqbYK0NEjmMAJKsYAIlcoKamBqqKnTt3Ri2T7AC4Y8cODgdH5BIMgGQVAyCRC8QbBg5IfgA0hoNbsmRJ7JUhIscxAJJVDIBELjB79myoKk6fPh21TLIDIIeDI3IPBkCyigGQyAUmTZoEVcW1a9eilkl2ALx69SpUFZMnT469MkTkOAZAsooBkCjJgoeBi/W3mOwAaAwHV1BQwOHgiJKMAZCsYgAkSrKOjg5zmLW+vr7o5ZIcADkcHJF7MACSVQyAREk2lGHggOQHQAAYN24ch4MjcgEGQLKKAZAoyc6fPw9VxbRp02KWc0MArKiogKriwoULMcsRkbMYAL3lFRGpE5E2CXyp34pTfuxAufDXHw/jMxkAiZLs2LFjUFVUV1fHLOeGAMjh4IjcgQHQW74qIoUi8m0ZXgB8QQKhz3h9aBifyQBIlGR79uyBqmL16tUxy7khAK5cuRKqin379sUsR0TOYgD0ruEEwD+y8DkMgERJZgwD19DQELOcGwLghg0bOBwckQswAHrXcALgRRG5LiKNIvJynGU+LIGdxXg9IwyAREm1bt06qCp27doVs5wbAqAxHNz69etjliMiZzEAetdQAuCLIvJTEXlJRL4gIvNF5ImIfDbGMioR2g0yABIlz+LFi6GqOHz4cMxybgiABw8e5HBwRC7AAOhdQwmAkewQkUUx5vMKIJHLzJo1C6qKM2fOxCznhgD4wQcfQFUxZ86cmOWIyFkMgN410gA4QUT2DqM82wASJdnEiROhqmhra4tZzg0BkMPBEbkDA6B3jTQANorI2mGUZwAkSiK/34+8vLy4w8AB7giA9+7d43BwRC7AAOgt/0VEPjPwgoj8auDf/2tg/jgRWRhU/m0R+aaIfEREPikiZSLSLyJfHMZnMgASJdFQh4ED3BEAg4eD6+rqilmWiJzDAOgtYyVyx87VA/OrRWR7UPl3RKRVRLpE5I6IvCsirw3zMxkAiZKkr9+PLQdPQ1VRVDwOff2xr6i5IQACT4eDW77zOPa0tsetNxHZjwGQrGIAJEqChpY2jCluwpj0pVBVvJ1TgjHFTWhoid4O0A0BsKGlDb/V8VBVfC59GUb56uPWm4jsxwBIVjEAEiVYQ0sbRg8ErtcyFkBV8dPsSRjtq8doX33UMJXsAGjU+2fZgYdWXs1YiFEDdY5VbyKyHwMgWcUASJRAff1+jCluMgPXVzPmQVXxz1nlZpgaU9wU8bZqMgNgcL1/mD0VqoqvZFSay8WqNxHZjwGQrGIAJEqgPa3tZmga5avHdzIDfQD+XdaMkOl7WtsHLZvMABhc7zezpkNV8e3M2SF1jlZvIrIfAyBZxQBIlEA1zVdDAtM/ZlVAVfG1zLkh02uarw5aNpkBMLje38icA1XF97OmDQqAkepNRPZjACSrGACJEij8CuBPsidDVfF6RnXKXAH8UkYVVBX/kj2FVwCJkoQBkKxiACRKIKMtnfEQyC9zSqGqeDl9cUq0ARztq8dfpgfGLv63nFK2ASRKEgZAsooBkCjBgp8C/m1uEVQVn01bkTJPAb+Uthyqit/kFPMpYKIkYQAkqxgAiZKgoaUNnyvcgpzcwDBwH09bmzL9AL5aWAdVRVZuHkb56tgPIFESMACSVQyAREly8+59c1i1puNtKTMSyJ2HT4ev23L0Mm/7EiUBAyBZxQBIlCSXrrVBVZGeWzCk4OWWANjR8wQZuQVQVVxpuxG3PBHZjwGQrGIAJEqSU2fOmsPApVoA/FVOYDzgD862xi1PRPZjACSrGACJkuRg85GBYeAmplwANIaDO3TkaNzyRGQ/BjuDIf0AACAASURBVECyigGQKEl27n4PqoofZk1NuQD4w6zAcHA7d++JW56I7McASFYxABIlScPmLVBVfC9rRsoFwO9lzYCqYtOWLXHLE5H9GADJKgZAoiRZs3YdVBVfz5yTcgHQGA5uzbp1ccsTkf0YAMkqBkCiJFm4aNHAMHBVKRcAXx8YDm7hosVxyxOR/RgAySoGQKIkmTlrFlQVf5m+OOUCoDEc3KxZs+OWJyL7MQCSVQyAREkyadIkqCpeSluRcgHwpbQVUFVMmjQpbnkish8DIFnFAEiUBH6/HwUFBQPDwK1JuQD48bQ1UFXk5+fD7+dIIESJxgBIVjEAEiVBZ2enOZzac77alAuAz/pqzfp3dnbGXYaI7MUASFYxABIlwe3bt81h4IYTvNwSAEf56pE+MBzcrVu34i5DRPZiACSrGACJkuDChQtQVfwqZ1zKBsC3c0qgqrhw4ULcZYjIXgyAZBUDIFESHD9+HKqKn2VPTNkA+NOB4eBaWlriLkNE9mIAJKsYAImSYN++fYFh4LKnpmwANIaD27t3b9xliMheDIBkFQMgURI0NTVBVfFm1vSUDYDGcHCNjY1xlyEiezEAklUMgERJsH79eqgqvpE5J2UD4Ncz50JVUVNTE3cZIrIXAyBZxQBIlARLly6FquJLGVUpGwBfz6iGqmLxYg4HR5RoDIBkFQMgURLMmTPHHAYuVQPgywPDwc2ezeHgiBKNAZCsYgAkSoIpU6YMDAO3PGUD4Gc5HBxR0jAAklUMgEQJFjwM3CfS1qRsAPyYby2HgyNKEgZAb3lFROpEpE0CX+q3hrDMWBE5LCI9ItIqIj8a5mcyABIlWFdXV8gwcKkaAIOHg+vo6Ii7HBHZhwHQW74qIoUi8m0ZWgB8VkQ6RGSSiHxMRH4pIn0i8uVhfCYDIFGCGcPAFRcXjyh4uSUAjvLVo6RkPFQVN2/ejLscEdmHAdC7hhIAx4vI8bBpy0Vk0zA+hwGQKMEuXrwIVUXZ1KkpHwArKqZBVXH+/Pm4yxGRfRgAvWsoAXCniJSFTXtLRB4M43MYAIkSzBgGbu68ypQPgPOrqqCqOHbsWNzliMg+DIDeNZQAeEZE0sOmvTGw7B9EWebDEthZjNczwgBIlFD79++HqmLpsuUpHwCXr1gJVcWePXviLkdE9mEA9C6nAqAOzA95MQASJc7WrVsDI2jU1qV8AKyr3wBVxZYtW+IuR0T2YQD0LqduAfMKIFGS1dYGnp5t3Lot5QPgtu07oKpYt25d3OWIyD4MgN411IdAWsKmLRU+BELkasuWLYOq4r19+1M+AO57/yCHgyNKAgZAb/kvIvKZgRdE5FcD//5fA/PHicjCoPJGNzClIvJREfmFsBsYItebO3cuVBVHWo6nfABsOXkKqopZs2bFXY6I7MMA6C1jJUL7PBGpHphfLSLbIyzTLIGOoM8JO4Imcj1jGLgz5y6kfAA8f+kyVBUTJ06MuxwR2YcBkKxiACRKIL/fj8LCQqgqrt28nfIB8Gb7Xagq8vLyOBwcUQIxAJJVDIBECdTd3W0On3b/cWfKB8CHnU/X5/Hjx3GXJSJ7MACSVQyARAnU3t5uDgNnJXi5JQB29DzB+PGB4eBu3LgRd1kisgcDIFnFAEiUQJcuXYKqYurUqZ4JgNOnT4eq4ty5c3GXJSJ7MACSVQyARAl04sQJqCoqKys9EwAXLFgAVcXRo0fjLktE9mAAJKsYAIkS6MCBA1BVLF++3DMBcM2aNYF+Dd97L+6yRGQPBkCyigGQKIG2bdsGVUV9fb1nAuCmTZs4HBxRgjEAklUMgEQJtH79eqgqtm/f7pkAuHv3bqgq1q5dG3dZIrIHAyBZxQBIlEBLly6FquLgwYOeCYDNzc1QVSxatCjuskRkDwZAsooBkCiBZs+eDVXF6dOnPRMAz549C1XFzJkz4y5LRPZgACSrGACJEmjSpEmBUUCuXfNMALx+/TpUFRMmTIi7LBHZgwGQrGIAJEoQv9+P/Px8qCoePHjgmQD48OFDczi4/v7+uMsTkXUMgGQVAyBRgjx+/NgcNq2vr88zAbC/v99cr0ePHsVdnoisYwAkqxgAiRLkxo0bUFWUlpYCsB68klE2WvnS0lIOB0eUQAyAZBUDIFGCtLa2QlUxY8YMAN4KgDNmzICqorW1Ne7yRGQdAyBZxQBIlCDh3aV4KQAuXLgQqoojR47EXZ6IrGMAJKsYAIkSZNeuXVBVrFu3DoC3AuDatWuhqti9e3fc5YnIOgZAsooBkChBGhoaoKpobGwE4K0AuHnzZqgqNm/eHHd5IrKOAZCsYgAkSpBVq1ZBVbF3714A3gqAxnBwa9asibs8EVnHAEhWMQASJUhVVRVUFS0tLQC8FQCPHDkCVcXChQvjLk9E1jEAklUMgEQJUlFRAVXFhQsXAHgrAIY/4UxEzmIAJKsYAIkSpLi4GKqK9vZ2AN4KgDdv3oSqYvz48XGXJyLrGADJKgZAogTo6ekxR8vo7u4G4K0A2NHRYa7fkyfx34OIrGEAJKsYAIkS4M6dO1BVFBUVwe/3A/BWAPT7/SgoKICq4t69e3Hfg4isYQAkqxgAiRLg0qVLUFVMnTrVnOalAAgAU6ZMgari8uXLcd+DiKxhACSrGACJEuDEiRNQVVRWVprTvBYA582bB1XFyZMn474HEVnDAEhWMQASJcD+/fuhqlixYoU5zWsBcMWKFVBV7N+/P+57EJE1DIBkFQMgUQJs3boVqooNGzaY07wWADds2ABVRVNTU9z3ICJrGADJKgZAogSoqamBqmLHjh3mNK8FwJ07d0JVUVNTE/c9iMgaBkCyigGQKAGWLFkCVcXhw4fNaV4LgIcPH4aqYtGiRXHfg4isYQAkqxgAiRJg1qxZUFWcOXPGnOa1AHj27FmoKmbOnBn3PYjIGgZAsooBkCgBJk6cCFVFW1ubOc1rAfDGjRtQVZSWlsZ9DyKyhgHQe/5NRC6KSLeI7BeRz8UoO1YCX37464+H8XkMgEQO6+/vR15eHlQVDx8+NKd7LQA+fvzYHA2kr68v7vsQ0cgxAHrLmyLSIyJvicjHRWSOiNwTkf8WpfxYCXz5L0gg9BmvDw3jMxkAiRz26NEjqCry8vLQ399vTvdaAPT7/cjPz4eq4v79+3Hfh4hGjgHQW/aLyLSg/39IRK6JSFqU8mMl8OX/kYXPZAAkclhbWxtUFRMmTAiZ7rUACACTJ0+GquLKlStx34eIRo4B0Dt+X0T6RORbYdMXiMj6KMuMlcCXf1FErotIo4i8HOdzPiyBncV4PSMMgESOOn36NFQVs2fPDpnuxQA4d+5cjgZClAAMgN7xPyTwRf5F2PRSCVwZjORFEfmpiLwkIl8Qkfki8kREPhvjc1QitBtkACRyzsGDB6GqWLp0ach0LwbA5cuXQ1Vx4MCBuO9DRCPHAOgdIwmAkewQkUUx5vMKIFGCvfvuu1BV1NXVhUz3YgCsr6+HqmLr1q1x34eIRo4B0DtGcgs4kgkisncY5dkGkMhhtbW1UFVs3749ZLoXA+COHTs4GghRAjAAest+EakI+v+HROSqRH8IJJJGEVk7jPIMgEQOM0YBOXToUMh0LwbAQ4cOQVWxePHiuO9DRCPHAOgtb0qg/78fisjHRGS2BLqB+e8D88eJyMKg8m+LyDdF5CMi8kkRKRORfhH54jA+kwGQXKW/vx9+vx8A0Nfvx57WdtQ0X8We1nb09fuTXLuRiTQKCODNAHjmzJmUHw0k0n7n9/tDuvAhSjYGQO/5pYhckkB/gPtF5PNB86pFZHvQ/98RkVYR6RKROyLyroi8NszPYwCkpPP7/WhubsasWbOQl5eHoqIiTJ1TjS8V1phBY5SvHmOKm9DQ0hb/DV2mtLQUqorr16+HTPdiALx+/XrELm9SRUNLG8YUN5nr95m0lfh5XjnyCwqRl5eHWbNmobm52fyRQpQsDIBkFQMgJVVPT495izT8lZObhy9mVJsn49EDr1QKgX19feb6dHR0hMzzYgBM5dFAGlraMDroB8frGdXIyc2LuG8uWbIEPT09ya4y/Q5jACSrGAApafr6+lBVVQVVRWFhIXbt2oU7d+/hS4U1eCu7zDzZjs1YGBICxxQ3pczt4Hv37kFVUVBQMOiqkRcDYPBoIKl0XOnr94dc+Xs1Y6G5/72VXYbPpq3E2KIN2LFzJwoLC6GqqKqqSrmQS97BAEhWMQBSQgW3r5q3ZDVUFePGjTNHjtjT2j5wEq7D97JmQFWRlZuPT6etCrkdvKe1PclrMjSXL1+GqqKsrGzQPC8GQODpaCBXr16N+15u8XS/q8en0lYjMzcQYr+XNQOjfHUh+92VK1cwbty4ga596j3RTpVSDwMgWcUASAkT3L7q1fTAFZZcVSzdss8sU9N8NehqXx3+NTsQJn6WPTHkRFzTnBrh4sSJE1BVVFZWDprn1QA4Z84cqCpOnToV973c4ul+V4df5EyAquKn2RMxOmifC97vjNFdVBWvpD+9Qp2q7VQp9TAAklUMgJQQwe2rnvfV4J3cwG20b2fODmnXF3wlZpSvHh9PW2NejXk9qD1gqlwB3LdvH1QVK1euHDTPqwFw2bJlUFW8//77cd/LLYz97q8zFkBVkZmbj4/61obsi8H7XUNLG76dORuqindyi/C8ryZl26lSamIAJKsYAMlx4e2r3syaDlXF2zkleNZXG9Kuzygb3Bj/jcx5UFX8NqcIz/lqU6oN4JYtW6CqaGhoGDTPqwGwrq4u5UYD6ev34wtFm/FObhFUFV/LnBsS/CLto8/5avF2TglUFW9mTU/ZdqqUmhgAySoGQHJcePuqnNzArbPPpy+NenUlOAA+56vFbwdOzF/OmJ9SV1fWrl0LVcXu3bsHzfNqAEzV0UCqaxqhqvh1TjGe9dWGBLpoV6k/n77UfGL9U2mrU7KdKqUmBkCyigGQHBfcru+HWVOhqvhx9pRBt9eC2/U1tLThc0WN5ryvZFRCVVE8fkJKdchbXV0NVcXRo0cHzfNqAGxuboaqYuHChXHfyy36+/tRVhZ48vzv8heG7Jfh7fqC9+dRvnr8ZKCd6g+zpkbdn4nsxgBIVjEAkuOMKyafTlsVePAjV/GZtJVR21cZHnb1mvOajl8zO1Q+efJkktZk+CoqKqCqOH/+/KB5Xg2A586dg6pi2rRpcd/LLY4fPw5VRWlpKe487DDXb9upm4Nu5Ya3U/1M2krkDlzVDn5anVcAyUkMgGQVAyA5zmgz9Y9ZFWa/atHaVwULDxpNTU1QVSxYsCBJazJ8xcXFUFXcvn170DyvBsDbt28HrtYWF8d9L7cwrtRu27Yt7vpFaqdq9Fv5D1kVbANICcEASFYxAFJC1Ow/g+yBURVeSlsetX1VsPATsdGpcrRA5Tbd3d1mfbu7uwfN92oA7OnpibnebnPnzh2zvvfv3x/S9ghvp/rnacuhqsjOzcPHfWtTqp0qpSYGQLKKAZASYvPmzVBV/Hve5Jjtq4JFOhEvXRpodN/U1JTI6o9IvCthXg2AAMyOkm/duhX3/ZKtsTHw8MfixYsBDH17hLdT/Vn2RKgqZi9Zm6iq0+8wBkCyigGQHNfb22sGgiPHT8ZsXxUs0onYaKs1ZcqUQUOruc358+djtoXzcgCcPj3Q1U9ra2vc90smv9+PSZMmhbQtHc72CG6numrrAagqSkpK0Nvbm4jq0+8wBkCyigHQRYKHSfPSsFKHDx+GqmLq1Kl43N1rKZgEh8mLFy8movojdvTo0ZhtFr0cABctWgRVxeHDh+O+XzJdunTJHI7wyZPAuox02z3u7jWfJG5ubk5E9RPCq8elVMcASFYxADos1sGzq6sLt2/fRkdHBzYeuxbSWXK826OpxBgabPfu3bYEk5qaGqgqamtrna66JTt37oSqYu3ayLcEvRwA169fD1XF9u3b475fMm3cuBGqinXr1pnTrGy7Xbt2QVUxd+5cp6ueEMHDN5rHpaJGrH+/Fe3t7ejs7Awpz7CYOAyAZBUDoIMiHTxfLtqEeas2YNq0aWbDc1XFb3KK8beZs/CCb92QHpBIFdeuXYOqIj8/H48fP7YlmLS2tkJVMWGCu/sErK+vj9le0csB8N1333V9SO/v78fEiYF2e6dPnzanW9l2jx8/Rn5+YOjCtrbU/bsFBj/o8qJvHb6TOQu/ySkOOXZVVFRg165dqDt0wbM/Yt2IAZCsYgB0SPjBc5SvHq+kL4JvYAxc42V0E2K80nML8MWgMW9TvUuJ2tpaqCpWr14NwJ5g0tfXh5KSwBBcly5dcrT+VhgPrEQbE9fLAfDQoUNQVSxZsiTu+yXLhQsXzDZ7fX195nSr22716tWuD7/xhA7fWIcvZlSbY3IHRj5RZGlByLHLl1uIV9JDO9H2wo9Yt2IAJKsYAB0QPvbtKF8dvps50zxQ/ipnHL5TsASPOzqxp7Udz/nW45X0Rfj3nFKzzPeyZmCUr858j1TsVLa7uxtFRUUh7fXsCibGEGubN292rP5WzZwZ+M7PnDkTcb6XA+DZs2ehqpg5c2bc90uWDRs2RByyzuq2M4JlUVFRSnSDE8nTzq7r8L2sGeZx6Zc5pXglfRH+xLceo3z12HHiKg4dPozf6HizzN9mzsTooGNXqv+IdSsGQLIq6QHQi21GgkcKGO2rMztADhwcZ5njjBrrHVz2G5lzzFEFvp81zQyBqTislDEkWEVFhfnErl3B5MSJE+aDJW59Gnj8+MBJ8caNGxHnezkA3rx5E6qK8ePHx32/ZPD7/ZgyZQpUFR988EHIPKvbzu/3myPApOrDIIHjUh3+YeDYlZur+EbmnJBgZxyX9rS241lfLb6TOcs8zv1jVsWgsqn4Izacm85XDIBklSMBcKh/JBEbGHugzcjTUFeHN7Omm7dMXstYEPHgGTxtlK8er2UsQM5ACPx25uyUPXgaoyvs2LHDnGZXMOnp6UFBQeAW1M2bNx2pvxXBnSF3dXVFLOPlANjV1WWuvxu7RDECakFBAXp6ekLm2bHtduzYAVVFdXW1I/V32p7Wdnwrc3bUY1dwqAv+ERt87Pr7rOkhdzFS8UdssOGer5wOiwyAZJXtATDWH0lvby/u3buHx48fY+Oxa4PayHmlzYgR6v5P5jzz1/OrGQsjHjwjDSs1yleP1zOqzRPoNwuXp9yV0eBRO+7du2dOtzOYGG3sggOmWwR3Ah3tCqWXA6Df7zdv/7e3u+/Hy+7du0M6fw5mx7a7f/9+xP0/VbS0HDfr/3pQm+RIt3XDf8S+mrHQvIvxRuY8T1wBjNSm++n5qg6175/DvXv3zB87ibi4wQBIVtkaACP9kbyUtgJ/nzUdvw57cixTC/CT7Mn464xq85aoV9qM9PX78bXCVeZB8KsZlTHXL9rBxWg3WFBYhPv37yd5rYbH6AIl/AqIncHk/fffh6pi/vz5ttbdDsaTytOnT49axssBEIB5G/T8+fNx3zPR5s+fD1XF/v37B82za9stWLDAtT9QYrl37575kNXfZs6M+yM90o/Yr2Y8/fH7cvqSlD+eh4e5Z321+OuMavwkezIyckMfhhlXOgl/nzUdn01b4ejFDQZAssq2ABj+R/Knaavwr9mTQ/4wjO5Awqf9Jqd44BaDN9qMPHjwAIXFJUG3QeIfBMKHlRrlq8dfFDViYvlMM0i5ta1buFhtoOwMJsZVxry8vKi3WZPF6Px60aJFUct4PQAaAejIkSNx3zOROjs7kZeXF/XqnF3b7siRI1BVlJeXp8zfbn9/vxmO586diw1Hrw46LkW6kjX4R2wdvp8V6OoqLbcQ6w+4e0SYWEKvcNbhtYwFg7rCUVXkRTi3/Wv2ZPxp2ipHLm4wAJJVtgXA4D+Sb2bONtuBZOfm4QdZ5Xg5fTGe99XgvbO3se7QZfxZ2kp8I3MOfptbZP6xvJVdFtIPXiq2GfH7/aiqqoKqorSsAmMKNw/5NkDwsFLGMGl37twxb6Xt27cvwWszMleuXIGqorCwcNBTkHYHEyNoGsN4uYXRD9769eujlvF6AFy3bh1UFTt37oz7nonU0tIS8+qsne1Ujb/dy5cv21Z/J+3fv99sunD37l0AkY9LkYT/iH3WV4v/yJsAVcXChQtTJgSHM9o4vuBbh7eyy8zz1W9zi/CNzDn4s7SVGO2rxbrDV7DjxFW8nL4YP8gqR3ZuntmG8psDbbntvLjBAEhW2RYAgxsCv54RCEA/yi7DJ9LWhOz44Q8+POerxdcz55h/LL/OKcanB34xpeIVwIMHD5pdQNy5c2fIB08g+snEuNVZXFyMhw8fJmI1LDE6QF6zZs2geXYHE2MkB7f1uTaUkTC8HgC3bt0KVUV9fX3c90wkYySZaF0I2bntjBDstv0zkocPH5r9kh44cMCcPpztEX68u3HjJgoLA32f7t692+lVcMSe1nZ8Om2V2YwpOzcPX8+cg+fCmi6FPxDzibQ1ZmAMb0dpx8UNBkCyypErgKN9dfjf6ctDdvjgP5JIbUY+k7YS/5ETGOM1PbcAXylcm3JtRh4+fGiOU7t3714A9pxM/H4/5s6dC9WnHSq71ZMnT8zuT1pbB9/2sTuYnDlzBqqKKVOmuOoKgzEWbqxuQLweAI0fLsuWLYv7nokS3P3L2bNnI5axc9udP38+0C5s3DhXPg0dbOXKleat3+C/Javbw+gUvKCgALdv33Z0HZxw4eIlZA50ev0fOePwmbSVIee0WA/EjPLVD5wL7W/exABIVtneBjDSwwyR2j5EevDhBd86/Dw7cMsgv7AIV6+m1i3gVatWQVUxe/Zsc4gyu04mbW1t5q2HCxcuOLUKlp08eRKqikmTJkUcps3uYBLcHYybTi7GUH/nzp2LWsbrAfD06dNQVcyaNSvueybKnTt3zLbI4d2/GOzcdsGB8/jx47asgxMuXbpktqe9fv16yDyr28Pv95s/iObPn++qH2rxXLlyxbwq+vPsiSFNlIzzWrwHYmKdB61gACSrHH8KONIfSXD58AbGXyjajEnTZ5u/mt3Yx1skxskuLy8vZAxQO08mdXV1EX+hu8ny5cuhqtiyZUvE+U4EE+Nhg0hPdCbDULtA8XoAvHHjBlTd1Rn0UJ4ct3vbGbfC3TosXvAdhki3qu3YHvfu3TP/JoJvL7vZjRs3zDs61dXVqG++PMIHYmKfB0eKAZCscqQfwKH8kRgitZHr6elBZWWleWvv0aNHttXPCT09Peav/PB2RXaeTB49emQeRE+cOGHrOtiho6PDfMo7WnB3IpgYne6uWLHCUv3t0tnZaV6tjXXbz+sBsLu729wO0a62JZpxm9OutplDKWv0CZmXl+fKY9nx48fNdsuR6mfX9ti3b5/Zltnt3Vo9evTIPKZXVlaa++9IH4iJdx4cCQZAssqRkUDsePChs7MT5eXl5hUvN7ef2bRpkxlWnRhVIJjxdGl5eXnIAPZuYDxBGOuWnxPB5PLly+aVJjdcGTWufJWWlsYs5/UACMDsT84NV/L9fr/ZPvXSpUtRyzmx7YwrbEbbYLfo6+vD1KlTY4Ziu7ZHf38/5s2b57p2oeF6e3sxZ84cqAaGsezs7DTnDWdbDOc8OBIMgGSVIwHQrgNGe3u7ecBeu3YtnvT1u2IcxuAhfjbtP2n2KXbmzJlBZe0+mXR3d2PChEA7yf0HDrhqe5SWBYa9e2/PnqhlnTi59vX1mVdGl20/mvRtsX574EnwSVOnj+jHjx3l3RIAZ84M9GO5cNPepH8vmw6cCjyMUFiEnt7o9XZi2x04cMDcJ9zy91rTfBUrG7ZDVTFx4sSEtIm8efOmeZfg+ImTrjp+1TRfxXtnb2PNmrXmD8o7d+6ElHXy72q4GAC9599E5KKIdIvIfhH5XJzyY0XksIj0iEiriPxomJ/n6gAIABcuXDAD1ncLFjt6SX0ogof4Ge2rwy9zSgO/FOdF7vDXiQOGcaXNp8Uho6gkc3t8Km212efVK0Ubo9bDie3R0NKGX+YFulswRl1J5rb4m4xAR7r/kl0Wsx5eD4ANLW34eV7gKv7fZMxP+vdiDM344+wptn0vQy1be/A8cjRwHDOeIk328etZX63ZoXHVushtdgHn2kSmaTE+4lvviuOXUYenQ3DmRXzYjgGQnPKmBILcWyLycRGZIyL3ROS/RSn/rIh0iMgkEfmYiPxSRPpE5MvD+EzXB0AAqFzdYPa/FDy8TqLHDQ5v3PvGwAklPbcAH/Wti1gPJw4YG45cMTvQNk6syd4e3x4YOP7H2VNi1sPu7WHU4WuZc83OxJO/LWZBVfFm1nTbtsVwyyc7ABrb43tZM6Cq+E7mrKR/Lz/OnjLwI2FeUvZRo084Y3i1ZB+/vjTQX+s7uUX4E19twgLxhiOXzS6/vpc1wxXHr1G+wOhVWbmBq5Nfz5ybsOP5SDEAest+EZkW9P8Picg1EUmLUn68iBwPm7ZcRDYN4zNdHwD7+v0YU9RoHjx/nVOM5301IQeNSI/V+/1+dPQ8QUfPkyG1C4tXPnyou0+krUHmwMHi9YyqqPWw+4Bh1OMrA1eZfpMTehXQju0xlLKh26POvJIwNmNhzHrYvm8M1OGltOVmGB890OdWrC4X7Nwe4fvGD7ICV72+ljnXtm0x3PLJDIDB28P4kfTPWVOTuo+O9tWZY7YaPyITvY/+VfoiM3Alex8Nvvr3lYzKmPVwYnuMSV8K1cBYwS+F/ahPxvH8T3zr8XZOoL3qT7InY7SvLiHHcysYAL3j9yVw9e5bYdMXiMj6KMvsFJGysGlviciDGJ/zYQnsLMbrGXF5ADQ61nzeV2P2xP4v2WWI17Gm3Se18PEgjasJP8ueGFIXK/UYSlmjHs/5aoOuAlaFbItE1mOUrx6fS18GVUVGbkHE3vGdqkd45+MZA4E8fBD2SJ2uOlWPUb56/Cx7YkgYTtQ+moiyQykfvD1eSV8IVcUvciYkdR/9s7SVA/to+YvUygAAIABJREFUvhm+Er2PPuurRdpACP2L9CVJ3UeDr/4F/80msh7GD6V/zxlv63cy/O1Rhx9kBYaU/G1uUUhff07vo1YwAHrH/5DAF/kXYdNLJXBlMJIzIpIeNu2Ngff5gyjL6MD8kJebA2Dw0DqfTVthDhn31Yx5IQeM8KF17D5gBNfj1YyF5i3pTwcN9G21HkMpG1yPr2RURrwKmOh6/MPAoO//kDVt0EneyXoE12GU7+ktvjcyY+8bTtfDCOYvpS23bVvYXWcn6xG8PV5KW2EGjUTuG+H1MP5WfpI9Oan76JtZgQel/imrPGn7aPDVP6PNbDLq8aJvnRmI4/3NOrmPfnGg3V9OruJz6csSuo9awQDoHYkKgAm5AmjnrYvwX65GA/uc3LyQE2yifjE+76vBO7mBsS2/mTln0MkkvB5239YKH0f5nYGw8aWwq4CJvBJpXHkLP3g6vT3C9w2jkb/RDjBaHezeHuFXeXJzA33fvRg2aoCVbTHc8k6VHUr54O3xom+d2Rdg+I+URF4B/GH2VLNtVzL3UaOpQlZufsgDEIncR6Nd/YtWDye3h/HQRWZuPj4eNG58oo7n4e3+En08t4IB0DsSdQs4nCNtAO00eGidOvwwa6rZHvAFX01C2lcZ9TCudr2dUzKktnd2C98eXx24svHrnGKM9tUmvC3iawNXQ3+dU4zgW+GJ2B7h2+LPB06uabmFGOWrS3i7ptG+evNp6MzcfHN7JGrfcIvQ76XOPMF+Mm11zO3h1D462ldn/mgL/pGSjH10lK/ObGv2xYzqhO+jz/pqzaY0wVf/knX8GuWrM5tMBB4gs972bijl+/r9eLlos/ld/Gv25IQfv6xiAPSW/SJSEfT/D4nIVYn9EEhL2LSl4oKHQOxmPK1lHDQ+4qsxnyL7l+wybDx2bdAyTtxeW950wGy4/L/DTiTJeHpttM+4ClhoXgVM1JONRj1+kj0ZqopvZc5OyvYI3hbP+mqRNdBE4E/TVsWsg93bw6jHF9KXQFXx/3JKkrJvuEXw92KcZMekL03o07dGPYxQnp2bZ17xStY+Osr39In1n2ZPSvg+alxxeye3MCnbwqhH8Pb4dNoqs2nPq+kLE/LEvN/vx7T5S8x2f8FX61Plb5YB0FvelED/fz+UQLcusyXQDcx/H5g/TkQWBpU3uoEpFZGPisgvxCXdwDghvL+mz6atMPvV2hOh42G7DxjBw729lf807IzyJb//KuNJy3d0HDYcHdyGB3Dm5Hrv3j3z9p5xdScZ2yN4W/x04GrCdwsWx6yDU2Hj7woWmVczkrVvuIXxvRg/El7PqE54/3sAsKBuW9ADW8nfRz+etsZsJlCz73TUZezeHv39/Rg3YdKgNnfJPn6N8tXjmwPdSBWVlKKrq2tQebuP5wcPHjT7+/tq4dNbz6n0N8sA6D2/FJFLEugPcL+IfD5oXrWIbA8rP1ZEmgfKnxOXdATtlOAe2/e0tmPfQIfI+fn5uHLlSkhZuw8YGzduhGpguLfOrm5X9WC/5v0LKBoXGDGlubk5YlknTq7btgVOrNXV1UnfHsa2mLm0BqqKNWvWxizvVNjYsmULVBXTFqxM6r7hFn39fsxbvCowGsiaDbaNjDKcsuvWBdohLlhd54p9tKb5KspnBX607dixI2p5u7fHkSNHoBoYonDnB9ddc/yqab6KXadvoLw88CRufX39oLJ2Hs/b2tpQUBB4+GTXrl2Dziup8jfLAEhWpVQADOf3+83B3adMmTLiMRvjlT937px5pau1tdX29bDD7t27oaqYOnUq+vv7B8134mrC5MmBKzstLS22rIMdzp49C1VFWVlZzHJOhY1Vq1ZFvSr9u2rnzp1QDQznGItT34kx1u3Zs2eHXXenGGFsypQpEf9eAXu3R39/PyoqKszQ40bnz583j7Pnzp0LmWfX8byrqwtlZYE+ZZcuXeqKscNHigGQrErpAAgE/qCNA/yyZcvMP2i7DhiPHj0yx96tq6tzbD2s6unpQWlpYFi6I0eODJpv98n19OnTUA2Ml/nkif1dHIxUd3e3OXRgrP3aqbAxd26gfdfJkydHVH8vOn78OFQVlZWVMcs58Z08ePAAqoq8vDx0d3ePqP5O6O3tRUlJoG3k6dORbwPbuT1aWlrMv1c3bYdwdXV1UA2MTfzo0SNzuh3Hc7/fj2XLlpk/EIMvGKQiBkCyKuUDIBB6Sb+xsRGAfQeMRYsCbbpmzJiB3t5eR9fDql27dkFVUVFRMeiqgt0nV+NAumnTJtvqb5dZs2bFvTLpVAA0Qnhbm/vbECXKtWvXzJN6LE58J0bwmTVr1ojq7qRNmzZBVbFkyZKI8+3aHn6/H9OnB/of3L59u231d0Jvb69Z10WLFtn6g95onlFQUIBr1wY/OJhqGADJKk8EQAA4evSoefvg4MGDeNjVax4Atp26GbddR6QDhjFoeWFhIW7dupWI1bCku7sb48cH2gIePXo0ZJ6dJ9f79++bV9ncuF2M9pobNmyIWsaJsNHT02Pug5Easv+u6uzsNLdLT09P1HJOfCf19fVQVTQ0NIy4/k5pb283t8vdu3cHzbdre5w4cQKqinHjxqXEfnnz5k0UFgZ6Nti2bRuA4QfA8OP/gfffN7d1+LExVTEAklWeCYAA8O677wb+yPPy8PWC0FEY4j3ZFX7AOHy42TxgRHuwwo127NgReAhh2rSQq4B2nlyNX9ILFiywvf52MG45xrrq40TYuHnzJlQVJSUlI667Vxm3O2/cuBG1jBPfyYwZM6CqOHHixIjr7qSFCxeG3LkIZsf28Pv9mDlzZkiYSgXNzc0hgW04P+gbWtrwuaJGs/xfpS9CzsB7uf0K6HAwAJJVngqAfr8f06oCg4zn5Obhr9IXmQeBWH07hR8w/jJ9sdnFTFNTUxLWZOS6u7vNk23wLVC7Tq49PT3m+3/wwQeOrINVDx8+jHslzomwYbSLdOPtxmSbM2cOVBWnTp2KWsbu7yT4ymNwezI3OXnypNk2L7yJiR3b49ixY+bVv1Rr89bY2DjQfjMfXysIHd872g96o4/BkPA30MfgD7IqIvYZm6oYAMkqTwXAvn4//qKoEf80MMh4Tq7ibzLmh4TA8N7dww8Yr6YvNA8Y/5xVnpIHjO3bt0NVUV5ejr6+PgD2nVwPHDhgPm3s5ifo4j356UQA3LdvH1QVy5cvt1R3LzKejn7vvfeilnHqQaWKigpLdXdSf3+/+VTq/v37Q+ZZ3R59fX3m38HOnTsdWwen+P1+VMxbZP6gfyV9Ycwf9MYoI0aZL2fMR85Af4v/lFWOZ6OMMpKqGADJKk8FQGN8x9G+Ovwgq8L89f/9rGn4kwjjbgYfMEb76vCtgc5IU/2A0d3dbT6MYJxU7Di59vf3myeUffv2OboOVhl9v23dujXifCcCoNH2cPPmzZbq7kVNTU1R+3gz2P2dGE0V1q9fb6nuTjN+VJWVldnabMN43wkTJsRse+lW4T/oVQMjDo2OMsSicfz/E996fH9gyE7jyt/ooGHeIo13nIoYAMkqTwXAmuarQbcJ6swhl1QVv8kpxusZVXjOV4ua5sBoGXta2zHaV4eX0xfj/+aMN8t+L2tGyh8wjIN/aWmgZ307Tq5Gu5zS0lLXn1AOHToEVUVVVVXE+U4EwMWLF5sPIVGow4cPm092RmP3d1JZWZkSbXh7e3vNH2zHjh0zp1vZHj09PZg4cWLEK4upIvgH/feyZpjH5/+bMx4vpy+GMXavcXxee/AiXs+owm8GxjrOzVV8LXMugsf4HeWrN4//qY4BkKzyVAA0DhghbUXSl5qDn6sqMnPzUT6rEuvWrcPkWfPNcXRVFWm5BXgtY8Gg90jFA0ZfX5/Z8WtTU5Plk2t/fz/Ky8td3ZFssNu3b5tPcEfqp9CJAGhcHT1//rzl+nvNhQsXzGYJ0dj5nfT29iI/Px+qijt37liuv9MiPbxlZXsY7eemTp1qNgNJNaE/6OvxWsYCpOcWmMfrd3IL8S/ZZZhauQQLFy5EQWGROe/XOcUYk7500LE8VX/QR8IASFZ5KgAat3RHh/3BP+dbjzcy55m/DMNf6bkF+G7mTLwQNCC4Fw4Yp06dMvu9unTthrk+8Z6ii3TiMUYuGD9+vOuv/gGB9kPGVZXLly8Pmm93AOzr6xtSB9S/q+7fvw/VwLCNiRj54uLFi2bfg25uq2ro6uoyu3A6dOgQgOFtj+CnZDccOG2GX7c+qDUUkX7Qv+Bbh+9mzgwJgsEvn47DG5nz8FxQk5/gdoOp2KQnGgZAsspTARB4+lBHeAgcPXArYfXO/9/e3UfHUZ1nAH9IcpKmpbRJmiaNcyLb0CaEkJCkh2CSEgopgZKkkLaBlJ5TQdMGCKenSUpX33plWbJjbIyxbNnGH7KDjGwJrC+QXbChRZYB1xa2c2yMZbBiowK2AVvYkvWxb/+4O6vZ0e7qY0a7O7PP75w5iUe76F5d7erZO3Pfu087Ozu1vb1dX3jhRb1pzuN6cag5bvDz+xtGOByOlpm4r2xRzKWQZGVx4l1OsrZ988Psn6Wuri5hm70OgFZNt4qKCl8EjlQLh8PRYu3xat6pejsm1vZzmzZt8qT9qbBz504VEV24cKEODAyM++cRW8WgRX9SbF6ri6pX+/p3MdEHevOhvlmvzH9Mf1S+Xv/n+ee1s7NTe3p69Kl9byR5/49fBcKvGADJrcAFQFXzhmhfDZYs8CQPjP5/w9i88xUtiqxqvq6gZlz9c9bc2rZtu/mDsmhRxu+GYtfR0aEi8XdamKoVp9XV1Z60PYiqqsyN+c59Xi1ejkltba2KiO7cudOTtqfC4OBgdEXws88+O67ad84qBt8pWKsiosWlZfrlvAbfv39N5v15Iu//fsYASG4FMgCqmk+PHV0ntbHzuHZ0nRyzcGgQ3zCsT9DWYpiC0nK9LO/xpDOczpqIX8mr1+JITcRMLaabyPHjx6OFmZ0zIV4HQGv2xk8zTqm2YYOp0blr1664X/dqTMLhsM6dO1dFxHdbfllFzMvKZut1c5qSvic5y55clve4FpaaS783F67y/RUMy2Tenyfy/u9XDIDkVmAD4EQF8Q1jZBVds95T/IC5FFwyX2c4Lnlb9zg6ZxOmh5r1vhJzH91Pih/0XU3E4eFhraioiLsDhdcB0NpyzG+Fw1Np69atKpJ4WzavxuTNN99UEdHKysqE9xtmqnA4rA8tX6Mioj9zvFads172e+RmhJr13hLzGr+7eIHvqxg4BfH92S0GQHKLATDA7Kvovpj3hOZFbpy+o2hJzP2AjZ3HR80m5IRa9PaipdFFMpeGnvDlbIJ1D+RLL70Uc97rAGh9nz179njW9qCxSvMkKgXjdbHy9evXe9b2VBkaDuu1FU9GFzncVrQ04X3JI6/vFr0jUvc03zHLb72+KXgYAMktBsAAc66iuzq/NloZ317rsKPrpOOxIzUUS0tFv5X/qG9nE6xdURoaGmLOex0AFy1apCKi3d3dnrU9aLq7u6P3ksbj1Zg0NDSoiD/3fbVeh9/MfzS6svX7hStHLYIYec226G2RD2olpaKz8mvjPpaChwGQ3GIADLB4q+iuL6iJ/mG5q3iRfrviqZjZhJmh5piiqzcXrvL1bMJrr70WXVlpvw/QywA4ODgY/Xm9//77nvchKM6ePRv9OcVbTOTVmFgr1v1Yj9E+a39z4aroz+u2oqUxpU0aO4/r6TO9em/Z4ugHtetti7wS3eNLwcEASG4xAAZcvFV0f1mwTosjK4Nnl8/RlpYWrWvdpj8sXK73l4wUU/1rR/jz42yCvSCwvfyIlwHwrbfeUhHRuXPn+rrsRipYtRl7ekbfwO/FmFj1BsvKynxRr9LJOWtv383o/pIK/WHhcr2xYLWuqq3XysrK6Irf6xwF7INSxYASYwAktxgAs0C8VXQ3zGnUBxYvjVtM9f7SipjLvn6fTVi1ysykvPzyy9FzXgbAAwcOqIjoypUrPW970KxZs2bUlmcWL8Zk3759vh6LeLP2s/Jr9f7Siriv1eXLl+vj7fsDWcWAkmMAJLcYALNEvFV04XBYu7q6tK2tTTdu3KhLa+r0uoJ1owpj+302wVp92tTUFD3nZQC0tvHavHmz520PmqamJhUR3b59+6iveTEm1mrsLVu2eN72VIk3az8z1KzXFazTHxdV6eJH1mlbW5sePnw4OuPMVbLZhwGQ3GIApBhBrIn4yiuvqIjokiVLoue8DIDWooP29nbP2x40O3bsUBHR+vr6UV/zYkyWLTP3rx44cMDztqdSEF+H5C0GQHKLAZBGCdpsgn3xgbVIw8sAaIWOQ4cOTUn7g8TaMWXZsmWjvuZ2TM6dOxeoxThBex2StxgAyS0GQMoKS5cujZkZ8ioADg8Pj7nHLY145513VES0vLx8VJFmt2NihUv7TC9RUDEAklsMgJQVWlpaYnah8CoAnjhxQkVEKyoquAJ4HOyB+dSpUzFfczsm8e71JAoqBkByiwGQsoK1OnTFihWq6l0A5ArgiVu+fLmKiB48eDDmvNsxWbFihYqI7t27d8raTpQpGADJLQZAygr2+nD9/f2eBUBrpxGuAB6/zZs3x92pw82Y9PX1aVmZqW155syZqWw+UUZgACS3GAApa1jbtR0+fNizAFhfX88VwBPU0dGhIqIbN26MOe9mTOKt9CYKMgZAcosBkLJGY2Ojiohu3brVswD48MMPq4hoV1fXVDY9UI4cOaIioosXL44572ZMtmzZoiKizc3NU9l0oozBAEhuMQBS1ti7d2909wQvAmB/f3+gyo6kir0sT39//8h5F2Ni3Ve4f//+qW4+UUZgACS3GAApa/T29kaDx8l3T7sOgEePHlUR0QcffHCqmx44CxcuVBHR3/72t9Fzkw2AJ987Ex3X3t7eqW46UUZgAAyOjwOoBXAGwHsAVgO4cIzn1MAMvv3YMsHvywBIWcWqB7hn7z7XAfCFF15QEdENGzZMdbMD59FHH1UR0V27dkXPTTYAvrz/NyoiWlVVNdXNJsoYDIDB0QbgZQDfAPAtAIcBbBjjOTWR533adnxsgt+XAZCySltbm1m129TkOgBa9xTG29eWknv66adH3bM32QDY3Pqkioi2trZOdbOJMgYDYDBcCjOIf247dyOAMIDPJHleDYBGl9+bAZCyirVa9KHFi10HwOrq6rj17GhsVv3E6urq6LnJBsCHH14SiP1/iSaCATAY7gLwruPchwAMAbg1yfNqYC4Xvw3gEIBqAJ+Y4PdmAKSs0t/fH60X98W8xycdAAcGBnT27NkqIvruu++moumBcvr06WhdxvPnz6vq5ALgZXmPR/87fX19qWg6UUZgAAyGApgA5/Q2gHuSPO92AD8AcDmAWwAcAPASgA8mec5HYH5ZrGMaGAApy6xatUpFRL9TUKM5oVbdfvAtHRpOvI1bvGDS3d2tIqILFizgFnCTZC0EOXr0qKpOLACe6RvQnFCr3lCwRkVEV69Zk4omE2UMBsDMNg+jF2k4jy9g8gHQaWbkv3l9ksdIvHYwAFI2eWRjs4qI5haPXAa+qvIZbdvfE/fx8YJJe3t73GLGNH51dXUxRbTHGwDb9vfolRVPa06oVe8sfkhFRP+hfG3C8SMKIgbAzPZJmICX7PgwJn8JOJ4TAH6a5OucAaSs1ra/R7+et1FFRAtLZ+uMULPmhFp1euSIFyLiBZPHHntMRUR37NiR6i4ExvPPP68iops2bVLV8QXAtv09Oj3ymBmhZi0sNZfhv5a3MeH4EQURA2AwWItAvm47dwPGXgTi9NnIc34wgefwHkDKGkPDYb2q8hnNCbXof5ZWqIjorPzaaOiYHpkJdF4OdgaTcDis8+fPH1XHjibm9ddfVxHRhQsXajgcHjMAjoyfecw38jeoiGiodI7mhFoSjh9REDEABkcbgD0ArgTwTQCvYnQZmFcwMiN4IYAHAFwFYDrMZd/dked9ZALflwGQskZH18loePhxUZWKiP6oaFn0nHV0dJ2MeZ4zmJw6dUpFRMvLy3VwMPm9apTYwMCAlpeXm8LcJ0+OGQDt45cTatW/KzKrsP+xaEnS8SMKIgbA4Pg4TODrBXAawBqMLgStAHIj//+jALbC3Cc4AOAogJUAPjXB78sASFmjsfN4NCR8K98UIv5lSaXmhFpiAkRj5/GY5zmDyZ49e8zCg9Wr09ST4Fi7dm20IPRYAdA+fjmhFv1lSaWKiP5F/q+Tjh9REDEAklsMgJQ17DNIM0NNWlRqysFckbdpQjOA9fX1LADtkeeee05FROvr6yc0A/jVvE0qIlpUOltnhpo4A0hZhwGQ3GIApKxh3UNmLSK4q3iRiojeUrhi3PcA9vad11/96lcqItrd3Z2mngSHVU5n/vz5+n7/wLjuAZweatVbCleoiOidxQ+NeQ8nURAxAJJbDICUVaxVpNNDrXptwToVEf1FyVydHllEMNYq4K7XTWCZO3euDg0NpaEHwTI0NKQVFWZBzuvHjicNgKrW+LXoz0vmqojoXxasG3MVN1EQMQCSWwyAlHXa9vfoVZXP6MWhpmgZke/O2TyuOoDPbH9WRUTr6upS3Org2rDBrOZ9etv2cdUB3PRcZ7SMz8WRy7/J6jgSBREDILnFAEhZaWg4rB1dJ/WhR9ariOiTTz2V8LH2ALhixcroogXyRmenCXRLly0bVwBsbW1VEdEV6x7Txs7j2tF1kpd9KeswAJJbDICU1V599VUVEZ03b54ODAzEfUy8fWd7e3tT3NLgOnv2bHR/5i/lNSQNgIODgzpv3jwVET1y5EiKW0qUORgAyS0GQMpq4XBYFy9erCKiu3fvjvsYa9/Z7xU+oiKiNTU1KW5l8K1fb2Ziv1f4SNL9mXfv3q0ioosWLdLh4eE0tJQoMzAAklsMgJT1duzYoSKi1dXVGg7Hho6RfWdb9BeRhQd/W/4o7zfz2Lrm7dEFOVZdRud9feFwWKuqqrgFH5EyAJJ7DICU9c6ePRtdiXrw4MHoefu+s7Pya1VEtKC0XC8JNXHFqYfa9vfoJaEmLSgtj9mez7my99ChQyoiWllZqX19fWluNVF6MQCSWwyARKq6bds2FRGtqqrS4eFhx76zLXpP8YKYreNYc84b9p/zj4qWqYjo3cULorOA1s95YHBIly0zX9+6dWu6m02UdgyA5BYDIJGq9vX1RQs8t7e3x+w6cU3+ryO7TpTpF0JPcNcJD9l/zpeGnojuznKNY3u32qb/ii7WOXfuXLqbTZR2DIDkFgMgUYS1wGD27Nm6fstOzQm16uV5DZoXuTR5a+HymFDCfWfdi93ft1VvLVyuIqJ5peV6eWRF8NX5tSqRVcKJFuoQZRsGQHKLAZAoIhwOa0NDg4qISlmZ3l28IFoo+r6S+Toj1DwqAHIG0B37DGBOqFVnhJr1vpL50ULPdxcv0JJSURHRhoaGUYt0iLIVAyC5xQBIZDM0NKSNjY0mBEaOe0se0M+HNscEFd4D6A3n/sw5oVb9fGiz3lvyQMwYPLF5M7feI7JhACS3GACJ4ujp6dF1zdt0Vv4GnRFZkGAPf1wF7B37/swjP+MWnZW/Qf+qYK02PL8v3U0kyjgMgOQWAyBREta+wfYAyH1nvcefM9HEMACSWwyARGOw9g3mvrNTiz9novFjACS3GACJiIh8hgGQ3GIAJCIi8hkGQHKLAZCIiMhnGADJLQZAIiIin2EAJLcYAImIiHyGAZDcYgAkIiLyGQZAcosBkIiIyGcYAMktBkAiIiKfYQAktxgAiYiIfIYBkNxiACQiIvIZBkByiwGQiIjIZxgAyS0GQCIiIp9hACS3LgKgx44d09OnT/PgwYMHDx48fHAcO3aMAZBcmQbzC8SDBw8ePHjw8N8xDUSTcAHML89FU3BY4XKq/vvpPtg//x9B7yP75/8j6H1k/9z/9y8AUYa5COYX/6J0N2SKsH/+F/Q+sn/+F/Q+sn9EART0X3z2z/+C3kf2z/+C3kf2jyiAgv6Lz/75X9D7yP75X9D7yP4RBdBHAEjkf4OI/fO/oPeR/fO/oPeR/SMiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiSpXpAFYDeB1AH4AjAMoAfNjxuM8BeBLAOQBvA3gAwIdS1kr3CgF0wLT/vQSPibdlz+0paZ174+mf38fQ6ShGj1deOhvk0s9g+tQP4EUAV6a1Nd4SjB6rV9LZIJeuAdACoAemL7c4vn4BgNkA/g/mffUZAH+aygZ6YKw+1mD0mG5JYfvcygewC0AvzPthI4DPOx4ThHEkSuhGAGsB3ABgJoAfAHgLwALbYz4IYD+ApwFcAeAmACcAVKa0pe6UAfg5gIVIHgBzAXzadvxOKhrngbH6F4QxdDoKoBix4/V76WyQC7cBOA/gTgBfBLASwLsA/jidjfKQAPgNYsfqj9LZIJduAjAHwK2IH45CMK/DvwHwZQBNAF6Df95PgLH7WAOgDbFj+rEUts+tLTDv95cB+ArMh+NuxL6HBGEciSbkfphfcstNAIYBfMp27m4ApzF6pjDT5SJ5AHS+yflNLuL3L0hjaDkK4N/T3QiPvAigyvbvDwB4A/6e0bQTAC+nuxFTxPm+cQHMjNF/2M79AczMrl+uKDglCoCNqW/KlPkkTD+vifw7iONINKY5AP7X9u/ZGP3mPQPmxfLVVDXKI7lIHgDfAHASwEsA7oL/Nu3ORfz+BWkMLUcBvAngFIBOmA8ufryk/WEAQxj9B3YdzIxDEAiAszCXE18DUAtzS0IQOMPRzMi5KxyP+28Ai1PVKI8lCoDvwVw+PQSgGsAnUtssT10C088vRf4dxHEkSuoSmFmhf7GdWwlgq+Nxvwvz4rgpRe3ySi4SB8BiAN+ECUQhmE96/5aaZnkmF/H7F6QxtPwCwLUwl2buhrlk+mA6GzRJn4EZh1mO8/NhZgaD4CYAfw8zVt+FuV+1G8Dvp7N7+9EpAAADU0lEQVRRHnGGo6sj5/7E8bhNADamqlEeixcAb4e5ZejyyNcOwHxw/mBqm+aJDwBoBdBuOxfEcaQsMQ/xFzXYjy84njMNQBeAVY7zmRoeJtPHXCQOgE5lAI550dBJ8rJ/mTqGTpPps+VOAIPw3xZO2RAAnf4Q5oPmP6e7IR7I1gDoZM2YXT/1zfFcNcwVhc/azgVxHClLfBLmD2Wyw37v12cAvApgPcynIbtMvXw40T4CEwuAN8P0MV2Bwsv+ZeoYOk2mz5bLYPrjXMmX6bLhEnA8uwDMTXcjPJCtl4DjOQHgp1PcFq9VwXzQn+E4H8RxJBplGkz4ewzxp++tBQT2FYn/CvMJ3m+zLbkYfwAsBPDO1DVlSuQi+SKQIIxhInfA9NFPKxEtLwJYYvv3BwAcR3AWgThdCHPJ3m+3WMSTaBHIL23nLoK/Fw+MJwB+FkAY5rKwH1wAE/7eQPzSLkEcR6IY0wAchqlvNA2xS/otVgmRrTDL5b8Lc+Ovn0qIfA7mk1wJTN2nKyLHhZGvfx/AT2BuAL4EwD0wN62XpbylkzNW/4IwhnazYFYAfwXmk/odMP1Zl85GuXAbzB+WfwJwKYAVMAHpU8me5CMLAHwbpu7o1TDliE7AzPj60YUYeY0pTAmmKzCysCUEM37WPXKN8F/5kGR9vBCmjuhVMGN6PYDdMBMJfvlAuQzmw/K3Eft376O2xwRhHIkSykXie63scgA8BVNE+ATMG7qfVlzWIH4fr418/UaYlaS9AN6HuVz6U4y+HJ6papC8f4D/x9DuawBegHkD74O5AT0f/vnjE899MAsjzsPMCH4jvc3xVB3MCuDzMDObdQAuTmuL3LkW8V9vNZGvWwWE34QJ9s8A+LNUN9Kla5G4jx+F+TD5NoABmPvnVsJfH1gS/d3LtT0mCONIREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREREQ0Yf8Pj4vSC9lReNoAAAAASUVORK5CYII=\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_k = 20\n",
    "k = np.arange(-n_k,n_k+1)\n",
    "k_cont = np.linspace(-n_k,n_k,1000)\n",
    "\n",
    "omega = 2*pi / period\n",
    "c_k = height * (width/period) * np.sinc(width/2 * k * omega / pi)\n",
    "c_k_cont = height * (width/period) * np.sinc(width/2 * k_cont * omega / pi)\n",
    "\n",
    "plt.figure()\n",
    "plt.stem(k,c_k, basefmt=' ')\n",
    "plt.plot(k_cont, c_k_cont, '0.5')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def set_stem_plot(handle, x, y):\n",
    "    ml, sl, _ = handle\n",
    "    ml.set_data(x, y)\n",
    "    for i_l, l in enumerate(sl[:x.shape[0]]):\n",
    "        l.set_data(np.stack((x,x)).T[i_l], \n",
    "                   np.stack((np.zeros(x.shape), y)).T[i_l])\n",
    "    del sl[x.shape[0]:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step-by-step reconstruction of time-domain signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var 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, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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INDW7zxgf3xlScplpHMGz7D7p6y10l0Hc16fxqZmm71+t9306tKUnsGz7phmw2aW2gHG3yLAauobbcScTXbuPW/H37sn3DrRrnvhXZu22p/hDVv31diwmaUtLjtf98K7oeisIAB6k7cBsKk5YuOWbrM+D8xK6e27ffyqwHyTcWMQ99kfXk49mV72+DybtW4XQRCBUrrrgN3w8pKUgeeXPznfJq/cEZhZ7/sO1dvjs0pTLmmdXjTVHpmxgYlYCJTahiZ7Zm5ZSg/2WXdMsyHT1tvuA3V+V8/MzJqbIzZz7S675rnUK2fXjlxky7bu97t6WSMAepN3ATASidjUVTvsh0OKU7rQh8/aaFWHg3sC2FFVa7ePX2UnJfVg/L+nF9iqyvz/toX8trO61m4esywl+P32xcWB7globGq2N5ZUpIy/PXPQVHt+/mZrZMIIfNTUHLFXSsrtG3cnxvd9576Z9nJJeaCHLcR6/pOHMN3w8hLbuq/G76p1GAHQm7wKgBt2HrCrRyxMGbvw2Nsb7GAerSG260Ct3fnWajvx1knxy9V/HrPMdoZ8VhaCp7ahyR57e4OdctvklEtAqyvz4/PAzJ1sxy+rtO8lBcHvP1RsM9fSw47cKynblzL055zBM+yVkvK8msVetueQ3fTa0vgXwhMHTLLBk9YEuoMlHQHQm7wIgFWHG2zQP1bHZyCeOGCS3Td5bV69IdNt3VdjN7y8JP5BcfLAyfb07E30XiAnpqzakTIm6bLH59nSPL7k09jUbC8s2GJfTVqL8JrnSvKy9wL5Z3vVYbv+pfdSlm4ZMWeT1TUGt8evPSu3Vdn/e3pB/Dmdfec0G7d0W158sSIAehP4ADh55Q772l2JrvRfPf+ule8Nz4f6kvL37bKkWVk/emSOLa/I3xMxgm1Xda395oXF8ffbtwbPyJsPdS+qaxts8MQ18R72Lw2cZE8Wb8yrHhjkj+bmiL24YIt9+W9T4ld0bnl9he09GIwxfp0ViURsxpqdKUMtfv7MwsCvdUsA9CawAXDPwTr7fdI3qvMfmGXF63f7Xa1u0dwcsVcXldvpRVPjazTdPn5VKNdngj8iETcu6bTb3Ynqi/0n2v1T1trh+vztoWjLpt0H7Yqn5sc/Py4aOievB7UjeMr2HLLLn0y8xy59fF5ox3TXNTbZozM2xGfhnzRgkj0+qzSwV6wIgN4ELgBGIm52b2ztseP7T7T7Jq8N9ODZrrLnYJ396ZXEZeE+D8yy98rf97tayHMV79fYlU8lLuX89LG5eTXOL1uRSMTGvLvVzkj6LBkybT29geiUpuaIPVG8MT6h7+SBk+25eWWBmSnfncr2HEoZh3/Z4/OsLCCrbiQjAHoTqABYVdNgvxu9OOVbe5BnInaX4vW77Zt3z4j3Bj4wZZ3VN3LSQseNW7rNTotenvrSwEk2Yk7hjTPde7AuZbztTx+b68t6hsh/Fe/X2OVPzE+5HFpo40wjkYiNXVwR/1w5eeBke2H+5kANIyEAehOYALhg09742l5f7D/RHpmxoaC/qVfVNNiNry6Nf9BcPHSOrd95wO9qIU9U1zbYH5N6ky97fF7gx+10t/HLKu0r0UvgJw2YZM/NK7PmAui1QdcYv6wyPoTi1Nsm22uLtgYq9OTatv2HUyaJ/PyZhYFZzYIA6I3vAbChqdkenLouPuW8zwOzmASRZOKK7fHL4V8aOKngP3TQvpKyffEZvsf3n2gPT19fcL1+rdlRVWs/fyZxCesXIxdxv2606UBtg930WuLL+KV8mYprbo7YyHll8cvhZ90xLRBj9QmA3vgaALfuq0m5L+Ffxi7z5dZtQbfrQOpJ60+vLMmrtQ+RG5FIxB6fVRpfyPU79820xVsYQ5ouEonYqHc2xwe0nzN4hi3ess/vaiGAVm6rit8u7bhbJthDU9cV9JWp1pTuOmgXDU2sf3jv5LW+fukkAHrjWwCcu2FPfHD2abdPsbeWV+a8Dvmkudmd3GNrIZ7/wKyCGMgPbw7VNdrvRydmzf/fa8v4ktCOVZVV8VtJHt9/og2ftZFLwogbt3SbfWmg+5Jw7j1v26LNfEloS21Dkw18c2X8M+g/h79jlfsP+1IXAqA3OQ+AkUjERszZFO+luOSxuVbxfmENou2MRZv3xcdKnjhgkr20sJxLwgVuy95DdsGQ2fGbzI9euMXvKuWNg3WN9oekCSLXPFdi+7gkXNAam5rtrgmrU94TVTX5e9OBXJuwfHt8gsgZg6bazHW7cl4HAqA3OQ2Ah+ubUpY5uXnMsoJY3qWr7TtUb9eOXBRvx7+OXU47Fqji9bvj60d+7a7p9i69FB0WiUTs5ZLy+Dimc+95uyBXH4DZ+4fq7aoRiYkN909ZWxDLu3S18r019tPH5sYXx35kxoac9q4TAL3JWQCseL8mfo/E4/tPtFHvBGvaeL6JXRJO7kn1q7sduReJuLXIYq//z4bNC8wMvHy1Znu1nXf/zPgs4dffq/C7Ssih1ZXV9u173eSpU26bbBNXbPe7SnmtrrHJbn1jRTxM/3LUu1Zdm5ueVAKgNzkJgPM37o3fo/Ord0yz+Rv3duvvKySz1++Oj6U8i7YtCDX1jSl3yen39+V5fc/RIKmqabC+z5XE2/b28asY9F8A/rGsMj7e7zv3zbS1Oxhf3VVeW7Q1PuHq/Adm2YYcLGdGAPSmWwNgJOKmiMcmLvzokTm2jV6qLrd1X41dPDTRuzpiziZ6V0OqfG+NXfjw7Ph6mS8u2MJr3cWamyP20NR18RB4+RPzbfeBcNzbFamamiM2eNKalLXs9tcwBrSrLdu6386Jjl3PRe8qAdCbbguAtQ1N9n+vLYv/Yd346lLGqXWjw/VNKQtH/+HlJaG9z2uhmrMh0dt79p3TmZXYzaau2mFfjg5m/8bd020Jt2UMlf019SnLaw2etIbxft1oz8G6lFtS3ju5+8ZXEgC96ZYAuL3qsF0SHQB63C0T6JHKkViP6xejPa4XD53DDOsQiEQi9tTsxHi/S4bNs+1V9KTnwsbdB+17D7qlYk681S3Ejvy3dkd1fH2/Lw2cZOOXsQxZLqTPsP7fZ7tnhjUB0JsuD4CLNu+zs++cFp8CPnfDni57bHizcNNeOytpzOU7G3kN8tXh+qaUZUr+MpaZ87l2sK7Rfv38u/HX4LZxKxkXmMcmrthup9w22Xr1m2Dfvvdt1lP1QfIai+fdP7PLb3NKAPSmywJgJBKxFxdsifc+Xfjw7IK7SXaQbNt/2H78aGJc4HPzyuiFzTNb99XEV9f/Yv+J9nzAbrheSJqbI/bIjA2JcYFPzrc9BxkXmE+amiN2/5S18dfwqhELuA2gj1ZVVsVvWXnqbZNt8sodXfbYBEBvuiQA1jU2Wb+/L4//YV3/0ntWU89dCPxW25A6LpB1F/PHvNI9SeP9ptnCTczuDoJpq3fGxwWeM3iGrahgvcB8UHW4wa5Jmt1914TV3B87APYdqk8ZF/jQtPVdsl4gAdCbTgfAndW18fv59r5lgj1RvJFeigDJdOcVxo8FV/rr9VPWdwyc0l0H7fzoLeROGjDJ3lyyze8qoQ0bdh6I3/LvpAGTbNxSXq8gaWhqtqJ/rEpaL3CRHejkeoEEQG86FQAXb3nfvn7XdOvVb4J95fYpVrx+d6deNHSf5Hsvn30nd4wIovQ75fzfa/TYBlV1bUPK3XjufIsepSCavHKHnRod78cdXoLt74sr4usFfu/BWbZx98GsH4sA6E3WAfCVknI74VY33u+HQ4pt855DWb9YyI3kNeROuHWivbSw3O8qIari/dS1HEcyZjPwmpsj9sCUxHqBV49YyJiygEhfy/HKpxbYXsZsBt7yiv3xe92f9rcp9vbanVk9DgHQmw4HwPrGZhvwZuL2Lr95YbEdrGO8X76oqW+0349O3EWi/xsrrL6Rngs/vbNxT/xOOWfdMc0WMN4vryTPKv33+962NduZVeqn6toG+0VS7+ygf9A7m092H6iz/3rinfiwskezuI8wAdCbDgXA9Bfmsbc30EuRhyIRdx/h3tFxZv85/B3bdYD7yOZaJBKxZ+Ym7pTzk0fncqecPJW8rtzJAyfbhOXcR9YPpbsO2vmxdRu5n3Peqm9stoFvrsy6o4kA6I3nALhs63775t2d75pFcMxct8tOu93NaPzm3TNs2db9flepYNQ2NNlNSTO0b+JOOXkv/c4S93XjnQ7QUvIM7W8NnmHLK/g8y3evlJTbibdOig8127LX21AzAqA3ngLgq4sSL0JnB2ciWDbtPmjff6g4/o157GK+MXe3rftq7EePJMb7PTuX8X5h0djUbIMnJu4te81zJVZ1uOvvdICEpvR7N7NGY6hkM9mUAOhNmwGwrrHJbnk9Md7vV8+/2+np2QieA7UN9stRiTsd3D5+FXc66Caz1yfu58tdWsIr+U4HfR6YZRu6+E4HcPbX1Kes78dnVzglLzd33C0T7Ml2lpsjAHrTagDcXnXYLhmWWN9v2MzSLlmgEcHU3ByxIdPWp8ya28eMxi7T3ByxYTMT4y4vYX2/0Fu5LfVOB1NWdd2dDmC2ujL1fr5vLOHqRZjVNTbZX8cmbjhxw8tL7HB95mEzBEBvMgbA+RsT95I9vWgq6/sVkCmrUtfNWlXJulmdVV3bYL9KupfsLa8vZ7xfgdh7sM6ueGp+/LUf0kV3Oih0by5J9LD++318ThWKSCRiLyTdcvbioXMy3nKWAOhNSgCMRCL29OxN8VmJrTUuwm3DzgP23fsT36zHL6v0u0p5a/3OA/G7Rpx46yR7pYS1FwtNyzsdMJQmW/WNzXb7+ERb/s+zJba/hisVhaakbJ+dfafrpDpz0FR7pzR1KA0B0Jt4ANx3qD5lZfsbX13aavcqwq/qcIP977Op985kvUDvIpGIvbqoPN5L8a3BM2wps6wL2ph3t6bc6aB0F5PpOmLL3kP208fmxj+THpy6jlnWBaxy/+H4++H4/hPtmaTJdARAb3pIsreXb44v8XLigEn2woItzEqENTVH7N7Ja+MfuJc8NtfzNPxCdqC2wf7wcuKWbj9/ZiGzEmFmZkuTltM6eeBke3VROZ+1Hry1vNJOiy7xcnrRVJu+mmXIEF1O67XEclrXvfCu7a+pJwB61EOS9bppjPXqN8HOf2CWra5kFXukmrxyh51e5GaufvlvU+zNJdxMvTUrKqrsvOjl8+P7T7THZzF5Cql2Hai1q0ck1gv8/ej3WCqmFbUNTdb/jcRKFP85/B0mTyFFJBKxkfPK4kvVnTN4hs1csblgAuD1krZIqpNUIukbHTi2hyT7/I1j7KbXltohbumGVlTuP2yXP5EYzH7Ta0u5BWCS5uaIjZizKX5/7HPvedsWb9nnd7UQUM3NEXuieGN8MDvvl5ZWV1bbBUNmx1eieGDKOm7phlat3FZlfaLjrXvdNKYgAuAVkuolXSvpVElPS9ov6dMej+8hyZ4vXuP3a4c80NQcsaHTN9hx0aVMzrt/pi3kvrVWvrfGLn9yfspliKoaenTQvqVb96f0GD80dV3Bj7VtbGq2YTNL41+mzr5zus3dwHqZaN/Buka76dWl9vkbCyMAlkgalvTzkZIqJd3i8fgO3QsYMDNbtHmfnTN4RsriqzX1hdcbGIlE7MUFW+yU6LI5p9w22UYvZPwsOuZAbYPdmHRbwAsfnm0rKgpzWZONuw/az6Lrz/bqN8F+/fy7jJ9Fh/19wYbQB8CjJTVJujRt+/OSxrdyzDFyDRIrPUUARBaqaxus398Ti3IWWm/g1n01Kfd9/e8n51v5XpZMQvYmLN8eX3/1+P4T7b7Ja62usTBWYmhsaranZ2+yk6KzpE+7fYq9/l4FX6aQlUKYBPJZuSd4Ttr2++V6BjMpih6TUgiAyFbx+t0pvYG3vL481HcQqW90l6diy7ucNGCSPTu3jIke6BJ7D9bZDUkzyL//ULHN3xjuL1bvlb9vFw2dkzJrnoke6AwCYGb0AKLLpfcGnjFoqo1euCV0a3Qt3LTXvv9QcQtzbcoAACAASURBVPx5XvHUfNu4m7Xc0PUmr9weX+g2dturHVW1flerS1XVNFj/N1bEb494xqCp9koJy+Kg8wohAGZzCTgdYwDRZUrK9tmFD8+On7R++thcKynL/5mNZXsO2e9GL44/r7PumGZvLOHyFLrX/pp6G/jmyvikq1Num2zDZ23M+9sI1jU22Yg5m+JLS/XqN8FuHrPM9jLWD12kEAKg5Hr6Hkv6+UhJ28QkEPiksanZnp1bFl+0tVe/Cdb3uZK8vFfnnoN1dtu4lfGlOo67ZYLd+sYKZvgip1Zuq7LLHk9MjPjm3TPspYXl1pBnS6JEIhH7x7JK+/f73o4/lx8OKbYFBTR2GLlRKAHwCrn1/66RdIqkp+SWgTnW4/EEQHSLXQdqrf8bK+L3lY5dxlq/84DfVWvXrgO1NnjSGjs1Oru3V78Jdu3IRbZuR/DrjnBqbo7Y6+9V2Ln3JMLTd++faW8u2Rb4tfGamiP21vLKlHF+X79rur26qDx0w0QQDIUSACXpBknlcusBlkj6ZgeOJQCiW5XtOZQyqL1Xvwn2i5GLbOGmvYG7hLp5zyEb+ObK+P1ae/WbYD95dK69s5E1yBAMdY1N9ty8spTxgefe87Y9M7cscAuzH65vslcXldv5scV5+02wU2+bbEOnbyjIZaOQO4UUADuDAIicWLmtyn7zwuL4gO9e/SbYjx+dYy/M3+zrbbAamppt8srtKUu69Oo3wS57fJ7NWLMzcCEVMDM7VNdow2aWxpeNiS2d8rdxK23lNn+HW2zafdDueGt1yhi/04um2pBp621/TXhXCEBwEAC9IQAip8r2HLJb31iR0st20oBJ9oeXl9ikFdtzcjvCpuaIzd+41wa8ucLOvnN6vB69b5lg1zxXYgsC2DsJZFLb0GQvLUztZevVb4JdNHSOPT17k23ecygn9ajcf9hGzNmUsohzr34T7Nv3vm1PFm8MXO8kwo0A6A0BEL54/1C9PTu3LGXWcK9+E+zEAZPsFyMX2XPzymzltqouG9+0dV+NvbZoq9346tKUy2fuVlPT7L7Ja23rPhZyRn5qbo5Y8frddv1L79mJt05KeX9//6FiGzxpjb29dmeX9cAdrm+y2et32+BJa+wnj85N+X29b3FjZmeu3cUYP/iCAOgNARC+ikQitmzrfrtrwmr7zn0zU04ksTFDVzw13wa8ucJGziuzGWt22vKK/Va5/7BV1TRYTX2j1TU2WdXhBtteddjW7Thgs9btspdLym3wpDX2v8+W2Nfvmt7icU8vmmp/HrPMZq7bVfD3XkW47K+ptxfmb7arRyyMz2BPD4R/eHmJDZ2+wf6xrNJKyvbZxt0Hbd+hejtQ22C1DU12uL7Jdh+os817DtniLfts/LJKGz5ro9346lK7YMjslMldsdB3+RPzbdQ7m23XgXCtV4j8QwD0hgCIwIhEIrZuxwEbNrPUrnmuxE67fUqLk1e25Yv9J9p/DH/HHpy6zt4p3ZN3S2gA2ag63GDjl1Xan8csa3GZuLPlnMEz7OYxy+z19ypsZzWhD8FBAPSGAIjAam6O2Jrt1fb3xRV27+S19qvn37UfPzrHvnn3jIw9G1/sP9HOGDTVLnx4tl07cpHdNm6ljV64xd4rf59Zh4C5W83NWLPTnijeaH8es8z+64l3rM8Ds1r9snXqbZPt3HvetsufnG83vbrUHpmxwWas2WmV+w8zThaBRQD0hgCIvBSJRKyxqdkO1zdZdW0Dl3GBTmpsarbahiY7WNdoB+saub818hYB0BsCIAAACA0CoDcEQAAAEBoEQG8IgAAAIDQIgN4QAAEAQGgQAL0hAAIAgNAgAHpDAAQAAKFBAPSGAAgAAEKDAOgNARAAAIQGAdAbAiAAAAgNAqA3BEAAABAaBEBvCIAAACA0CIDeEAABAEBoEAC9IQACAIDQIAB6QwAEAAChQQD0hgAIAABCgwDoDQEQAACEBgHQGwIgAAAIDQKgNwRAAAAQGgRAbwiAAAAgNAiA3hAAAQBAaBAAvSEAAgCA0CAAekMABAAAoUEA9IYACAAAQoMA6A0BEAAAhAYB0BsCIAAACA0CoDcEQAAAEBoEQG8IgAAAIDQIgN4QAAEAQGgQAL0hAAIAgNAgAHpDAAQAAKFBAPSGAAgAAEKDAOgNARAAAIQGAdAbAiAAAAiNfA+AAyTNl3RYUlUr+3xB0sToPrslPSDpAx38PQRAAAAQGvkeAAdJuknSQ8ocAI+StFLSdElnSrpY0h5Jgzv4ewiAAAAgNPI9AMb0VeYAeLGkZknHJm37raRqSUd34PEJgAAAIDTCHgDvkLQsbdtxck/4q2083jFyDRIrPUUABAAAIRH2APi0pKlp2z4i94QvbuPxiqL7pBQCIAAACIMgBsB7lSF8pZWT047pq64NgPQAAgCA0ApiAPyUXMBrq6SP3+urrr0EnI4xgAAAIDSCGACz0VdtTwL5dNK26+QmgRzTgccnAAIAgNDI9wD4BbnlXf4m6WD0/8+U9NHov8eWgZkq6QxJF8qtBcgyMAAAoGDlewAcpcxjBPsk7dNL0iS5haD3SHpQLAQNAAAKWL4HwFwhAAIAgNAgAHpDAAQAAKFBAPSGAAgAAEKDAOgNARAAAIQGAdAbAiAAAAgNAqA3BEAAABAaBEBvCIAAACA0CIDeEAABAEBoEAC9IQACAIDQIAB6QwAEAAChQQD0hgAIAABCgwDoDQEQAACEBgHQGwIgAAAIDQKgNwRAAAAQGgRAbwiAAAAgNAiA3hAAAQBAaBAAvSEAAgCA0CAAekMABAAAoUEA9IYACAAAQoMA6E0PSVZRUWHV1dUUCoVCoVAoeV0qKioIgB70lmskCoVCoVAolDCV3kKresg1Us/o/1MSpSdtQ9vQNrQLbUPbBLTQNu23TQ+hVT1EI7WGtmkdbdM62iYz2qV1tE3raJvW0Tato208oJFaR9u0jrZpHW2TGe3SOtqmdbRN62ib1tE2HtBIraNtWkfbtI62yYx2aR1t0zrapnW0TetoGw+OkVQU/S9S0Tato21aR9tkRru0jrZpHW3TOtqmdbQNAAAAAAAAAAAAAAAAAAAoCCdJGi9pr6QDkuZJOt/XGgXLjyWVSKqVtF/SOH+rEzjHSFomN/PqTJ/rEgS9JT0rabPce2aTpEGSjvaxTn66XtIWSXVyf0ff8LU2wdBf0ruSDkraLfeZ8iVfaxRMt8h9rgz1uyIB0VPSaEn75D5bVkr6mq81CoajJN2p1M/c2yQd4Wel8sUGSRMlnS7pREmPS6qR9Bk/KxUQ/ynpfUm/lQvKp0r6b19rFDyPSJokAmDMRZJGSrpA0vGSLpG0S9KDflbKJ1dIqpd0rdzfztNyX6I+7WelAmCKpL6SvizpDLnP33JJ/+RjnYLm63In9OUiAErSv8h9kRop9yXqOLnPmC/6WKeguFWuA+vHcl/A/0vuy9UffaxTXvik3In7O0nbPhbd9gNfahQcH5C0TdIv/a5IgF0saa3cyZ0A2Lq/SCrzuxI+KJE0LOnnIyVVyvXsIOFTcn8/5/ldkYD4qFzHxA8kFYsAKEn3SprrdyUCaoLcVZdkr8v1lqINR0haJ2mE3LfPD8idrHbJfeMoZN+Q+1C+VtJSSTskTZZ0mp+VCpBj5QLy1+S+dREAW3eXpMV+VyLHjpbUJOnStO3Pyw05QcIJcn8/fLY4z0t6OPr/xSIAStIauTYZKzdsYKmkX/tao+C4Va539KToz2fIZZir/apQPvmc3MkpIveBvV3SV32tUTBcKfehXC53KfhsSS/LdTV/wsd6BcERcmF4YPTn3iIAtuYESdUqvA/rz8q9J85J236/XM8gnCPlejDm+V2RgLhSbmzbh6I/F4sAKLkxtHWSBsudn6+TG+92jZ+VCogj5XpII5Iao//t72uNfHav3IdvW+VkuRP5eLkxXN+WdJak4XI9O/+W81rnhte2uSr6/9clHXuMpD2SfpPD+uaS17b5o9wJ66jo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width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dcf3c825ea424af9b9e67161cf339ac6"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.plot_square_wave>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_axis = np.linspace(-8,8,1000)\n",
    "k_lim = 20\n",
    "k_axis = np.arange(-k_lim,k_lim+1)\n",
    "\n",
    "w = 2  # width of a rectangle\n",
    "h = 1 # height of rectangles\n",
    "p = 6  # period\n",
    "squeeze = 1\n",
    " \n",
    "# setting up the plots\n",
    "fig, ax = plt.subplots(2,1)\n",
    "ax[0].set_xlim([-8,8])\n",
    "ax[0].set_ylim([-15,15])\n",
    "ax[0].set_xlabel('t [s]')\n",
    "ax[0].set_title('Time-domain signal x(t)')\n",
    "ax[1].set_xlim([-k_lim-1,k_lim+1])\n",
    "ax[1].set_ylim([-3,5])\n",
    "ax[1].set_xlabel('k')\n",
    "ax[1].set_title('Spectrum $c_k$')\n",
    "sig_plot, = ax[0].plot([],[])\n",
    "spec_zeros = np.zeros(k_axis.shape)\n",
    "spec_plot_gr = ax[1].stem(k_axis, spec_zeros, basefmt = ' ')\n",
    "spec_plot_red = ax[1].stem(k_axis, spec_zeros, basefmt = ' ')\n",
    "plt.setp(spec_plot_gr[0], 'color', '0.6')\n",
    "plt.setp(spec_plot_gr[1], 'color', '0.6')\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "# wrapper for interactive mode\n",
    "def plot_square_wave(n_coef = 2):\n",
    "    global spec_plot_red\n",
    "    delay = 0\n",
    "    height = 10\n",
    "    sq_wav = height * square_wave(squeeze*x_axis-delay,w,h,p)\n",
    "    \n",
    "    # positive part of spectrum\n",
    "    c_k_pos = c_k[n_k:]\n",
    "    \n",
    "    # summing cosines corresponding to n_coef coefficient from the spectrum\n",
    "    summed = np.zeros(x_axis.shape)\n",
    "    for k in range(n_coef):\n",
    "        mult = 2 if (k != 0) else 1 # cosine has 2x amplitude of the coefficient in the spectrum\n",
    "        summed += mult * np.abs(c_k_pos[k]) * np.cos(k*omega*x_axis + np.angle(c_k_pos[k]))\n",
    "        \n",
    "    # spectrum\n",
    "    spec_sq_wav = spectrum_square_wave(k_axis/squeeze,w,height,p)\n",
    "    \n",
    "    sig_plot.set_data(x_axis, summed)\n",
    "    set_stem_plot(spec_plot_gr, k_axis, spec_sq_wav)\n",
    "    k_axis_chosen = k_axis[-n_coef + 1 + k_lim: n_coef + k_lim]\n",
    "    spec_sq_wav_chosen = spec_sq_wav[-n_coef + 1 + k_lim: n_coef + k_lim]\n",
    "    \n",
    "    # this is ugly, but the interactive stem plots are hell\n",
    "    try:\n",
    "        spec_plot_red.remove()\n",
    "    except ValueError:\n",
    "        pass\n",
    "    \n",
    "    if n_coef > 0:\n",
    "        spec_plot_red = ax[1].stem(k_axis_chosen, spec_sq_wav_chosen, basefmt = ' ')\n",
    "    plt.setp(spec_plot_red[0], 'color', 'red')\n",
    "    plt.setp(spec_plot_red[1], 'color', 'red')\n",
    "    plt.draw()\n",
    "    \n",
    "widgets.interact(plot_square_wave, \n",
    "                 n_coef = (0,k_lim+1,1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": []
  }
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