lab_convolution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convolution is the mathematical procedure that defines or represents the action of a linear and time-invariant (LTI) system on an input signal.  Specifically, if a system with an impulse response $h(t)$ is driven by an input signal $x(t)$, then the output is\n",
    "$$\n",
    "y(t) = h(t) \\ast x(t) = \\int_{-\\infty}^{\\infty} h(\\lambda) x(t - \\lambda) d\\lambda.\n",
    "$$\n",
    "Every LTI system has an impulse response $h(t)$, which is the output when the input is the signal $x(t) = \\delta(t)$.\n",
    "\n",
    "The expression above is useful if you have expressions for the signals such as $h(t) = e^{-t} u(t)$ and $x(t) = u(t)$, and a symbolic math package can help in this case.  However, in reality we can't specify the signals we see and care about using simple analytical expressions, particularly for input and output signals.  Yet we still want to work with them.\n",
    "\n",
    "We saw in a previous lab that if signals are bandlimited then they can be reconstructed from discrete samples.  In other words, the discrete signal $x[n]$ obtained by sampling a continuous-time bandlimited $x(t)$ according to $x[n] = x(nT)$ can be used to represent or reconstruct $x(t)$.  If we have a symbolic expression for the impulse response, which is often the case, then we can use the sampled input to generate samples from the corresponding output.  If all signals involved are represented using samples, then it turns out that we can effectively consider convolution in continuous-time using discrete-time convolution on the samples of the signals involved.  This lab explores all of these concepts and their application."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representing a continuous-time signal from samples\n",
    "\n",
    "A previous lab investigated the topic of reconstructing a continuous-time bandlimited signal $x(t)$ from a sampled representation $x[n]$, with $x[n] = x(nT)$.  The process involves using the discrete signal $x[n]$ to construct a modulated impulse train \n",
    "$$x_s(t) = \\sum_{n=-\\infty}^{\\infty} x[n] \\delta(t-nT).$$\n",
    "This is an interesting signal that has both continuous-time and discrete-time characteristics:  it is formulated on the continuous-time axis, but contains exactly and only the information contained in the samples $x[n]$.  As such it forms the link between the two domains.  The signal $x_s(t)$ is then filtered with a reconstruction filter $b_T(t)$ to interpolate between the sample points: \n",
    "$$x(t) = x_s(t) \\ast b_T(t).$$\n",
    "The ideal reconstruction filter is the *sinc* function that corresponds to perfect bandlimiting.\n",
    "\n",
    "The cell below plots the two example signals mentioned above, which will be used for demonstration.  Also shown is the discrete set of values obtained by sampling the signals with a spacing $T$, starting at $n=0$.  It should be noted that neither of these signals are in fact bandlimited, so there will be errors in the approximation, but these errors will be reduced as $T$ becomes smaller."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "/* 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",
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       "    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",
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       "    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",
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       "    var fig = this;\n",
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       "    this.waiting = false;\n",
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       "    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",
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       "\n",
       "    this.imageObj.onload = function() {\n",
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       "    this.ws.onmessage = this._make_on_message_function(this);\n",
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       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
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       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
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       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
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       "\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",
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       "            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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qQiA1F7RAJiZeeWV7U8BXnTR3K0PAADMOgEQqmdDNG/I70wx74AYu3k/P411PtTy+d+eYM4XYuy3CH9tGmtMRQCk9ooHwEYj88QTxwfAPffM/MEP5m4PAADArBIAoVr2jrEb8pou5t8/Mvffp7HWfhHxtZHPPxjNJ/xeGBHPjIjTI+Lakb89HBFvnMbxI5r/UZlsHBsCIDVXPABmZn7ve+0vBDnppGYcBAAABp4ACNXyuBi7IT/Xxfx7RuaumeZ6e0TE2REx1LJu6/hiNIPgdHU6ZschAFJXHQPgby6Z+42cf377V4GvuGLu9wEAAPSdAAjVcliM3ZBXdjF/3cjcoWmu9+yI+HZENKJzmBuO5puIHz3N4wuAMIXKBMD7789cuHB8AHzsYzM3bJj7vQAAAH0lAEK1zOUTgC+L5ld/MyK+GxEviYhfiog9I2JRRCyLiK0jf781Ip4wjTV8BRim0DEAnry0zGa+8pX2pwBf+9oyewEAAPpGAIRqmavfADyo5bPfj+bvAXZySow9HfjFHtfohpeAUHuVCoCZmS99aXsEvO66cvsBAABmTACE6tkYs/8W4Le0fPbMKeZ+c2TezpE1+0kApPYqFwDXr8/cf//xAXDx4szt28vtCQAAmBEBEKpnVTRvyPuj+ZKOiZwQYzfvJT2u8amWz/7aFHM/0jL3+B7XmYoASO11DIDPf0HZTV16aftTgB/8YNk9AQAA0yYAQvV8OLoLbhe2zFva4xqfaPnsU6eY+/GWuc/ocZ2pCIDUXiUD4MMPZz7jGeMD4N57Zw4Nld0XAAAwLQIgVM9xMXZTfmqCOQui+WKOjIhN0XxxRy/+pGWNc6aYe+PIvEZEPLbHdaYiAFJ7lQyAmZk33ZS5YMH4CHjKKZmNRumdAQAAPRIAoZpGvwb8UDS/6rur82Psxr24w9/PmuLvvxZjL/dYHxFPnGAfb2g5zuou994LAZDa6xgAT/nt0ttqevOb278K/Dd/U3pXAABAjwRAqKZjImJrNG/MLRGxLCKeFREnR8RlMXbT3h4R+3f4/FkxeQCMiPibljn3RsS7IuK5EXF0RJwaEZ9p+fvDEfGbMzynTgRAaq/SAfC++zIPPXR8AHz0ozN/8pPSOwMAAHogAEJ1nRoR98XYDbrruD0ijprgs2fF1AHwERHxuUmOPzruj6nfFDxdAiC11zEA/tYLS29rzDXXtD8F+JKX+CowAAAMEAEQqm1hRCyPZux7IJq/93djRFwQEftO8rmzYuoAOOrkiPi7kTXuj+bXjn8eza/8vj9m9z8MAiC1V/kAmJn5yle2R8AvfKH0rgAAgC4JgEBJAiC1NxABcMOGzAMPHB8AH//4zJ//vPTOAACALgiAQEkCILXXMQAueVHpbbX77GfbnwL8gz8ovSsAAKALAiBQkgBI7Q1MAGw0Mk89tT0Cfu1rpXcGAABMQQAEShIAqb2BCYCZmXfdlfmoR40PgAsXZm7ZUnpnAADAJARAoCQBkNrrGACXvrj0tiZ22WXtTwG+6U2ldwUAAExCAARKEgCpvYELgDt3Zp50UnsEvPba0jsDAAAmIAACJQmA1F7HAPiC3ym9rcmtXZu5997jA+Av/7KvAgMAQEUJgEBJAiC1N5ABMDPz4x9vfwrwnHNK7woAAOhAAARKEgCpvYENgA8/nHniie0R8BvfKL0zAABgFwIgUJIASO11DIC/fWrpbXVnaChz333HB8BDD83cvLn0zgAAgBYCIFCSAEjtDXQAzMz85CfbnwJ87WtL7woAAGghAAIlCYDUXscA+MLfLb2t7u3cmXnKKe0R8CtfKb0zAABghAAIlCQAUnsDHwAzM++8M3P//ccHwIMPzty4sfTOAACAFACBsgRAam9eBMDMzE9/uv0pwDPOKL0rAAAgBUCgLAGQ2usYAF90Wult9a7RyHzRi9oj4Oc+V3pnAABQewIgUJIASO3NmwCYmfmTn2Q+5jHjA+BjHpPp/gYAgKIEQKAkAZDam1cBMDPzM59pfwrw+c9vviwEAAAoQgAEShIAqb15FwAzm7/9t2sE/NjHSu8KAABqSwAEShIAqb15GQA3bco87LDxAXCvvTK/853SOwMAgFoSAIGSBEBqr2MAfPFLSm9r5v7lXzJ32218BHzKUzK3bi29MwAAqB0BEChJAKT25m0AzMy84IL2rwK/+c2ldwUAALUjAAIlCYDU3rwOgNu3Zx59dHsE/NrXSu8MAABqRQAEShIAqb2OAfB3fq/0tvrn1lsz9957fAA8+ODMDRtK7wwAAGpDAARKEgCpvXkfADMzP/GJ9qcATz01s9EovTMAAKgFARAoSQCk9moRABuNzBe+sD0CXnpp6Z0BAEAtCIBASQIgtdcxAJ76v0pvq/9+9rPMxz9+fADca6/Mm28uvTMAAJj3BECgJAGQ2qtNAMxsvvxj16cAjzoqc3i49M4AAGBeEwCBkgRAaq9jAPzdl5be1uy54IL2CPjKV/o9QAAAmEUCIFCSAEjt1S4A7tiRefzx7RHwiitK7wwAAOYtARAoSQCk9moXADMz//u/Mx/1qPEBcN99M2+7rfTOAABgXhIAgZIEQGqvYwA87WWltzX7Pv/59qcAn/a0zG3bSu8MAADmHQEQKEkApPZqGwAzM9/4xvYIeN55pXcFAADzjgAIlCQAUnu1DoBbt2Y+9antEfCzny29MwAAmFcEQKAkAZDa6xgAX/Ly0tuaO9//fuY++4wPgPvtl3nrraV3BgAA84YACJQkAFJ7tQ+AmZl/+7ftTwEuXpy5ZUvpnQEAwLwgAAIlCYDUXscA+Hu/X3pbc+91r2uPgGeemdlolN4ZAAAMPAEQKEkApPYEwBFbt2YefXR7BPyrvyq9MwAAGHgCIFCSAEjtCYAthoYyH/3o8QFwr70yb7ih9M4AAGCgCYBASQIgtdcxAP6v00tvq5x//Mf2pwAXLszcuPF/pgxv25Fr7x7OW9ZtyrV3D+fwth3l9gsAAANAAARKEgCpPQGwg/PPb4uAjRe9KK9fe2+ec9VNuWjZinHXa9GyFXnu1Tfl9UMbsuE3AwEAoI0ACNW2MCI+HhG3RcQDEfGLiLgxIs6PiH37uM5uEfHSiPhCRPwoIraNrPWDiLg6Il4bEbv3cb1RAiC1JwB28NBDmc997v/EvzUHHZlLzv5k23XqNJYsvzbXrN9c+gwAAKBSBECorlMj4r4Yu0F3HbdHxFF9WOfwiPjXSdYZHY/pw1q7EgCpvY4B8KWvKL2t8n7608yDDspVRxydi9/2ha7i3+hYfNHKXLX23tJnAAAAlSEAQjUdExFbo3ljbomId0XECRHx/Ii4PMZHwP1nsM5hEfHfI8d6OCKuiOaTgMdGxHERcXpE/HVEbAwBEGaFADixNV/+557jX2sE9CQgAAA0CYBQTauieVM+FM3wt6vzY+zGvXiaa+wWEdeNHOMXEfGsSebuMTK/3wRAaq9jAHzZGaW3VVyj0cgly6+dVvwbHUuXX+c3AQEAIAVAqKLjYuym/NQEcxZExK0jczZFxJ7TWOdVLeu8bBqf7wcBkNoTADu7fmjDjOLf6Fg9tHHqxQAAYJ4TAKF6PhxjN+Xxk8y7sGXe0mms8x8jn71tGp/tFwGQ2hMAOzv36pv6EgDPu/rm0qcCAADFCYBQPaNf/70/ml+9ncgJMXbzXtLjGoe3fPajLf9+z4g4Ipq/DTidpwp7JQBSex0D4MvPLL2tooa37chFy1b0JQAuWrYih7ftKH1KAABQlAAI1bMhmjfkd6aYd0CM3byf73GNl7d89jURcXBE/G1EPNDy7x+IiH+MiKN7PHYvBEBqTwBst/bu4b7Ev9Fxxz3DpU8JAACKEgChWvaOsRvymi7m3z8y9997XOd9Leu8NSLubfnnXceOaP5e4HQcOsU4NgRAak4AbHfLuk19DYC3rNtU+pQAAKAoARCq5XExdkN+rov594zMXdPjOpe2rLNt5P9eFRFPjYi9IuKJ0fyNwe0xFgGf0eMaERNHxbYhAFJXAmA7TwACAEB/CYBQLYfF2A15ZRfz143MHepxnU/H+AD3NxPMO6Nlzsoe14gQAGFKAmC7fv4G4JF+AxAAAARAqJi5egLwEy3rPBQRB00y98aReTsj4jE9ruMrwDCFjgHw919ZelvFeQswAAD0jwAI1TJXvwH4py3r3DjF3A+2zD2lx3Wm4iUg1J4A2Nn1Qxv6EgBXD20sfSoAAFCcAAjVszFm/y3A57V89h+mmPvGlrmv6HGdqQiA1J4A2Fmj0cgly6+dUfxbuvy6bDQapU8FAACKEwChelZF84a8PyL2mGTeCTF2817S4xontXz2y1PMbY2FL+txnakIgNRexwB4+qtKb6sS1qzfnIsvWjmt+Lf47V/MNd/779KnAAAAlSAAQvV8OMZuyuMnmXdhy7ylPa6xX0Rsje5+P/DjLeuc0OM6UxEAqT0BcHKr1t7bcwRc/LYv5Kojjs58znMyH3yw9CkAAEBxAiBUz3ExdlN+aoI5CyLi1pE5myJiz2ms8w8jn29ExJMmWWdoZN4DEfGIaawzGQGQ2usYAF/x6tLbqpQ16zd3/XXgpWd/ItccdGRmRHO88pWZvgYMAEDNCYBQTaNfA34oOj91d36M3bgXd/j7WVP8PWJ8aPxGdI6I72mZ84ku994LAZDaEwC702g0cvXQxjz7ihvarteiC5tv+119w9psHHbYWPwbHe9+d+ntAwBAUQIgVNMxMfYV3S0RsSwinhURJ0fEZTF2094eEft3+PxZMXUAjIj4ZMu8/4zmSz6eHhEviIirWv62LiIOnNEZdSYAUnsCYG86Xa8fb7x/bMJ3vpO5337tEfDyy8ttGgAAChMAobpOjYj7YuwG3XXcHhFHTfDZs6K7ALh7RPzdJGtkRNwREb86kxOZhABI7XUMgGe8pvS2Kqvj9dqyy+/8rViRuWDB+AC4++6ZX/1qmU0DAEBhAiBU28KIWB7N2PdANH/v78aIuCAi9p3kc2dFdwFw1G9HxN9HxPqI2B4RP4/m15DfEhF7T2vn3REAqT0BsDddBcDMzMsua38KcL/9Mm++ee43DQAAhQmA0G5RRLw8It4ZEX8eEZdH86uyH4qIN0bEiTF5fKN7AiC1JwD2pusAmJn5rne1R8CDD8780Y/mdM8AAFCaAAhNJ0cz9K2LiJ1djAcj4l8i4s0R8fgC+50vBEBqr2PQOvMPSm+rsnoKgI1G8y3Au0bAxYszf/GLud04AAAUJABSZ/tExFsjYijGwl6jx7Ezml+Z/Ww036pLbwRAak8A7E1PATAzc/v2zJNPbo+AJ52U+eAknwMAgHlEAKSOdo9m+Ls7xke/H0bE/x3523Oj+eKLx0XEHtF80+7CiDg6In4/Ij4aEddF8029rTHwmoh48tydysATAKm9jkHrlWeV3lZl9RwAMzM3bcp8ylPaI+DLXpb58MNzs3EAAChIAKSOboux8HdXRHwsIo6Z5rEeGRGviYivRcRDI8fcERGvmvk2a0EApPYEwN5MKwBmZt55Z+Yhh7RHwDe+sflVYQAAmMcEQOqoERHfj4gzImJBH497eERcFs3fB3xvH487nwmA1J4A2JtpB8DMzFtuydx///YI+J73zO6mAQCgMAGQOnpZROw2i8c/NCJOmMXjzycCILXXMWi96rWlt1VZMwqAmZnf/nbmXnu1R8BLL529TQMAQGECIFCSAEjtCYC9mXEAzMz84hczFyxoj4Cf+czsbBoAAAoTAIGSBEBqTwDsTV8CYGbm5Ze3B8A99shcubL/mwYAgMIEQBjz/0XE30TEIT185nEtn6N3AiC11zFovfrs0tuqrL4FwMzMD32oPQLuu2/m6tX93TQAABQmAMKYRjTfDvzkHj5zZMvn6J0ASO0JgL3pawBsNDLf+tb2CHjAAZnf/W5/Nw4AAAUJgDBGAJx7AiC11zFoveZ1pbdVWX0NgJmZO3dmvupV7RHw8Y/P/MEP+rdxAAAoSACEMdMJgE8Z+dzWWdnR/CcAUnsCYOaPjpcAACAASURBVG/6HgAzM3fsyHzRi9oj4BOekDk01J+NAwBAQQIgjJlOAHzDyOd+NCs7mv8EQGpPAOzNrATAzMwHHsh83vPaI+DChZnr1s38+AAAUJAASJ29d5cxGgA/0eFvu44PRcTnovnk386IuHqO9z5fCIDUXseg9Qd/WHpblTVrATAzc3g48/jj2yPgk56U+bOf9WcNAAAoQACkzkaD3+hodPh3U43Rr/8+bY73Pl8IgNSeANibWQ2AmZm/+EXm0Ue3R8CnPCVzw4b+rQMAAHNIAKTOGruMXUPgZGNrRPwwIq4K8W8mBEBqTwDszawHwMzMe+/NfPKT2yPg05+euWlTf9cCAIA5IADCmOn8BiAzIwBSex2D1lmvL72typqTAJiZ+dOfZh51VHsEPP74zM2b+78eAADMIgEQxvw4mi/zOKrwPupEAKT2BMDezFkAzMy8887Mww8XAQEAGHgCIFCSAEjtCYC9mdMAmJk5NJR5yCEiIAAAA00ABEoSAKk9AbA3cx4AMzN/8IPMgw5qj4DHHScCAgAwEARA6mjvebLGfCAAUnsCYG+KBMDMZgQ8+ODOEdCLQQAAqDgBkDr6WUS8PSL2mYVjHxcR10TERbNw7PlIAKT2Ogat176h9LYqq1gAzJw4Aj7zmSIgAACVJgBSR6Nv+70nIi6JiF+Z4fH2jojfj4ivjxx3ZwiA3RIAqT0BsDdFA2CmCAgAwEASAKmj50fE92IsBO6MiBsj4sKI+M2I2L+LYyyOiD+IiCsj4r6RYzQiYktEvD8iHtnvTc9TAiC11zFonf3G0tuqrOIBMDPztts6R8BjjsncsGFu9wIAAF0QAKmr3SLizIj4f9EMd60x8OGIWBsR/xYRX4lm5PtCRPxzRPxXjAW/0dGIiAci4pMRcdBcnsQ8IABSewJgbyoRADObEbDT24Gf/OTMn/xk7vcDAACTEAAh4rci4nPRjHiNaA+Cu8a+1vGdiPijiHj0nO96fhAAqT0BsDeVCYCZE0fAI4/M/PGPy+wJAAA6EABhzCMi4nkR8e6IWBER342In0bEgxGxOSLuiIjVEXFZRLwqIhaW2ea8IgBSex2D1uvOKb2tyqpUAMzMvOOOzMMPb4+Ahx2Wefvt5fYFAAAtBECgJAGQ2hMAe1O5AJiZeeedmU96UnsEPOigzO99r+zeAAAgBUCgLAGQ2hMAe1PJAJiZ+bOfZT71qe0R8Jd+KfPGG0vvDgCAmhMAgZIEQGqvY9D6w3NLb6uyKhsAMzM3bsw89tj2CLj//pnXXlt6dwAA1JgACBPbPyJ+IyKeE83fBpxq0DsBkNoTAHtT6QCYmbl5c+aJJ7ZHwEc8IvOLXyy9OwAAakoAhHavj4hbIuLh6Pwm4E7j4SI7HXwCILXXMWi9/rzS26qsygfAzMz7789csqQ9Ai5YkHn55aV3BwBADQmAMGb3iPhSjEW9Rg9jZ4H9zgcCILUnAPZmIAJgZua2bZm/93vtETAi8wMfyGw0Su8QAIAaEQBhzB/FWND7WUR8OCJeGhEnR8RJXQx6JwBSewJgbwYmAGZmPvRQ5utf3zkC/vEfZ+7cWXqHAADUhAAIY/4zmvHv+xFxQOG91IUASO11DFpv+KPS26qsgQqAmc0n/d7zns4R8PTTMx+s8N4BAJg3BEAYMxzNr/KeXnojNSIAUnsCYG8GLgCO+ou/yNxtt/YI+Fu/lTk8XHp3AADMcwIgjBkNgEeX3kiNCIDUngDYm4ENgJmZn/1s5p57tkfAo4/OXL++9O4AAJjHBEAYc3M0A+DzS2+kRgRAaq9j0HrjH5feVmUNdADMzPzGNzL32689Ah56aOZ3v1t6dwAAzFMCIIw5P5q/Abi89EZqRACk9gTA3gx8AMzMvPHGzAMPbI+A+++f+fWvl94dAADzkAAIYx4REbdExLaIeG7hvYxaGBEfj4jbIuKBiPhFRNwYzVi57yyteUhEbIqx/zBcO0vrRAiA0DlonfOm0tuqrHkRADMz77gj86ij2iPg7rtnfvrTpXcHAMA8IwDCeI+PiH+LiAcj4s+i+XuAexfay6kRcV+M3aC7jtsj4qhZWPfvd1nn2llYY5QASO0JgL2ZNwEwM3PDhsznPKfzG4Lf/e7mG4QBAKAPBEDqaGcXo9HlvNHxcJ/3eExEbI3mjbklIt4VESdE8/cJL4/xEXD/Pq576shx7wkBEOaEANibeRUAMzO3bcs8/fTOEfCMMzIfHOBzAwCgMgRA6qgxC2Nnn/e4Kpo35UPRDH+7Oj/GbtyL+7TmIyNi3cgxXx0CIMyJjkHr3DeX3lZlzbsAmJm5c2fmhRd2joDPeU7mPfeU3iEAAANOAKSO3jdLo1+Oi7Gb8lMTzFkQEbeOzNkUEXv2Yd2/GDnet0f+WQCEOSAA9mZeBsBRl13W/A3AXSPg4Ydnfuc7pXcHAMAAEwChej4cYzfl8ZPMu7Bl3tIZrnlcNJ9i3B4Rvzry7wRAmAMCYG/mdQDMzFy5MvORj2yPgPvum/kP/1B6dwAADCgBEKpn9Ou/90fEHpPMOyHGbt5LZrDeHhHx3ZHjvL/l3wuAMAc6Bq3z3lJ6W5U17wNgZvNpv8MP7/yV4A98wMtBAADomQAI1bMhmjfkd6aYd0CM3byfn8F6o08S3hHj33gsAMIcEAB7U4sAmNn83b+J3hD8ildkPvBA6R0CADBABEColr1j7Ia8pov594/M/fdprndkjL1teNevEfcjAB46xTg2BEBqrmPQ+qO3lt5WZdUmAGY23wD82td2joDPeEbm+vWldwgAwIAQAKFaHhdjN+Tnuph/z8jcNdNc75uTrNWPAJjdDgGQuhIAe1OrAJjZ/Lrv8uWZCxa0R8CDDspctar0DgEAGAACIFTLYTF2Q17Zxfx1I3OHprHWa0Y+e19EHNLh7wIgzAEBsDe1C4CjVq7MfNSj2iPgHntkXnrphL8LOLxtR669ezhvWbcp1949nMPbdszxxgEAqAIBEKplrp4APDDGfmvwjyeY4yvAMAc6B8C3ld5WZdU2AGZm3npr5lFHdf5K8Jln/s/vAjYajbx+aEOec9VNuWjZinHXatGyFXnu1Tfl9UMbsuFlIgAAtSEAQrXM1W8AXjnyuRsjYsEEc7wEBOaAANibWgfAzMyf/zzzBS/oHAF/4zdyzX98P5csv7btGnUaS5Zfm2vWby59RgAAzAEBEKpnY8zuW4Cf0PK5/x0Rr5hgjM65teXfHd/DOt0QAKk9AbA3tQ+AmZkPP5z5nve0BcBVRxydi9/+913Fv9Gx+KKVuWrtvaXPCACAWSYAQvWsiuYNeX9E7DHJvBNi7Oa9pIfjH9HyuV7HFT2s0w0BkNrrGLT+WACciADY4ktf+p/fBVxz0JG5+G1f6Cn+tUZATwICAMxvAiBUz4dj7Kac7Im7C1vmLe3h+EeEAAiVIQD2RgDcxe23Z+PJT84lZ39yWvFvdCxdfp3fBAQAmMcEQKie42LspvzUBHMWRPOruRkRmyJiz1nYh98AhDnQMWi96e2lt1VZAmC769esm1H8Gx2rhzaWPhUAAGaJAAjVNPo14Iei+VXfXZ0fYzfuxR3+ftYUf++GAAhzQADsjQDY7tyrb+pLADzv6ptLnwoAALNEAIRqOiYitkbzxtwSEcsi4lkRcXJEXBZjN+3tEbF/h8+fFQIgDAQBsDcC4HjD23bkomUr+hIAFy1bkcPbdpQ+JQAAZoEACNV1akTcFxP/Ht/tEXHUBJ89KwRAGAgdg9ab/6T0tipLABxv7d3DfYl/o+OOe4ZLnxIAALNAAIRqWxgRy6MZ+x6I5u/93RgRF0TEvpN87qwQAGEgCIC9EQDHu2Xdpr4GwFvWbSp9SgAAzAIBEChJAKT2Ogatt7yj9LYqSwAczxOAAAB0QwAEShIAqT0BsDcC4Hj9/A3AI/0GIADAvCUAAiUJgNSeANgbAbBd394C/Lf/UfpUAACYJQIgUJIASO11DFpvPb/0tipLAGx3/dCGvgTA1c9ckvlv/1b6dAAAmAUCIFCSAEjtCYC9EQDbNRqNXLL82hnFv6VnfyIbEZkLFmS+972ZDz1U+rQAAOgjARAoSQCk9gTA3giAna1ZvzkXX7RyWvFv8du+kGsOOjIzYmwce2zm//t/pU8LAIA+EQCBkgRAaq9j0HrbBaW3VVkC4MRWrb235wi4+N1fzVW/8+rx8W90POIRmR/9aObDD5c+NQAAZkgABEoSAKk9AbA3AuDk1qzf3PXXgZcuvy7XrN/cDHwf/GDm7rt3DoHPfnbm2rWlTw0AgBkQAIGSBEBqr2PQevs7S2+rsgTAqTUajVw9tDHPvuKGtmu16MJr8ryrb87VQxuz0WiM/+B//mfmr/5q5wi4zz6Zf/mXmTt3ljkpAABmRAAEShIAqT0BsDcCYPc6Xasfb7x/8g9t3Zr59rdn7rZb5xB48smZP/rRnOwfAID+EQCBkgRAak8A7I0A2L0ZXatVqzIXLeocAR/5SE8DAgAMGAEQKEkApPY6Rpo/ubD0tipLAOzejK/Vli2Z553XOQJGZJ5wgjcFAwAMCAEQKEkApPYEwN4IgN3r27X65jczDzuscwTca6/MSy7J3L69/ycAAEDfCIBASQIgtScA9kYA7F5fr9XmzZl/+IcTPw34lKdk/vu/9/cEAADoGwEQKEkApPY6Rpp3LCu9rcoSALs3K9fq29/OPPLIzhFwt90y3/KW5leHAQCoFAEQKEkApPYEwN4IgN2btWu1dWvmBRdk7r575xB42GGZ//APmY3GzNcCAKAvBECgJAGQ2usYac5/V+ltVZYA2L1Zv1Y335x59NETfy34RS/K/OEP+7ceAADTJgACJQmA1J4A2BsBsHtzcq127Mj8yEcy9967cwTce+/MD3wg80H/PwIAKEkABEoSAKk9AbA3AmD35vRarV2becopEz8N+KQnNd8mDABAEQIgUJIASO11jDQXvLv0tipLAOzenF+rRiPzs5/NPPjgiUPg6adn/uQns7cHAAA6EgCBkgRAak8A7I0A2L1i12rz5sw3vzlzwYLOEXC//TI//OHMbdtmfy8AAGSmAAiUJQBSewJgbwTA7hW/Vv/1X5nHHz/x04C//MveFgwAMEcEQKAkAZDa6xhp3vme0tuqrOJRa4BU4lrt3Jl5+eWZBxwwcQg85ZTMNWvmdl8AADUjAAIlCYDUngDYm0pErQFRqWt1772Zr3td5m67dY6ACxZk/tEfZW7cWGZ/AADznAAIlCQAUnsCYG8qFbUqrpLX6uabM088ceKnAQ84IPPSSzO3by+7TwCAeUYABEoSAKk9AbA3lYxaFVXZazX6tuBDD504BB55ZObnP+/3AQEA+kQABEoSAKk9AbA3lY1aFVT5a/XAA5nve1/m3ntPHAKPPz7zX/+19E4BAAaeAAiUJABSex0jzYUXld5WZVU+alXIwFyrO+/MPP30iSNgROZpp2X+4AeldwoAMLAEQKAkAZDaEwB7MzBRqwIG7lr9679mPutZE0fA3XfPPOeczJ/9rPROAQAGjgAIlCQAUnsCYG8GLmoVNJDXqtHI/MIXMo86auIQuO++mRdemPnzn5feLQDAwBAAgZIEQGqvY6RZ9t7S26qsgYxahQz0tdq+PfMv/zLzwAMnDoGPelTm+9+fed99pXcLAFB5AiBQkgBI7QmAvRnoqDXH5sW1uu++zHe/O3OffSYOgY99bOZHP9p8qQgAAB0JgEBJAiC11zHSvOt9pbdVWfMias2ReXWt1q/PfN3rmr8DOFEIPOSQzE98IvPBAT1HAIBZJAACJQmA1J4A2Jt5FbVm2by8VrffnnnGGZm77TZxCFy4MPPyy5tfI+7B8LYdufbu4bxl3aZce/dwDm/bMTvnAABQgAAIlCQAUnsCYG/mZdSaJfP6Wn3ve5mnnTZxBIzIPOyw5hOB27ZNeJhGo5HXD23Ic666KRctWzHuWi1atiLPvfqmvH5oQzYajTk8OQCA/hMAgZIEQGqvY6R598Wlt1VZ8zpq9VktrtUNN2QuXTp5CDzkkMw///O23whcs35zLll+bds16jSWLL8216zfXOgkAQBmTgAEShIAqT0BsDe1iFp9Uqtrdd11mSeeOHkIfPzjM//szzK3bMlVa+/NxRet7Cr+jY7FF63MVWvvLX2mAADTIgACJQmA1F7HSPOeS0pvq7JqFbVmqHbXqtHI/MY3Mp/73ElD4JpfeXoufueXe4p/rRHQk4AAwCASAIGSBEBqTwDsTe2i1gzU+lpde23mKae0xb9GRC45+5PTin+jY+ny6/wmIAAwcARAoCQBkNoTAHtT66jVI9cqM6+/PvO3f/t/AuD1h//6jOLf6Fg9tLH0mQEA9EQAhGpbGBEfj4jbIuKBiPhFRNwYEedHxL4zPPajI+KVEfG3EfHdiLgvIh6KiA0R8S8R8ScR8ZgZrjEVAZDa6xhpLnp/6W1VlqjVPdeqxQ03ZJ56ap572oV9CYDnXX1z6TMCAOiJAAjVdWo0o1xOMG6PiKOmeewXRsSDkxx7dPwsIk6e9hlMTQCk9gTA3oha3XOtxhvetiMXXTjz+LfwndfkomUrcnjbjtKnBADQNQEQqumYiNgazRtzS0S8KyJOiIjnR8TlMT4C7j+N479q5PM7I+JrEfHWaIa+Y6IZHj/XssYDEXH09E9lUgIgtScA9kbU6p5rNd7au4f7Ev9Gxx33DJc+JQCArgmAUE2ronlTPhTN8Ler82Psxr14Gsc/PSI+FRGHTzLnTS1rfHsaa3RDAKT2Okaa936g9LYqS9Tqnms13i3rNvU1AN6yblPpUwIA6JoACNVzXIzdlJ+aYM6CiLh1ZM6miNhzlvZyY4w9KXjgLBxfAKT2BMDeiFrdc63G6/sTgHd7AhAAGBwCIFTPh2Pspjx+knkXtsxbOkt7+WjLGs+cheMLgNRex0jzvg+W3lZliVrdc63GG962IxctW9GX+HfkO76Uw099WuZf/VXmsBAIAFSfAAjVM/r13/sjYo9J5p0QYzfvJbO0l79oWePps3B8AZDaEwB7I2p1z7Vqd+7VN/UlAJ532jszI5rjkY/MPOeczO9+t/TpAQBMSACE6tkQzRvyO1PMOyDGbt7Pz9Jevjty/B0R8ahZOL4ASO0JgL0RtbrnWrW7fmhDXwLg6sN+fSwAto4TTsi88srMbdtKnyoAwDgCIFTL3jF2Q17Txfz7R+b++yzs5cUte/nKNI9x6BTj2BAAqbmOkebiD5XeVmWJWt1zrdo1Go1csvzaGcW/pef+dTY6xb/W8djHZr7jHZl33FH6lAEAMlMAhKp5XIzdkJ/rYv49I3PX9HkfvxQRPx459sMRccw0j5PdDgGQuhIAeyNqdc+16mzN+s25+KKV04p/iy9amWvu2pT5jW9knnZa5oIFk4fAiMwlSzI///nMB117AKAcARCq5bAYuyGv7GL+upG5Q33cw+4RsbJlHxfP4FgCIExBAOyNqNU912piq9be23MEXHzRyly19t7xB1q3LvOiizIPOWTqEPjYx2a+5S1+KxAAKEIAhGqpwhOAl7Xs4SvRDILT5SvAMIWOkeaSD5feVmWJWt1zrSa3Zv3mrr8OvHT5dblm/eaJD7ZjR+bf/33mKadMHQIjMp/xjOYbhDdtmrsTBgBqTQCEain9G4B/2rL+qojYp0/HnYiXgFB7AmBvRK3uuVZTazQauXpoY559xQ1t12rRhdfkeVffnKuHNmaj0ej+oLffnvn2t2cecMDUIXDvvTPPPDPzW9/K3Llz9k4UAKg9ARCqZ2OUeQvwO1uOd3PMzlt/dyUAUnsdI837/7T0tipL1Oqea9W9Ttfqxxvvn9lBt27N/Lu/yzzppO6eCly4MPNd78q89dZ+nBIAwDgCIFTPqmjekPdHxB6TzDshxm7eS2a45nktx7o1Ig6c4fG6JQBSewJgb0St7rlW3Zv1a3XHHc2494QndBcDn/70zOXLM3/60/7tAQCoNQEQqufDMXZTHj/JvAtb5i2dwXqvjojGyHF+GBFPmMGxeiUAUnsCYG9Ere65Vt2bs2v18MOZX/1q5ktfmrnnnlOHwAULMpcuzbzqqswtW/q/HwCgNgRAqJ7jYuym/NQEcxZE80m9jIhNEbHnNNf6XxHx8Mhx7oqII6Z5nOkSAKk9AbA3olb3XKvuFblW996b+ed/nvnUp3b3VOC++2a+8pWZK1Zkbt8+u3sDAOYdARCqafRrwA9F86u+uzo/xm7cizv8/awp/h7RfGpw+8iceyLiV2ew3+kSAKk9AbA3olb3XKvuFb1WjUbmf/1X88UhBx/cXQw84IDMs8/O/NrXmm8gBgCYggAI1XRMRGyN5o25JSKWRcSzIuLkiLgsxm7a2yNi/w6fPysmD4DPiogHRv6+IyLOjIinTjEe04fz2pUASO0JgL0RtbrnWnWvMtfq4Yczv/GNzNe8JnO//bqLgb/0S5l/+IfNzz300NzvGQAYCAIgVNepEXFfjN2gu47bI+KoCT57VkweAC+e5LgTjbNmeD6dCIDUXsfw8IGPlN5WZVUm1AwA16p7lbxW99+f+X//b+aLXpS5++7dxcADD8x8wxsy//mfxUAAYBwBEKptYUQsj2bseyCav/d3Y0RcEBH7TvK5s0IAhIEgAPamkqGmolyr7lX+Wt1zT+all2aecEJ3ITAi83GPy3zd6zKvuSZz27a+bmd4245ce/dw3rJuU669eziHt/kaMgBUnQAIlCQAUnsdw8MH/3fpbVVW5UNNhbhW3Ruoa3XnnZkf+1jmccd1HwMf+cjMl7888zOfydy0aVrLNhqNvH5oQ55z1U25aNmKcddq0bIVee7VN+X1Qxuy0Wj0+YQBgH4QAIGSBEBqTwDszUCFmsJcq+4N7LX60Y8y/+zPMo89tvsYuOeemUuXZv7VX2X+5CddLbNm/eZcsvzatmvUaSxZfm2uWb95ds8bAOiZAAiUJABSewJgbwY21BTgWnVvXlyrH/4w8yMfyXz607uPgRGZxx+f+cEPZt5yS/ONxLtYtfbeXHzRyq7i3+hYfNHKXLX23gIXAQCYiAAIlCQAUnsdw8OH/qz0tiprXoSaOeJadW/eXauhoebXhE88MXO33bqPgU98YubrX5/5pS9lbtmSa9Zv7jn+tUZATwICQHUIgEBJAiC1JwD2Zt6FmlnkWnVvXl+ru+/O/Ou/znzxizP32qvrGNjYa69c8uYrphX/RsfS5df5TUAAqAgBEChJAKT2BMDezOtQ02euVfdqc62GhzM///nMM8/MfNSjJg2A1x/+6zOKf6Nj9dDG0mcNAKQACJQlAFJ7HcPDhz9aeluVVZtQ0weuVfdqea22b8/8+tcz3/SmzEWL2gLguadd2JcAeN7VN5c+UwAgBUCgLAGQ2hMAe1PLUDNNrlX3an+tGo3MH/yg+buBJ5+cw/vun4vO/3JfAuCiZStyeNuO0mcIALUnAAIlCYDUXsfw8KcfK72tyqp9qOmBa9U912q8tUM/7Uv8Gx133DNc+pQAoPYEQKAkAZDaEwB7I9R0z7Xqnms13i3rNvU1AN5y8u9mvuMdmddck3nffaVPDwBqSQAEShIAqT0BsDdCTfdcq+65VuOtvXu4v08APvbQsd8XXLAg85nPzLzggsyvfrX5YhIAYNYJgEBJAiC11zE8fOTjpbdVWUJN91yr7rlW4w1v25GLlq3oS/w78h1fyuG99pn4jcO77555/PGZF17YfELwF78offoAMC8JgEBJAiC1JwD2RqjpnmvVPdeq3blX39SXAHjeae+cOP5NNJ7ylMw3vjHzyisz//u/my8pAQBmRAAEShIAqb2O4eF/Ly+9rcoSarrnWnXPtWp3/dCGvgTA1X//rcz3vjfzec/L3Guv3mNgROYhh2S+/OWZ/+f/ZN50U+ZDD5W+PAAwcARAoCQBkNoTAHsj1HTPteqea9Wu0WjkkuXXzij+LV1+XTZan97bujXzn/8586KLMk88MXPPPacXBPfbL/OUUzLf/e7Mf/qnzHvuKXehAGBACIBASQIgtScA9kao6Z5r1T3XqrM16zfn4otWTiv+Lb5oZa5Zv3nyBR54IPOb32yGvJNOytx77+kFwYjM/5+9e4+zqq73P/72hrcsLT3dVEg9pmUmhRcsNS2xOt66aOrpQv46Knb1goJlYsdMSynNTC0VFdM0NRXkZGVIigV6vJCWOBkhlcIoiCjCwHx+f6w9Z+9hbu/vsPesNWu/no/H99EjZ82sxau18Tuf9mXo0Igjj4y48MKI++7LfnYBLF2+MuY+uzQenr845j67NJYuX5n3JQEAmhQDQAB5YgCIptft4OG738/7sgqLQY2PVj5a9WzG3IXJQ8Cdz5wWM+YuTD/ZihURDzwQccEFEYcfHrHVVv0fCK63XsTw4REnnBBx9dURTzwRsXp13ft0p729Pe5vWRQnXPdglw9T2W781Bgz+cG4v2VR52dHAgDQYAwAAeSJASCaHgPANAxqfLTy0ap3cxYssV8OPGrivX0/88/V3h7x5JMRV14ZceyxETvu2P+BoBSx2WbZexGedFLEdddlQ8FVq+pzrRUprQ6cOL1+rQAA6AMDQAB5YgCIpscAMA2DGh+tfLTqW3t7e8xsaY1jJ83q0mq7cVPixMkPxcyW1sY/q+255yJuuy3itNOylw1vuunaDQU32SRi770jvvzl7JmCjz7a7w8ZGdBnSwIAkIgBIIA8MQBE0+t28PC9H+R9WYXFoMZHKx+tfN21mte6LL8LWrUq4rHHIn7yk4gvfCHiXe+KWHfdtRsKbrRRxB57ZC8fvuKKiD/+MWJZ73/Ghr9fIgAAa4kBIIA8MQBE02MAmIZBjY9WPlr5BkWrl16KmD494vzzIz7+8Yi3vnXtBoJSxDrrRPz7v0d84hMRZ5+dPQvxr3+NWL26MZ+YDABAnTEABJAnBoBoet3+Mn3BRXlfVmENiuFDbU2WAwAAIABJREFUQdDKRyvfoG31j39E3HFHxIQJEYceWp+hoBTxmtfE/R8+aq2Gfx1rZktr3pUAACXGABBAnhgAoukxAEwzaIcPOaCVj1a+UrV69tmIadMizjkne6bgsGH9GgKOOWxcXQaAJ05+KO8iAIASYwAIIE8MANH0GACmKdXwocFo5aOVr/StWlsjfv3r7OXDRx4ZsdNOvb6n4NIhG8d2Y2+vywBwu/FTY+nylXkXAACUFANAAHliAIim1+0v0xdenPdlFVbphw91RCsfrXxN2eqVVyIefDDiqqsivvrViP33j3j96yOkmPuGbeoy/OtYT405JWLixIgpUyLmzo1YyUAQAFAfDAAB5IkBIJoeA8A0TTl86Cda+Wjlo1VFe3vEP/4RD//8rroOAB9+846dn2W4/voRO+4YcfDBEaecEnH55RG/+132noYl+9CQpctXxtxnl8bD8xfH3GeX8mxIAKgzBoAA8sQAEE2PAWAahg8+Wvlo5aNVZ3OfXVrfZwC+YWv//Qc33TRi+PCIT30q4swzI669NuK++yL+9a9BMxxsb2+P+1sWxQnXPRjbjZ/a5SXRYyY/GPe3LOITkgGgDhgAAsgTA0A0PQaAaRg++Gjlo5WPVp0tXb6yy+Cqv2v7U38ZS4dsXJ9PJ95kk4hddsk+8fhrX4v44Q8jpk6N+POfI14txv9ecxYsiQMnTrfaHDhxesxZsCTvSwaAQY0BIIA8MQBE02MAmIbhg49WPlr5aNXVmMkP1mUAeOI3JkeMHh2x994Rb3hDfQaB3a111onYeuuI/faL+PznI/77vyN+9rOImTOzlxavXt3wZjPmLoydz5yW1GfnM6fFjLkLG35tAFBWDAAB5IkBIJpet79MT/xh3pdVWAwffLTy0cpHq67ub1lUlwHgzJbWzj+4tTXigQcirrkm4utfjzjiiIh3vzti4zo9S7CnNWRIxPbbRxxwQDaQPOus7ANQfvvbiJaWiBUr1qrXnAVLkod/tUNAngkIAP3DABBAnhgAoukxAEzD8MFHKx+tfLTqqr293X4pa09r1MR7/fe5W7064plnsoHcj38ccdJJER/9aMTb354N7xo5HOx4BuGb3xyx117Z+w+edlrEj36UfXLxI49ELFrU43sQDngrAMD/YQAIIE8MANH0GACmYfjgo5WPVj5ada8wz2rrGA5On549a+8b34g4+uiIPfeM2HLLxg8HO9aGG2bPItx334hjjokYOzbioovi/qtubcyzJZsMn5gMoD8YAALIEwNANL1uf5n+/iV5X1ZhMXzw0cpHKx+tejYo3tfuxRezZ+ndckvE974XccIJEaNGReyww4A8e3DMYePqMgA8cfJDA9esIPjEZABriwEggDwxAETTYwCYhuGDj1Y+Wvlo1buUT7YdNfHeYr2f3erVEf/8Z/a+gzfeGHH++REnnhhx8MER73pXxGtfu1bDv6VDNo7txt5elwHgdqffGUsvvTzil7+M+MMfIv7+98J8unEj8InJAOqBASCAPDEARNNjAJiG4YOPVj5a+WjVt/b29pjZ0hrHTprVdXA1Lnv22syW1sH5TK3Fi7NnEN5+e8TFF0ecemr24SR77BHxpjdl7w/YwwBw7hu2qcvwr2M99Yatu57n9a+PeMc7sg8w+c//zN4f8dxzI3760+yaH3gg+yCTpUt7fJ/CohkUzywtOF4yDWQYAALIEwNANL1uf5n+wY/yvqzCYvjgo5WPVj5a+bprNa91Wd6X1VgrV2bPxps5M+KmmyK+//2IU06JOOqoePjDR9R1APjwm3dc+/cp3GabiPe8J+LDH474zGeyaz3vvOz9E++8M+KPf4x4+umIZfn871aY95YchHjJNNAVA0AAeWIAiKbHADANwwcfrXy08tHKR6vO5j67tPHPAGzk2njjiK23jth114j994/45Ccjjj8+Yvz4iAsuiLj66og77oi4776IP/85YuHCiLa2fvfiE5P7j5dMA91jAAggTwwA0fS6/QXxokvzvqzC4hdqH618tPLRykerzpYuX9nlmVj9Xdufdkcs3XufiG23HZAPL1mr9brXRWy3XcTuu2fPNDzmmIgvfzliwoTsZdTXXRcxZUo2OPzTnyIWLIh4+eW4/6lFdWnVbJ+YzEum1w4vly43BoAA8sQAEE2PAWAafqH20cpHKx+tfLTqaszkB+sy1Or0KcDt7REvvBDx+OMRv/1txPXXZ8/IO/XUiM99LuIjH4kYMSIbFm60Uf4DQXON+dgZ9W9Vcrxkun94uXTzYAAIIE8MANH0GACm4RdqH618tPLRykerru5vyflZbe3tES+9FPHXv2afHnzHHRFXXhnxne9EnHxyxKc/HXHQQRHDh2cv983p2YV1/cTksbfH0t1HRnzgAxGHHpr9GceMiTj99Ihvfzvihz+MuOaaiNtuywaos2dH/OUv2SdCL1s2aD4shZdM9w8vl24uDACBYhsq6UJJf5H0sqQXJM2WNFbSJnU8z9GS7pb0rKRXJf1d0mRJI+t4ju4wAETT6/YXxIt/nPdlFRa/UPto5aOVj1Y+WnU16IY07e0RS5ZEPPVU9sEmd96ZDcsmToz4+tcjTjgh4sgjIz74wYjddss+VGTTTdd6ADggn5jsrnXXjdh88+wZlLvsErH33tlLmY84IuLzn89ezjx+fMQ550T84AfZJy7fcEPW6ne/i5g1K+KJJyLmz494/vmIFSsa8j9V7sPlQYiXSzcfBoBAcR0i6UVVH6Brricl7bCW59hY0tRezrFa0llreY7eMABE02MAmIZfqH208tHKRysfrbrXFC/TXL484h//iHjssYjp0yNuuSXiiiuyZxqOHRtx7LERhx0W8f73R7zrXdmzDV/zmv8buj385h3rOgBc609MrvfaYIOILbbI/tw77ZS9RHu//SL+4z8iPvWprM9XvhJxxhnZsxQvuijrN3lyxK23RkybFnHvvdmzFR9/POLpp2PMT++vS6tmecl0UzwO0QUDQKCYhkt6RdkD8yVJZyh7Nt4Bkq5Q5yHgZmtxnhtqftY9kg6TtLuk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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib notebook\n",
    "\n",
    "# Dense set of values for plotting underlying functions\n",
    "tvp = np.linspace(-1, 5, 2000);\n",
    "hvp = np.where(tvp<0, 0, np.exp(-tvp));  \n",
    "xvp = np.where(tvp<0, 0, 1);\n",
    "yvp = np.where(tvp<0, 0, 1-np.exp(-tvp));\n",
    "\n",
    "# Discrete samples starting from n=0\n",
    "T = 0.5;  nv = np.arange(0,np.floor(np.max(tvp)/T),1,np.int32);\n",
    "tv = nv*T;\n",
    "hv = np.where(tv<0, 0, np.exp(-tv));  \n",
    "xv = np.where(tv<=0, 0, 1);\n",
    "\n",
    "# Plots\n",
    "fh = plt.figure;\n",
    "plt.subplot(211);  plt.plot(tvp,hvp,'r-');  plt.stem(tv,hv);  plt.ylabel('h(t)');\n",
    "plt.subplot(212);  plt.plot(tvp,xvp,'g-');  plt.stem(tv,xv);  plt.ylabel('x(t)');  plt.xlabel('t');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fully discrete convolution\n",
    "\n",
    "Suppose now that we want to numerically approximate the convolution\n",
    "$$y(t) = h(t) \\ast x(t).$$\n",
    "If $h(t)$ and $x(t)$ are bandlimited then we can sample them according to $h[n] = h(nT)$ and $x[n] = x(nT)$, and the following reconstruction formulae hold:\n",
    "$$x(t) = x_s(t) \\ast b_T(t) \\qquad \\text{and} \\qquad\n",
    "h(t) = h_s(t) \\ast b_T(t).$$\n",
    "The quantity $h_s(t)$ is the modulated impulse train corresponding to $h(t)$, namely\n",
    "$$h_s(t) = \\sum_{k=-\\infty}^{\\infty} h[k] \\delta(t-kT),$$\n",
    "and $b_T(t)$ is a reconstruction filter.\n",
    "\n",
    "If we use an ideal lowpass reconstruction filter then $b_T(t) \\ast b_T(t) = T b_T(t)$, and the required convolution is given by\n",
    "$$\n",
    "y(t) = (x_s(t) \\ast b_T(t)) \\ast (h_s(t) \\ast b_T(t))\n",
    "= x_s(t) \\ast h_s(t) \\ast T b_T(t).\n",
    "$$\n",
    "If any other reasonable reconstruction filter is used then this expression can be considered approximate.\n",
    "\n",
    "Since $y(t)$ is the result of a convolution with $b_T(t)$ it is also bandlimited, and can be expressed as $y(t) = y_s(t) \\ast b_T(t)$.  We must  therefore have the following:\n",
    "\\begin{align}\n",
    "  y_s(t) &= T x_s(t) \\ast h_s(t) = T \\int_{-\\infty}^{\\infty} x_s(\\lambda) h_s(t-\\lambda) d\\lambda \\\\\n",
    "  &= T \\int_{-\\infty}^{\\infty} \\sum_{k=-\\infty}^{\\infty} x[k] \\delta(\\lambda-kT) \\sum_{m=-\\infty}^{\\infty} h[m] \\delta(t-\\lambda-mT) d\\lambda \\\\\n",
    "  &= T \\sum_{m=-\\infty}^{\\infty} \\sum_{k=-\\infty}^{\\infty} x[k] h[m] \\int_{-\\infty}^{\\infty} \\delta(\\lambda-kT) \\delta(t-\\lambda-mT) d\\lambda \\\\\n",
    "  &= T \\sum_{m=-\\infty}^{\\infty} \\sum_{k=-\\infty}^{\\infty} x[k] h[m] \\delta(t-kT-mT) \n",
    "\\end{align}\n",
    "\n",
    "The steps above follow because the order of summation doesn't usually matter (which is probably true for the signals we care about), and the integral can be evaluated using the sifting property of the Dirac delta.\n",
    "\n",
    "The change of variables $m=n-k$ is useful, and gives the result\n",
    "\\begin{align}\n",
    "y_s(t) &= T \\sum_{n=-\\infty}^{\\infty} \\sum_{k=-\\infty}^{\\infty} x[k] h[n-k] \\delta(t-kT-(n-k)T) \\\\\n",
    "  &= \\sum_{n=-\\infty}^{\\infty} \\left( T \\sum_{k=-\\infty}^{\\infty} x[k] h[n-k] \\right) \\delta(t-nT) \\\\\n",
    "  &= \\sum_{n=-\\infty}^{\\infty} y[n] \\delta(t-nT) \n",
    "\\end{align}\n",
    "where we have let\n",
    "$$\n",
    "y[n] = T \\sum_{k=-\\infty}^{\\infty} x[k] h[n-k].\n",
    "$$\n",
    "This is the operation corresponding to discrete-time convolution:  it takes the discrete-time signals $x[n]$ and $h[n]$, and combines them to produce the discrete time output $y[n]$.  We use the same notation as for the continuous-time case, namely $y[n] = T x[n] \\ast h[n]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are standard functions implemented for discrete convolution.  They usually take two inputs in the form of vectors representing portions of signals, and produce an output that contains a set of convolution results.  Implicitly the signals are assumed to be zero where they are not specified.  Different variants can select different intervals for the output sets.  The code below implements the desired computation directly, and also shows the result of a full discrete convolution as implemented by standard methods.  This output produces a result for every possible shift that yields a nonzero overlap between the signals.  Evidently all the required convolution values have been calculated in the full convolution, but knowing which portion to extract requires some effort."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        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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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x119d6e5c0>"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Explicit discrete convolution sum\n",
    "yv = np.zeros(nv.shape);\n",
    "for n in nv:\n",
    "    for k in nv:\n",
    "        xcurr = 0 if n-k<0 else xv[n-k];\n",
    "        yv[n] += hv[k]*xcurr;\n",
    "yv *= T;\n",
    "   \n",
    "# Standard full-length convolution between vectors \n",
    "yvf = T*np.convolve(hv, xv, 'full');\n",
    "\n",
    "# Plot discrete convolution results\n",
    "fh = plt.figure();\n",
    "plt.subplot(211);  plt.stem(nv,yv);  plt.ylabel('direct')\n",
    "plt.subplot(212);  plt.stem(yvf);  plt.xlabel('n');  plt.ylabel('\"convolve\"')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpretation\n",
    "\n",
    "The preceeding discussion is admittedly quite technical, but the result is simple.  Suppose we want to find the convolution\n",
    "$$y(t) = h(t) \\ast x(t).$$\n",
    "If $h(t)$ and $x(t)$ are bandlimited then by the Nyquist criterion they can be represented by samples taken with a sufficiently small $T$.  All that is required is that they be sampled at a frequency that is more than twice the highest frequency present in either.  We can then perform discrete convolution \n",
    "$$\n",
    "y[n] = T h[n] \\ast x[n] = T \\sum_{k=-\\infty}^{\\infty} h[k] x[n-k]\n",
    "$$\n",
    "on the discretised signals to produce the sampled output $y[n]$.  The corresponding continuous-time output is\n",
    "$$y(t) = \\sum_{n=-\\infty}^{\\infty} y[n] \\delta(t-nT) \\ast b_T(t) = y_s(t) \\ast b_T(t).$$\n",
    "The above equation is exact if\n",
    "$$b_T(t) = \\text{sinc}(t/T) = \\frac{\\sin(\\pi t/T)}{\\pi t/T}.$$\n",
    "\n",
    "The code below takes the calculated $y[n]$ and plots the corresponding $y_s(t)$.  The `plot` function applied to the same input effectively 'joins the dots', which as seen before is linear interpolation and corresponds to a low-quality reconstruction filter.  The actual ideal output $y(t)$ calculated analytically is also shown.  Observe that there is some error in the approximation obtained by discrete processing.  This is primarily a consequence of the signals not in fact being bandlimited.  If you decrease $T$ you should observe that the correspondence improves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "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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EGwoFAEAAHqL5mapIl/K2eB9HmDc36U5v/IWeIMvDVhJeCr6S8qNuk5bo+5RfORDmhPxuMZFPK/w8Dd1LHVhjy4JbfE8wItDQWaHvNyDQhFAsKFQBAAArlZd26Dsompl5lcou6ha1bUNTp9S506fkPLTpcxPpHVDpYXPSR884H0jcYAKw6yo27Qs8lG9F/G8Xg8L1eOhMfpu6HTdFLKo3cLs2rDYnpGnn/E8wK6jILNDXu5BoQgg2FAoAgAA1/F4PErOKdXLczJavYCkpfAJi9UrczOUnFPqbOHTUCsV7/XeBpw0VloyUProEWn0NYFZaTj4Mmn8ndLcp7R23IsKC/+LfhM2WveGzNHVISu69GzAgXO3OZdfEOB5gPYoyOyQl3tQKAIINhSKAADAVWxuSX0kJiGwt6Q2N0sVeVLOemnLVCn2LWn249K4W6RBlwSmOBxzgzTjJ9Ky16Tk96X9cVJpttR0diVhck5plwrE80dKTlngsusBKHvskZkd8nIPCkUAwYZCEQAAuIZjL82oKZfy06TMedLawdKCZ6VJ90vDvhyY0nDEldKU70ufveB94cmuz6Sj26XaKp9O1+Px+Fy6dvR8QLff0kvZY4/M7JCXe1AoAgg2FIoAAMAVsgorrcvE1qVipysVG05LRbulPUulpHelz1/2vsn47T6BKQ2HfEF6/y5p3q+lVeHS1hnSkU1S9XHJD0VewPNyAcoee2Rmh7zcg0IRQLChUAQAAL2e31bcNTVKJ3Klg2ulLVOk2L9JH/9CigngLcrv3ijNfExa/rqUPEHaHy+VHjznFuVAcWxFZy9B2WOPzOyQl3tQKAIINhSKAACg17N7JuAK3RHyiR4PjdHfwv+mSRHPKi7yIe2PulnNQy4P0C3KX/PeorzoRWnjqJZblDOlumqno7N65uSAmERWJrZC2WOPzOyQl3tQKAIINhSKAACg13tlbkabBdiNIYv127C3NTr8D1oU+Zi2Rd2liuivBvAW5buleU9LqyOkjJkttygX+eUW5UDyeDxKySnTC7PSL8iwb6j3bc4pOWWuf2bi+Sh77JGZHfJyDwpFAMGGQhEAAPRq1bUN6hsW670dN2SRngsboYkRz2pr1D2qj74sALco39Ryi/IbUspE6cAqqSxHamp0OoqL1lZ5kVt2yunTClqUPfbIzA55uQeFIoBgQ6EIAAB6r9oqFaYt0eSI32l71F1qjL7UP6XhyK9LU38gLfqDtPFtKWuRdGyHVHfS6SsOKMoLO+Rlj8zskJd7UCgCCDYUigAAoPc4XSHtj/O+9Xjqg9LgrheI9dGX6WDUTVoT2V+TI57R38P/qqdCxyjrQHbQ36IcKJQXdsjLHpnZIS/3oFAEEGwoFAEAQM9VUy7tXSHFh0qTv9OlNy03Rl+qzKg7NSficQ0Jf1W/Dxum74d+pL4hy9p87uLBYudflOIUygs75GWPzOyQl3tQKAIINhSKAACg5zhVKu1ZKsW+JU26v0srDxuiL1NG1N2aFPGsngsboZtDPvP5DdDXhsWqurbB6RQcQ3lhh7zskZkd8nIPCkUAwYZCEQAABK+TxVLWYmnFX6SJ3+ra7ctDL9fBUd/R+Ij/0jNho3RTyCKfC8Tzx8C525xOxFGUF3bIyx6Z2SEv96BQBBBsKBQBAEDwqDoq7fxUWv669P7dXSwQvyTN+Im0YaR0OFFqOK3knNIul4itR0pOmdMJOYrywg552SMzO+TlHhSKAIINhSIAAHBOZYG0Y7609FVp/B1dKxCHfUWa9VMpYbR0ZLPUUHvBYTwejx6JSbioMnFATKI8Ln0ZyxmUF3bIyx6Z2SEv96BQBBBsKBQBAED3OZErbZ8rLXlFGndr1wrE4V+VZv9SShwj5aVKjfU+HTqrsFL9ouK7VCb2i4pXVmFlgMMJfpQXdsjLHpnZIS/3oFAEEGwoFAEAQGB4PFJZjrTtY2nxS1LMN7tWII74mjTnCWlTjJSfLjV1/aUoSdkl1qViv6h4JWWX+DGYnovywg552SMzO+TlHhSKAIINhSIAAL1IdW2DsouqlZlfoeyi6u59I7HHI5VmS1tnSItelN69qWsF4sirpHm/ljaPlwq3SU2Nfj3NrMJKn29/HhCTyMrEVigv7JCXPTKzQ17uQaEIINhQKAIA0MN5PB4l55Tq5TkZ6hsWe87Esm9YrF6Zm6HknFL/P//P45GK90np06RPn5fGXN+1AnHUN6RPfiulTJKO7ZCam/x7nm2eukcpOWV6YVb6BZPxvqHetzmn5JS5/pmJ56O8sENe9sjMDnm5B4UigGBDoQgAQA9ms9rukZiEi1tt19wsFe2WtkyVFj4nje7btQJx9DXSgmelLVOk41ne/Tqkrcl4btkpx84n2FFe2CEve2Rmh7zcg0IRQLChUAQAoIcK+PMAm5ulYzul1A+k+c9Ib/fpWoH4znXSp7+X0j6Uivd6VzYGCSbjdsjLDnnZIzM75OUeFIoAgg2FIgAAPVBA3ljc1Oh9ZmHy+9K8p6VRV3WtQHz3RumzF6St06WSA0FVIJ6Pybgd8rJDXvbIzA55uQeFIoBgQ6EIAEAP4/F4fL7Nub0xICZRnqYGqSBD2jROmvukNPLrXSsQx94sLf6jlDHL+1bnIC4Qz8dk3A552SEve2Rmh7zcg0IRQLChUAQAoIdJzintUol4XchSPR4ao9Hhf1RC5HfVNOyrXSsQx90iff6ytH2OdOJIjyoQz8dk3A552SEve2Rmh7zcg0IRQLChUAQAoId5ZW6GTwXi9SFL9GTouxoT/qKSIh9QTfSXulYgvne7tHSgtGO+VJHv9OX7FZNxO+Rlh7zskZkd8nIPCkUAwYZCEQCAHqS6tkF9w2LbLRHvCZmrUeEvKTny26qN/mLXCsT375KWvy7t/FSqOur0JQcUk3E75GWHvOyRmR3ycg8KRQDBhkIRAIAeJLuouo0icYV+EzZaKyIfUUP0ZfYF4sRvSSv+ImUtkqqPO32J3YrJuB3yskNe9sjMDnm5B4UigGBDoQgAQA+SmV/xj0njbSELNDR8oHKibrQqEPdGfVMzI57Uy2FRyjpw0OlLchSTcTvkZYe87JGZHfJyDwpFAMGGQhEAgB4k+3iVHg+N0aLIx1Tnwy3NzdGXaHfUrZoe8Wu9FDZId4R8cs7E82BxtdOX5Cgm43bIyw552SMzO+TlHhSKAIINhSIAAD1BXbWU/pGaJj3QaYl4OvpyLYz4mV4MG6JbQxa0+7zFa8NiVV3b4PSVOYrJuB3yskNe9sjMDnm5B4UigGBDoQgAQDA7vkta/oY04spOi8QDUf0UHf6abg1Z2G6J2HoMnLvN6atzHJNxO+Rlh7zskZkd8nIPCkUAwYZCEQCAYNNwWsqcJ017qNMSsT76Mi2N/JGeDH1XV4es8KlIPDNScsqcvlLHMRm3Q152yMsemdkhL/egUAQQbCgUAQAIFqXZUnyoNOobnRaJR4fcoJHhf9JdIfOsSsQzY0BMojwej9NX7Dgm43bIyw552SMzO+TlHhSKAIINhSIAAE5qrJeyFkszH+v8Dc2DL5PmPyMdXKesghPqFxXfpTKxX1S8sgornb7yoMBk3A552SEve2Rmh7zcg0IRQLChUAQAwAkncqW1g6V3ru28SHz3JmnjKKmy8JxdJGWXWJeK/aLilZRd4tBFBx8m43bIyw552SMzO+TlHhSKAIINhSIAAN2luUnaHyfNfVIadEnnReLsx6W9K6SmxnZ3mVVYqUdiEny+zZmViediMm6HvOyQlz0ys0Ne7kGhCCDYUCgCABBo1celhHeksTd3XiKOvkZaEy2VH/J59x6PRyk5ZXphVvoFE8u+od63OafklPHMxDYwGbdDXnbIyx6Z2SEv96BQBBBsKBQBAAiE5mYpZ4O04FlpyBc6LxJn/Fja9ZnU2PWJYFsTy9yyU368qN6Hybgd8rJDXvbIzA55uQeFIoBgQ6EIAIA/1ZRLye9L4+/svEQceZUU+5ZUvM8vh2ZiaY/M7JCXHfKyR2Z2yMs9KBQBBBsKRQAALpbHI+WlSov/KA39UudF4tQfSNtmS/X+XT3IxNIemdkhLzvkZY/M7JCXe1AoAgg2FIoAAHRVbZWU9qE06f7OS8ThV0jL/iwd3R6w02FiaY/M7JCXHfKyR2Z2yMs9KBQBBBsKRQAAbB3bIS17TRr+1c6LxIn3eUvH2sC/XZmJpT0ys0NedsjLHpnZIS/3oFAEEGwoFAEA8EV9jbR9jvRh/85LxKGXS4v+4L0NuhvfrMzE0h6Z2SEvO+Rlj8zskJd7UCgCCDYUigAAdKRkvxT3d+8LVDorEt+7Xdo8XjpV5sipMrG0R2Z2yMsOedkjMzvk5R4UigCCDYUiAADna6yTdn0mzfhJ5yXi4MukBb+TctZLzc2OnjYTS3tkZoe87JCXPTKzQ17uQaEIBNaXjTE/NcYMNcbEG2PKzNkv3KwAHfO3xpg1xpgiY0ydMSbPGDPXGHO/xT4uN95z3mWMqW4Zu1r+2Rf9ebJtoFAEAOCME0ektYOk0X07LxLH9pMSRktVxxw+6bOYWNojMzvkZYe87JGZHfJyDwpFILDUwZjl52P9uzEmtoPjNRtjBvmwn/uMMcc72M8xY8y3/HzurVEoAgDcralR2rdSmvMradAlnRSJl0hznpD2xXp/L8gwsbRHZnbIyw552SMzO+TlHhSKQGC1/oLlGWNWm8AVivNb7XuDMeYXxph7jTEvGGNyWv3spQ72cZUxpqRlu0ZjzGhjzPdaxuiWfyZjTLEJ3H8wKBQBAO5UdVTa+LZ3pWFnqxFH9/WuXDxxxOGT7hgTS3tkZoe87JCXPTKzQ17uQaEIBNYQ473l+Sst/7+PCUyh+MNW+11ujPnn835+ufEWmjLGVBhjLmtnP7Nb7eepNn7+axO4QvQMCkUAgHs0N0sH10nzn/E++7CzInHmY1LWIqmx3ukz9wkTS3tkZoe87JCXPTKzQ17uQaEIdK8+JjCFXJw5u6qwvS/yb1od+602fn6F8d4WLWPMqg6OtcqcvYX6ii6eb0coFAEAQa26tkHZRdXKzK9QdlG1qmsb7HdyqlTa/J73LcydlYijrpLiQrxvd+5hmFjaIzM75GWHvOyRmR3ycg8KRaB79TH+LxT/wxhT37LP+A62+1djTFXLdilt/PylVuf2dAf7aV1MdnT7dFdRKAIAgo7H41FyTqlenpOhvmGx50yU+obF6pW5GUrOKZXH4+loJ1JuirToRWno5Z0XiR/+UNo+V6qv6b4L9TMmlvbIzA552SEve2Rmh7zcg0IR6F59jP8Lxda3O4d2su2ZZzg2GmP+5byftb7duaOVh19ttd3HXTjfzlAoAgCCSlZhpR6JSbhggtTWeCQmQVmFlefuoLZS2jJVmnhf5yXi8K9Ky1+Xju1w5mL9jImlPTKzQ152yMsemdkhL/egUAS6Vx/j/0Lxz632+ctOth3fatubz/tZRss/r/ThmGdWOqZbnalvKBQBAEEjKbtE/aLifSoTz4x+UfFKyi6Rjm6Xlr4qDb+i8yJx0v1S+jSptsrpS/YrJpb2yMwOedkhL3tkZoe83INCEehefYz/C8W3W+3znk62/VurbR8972dFLf98tw/H3N2y7XGrM/X6eifjHkOhCAAIAlmFldZl4k0hi/RW+F+1K/qOzkvEoV+SFr8k5W3x3g7dCzGxtEdmdsjLDnnZIzM75OUeFIpA9+pj/F8oTmq1z5s62faVVts+cd7Palr++RYfjpnWsu1JqzP1kq+DQhEA4BSPx+Pzbc5Xh6zUw6FTNCPiKVVF+7AacfydUvIEqabc6csMOCaW9sjMDnnZIS97ZGbHrXl5PB41NXtU19ikmvpGVdc2qKKmXmUn61RcVatjlaeVX16j3LJTyik5qQNF1dp7rEpZhZXakV+hjNwTSj9SrpScMlXU1Dt9OT6hUAS6Vx/j/0Jxeqt99u1k2xdabfvseT8784bnJB+OmdSybZPVmXpRKAIAgl5yTmmnJeL1IUv0Wt4T3VMAACAASURBVFiYtkR9q/MSccgXpIXPSYc2Ss3NTl9et3HrxPJikJkd8rJDXvbIzE5beeWWndKJU/Uqqa77R7F2uPSUsouqtedolXYVVGpb3gmlHS5Xck6pEg+UaP2+Iq3efVyxu45paWahFm8r0ML0fM3bkqePU47oo02HNTUxRxM3HNR7a7M1dvV+vR2/T8NX7tHg5bsVuSRLoYt36m+f7tCbCzL16rxtenlOhl6ctVXPz0jTsx9t0TPTUvXrKSl6cnKyfjlps34+YZN+Mj5Jj45L1MNjE9R/zEZ9/50NemDUen175DrdM3yt7hq6RrcNXq1vRq/STZHxuj487oKXtV3s2JRd6vS/Rp9QKALdq49hhSK3PAMAgt4rczPa/UP/7pB5mhzxO5VFf63TIrF82PVS4jtS9XGnL8kRTMTtkZkd8rJDXvaCKTOPx6OGpmadrGvUiVP1Kq6qVcGJGh0qOan9x6uVVegt5rYcKtOm7FJt2FesVbuPa8XOo/p8u7eQm5Oaqxmbz5ZxMWsOaHRLETdo2W6Ffb5Lf/t0h96Yv10D527THz7eqt/PSNMz01L11OQU/WLiZv1kfJIeiUnQgy1l2z3D1+r2Id6S7fpw/5Zrbhwb9xc78vmyRaEIdK8+hmcodoaXsgAAHFVd29DOaoMV+nNYuE5EX9lhidgcfYnWRT6o/w4bquvCVqi6tsHpS3JMME3Eewoys0NedsjLXluZ7TtWpbyyGh0sPlvipeSUaeP+Yq3efVzLdxzVoowCzduSpxmbD2tKQo7Gr8vWmFX7NXzlHkUtzVLIop16c0GmBs7dphdnpevZj7boqSkp+vnEzfrRe0nq/+5Gfedtb1l366BVujEyTn1CnS+7GIEf6/YWOf2x9wmFItC9+hje8twZCkUAgKOyi6ov+OP+rpB5io18uMMisST6Kk2IeE7fCZ15zu8eLK52+pIcQ3lhj8zskJed3pZXY8tqvdKTdcovP1vwpR8pV1J2idbsKdKyHUe1cGu+Zqcc0dREb7H3dvw+DV6+W6GLd+nNBZl6eU6Gnp+RpqenelfgPTouUQ++s0H3jVinWwevcrxgYvTOcU3oSl0fHqebIuP1zehVum3wat05dA0rFAG0qY/xf6H4w1b7DO1k29Ut2zUaY/7lvJ/NbrWfKzrYx1dbbfdxF863MxSKAABHZeZXnPMH/ythkR3e3rw58n69Ehap60KWtjlhyMyvcPqSHNPbyovuQGZ2yMuOE3k1NXtUXdugoqpaHS49pd1HK7X1SLkSDpQoPuuYFm8r0JzUXE1NzNG4tQc0MnavIpbs0l8Weou+/5qepicnJ+sn45PUf8xG3TdinW4ZtErXcWttrxhnSrV+UfG6ddAq3Tl0je4dvlYPjFqv743eoP7vbtSAmET9+L0k/XzCJj0+abOempKiZ6al6rnpaXphZrpemr1VA+du0+vzt+t/Fu7Q3z/bqfDPd2nQst0aumKPRsbt1ZhV+xWz5oAmrM/WBxtz9GHiIU3fdFizko9oTmquPknL08Kt+VqUUaClmYVasfOo4nYd0+rdx7Vub5E27i/WpuxSJeeUKu1wuTJyy5WZX6GswkrtOVqlA0XVOlh8UkdKTym/vEZHK06ruKpWpSfrVFFTr6raBtXUN6qusUmNTc3yeDwB/d51BwpFoHv1Mf4vFP/DGFPfss/4Drb7V3N2ZWFKGz9/qdW5Pd3Bfn7TaruXunC+naFQBAA46swKxTtCPtGKyAHtFokrIh9R/9APO50ssUKRsscGmdkhLzu+5NXY1KzKmgYVVpzW/uPVysg9ocQDJYrddUwLt+Zr+qbDen9dtkbG7VX457v0xvztenFWup6emqKfTdikh8Ym6IFR63X7kNW6PiLO8cLKTeP68DjdHBWv24es1j0tpdyD72zQw2MTvIXcxM16cnKyfvthqv5reppenLVVr8zN0Ovzt+uvn+5Q6OJdil6apWEr9ujt+H0a21LATUnI0fRNhzU7NVcL0vO0eFuBlu84qvis41q/r0hJ2SVKPVSmjNxyJR4oueC8so5WqriqVmUn61R5+myx1tzc80s1N6NQBLpXH+P/QtEYY+LM2ZWH7X2RWxeBb7Xx8yvM2Tc9r+rgWKtatmk2Ha9k7CoKRQCAo6prG/Ry+GCVRH+97RetRF+pgWGRPk3urg2L5RmKlD1WyMwOeZ3V1OxRRU298strlFVYqeScUsVnHdenW/P10abDGr8uW5FLsi7Ia0DLyzXuHrZGN0ZSANqOa8NidXNUvO4cukb3jVin77cUeI+9n6RffZCs30xN1e9npOmPH2/Vnz/xFndhn+/S4OW7NTJur8auOaCJGw5qWtIhzU45ogXpeVqyvVBxu45p3d4ibcr2rojbkV+hfcerdKjkpApO1Kikuk6VNd5yriGIVrzxnXQPCkWge/Ux9oXi861+Z3A727S+7XmZMeafz/v55caYvJafVxhjLmtnP61ve36yjZ8/ZQJTiLZGoQgAcE5NubToxXZXJcZFPqS7Q+b5PNEcOHeb01fkKCaW9sjMTm/Kq76xWaUn63So5KR25FcoKbtEK3ce0ydpeZqamKMxq/YrammW3lyQqRdmpuvJyckaEJOo+0eu0zejec7fmXF9eJxuGbRK9w5fq++N3qBHYhL08wmb9NSUFD03PU0vzd6q1+dv198/26lBy7ylXsyaA5qckKOZmw9rflqelmYWKj7ruDbuL9aa3ccvOMbhklM6Xd+kJlbYXaA3fSfRMQpFILC+a7yF4JnR+i3Lm8/72fPt7ON503mhaIwx81ttt8EY83Pjfevzfxtjclr9rKPblK8yxpSYs6sd3265hu+2/O/Glp+VmMD9B4NCEQDgjH2x0pjr2ywST0RfqT+HhevqkBVWE9uUnDKnr8pRTCztkZmdYMyrtqFJxytrte94lVIPlSk+67jmp+VpckKORsXtU+jinXp5ToZ+MzVVj45L1LdHrtNNkfGOF3HdNfqGxeqWQav0rRFr9YMxG/Xj95L05ORkPTc9TX+anaG/LMxUxJJdGhHrLfqmJuZodmquFmUUKG7XMSUcKFH6kXJlFVbqYPFJFVacVtnJOp2qawxIwReMn7FgRl7uQaEIBNYsc/YL5stoy/PGt0Lx340xsR3su7mT3z/jPmPM8Q72c7xlm0ChUAQAdK/TJ6TFL7W7KnFNZH/dEzLXetI8ICYxaG5BcwoTS3tkZieQeXk8HlXVNuhI6Sll5J7Qmj1FWpCepw825mhk3F79/bOdemn2Vv16SooeHZeo+0as0w298JmBN0fF697ha9V/zEb9bMIm/WZqqv7w8Va9uSBTkUuyNCpunyasz9aMzYe1cGu+Vuw8qvX7ipR6qEw7Cyp0sLhahRWnVVFTr7rGph7330W+k3bIyz0oFIHAmmW6r1A84xljzBpjTLHxvqwl3xgzzxhzv8V5X26MGWaMyTLGnGwZu1r+2Rct9tMVFIoAgO5zYJX07o1tFolNI76uv0fZr0q8OmSl+kXFK6uw0umrcxwTS3tkZscmr6Zmj8pO1im7qFqph8oUu+uY5qTmavy6bA1atlt//mS7npnmXTV47/C1Pfotwn3DYnXHkNX6/jsb9Nj7SfrN1FT98eOtGjgn44JtZyYfUXzWcW3KLtX2vBM6WFytY5WnVV3bwC294jtpi7zcg0IRQLChUAQABN7pCmnJwHZXJWruU1LVMSVll6hflN2tiP2i4pWUXeL0FQYFJpb2yMxOUdXpC/Ias3qfBi/3FoRPT03RQ2MTdOfQNeoT6nzR5+u4ISJOdw9bq/7vbtQvJm7Wc9PTNHDeNoUu3qWRcXs1ccNBzU45oqWZhdqwr1hbj5TrQFG1jlfW6lRdY7urAPl82SMzO+TlHhSKAIINhSIAILAOrpXG9mu7SBx5lbR9rtRqMp5VWKlHYhJ8KgEGxCSyMrEVJpb2yMx7q3H5qXrtP16tTdmlWrK9UB8mHtKI2L36y4JMPfvRFj06LlF3DV3jePHX0egTulK3DfauEvz5hE16bnqaXvtku6KXZmnsmgOavumwFm8r0IZ9xdqWd0I5JSdVUl2n2oamgGXL58semdkhL/egUAQQbCgUAQCBUVslLftz+6sS5/xKqixs81c9Ho9Scsr0wqz0CyZKfUO9b3NOySnrcc8GCzQmlvZ6e2a1DU06UnpKqYfKtDSzUFMTczRk+R4NnLtNT3yQrO+8vV7XhwffcwhviIjT/SPX6bH3k/Tc9DS9Pn+7Bi3brZg1BzRj82F9vt1bDG7PO6HDpad04lR9UN4u3Ns/X4FAZnbIyz0oFAEEGwpFAID/5WyQxt7cdpE44mvSto/PWZXYnrYmSrllp7rhAnomJpb2empmHo/3+YS7Ciq1Zk+RZqfmasyq/frbpzv07Edb9EhMgm4dtMrxYvDMuCV6lb7/zgb9ctJmvTgrXW99tkOj4vZpamKOPsvwloM78iuUX16jmvpGp+P1m576+XISmdkhL/egUAQQbCgUAQD+U1ctLX+j/VWJH/9cqsj3eXdMlOyQl71gzay2oUmHS09p88FSLdyar3FrD+itz3bod9O2qP+YjUH1duOnp6bqfxbu0Mi4vZqWdEhLMwu1KbtUe45WqaiqVnWNgbulONgF6+crmJGZHfJyDwpFAMGGQhEA4B+HEqSYW9pZlXiltHWGT6sSW2OiZIe87DmR2ZlnFu7Ir1DcrmOalnRIQ5bv0Z9mZ+hnEzbp7mHOPavwjiGr9fDYBP32w1S9Pn+7hq3Yo8kJOVqUUaDEAyVKOVjKZ8wC30l7ZGaHvNyDQhFAsKFQBABcnLqT0sq/tr8qcdZPpRO5Xdo1EyU75GUvUJmdrm9SdlG11u0t0szNhzVk+R794eOtenRcom62fJO5P8bNUfHq/+5G/WZqqt5ckKlRcfs0c/Nhxe06pm15J1RYcVr1jc2O5dVbkZc9MrNDXu5BoQgg2FAoAgC67shm6b3b2i4Sh18hpX0oNXdeUrSHiZId8rLX1cyamz0qOFGj5JxSLUzP15hV+/X6/O16fNJm3T1sbbcVhdeErtR9I9bp5xM366XZWxW9NEsTNxzUoowCbT5YqoPFJ1Vd2+B4Xm5FXvbIzA55uQeFIoBgQ6EIALBXXyPFhbS/KnHGj6Xywxd9GCZKdsjLXkeZNTd7dLTitJIPlmrullwNX7lHL87aqofGJuj6bnqG4a2DVunRcYl6YWa6Ipbs0qSNB7U0s1DpR8pVWHFajU1dL+z9nRcuRF72yMwOebkHhSKAYEOhCACwk5cqjb+j7SJx2Fek1MkXtSqxNSZKdsjLXml17QWZPT8jTQNiEnVjZGBLw75hsXpg1Ho9NSVFby7I1Dur9mnullxt2F+sA0XVfl1Z6C98xuyQlz0ys0Ne7kGhCCDYUCgCAHzTcFpaFS4NuqTtMvGjAVJZjl8PyUTJDnm1r76xWdlF1YrbdUwT1mfrjfnb9dj7SbopwKXh3cPW6BcTN+u1T7brnVX7tCA9T8kHS5VfXtPtqwv9gc+YHfKyR2Z2yMs9KBQBBBsKRQBA5/LTpffvamdV4pellIlSc5PfD8tEyQ55SdW1DcrMr9CijAK9Hb9Pf/h4q/q/u1F9w2IDUhj2i4rXo+MS9eKsrRq8fLdmbD6stXuKtP94tWrqG52Ow+/4jNkhL3tkZoe83INCEUCwoVAEALSvoVZaEyUNvrTtMnHaw1JpdsAOz0TJjpvyOlnXqIzcE/okLU+Dlu3W76Zt0X0j1gWsNPzRe0l6ZW6GRsfv08Kt+Uo/Uq6S6jp5PB6no+hWbvqM+QN52SMzO+TlHhSKAIINhSIAoG0FGdKEe9suEod+Sdo8PiCrEltjomSnN+ZV39is/certTSzUKPj9+nFWen6ztvrA1IcnhnRS3drflqeUg+Vqaiq1nWlYUd642cskMjLHpnZIS/3oFAEEGwoFAEA52qsk9YObn9V4of9pZL93XIqTJTs9OS8PB6PCitOa+2eIk3ccFCvfbJdA2ISdV24f29Vvnf4Wv32w1RFLsnSrOQjitt1rMdm5oSe/BlzAnnZIzM75OUeFIoAgg2FIgDgrKPbpUnfbmdV4uVS0lipqfueC8dEyU5Pyaup2aPsomot2V6o4Sv36Lcfpur2Iav9VhpeE7pSD76zQS/OStfIuL1auDVf2/JOqPL0hW9N7imZBQvyskNe9sjMDnm5B4UigGBDoQgAkBrrpfXDpcGXtV0mTvm+VLSn20+LiZKdYMyrtqFJmfkVmrclT+Gf79IvJm7WjX56s/I1oSv1w3c3auDcbRq39oBW7jymfcerVNvg+634wZhZMCMvO+Rlj8zskJd7UCgCCDYUigDgdsd2Sh880HaROOSLUuI7UtOFK7u6AxMlO07nVdvQpG15JzRz82H9ZUGmHolJ8Nvblb89cp3+a3qaRsbu1eJtBcoqrLQqDtvjdGY9DXnZIS97ZGaHvNyDQhFAsKFQBAC3amqQNo6Shnyh7TJx8nek41mOniITJTvdmVdjU7P2HqvS/LQ8hS7epZ+MT9K1figPbxm0Sk9OTlbEkl2anZqrtMPlqqwJXKHNZ8wOedkhL3tkZoe83INCEUCwoVAEADc6niVN/m47qxK/4C0aHVqV2BoTJTuBysvj8ehI6SktzSzUkOV79MQHyX65bfm+Eev0wsx0vbt6v+Kzjim/vKbb36jMZ8wOedkhL3tkZoe83INCEUCwoVAEADdpavTewjzki22XiZPul47tcPos/4GJkh1/5VVT36iUnDJN3HBQ/z0z/aJfmNIndKX6v7tRr87bpg825ijxQIlKg+TfI58xO+Rlh7zskZkd8nIPCkUAwYZCEQDconiv9+UqbRWJgy+T1g/zvpwliDBRstOVvDwej/LLa7Q0s1DRS7P02PtJF/Xcwz6hK/Xw2AT9z8IdmpV8RBm55TpV131vBrfFZ8wOedkhL3tkZoe83INCEUCwoVAEgN6uqVFKGisNvbztMnHifVLhNqfPsk1MlOz4kld9Y7O25Z3QtKRDenlOhu4dvvaiVh9+5+31Gjh3m6Ym5ij1UJlOBnF52BY+Y3bIyw552SMzO+TlHhSKAIINhSIA9GYl+6UP+7ezKvFSae1gqTF4Jx5MlOy0ldfRitNKPVSm99Zm65lpqRf17MO7h63Rf89M17i1B7Rhf3Gv+HfBZ8wOedkhL3tkZoe83INCEUCwoVAEgN6ouUnaPF4a+qW2y8QJ90gFGU6fZaeYKNlpK6/runj7ct+wWP30/U0atGy3lu04qoIT3f/ClO7AZ8wOedkhL3tkZoe83INCEUCwoVAEgN6m9KA07eH2VyWuiZIaap0+S58wUercybpGbdhXrJFxe/XY+0ldXn14+5DVemFmuiZuOKjUQ2Wqqe9Zty53FZ8xO+Rlh7zskZkd8nIPCkUAwYZCEQB6i+YmKWWiNOzLbZeJ798l5ac5fZZWmChdqL6xWWmHyxWz5oCe+CBZ13ZxBeLDYxMUuninPt2ar5ySk71y9aEv+IzZIS875GWPzOyQl3tQKAIINhSKANAblOVI0x9tu0gcdIm0KlxqOO30WVpjoiQ1N3u052iVpiUd0u9npKlfVLx1eXhN6Eo99n6Shizfo1W7j6v8VHC9zdtJfMbskJcd8rJHZnbIyz0oFAEEGwpFAOjJmpulLVOkYV9pu0wcf4eUm+L0WXaZWydKBSdqND8tT3/+ZLvuGrqmy7cxXx2yUksyC1RV2+D0JQUtt37Guoq87JCXPTKzQ17uQaEIINhQKAJAT1V+WJrxk3ZWJf6nFBci1dc4fZYXxS0TpbrGJm3KLtWwFXv00NgE69LwuvBYPTk5WUOX73FFXv7kls+Yv5CXHfKyR2Z2yMs9KBQBBBsKRQDoaZqbpbQPpeFfbbtIfO826cgmp8/SL3rzRCmvrEazU47ohZnpuinS/jbmH72XpOEr92jD/mKdqvO+QKU35xUoZGaHvOyQlz0ys0Ne7kGhCCDYUCgCQE9yIlea9dP2VyWu/KtUd9Lps/Sb3jRRqm1o0sb9xRq8fLf6j9loXSB+d/R6hS7eqeU7jrabQW/Kq7uQmR3yskNe9sjMDnm5B4UigGBDoQgAPYHHI22dLo24su0iMeYW6VCC02fpdz19olR2sk6fbs3XS7O3Wq9CvH3Iar06b5s+SctTXplvt6739LycQGZ2yMsOedkjMzvk5R4UigCCDYUiAAS7inzp41+0vypxxZtSXbXTZxkQPW2i5PF4dLD4pCYn5OiJD5LVJ9T3ArFP6Er9fOJmxaw5oO15J9TU7LE+fk/LKxiQmR3yskNe9sjMDnm5B4UigGBDoQgA3ay6tkHZRdXKzK9QdlG1qtt7A6/HI237WBrxtbaLxLE3Sznru/fku1lPmCg1NjVry6EyDV+5Rz+wvJX5rqFr9OaCTC3NLFT5qfqLPpeekFewITM75GWHvOyRmR3ycg8KRQDBhkIRALqBx+NRck6pXp6Tob5hsef84d83LFavzM1Qck6pPJ6WVWmVhdKcX7W/KnHZn6XaKmcvqhsE60SprrFJG/YV62+f7tAdQ1b7XCBeE7pSj0/arPHrsrWzoELNXViF2JFgzSuYkZkd8rJDXvbIzA55uQeFIoBgQ6EIAAGWVVipR2ISfCqcHhm7UQUbpkkjr2q7SHz3Jil7rdOX1G2CaaJU29Ck1buP680FmbolepXPJWK/qHj9aXaGPssoCPi5B1NePQWZ2SEvO+Rlj8zskJd7UCgCCDYUigAQQEnZJeoX5dvLOO4NmaN1kQ+2vypxySvS6QqnL6lbOT1Rqqlv1Mqdx/TqvG0+/3u8OmSlvjVircI/36UN+4tV29DUbefrdF49EZnZIS875GWPzOyQl3tQKAIINhSKABAgWYWVPpZQK/RGWKgqo69ou0gcc4N0YJXTl+MIJyZKNfWNWrbjqP40O0M3Rsb5XCL++L0kjV1zQLsKKs/eut7NmFjaIzM75GWHvOyRmR3ycg8KRQDBhkIRAALA4/H4dJvzPSFztTqyf7urEj2L/yidPuH05TimuyZK9Y3NWrunSK99sl03Rfq+EvFXHyRrWtIhFZyo8fs5dQUTS3tkZoe87JCXPTKzQ17uQaEIINhQKAJAACTnlHa6KvG1sHCdiL6yzSKxJPoq/SFssFJyypy+FEcFcqLU1OxRSk6ZQhfv1G2DfXuxyjWhK/X01BTNSj6i45W1fjkPf2JiaY/M7JCXHfKyR2Z2yMs9KBQBBBsKRQAIgFfmZrRbSt0VMk9xkQ+1uypxSeSPdHvIfF0dslID525z+lIc5e+Jksfj0c6CCg1dsUffGrHWpxKxb1isnv1oi+ZtyVNpkE/SmFjaIzM75GWHvOyRmR3ycg8KRQDBhkIRAPysurZBfcNi2yynfhA6TUXR32izSCyN/rpeCou+oMyqrm1w+pIc46+JUmHFaU1Yn63+Yzb6XCI+Nz1NC7fm68Sp+gBcWWAwsbRHZnbIyw552SMzO+TlHhSKAIINhSIA+Fl2UXWbJdU9IXOUH3Vtm2XiisgBujPkkzZ/72BxtdOX5JiLmSjV1Ddq8bYCPTMtVX1COy8Rrw5ZqSc+SNbslCNBvxKxPUws7ZGZHfKyQ172yMwOebkHhSKAYEOhCAB+lplfccEf97eEfKo9UbdeUCSWR1+pgWGRHZZcmfkVTl+SY2wnSs3NHqUeKtPfPt2hm316w/ZK/ei9JH2wMSdoXqxyMZhY2iMzO+Rlh7zskZkd8nIPCkUAwYZCEQD87PwVijeEfK6UyG9fUCbujLpdd4fM67TwYoVi5xOl/PIaxaw5oO+OXu9Tifi90Rv07ur9yi7qXdkysbRHZnbIyw552SMzO+TlHhSKAIINhSIA+FnrZyheE7JcKyMfvqBMPBx1ve7yoUy8lmcotjtRamhqVtyuY3pueppPtzTfMmiVwj7fpYzcE/J4PA5fWWAwsbRHZnbIyw552SMzO+TlHhSKAIINhSIABID3Lc8rNCviiQvKxJLoq/Td0Ok+raTjLc8XTpQy805oVNw+3T2s87c0XxO6Ur+fkablO46qtqHJ6csJOCaW9sjMDnnZIS97ZGaHvNyDQhFAsKFQBIAASM4p1ZjwFy8oE6ujv6KfhE70qUy8OmSlUnLKnL4UR7U1UfJlPDw2QVMSclRUVev0JXQrJpb2yMwOedkhL3tkZoe83INCEeg+Vxtjxhpj9htjaowxJ4wxW40xbxlj/r+L2O8PzNkvsa8joZ195fr4+7kXcb6doVAEgADwZMy6oEysi/6CfhM22udSbEBMYq+9NddXO/JP+JzXLYNWKXJJlnYWVLg2NyaW9sjMDnnZIS97ZGaHvNyDQhHoHj8zxlSZ9gu6A8aY67q47x90sN/2xtR29pXr4+/ndvFcfUGhCAD+ti9WGnzpOWVic/Qlnb7NufXoFxWvrMJKp6/EEc3NHm3YX6znZ6T5lNWTk5O1KKNAp+t7/y3NnWFiaY/M7JCXHfKyR2Z2yMs9KBSBwLvTGHPaeL9kJ40x4caY+40xPzTGfGjOLRX/owv7/7/GmFt8GAmtjvVAO/vKbfn50k72dUMXztNXFIoA4E95qdKwL1+wOjE6/DWrMjEpu8TpK+l2lTUNmpZ0SN9/Z0OnGd0+ZLWGLN/T697SfLGYWNojMzvkZYe87JGZHfJyDwpFIPCSjPcL1mi8ReL53jJnv4SDA3QOlxpj6lqOcbCD7XJbtpkVoPPwBYUiAPhL8V5p1FUXlInFS8L1SEyCz7c5u21l4t5jVQpdvEs3Rcb7lNHc1FxXvGClK5hY2iMzO+Rlh7zskZkd8nIPCkUgsL5lzn7BprSzzf8yxuxt2abCGPMvATiPP7U6j+gOtss1FIoA0DtUFkhj+11QJmrpQMnjkcfjUUpOmV6YlX7BH/59Q71vc07JKXPNs/+amj2Kzzqmp6ak+Lxyk4lS55hY2iMzO+Rlh7zsgqiZYAAAIABJREFUkZkd8nIPCkUgsEaas1+w+zrYLrTVdgMCcB7JLfv2GGP6dLBdrqFQBICer6ZcmnDvhWXivF9LTY3nbNrWH/65ZaccOvHuV1PfqFnJR3y6rfnRcYn6MOkQEyULTCztkZkd8rJDXvbIzA55uQeFIhBYZ253PmWM+d8dbHe/OftFHOLnc7i21b4TO9k211AoAkDPVl8jTXv4wjJx2sPen53HrX/4F1XVanT8Pt02eHWHJWLfsFgNnLdNaYfL5fF4XJtXV5GXPTKzQ152yMsemdkhL/egUAQCq9R4v1w7OtnuMnP2i/ipn89hSKt9v9DJtrkt2x023nM+abwvlDlijFlojPmlMeaf/Hx+56NQBICuamr0rkI8v0yccK931WIb3PaH/56jVfrLwkxdFx7bYZF497C1GrvmgI5X1p7z+27L62KRlz0ys0NedsjLHpnZIS/3oFAEAuf/mLNfrpU+bH+qZdtUP57DPxljDrXs97Tp/C3SuebsObc3NhtjvnYR5/T1TsY9hkIRAOx5PN7nI55fJo7t532eYjvc8Ie/x+NR4oES/W7alk5va/7J+CR9vr1A9Y3Nbe7LDXn5E3nZIzM75GWHvOyRmR3ycg8KRSBwvmTOfrkW+LB9ccu2WX48h++1Ood5PmyfbYxZZox51RjzoDHmDmPMD4wxYcaY/Fb72muMuaSL59RZYfmPQaEIABbWDbmwTBx1lfdNzx3ozX/4Nzd7FLfrmH76/qZOi8QXZqYrOae005fQ9Oa8AoG87JGZHfKyQ172yMwOebkHhSIQOFeZs1+u2T5sf6awy/HjOXzY6hwe9WH7Szv42X8YY1a32l9MF8+JQhEA/G3LlAvLxGFflvJSO/3V3viHf0NTsz7dmq/+727ssES8ISJOoYt36WDxSZ/33RvzCiTyskdmdsjLDnnZIzM75OUeFIpA4Di9QvH/GGMqWvZ51Bjzz37Y5yXGmHJz9kUz/9qFfXDLMwD4U9ZiadAl55aJgy+V9sX69Ou96Q//0/VNmrn5sO4fua7DIvHuYWv03trsLl1nb8qrO5CXPTKzQ152yMsemdkhL/egUAQCx+lnKP661fHf8dM+jTFmUqv9PuDH/Z7BS1kAwFeHEqShl1+4OjFjls+76A1/+FfXNmjihoO6a+iaDovEB9/ZoE/S8lTb0NTlY/WGvLoTedkjMzvkZYe87JGZHfJyDwpFILDKjHNveV7Zap+3+Gmfxnifr3hmv0/5cb9nUCgCgC+O7ZBGfO3CMjHhHavd9OQ//KtrGzRhfbZuG7y6wyLx0XGJWr7jqJqaO34+oi96cl5OIC97ZGaHvOyQlz0ys0Ne7kGhCARWkjl7e/D/7mC7+83ZL+IQPxz3y8aYxpb9bfPD/lobaCgUAcBZ5Yeld667sExc+Vfv254t9MQ//E/WNWrihoO6fUjHReKvPkjWhn3Fnb5oxUZPzMtJ5GWPzOyQlx3yskdmdsjLPSgUgcAaac5+we7rYLvQVtsN8MNx32y1vzf8sL/WJrba93f8vG9jKBQBoGMnS6Txd1xYJi58Tmq2v5W3J/3hf6quUZM2HtQdnRSJz01P05ZDZX4tEs/oSXkFA/KyR2Z2yMsOedkjMzvk5R4UikBgfcuc/YJNaWeb/2WM2duyTYUx5l/8cNztLftrMN6Xw/jLJebsbdw1xph/8+O+z6BQBID21FVLU75/YZk48zGpobZLu+wJf/jX1DdqckLO/9/encfJUdf5H39777rrIoqKCptwKB6ooAiiqIAC6yrqruJ9ZD3Y9fjt4gFJIAnDKWe4EfDgEBVEBSEhJFxJ5JCES8KVAxJCgNz3OUd/fn/0TLo71d0z75mprp6u1/Px+D58kK6u+s77UZ18521VV+zdy3ckHnnVzJi1aHWqcxkKeTUT8vKRmYe8POTlIzMPeeUHhSKQvp7bnjtUvLV5W0er9CFsq/L6iF5e39Y7y7a/0Zjnv0n6xzqv/7OkyWX7Pt/Yt4NCEQCq6dgSceWnk2XixR+K2NT/Eq2ZF/6bOzrj13c93evDVr575cx49Ll0i8QezZxXMyIvH5l5yMtDXj4y85BXflAoAunbW9JGFT9k6ySNlvQBSQdJulSlD+BsSa+q8v4R8grFM8q2/5wxz6mSVkj6haRvSjpA0l6SPto952fK9vukpNcY+3ZQKALAtrq6Iq77VrJMPGfPiLUvDGjXzbjw7+wqxJ8eeDY+dNrtdYvE71yZ/hWJ22rGvJoZefnIzENeHvLykZmHvPKDQhFojMMlrVHpw7btmC1p9xrvHaG+F4ovlvRc97YrJb3cmOPUOvMrH1MlvdnYr4tCEQDKFQoRk0Yly8TTd4lYNnfAu2+mhX+hUIjbHl8ch46fVrdI/PYVMxpeJPZopryGAvLykZmHvDzk5SMzD3nlB4Ui0DjDJI1XsTzcoOL3Jc6UdIykV9Z53wj1vVA8pGzbn5vz20fSSEk3SHpC0jIVb9Ne0/3fV0g6TNKLzP26KBQBoNxfz0mWiSe/MWLR/YOy+2ZZ+M+YvyI+d/HddYvE/7p8Rvz92VUNn1u5ZslrqCAvH5l5yMtDXj4y85BXflAoAmg2FIoA0OOh3yXLxBNeEzH3tkE7RNYL/ydeWBPfunxG3SLx8z+/O2bOX9GwOdWTdV5DDXn5yMxDXh7y8pGZh7zyg0IRQLOhUASAiIjZkyPatk8Win+/dlAPk9XCf8naTTHqT3+PXUbVLhIPO2da3PHEkigUCqnPp6/4RclDXj4y85CXh7x8ZOYhr/ygUEQre52k/SR9RtJXJB2h4i3Be0h6SYbzQn0UigDw7MyIk3dMlol3XzDoh2r0wn9Te2dceMfceMfYSTWLxANOvz2uf3BRdHU1T5HYg1+UPOTlIzMPeXnIy0dmHvLKDwpFtJJ/UrE4/I2khZK66oyNku6WdLykd2cxWdREoQgg35bNiThteLJMnHxcKodr1MK/q6sQNzy0KPY/9baaReL7TpoSV9w9P7Z0dA368QcLvyh5yMtHZh7y8pCXj8w85JUfFIpoBXtL+rWkdSoVhoU+jp7tH5H036r/cBQ0BoUigPxa81zE+Hcmy8Q/fTeiK52SrREL/5nzV8SnL7yrZpH4tjGT4txb58T6zR2Detw08IuSh7x8ZOYhLw95+cjMQ175QaGIoWxvSROULBGfV/FJxWNVLAmPkPRxSYdL+qakoyRdrOITlreoslxcKumnkl7RwJ8DlSgUAeTTxlURF30gWSb+5j8jOttTO2yaC/9FqzbG969+oGaROHzUhPjpHx6OxWs2DcrxGoFflDzk5SMzD3l5yMtHZh7yyg8KRQxVl0vqVKkMvF/SjyT9q7mfl6tYNl4uabVKxeLTkg4YrMnCQqEIIH/aN0X8+hPJMvHSAyM2r0v10Gks/De1d8YFt8+JPcbcXLNM/NKl98asRasH6adoHH5R8pCXj8w85OUhLx+ZecgrPygUMVQVJG2WdKmktw7SPl8h6WuSHu/e/7hB2i88FIoA8qWrM+L3X0mWieftHbF+WeqHH+yF/+1PLI6PnHFHzSLxwDPvjCmPLW6qJzc7+EXJQ14+MvOQl4e8fGTmIa/8oFDEUHWhpJ1T2veLJH1B0pdT2j/qo1AEkB+FQsSN/5csE898a8TKBQ2ZwmAt/BcsXx/funxGzSLx3W2T49d3Pd3UD1zpC35R8pCXj8w85OUhLx+ZecgrPygUATQbCkUA+XHnz5Jl4qk7Rbwwq2FTGOjCf+OWzjhr8pPxluOq3948fNSEOO76R2Ll+i0p/hSNwy9KHvLykZmHvDzk5SMzD3nlB4UigGZDoQggH2b+KlkmnrhDxNPTGzqNgSz8pzy2OD74s9trXpX4HxfdNSS/J7EeflHykJePzDzk5SEvH5l5yCs/KBTRar7RPf7FeM8/l70P2aNQBND6Hr8xou3V2xSK20U8dkPDp9Kfhf/zqzfGkVfNrFkkvu+kW+OP9z8bXV1D83sS6+EXJQ95+cjMQ14e8vKRmYe88oNCEa2m5ynN7zDes1v3+zpTmRFcFIoAWtv8uyJOfF3y6sQZv8hkOs7Cv7OrEL++6+l4x9hJVYvEXUdPjBNveizWbGpv8E/ROPyi5CEvH5l5yMtDXj4y85BXflAootUMpFDsSmVGcFEoAmhdix+NOHXnZJl4xymZTamvC/9Zi1bH4Rf8teZViV+89J6YvXhtBj9BY/GLkoe8fGTmIS8PefnIzENe+UGhiFbTn0Lxrd3v25LKjOCiUATQmlY9E3HWHsky8cb/LT7tOSO9LfzXb+6Ik256LHYZVb1I3PvEKfHnB5+NQoY/QyPxi5KHvHxk5iEvD3n5yMxDXvlBoYhW059C8fDu972QyozgolAE0HrWL484/33JMvF3X47o7Mh0avUW/lNnL6370JWjr3u4ZZ7e3Ff8ouQhLx+ZecjLQ14+MvOQV35QKGKo+8g2o6dQ/GaV17Ydh0j6H0nzut8zqcFzR3UUigBay5b1EZcdnCwTf3VYRPvGrGdXdeH/9LL18dM/PFyzSDzorDvj3qeWZz31TPCLkoe8fGTmIS8PefnIzENe+UGhiKGup0DsGYUqf9bb6Nn+sw2eO6qjUATQOjrbI37zuWSZeNEHIjauzHp2EVF94b/PSVOqFolvOfbmOPfWObG5ozPraWeGX5Q85OUjMw95ecjLR2Ye8soPCkUMdYVBGAtVvFIRzYFCEUBrKBQi/vw/yTLx7HdErF6U9ey2qrbwrza+eOk9MW/puqynmzl+UfKQl4/MPOTlIS8fmXnIKz8oFDHUfbRsHKjS1YYjtnlt2/ERSftK2rnRE0avKBQBtIYp45Jl4mnDIpY+mfXMKvRWKL5z3C1x9d8W5OahK73hFyUPefnIzENeHvLykZmHvPKDQhGtpj8PZUFzoVAEMPTdc1GyTDzpDRELZ2Q9swor12+J71w5o2aZ+PVf3ReLVmX/PY/NhF+UPOTlIzMPeXnIy0dmHvLKDwpFtJph3eOlWU8E/UahCGBoe+S6ZJnYtn3E7FuynlmFO59cEu8/+daqReI7xk2Ka2cu5KrEKvhFyUNePjLzkJeHvHxk5iGv/KBQBNBsKBQBDF3zbo844bXJQvHBq7Oe2VYbtnTEcdc/Uvc258efX5P1NJsWvyh5yMtHZh7y8pCXj8w85JUfFIoAmg2FIoCh6bkHI055U7JMnH521jPb6sFnVsaBZ95Zt0xk4V8fvyh5yMtHZh7y8pCXj8w85JUfFIoYqm6U9N6U9v2Pkn4qnvycFQpFAEPP8nkRp++aLBNvPqb4tOeMtXd2xdmTn4xdR0/stUxk4V8fvyh5yMtHZh7y8pCXj8w85JUfFIoYqnoevjJB0kGDtM8dJY2WtKR73+MGab/wUCgCGFrWLo44993JMvEPIyK6urKeXcxdsi4+df5fqxaHbxszKS6ZOo+Fv4FflDzk5SMzD3l5yMtHZh7yyg8KRQxVJ0raqFKx+KykMyR9QNLLjP0Mk/QtSbdJ6ujeV0HSNEnvHMT5ou8oFAEMHZvWRPz8gGSZeMXhER3ZLp4LhUJcM+OZeNuYSVXLxM9ceFc8vWw9C38TeXnIy0dmHvLykJePzDzklR8UihjKdpZ0maQtKhWLXZI2S5rZ/drJkn6iYmn4A0ljJY1X8crGJWXvKXSPWZI+1cgfAgkUigCGho7NEVd8Klkm/vyAYtGYoTWb2uMHv32gapG42+iJcd5tc6Kjs3j1JAt/D3l5yMtHZh7y8pCXj8w85JUfFIpoBW+SdIqkRSoVg+UFY63Rs90WSddJOqTRE0dVFIoAml9XV8QfvpksE899T8S6JZlO7YFnVsaHTru9apl48Fl3xt+fXVWxPQt/D3l5yMtHZh7y8pCXj8w85JUfFIpoJS+S9GEVv/vwVknrVFkwlo/Zkn4p6ZuSXpfFZFEThSKA5lYoREw8OlkmnrFbxIqnMptWV1chLrpzbuxW48Erx13/SGxq70y8j4W/h7w85OUjMw95ecjLR2Ye8soPCkW0uu0lvVXF71bcS9KbJb080xmhNxSKAJrb9LOSZeIpb4p47qHMprRkzab46i/+VrVIfHfb5Jg064Wa72Xh7yEvD3n5yMxDXh7y8pGZh7zyg0IRQLOhUATQvB78TbJMPOG1EfPuyGxKU2cvjfeeOKVqmfj5n98di1ZtrPt+Fv4e8vKQl4/MPOTlIS8fmXnIKz8oFNFqfirp9VlPAgNCoQigOT05KaJt+2Sh+Mh1mUyns6sQZ0+ZHcNHJYvEXUZNiLOnzN764JV6WPh7yMtDXj4y85CXh7x8ZOYhr/ygUESr6XnIyvWSDpf04myng36gUATQfBbeF3HSG5Jl4r0XZzKd5es2x9d+Wf0W5/1OuS3ufWq5tS8W/n1HXh7y8pGZh7w85OUjMw955QeFIlrNtk94fkHS6ZLeluWkYKFQBNBclj4ZcdqwZJl46/GZTOf+BStiv1Nuq1omfvuKGbFy/RZrfyz8PeTlIS8fmXnIy0NePjLzkFd+UCii1bxT0nhJS5QsF++R9G1J/5zZ7NAXFIoAmsfqRRFnvyNZJl7/veLTnhuoUCjEL//6dNWnOO86emJcNu2pKPRjTiz8PeTlIS8fmXnIy0NePjLzkFd+UCiiVb1U0mcl/UVSuyqLxXWSLpf0kcxmh3ooFAE0h40rIy7cL1kmXv35iM72hk5l7ab2+N7V91e9KvH9J98aM+av6Pe+Wfh7yMtDXj4y85CXh7x8ZOYhr/ygUEQevF7Fh7U8quRVi3MkjZb0psxmh21RKALIXvvGiF8dliwTf/GxiC3rGzqVuUvWxkFn3lm1TPzyZffG0rUDW6Sz8PeQl4e8fGTmIS8PefnIzENe+UGhiLzZV9IlklapslzskHSzpM9Jellms4NEoQgga50dEb/7UrJMvGCfiA39vxKwP6Y8tjjeOe6WqmXimbc8GZ1dA7/tmoW/h7w85OUjMw95ecjLR2Ye8soPCkXk1T9I+pqk55W8anGppNMk7ZjZ7PKNQhFAdgqFiL/8MFkmnrVHxKqFDZtGV1chzrl1dtUi8d1tk+P2JxYP2rFY+HvIy0NePjLzkJeHvHxk5iGv/KBQRB4Nk3S8pKdVKhEL24wuSRsk/SijOeYZhSKA7Nx+crJM/NnOEYsfa9gU1m5qj+9cObNqmfjJ86fHwhUbBvV4LPw95OUhLx+ZecjLQ14+MvOQV35QKCIveq5IvF1SpypLxCclHa3iFYkfl/R7VT7I5WsZzDfPKBQBZOO+y5Jl4omvi1hwd8Om8NTSdfGxs6dWLROPuuah2NTeOejHZOHvIS8PefnIzENeHvLykZmHvPKDQhGtbn9Jl0larcqrETdIulLSh2u8bzdJD3Vv+0D600QZCkUAjffo9RHHb1dZJra9OuLxmxo2hTueWBJ7Hp/8vsRdR0+MX0x/KgqFgX9fYjUs/D3k5SEvH5l5yMtDXj4y85BXflAoohW9UdJISU8oeUvzA5K+J+lf+rCfQ7vfsy6daaIGCkUAjfX09IgTd0henTjz1w05fKFQiEunzYvho5JXJb7nhMlx19xlqR6fhb+HvDzk5SMzD3l5yMtHZh7yyg8KRbSam1V8YnN5ibhK0kWS9jb3tbtKtz2jcSgUATTOC49EnLpTsky887SGHH5LR1ccc93fq97ifNg50wb9+xKrYeHvIS8PefnIzENeHvLykZmHvPKDQhGtpvzBKtMkfV3F70/sjzdJmirpzkGZGfqKQhFAY6ycH3HmW5Jl4k1HFZ/2nLJVG7bEFy+9p2qZ+P3fPhAbtnSkPocIFv4u8vKQl4/MPOTlIS8fmXnIKz8oFNFqFks6XdJbsp4I+o1CEUD61i+LOG/vZJl4zVcjugb/wSfbemrpujjwzDurlokX3jE3te9LrIaFv4e8POTlIzMPeXnIy0dmHvLKDwpFtJqXZj0BDBiFIoB0bV4XcemByTLx1/8e0b4p9cPfPW9ZvLttcmKxvceYm2PSrOdTP/62WPh7yMtDXj4y85CXh7x8ZOYhr/ygUAQaZ5iksyU9qeJTpldKminpaEmvHOC+21T6IPc2DuzD/naQdKKkRySt7R6PdP/Zawc4195QKAIYkLWb2mPO4rXx0MJVMWfx2li7qb30YseWiKv+I1kmXrR/xMZVqc/t9/c9E7uNnphYaO97yq3xyLOrUz9+NSz8PeTlIS8fmXnIy0NePjLzkFd+UCgCjXG4pDWqXfLNVvEhMP3VVmffbqG4n6QX6rz/eUn7DmCuvaFQBGArFApx97xl8T+/uT923aaw23X0xPje1ffH3XOXROFP30mWieP3jFiT7pWBXV2FOHXi41Vvcf7386bHC6vTvzKyFhb+HvLykJePzDzk5SEvH5l5yCs/KBSB9O0taaOKH7J1ko6VtL+kgyVdpspS8VX9PEZb2X727GX8U5397Cxpafd+OlT8PsoPd4/Tu/8sJC1Ren9hUCgCsMxatDoOGT+1allXPi457svJMvG04RHL5qQ6v80dnfHD3z1YdU7fvXJmwx6+UgsLfw95ecjLR2Ye8vKQl4/MPOSVHxSKQPqmq1TQ7V/l9aNV+hC29fMYbWX7GIiryvZzRJXXv1D2+hUDPFYtFIoA+mz6nKXx9rGTei0TTzr2e8ky8eQdI56dmer8Vm9sr/kk51Nvfjy6uhr38JVaWPh7yMtDXj4y85CXh7x8ZOYhr/ygUATSta9KH7BLamzzYkmPd2+zStLL+nGcNg28UNxRUlf3Pm6ps90t3dt0db9nsFEoAuiTWYtW96lM/L/RoxJlYvu47WP+vTekOr/nVm2MQ8dPS8xnt9ET49oZC1M9toOFv4e8POTlIzMPeXnIy0dmHvLKDwpFIF2nqvQB26/OdqPKtju0H8dp08ALxSPL9vHFOtt9qWy7IwdwvFooFAH0qlAo9Ok256+PPiXax22fKBSPGj0yDh0/LQqFdK4QfOKFNbHfKbcl5vOOsZNi6uylqRyzv1j4e8jLQ14+MvOQl4e8fGTmIa/8oFAE0tVzu/N6SS+ts93+Kn0QT+jHcdo08EKx/HbnelcevrFsuysHcLxaKBQB9Oruect6LRMPH3VerB/3ukSZeMqx/711m3vmLR/8uc1dFnuOuyUxn31OvjVmLcrmSc71sPD3kJeHvHxk5iEvD3n5yMxDXvlBoQika5mKH66He9lue5U+iH/ox3Hayt4/RcUHq7R3/+9UFa+A3L6Xfdzf/f7VfThezxOrZ/Rjrr2hUATQq+9dfX/dMvHAUb+I5ePenCgTLzvuSzFs5E1bt/v+1Q8M6rxueGhR7H7sxMR8Djrrzli4YsOgHmuwsPD3kJeHvHxk5iEvD3n5yMxDXvlBoQik5x9U+nBN6MP267u3vbcfx2orO1atsUrSZ+rsY3H3do/24XiPdm/7Qj/mulMvYx9RKAKoY+2m9th1dLK023ol4MirY+HY3RJl4p/HfCKGj7yxYttdR0+MtZvaB2Vev77r6arz+c+L746V67cMyjHSwMLfQ14e8vKRmYe8POTlIzMPeeUHhSKQntep9OG6pg/bL+nedlY/jtUm6RFJJ0r6lKT3qvidjd+QNLlsHp2SPlFjHxu6t/lbH453X/e26/ox196Kz62DQhFANXMWr617deKUMQcmysRpYz4Uu4+8oer2c5esHdB8CoVCjJ8yu+q+j7xqZmxq7xyknzwdLPw95OUhLx+ZecjLQ14+MvOQV35QKALp2VmlD9dVfdh+Yfe28/pxrFf38vp/l83lORWvntxWzxOep/fheD3fDdlpzLEHhSKAAXlo4aqaZeIXR5+RKBMfHrtXvGPkdTXf89DCVf2eS1dXIY7/y6NV9zvuhlnR2ZXOQ18GEwt/D3l5yMtHZh7y8pCXj8w85JUfFIpAehp5hWJf/LJsPl+t8nqjrlDklmcAA1LrCsXhI2+Mh8fuVVEmLh23U7x35G/rXtHY3ysU2zu74qhrHqq6zwvvmJvaE6QHGwt/D3l5yMtHZh7y8pCXj8w85JUfFIpAehr5HYp98f6y+VxW5fVGfYdib3goC4C6an2H4g9HH5u4OvHYY4+qWybu1s/vUNzU3hnfunxGstQcNSGuundBCj91elj4e8jLQ14+MvOQl4e8fGTmIa/8oFAE0rVcjXnKc1/8U9kxJlZ5nac8Axgytn3K81tGXp94EMu8sXvEriP/UrdQ7M9Tntdsao8jLrmnajn5l4efS+GnTRcLfw95ecjLR2Ye8vKQl4/MPOSVHxSKQLp6vmtwvaSX1tluf5U+iCekNJdXqn6heFXZ6zvW2c8by7a7cpDnKFEoAuiDu+ctq1ionnjs9xNXJ35ndFvdMnHYyAlxz7zl1nFXrt8Snzx/emI/e4y5Oe54cklKP226WPh7yMtDXj4y85CXh7x8ZOYhr/ygUATSdapKH7D96mw3qmy7Q1Oay9bvJpT0iyqvH1n2+hfr7OdLZdsdOchzlCgUAfRBoVCIQ8ZPjWEjJ8S7Rl4Tq8a9saJMvG/s+2PYyJvqlomHjp9mfc/h0rWb47BzpiX2s+fxt8TM+StS/GnTxcLfQ14e8vKRmYe8POTlIzMPeeUHhSKQrn1V+oBdUmObF0t6vHubVZJeltJcflE2l69VeX1HlZ70fEud/dzSvU2X6l/J2F8UigD6ZNai1fH2sZPi58d9JXF14mdHnVO3THz72Ekxa9HqPh9r8ZpNcfBZdyb2876Tbo3HnluT4k+ZPhb+HvLykJePzDzk5SEvH5l5yCs/KBSB9PXc9tyh4q3N2zpapQ9hW5XXR/Ty+rsk7d7LHMqvPnxBxe9TrKb8tufPV3n9iLLXr+jlmP1FoQigz+578KHYPO61FWXiTWMO6bVMnD5naZ+P8dyqjfHRM+5I7OeDP7s95i9bn+JP1xgs/D3k5SEvH5l5yMtDXj4y85BXflAoAunbW9JGFT9k6ySNlvQBSQdJulTKrqj+AAAgAElEQVSlD+BsSa+q8v4R6r1w7JR0q6QfSzpE0ntVvDryG5Iml72/U9Lhdea6s6SlKhWgp0k6oHuc1v1n0b1NWn9hUCgC6Ls/HVlRJraP2z4+MuqXdW9zdq5MXLhiQ3zotNsT+zng9Nvj2ZUbUvzBGoeFv4e8POTlIzMPeXnIy0dmHvLKDwpFoDEOV+nJyNXGbNW+ynCEei8Ua+23fCyX9Jk+zHU/Fa9irLWfF1T/+yAHikIRQN88/3DE8dtVFIq3nv2NxCJ211HFpznfM2+59Z2JTy9bHx849bbE/g488854fvXGFH+wxmLh7yEvD3n5yMxDXh7y8pGZh7zyg0IRaJxhksarWB5uUPH7EmdKOkbFJzDXMkL1C8XXS/qWit+ReL+kZ1W8InKTpOck3SzpfyX9izHXHSSdJGmWildVrpP0SPefvdbYT39QKALoXaEQceWnK7878dSdYsWSRYlF7ILl/m3Jc5esjX1OvjWxr4+fPTWWrNmUwg+UHRb+HvLykJePzDzk5SEvH5l5yCs/KBQBNBsKRQC9m3tr4kEsMf2sQVnEzl2yNt530pTEfg47Z1pLLohZ+HvIy0NePjLzkJeHvHxk5iGv/KBQBNBsKBQB1NfVGXHxByvLxLPeFrFlw4AXsfOWrqt6ZeKnzv9rrFy/JcUfKjss/D3k5SEvH5l5yMtDXj4y85BXflAoAmg2FIoA6nvw6uTViQ9eHREDW8Q+vWx9vL9KmfjZi+6K1Rvb0/yJMsXC30NeHvLykZmHvDzk5SMzD3nlB4UigGZDoQigtvaNxasRy8vEi/YvXrUY/V/ELli+PvY7JfkAls9edFes3dS6ZWIEC38XeXnIy0dmHvLykJePzDzklR8UigCaDYUigNqmn528OnHOrVtf7s8iduGKDbF/lac5f/qCv8aaFi8TI1j4u8jLQ14+MvOQl4e8fGTmIa/8oFAE0GwoFAFUt35ZxKk7VZaJVxxefOJzN3cR++zKDfGh025PvOdT5/+1pW9zLsfC30NeHvLykZmHvDzk5SMzD3nlB4UigGZDoQigupuPSV6d+PzDFZs4i9jnVm2MA05PlomfOHd6rNrQmg9gqYaFv4e8POTlIzMPeXnIy0dmHvLKDwpFAM2GQhFA0vJ5ESe8prJM/NN3k5v1cRG7dO3mOPDMOxPbHnbOtJZ9mnMtLPw95OUhLx+ZecjLQ14+MvOQV35QKAJoNhSKAJKu/UZlmXji6yJWPZPYrC+L2NUb2uOwc6Yltjtk/NRcLnhZ+HvIy0NePjLzkJeHvHxk5iGv/KBQBNBsKBQBVHp2ZvJW58ljqm7a2yJ2/eaO+OxFdyW2+djZU2Pp2nwudln4e8jLQ14+MvOQl4e8fGTmIa/8oFAE0GwoFAGUFAoRv/q3yjLxZ/8asXFl1c3rLWI3tXfGly+7N/H6h0+/Ixav2dTIn6qpsPD3kJeHvHxk5iEvD3n5yMxDXvlBoQig2VAoAih5YkLy6sS7L6i5ea1FbHtnV3z7ipmJ1/Y75bZYuGJDA3+g5sPC30NeHvLykZmHvDzk5SMzD3nlB4UigGZDoQigqLMj4vz3VZaJ5+wZ0VF7UVptEbt0zab4v98/mPjzvU+cEnOXrG3gD9ScWPh7yMtDXj4y85CXh7x8ZOYhr/ygUATQbCgUARTN/FXy6sRHrqv7lmqL2B9f+1Diz/Ycd0vMWrS6QT9Ic2Ph7yEvD3n5yMxDXh7y8pGZh7zyg0IRQLOhUAQQsXldxBm7V5aJl3wkoqur7tuqLWK3HXuMuTlmzF/RoB+k+bHw95CXh7x8ZOYhLw95+cjMQ175QaEIoNlQKAKIuOPU5NWJT0/r9W29FYq7Hzsxps5e2oAfYOhg4e8hLw95+cjMQ14e8vKRmYe88oNCEUCzoVAE8m7tCxEnv7GyTLz6iD69tV6huMuoCXHzI8+nPPmhh4W/h7w85OUjMw95ecjLR2Ye8soPCkUAzYZCEci7G/+vskxse3XE4sf69NZ6heI1M55JeeJDEwt/D3l5yMtHZh7y8pCXj8w85JUfFIoAmg2FIpBnS5+MaNu+slC84Qd9fvvdc5dVLRMvuH1OipMe2lj4e8jLQ14+MvOQl4e8fGTmIa/8oFAE0GwoFIE8+92XKsvEk94QsaZvtykvXLEh3nvilMQi9ujrHo5CoZDyxIcuFv4e8vKQl4/MPOTlIS8fmXnIKz8oFAE0GwpFIK/m35V8EMvtJ/XprcvXbY4Dz7yz6tWJS9ZsSnniQxsLfw95ecjLR2Ye8vKQl4/MPOSVHxSKAJoNhSKQR4VCxGUHVZaJp+8asWlNr29dv7kjPn3BX6uWiSxie8fC30NeHvLykZmHvDzk5SMzD3nlB4UigGZDoQjk0aw/Ja9OvO+yXt/W2VWIb10+o2aZyCK2dyz8PeTlIS8fmXnIy0NePjLzkFd+UCgCaDYUikDedGyJOPfdlWXieXtHdLb3+tbj//Jo3TKRRWzvWPh7yMtDXj4y85CXh7x8ZOYhr/ygUATQbCgUgby59+Lk1YmP/aXXt/36rqcTC9Z3td3CItbEwt9DXh7y8pGZh7w85OUjMw955QeFIoBmQ6EI5MnGVRGnDa8sE395SPE7FeuY8tjiGD6qcrH6lmNvjlsfW8wi1sTC30NeHvLykZmHvDzk5SMzD3nlB4UigGZDoQjkya3HJ69OfOZvdd/yyLOr421jJiUWqzc8tIhFbD+QmYe8POTlIzMPeXnIy0dmHvLKDwpFAM2GQhHIi9XPRpz0+soy8Zqv1n3LolUbY5+Tb00sVM+7bU5EsIjtDzLzkJeHvHxk5iEvD3n5yMxDXvlBoQig2VAoAnnx5/+pLBNPeE3Esrk1N1+7qT0OO2daYpH642sfjkL3LdIsYn1k5iEvD3n5yMxDXh7y8pGZh7zyg0IRQLOhUATy4IVHIo7frrJQnPCTmpt3dHbF1391X2KB+sVL74ktHV1bt2MR6yMzD3l5yMtHZh7y8pCXj8w85JUfFIoAmg2FIpAHV/1HZZl4ypsi1i2tufm4G2YlFqcHnXVnrN7QXrEdi1gfmXnIy0NePjLzkJeHvHxk5iGv/KBQBNBsKBSBVjfv9uSDWKaeUXPz3/7tmcTC9L0nTolnlm9IbMsi1kdmHvLykJePzDzk5SEvH5l5yCs/KBQBNBsKRaCVdXVFXPyhyjLxrD0itiTLwYiIe59aHruNnlixKH3LcTfH/QtWVt2eRayPzDzk5SEvH5l5yMtDXj4y85BXflAoAmg2FIpAK3v498mrEx+4suqmC1dsiL1OmJxYlF7/4KKau2cR6yMzD3l5yMtHZh7y8pCXj8w85JUfFIoAmg2FItCq2jdGnP2OyjLxwv0iujoTm67b3FH1ic4/u/mJuodgEesjMw95ecjLR2Ye8vKQl4/MPOSVHxSKAJoNhSLQqv56TvLqxNmTE5t1dRXiu1fOTCxGv3X5jOjsKtQ9BItYH5l5yMtDXj4y85CXh7x8ZOYhr/ygUATQbCgUgVa0YUXEqTtXlomXfzKikCwIz5r8ZGIh+vGzp8baTe1VdlyJRayPzDzk5SEvH5l5yMtDXj4y85BXflAoAmg2FIpAK5o0Knl14qIHEpvd+PBziUXou9smx4Ll6/t0GBaxPjLzkJeHvHxk5iEvD3n5yMxDXvlBoQig2VAoAq1mxdMRJ7y2sky87luJzWYtWh17jLm5YgG66+iJcffcZX0+FItYH5l5yMtDXj4y85CXh7x8ZOYhr/ygUATQbCgUgVZz3X9Vlokn7hCxcn7FJivXb4kPnXZ7YgF65T3zq+6yFhaxPjLzkJeHvHxk5iEvD3n5yMxDXvlBoQig2VAoAq1k0f3JW51vObZik86uQnztl39LLD5H/emRKFT5jsV6WMT6yMxDXh7y8pGZh7w85OUjMw955QeFIoBmQ6EItIpCIeLX/15ZJv5s5+IDWsqcccsTiYXnf158d2zp6LIPySLWR2Ye8vKQl4/MPOTlIS8fmXnIKz8oFAE0GwpFoFU8OSl5deJd51VscsujLyQWnfucfGssXrOpX4dkEesjMw95ecjLR2Ye8vKQl4/MPOSVHxSKAJoNhSLQCjo7Ii54f2WZOP6dEe2lonDe0nXxznG3VCw4dxs9MWbMX1Fnx/WxiPWRmYe8POTlIzMPeXnIy0dmHvLKDwpFAM2GQhFoBfdfnrw68eFrtr68bnNHfOzsqYkF5+V3PT2gw7KI9ZGZh7w85OUjMw95ecjLR2Ye8soPCkUAzYZCERjqtqyPOPMtlWXizw+I6Cp+J2KhUIjvXX1/YrF51DUP2Q9h2RaLWB+ZecjLQ14+MvOQl4e8fGTmIa/8oFAE0GwoFIGhburpyasTn7pz68uXTpuXWGj+27nTY+OWzgEfmkWsj8w85OUhLx+ZecjLQ14+MvOQV35QKAJoNhSKwFC2bknEKW+qLBN/859bX54xf0XsOnpixSLzXcffEs8s3zAoh2cR6yMzD3l5yMtHZh7y8pCXj8w85JUfFIoAmg2FIjCU3fSjba5O3C7ihVkRUVxg7nvKrRULzOGjJsQdTy4ZtMOziPWRmYe8POTlIzMPeXnIy0dmHvLKDwpFoHGGSTpb0pOSNkhaKWmmpKMlvXKA+95O0lclXS7p75LWSOqQtEzSnZJ+IunVfdjPApX+Qqg3FgxwvvVQKAJD1bI5EW3bVxaK138/IiK6ugrx9V/dl1hgjp8ye1CnwCLWR2Ye8vKQl4/MPOTlIS8fmXnIKz8oFIHGOFzFkq9WQTdb0u793PcnJG2us++e8YKkg3rZ14I+7IdCEUB1v/9KZZl40usjVi+KiIgLbp+TWFx+5Rf3RmfXwB7Csi0WsT4y85CXh7x8ZOYhLw95+cjMQ175QaEIpG9vSRtV/JCtk3SspP0lHSzpMlWWiq/qx/6/1v3+Lkm3SDpKxeJwbxWLzGvKjrFB0l519rWge7sbJO1ZZ7y1H/PsKwpFYChacE/yQSy3tkVExN3zlsUuoyoXlvucfGssXTv4i0sWsT4y85CXh7x8ZOYhLw95+cjMQ175QaEIpG+6ih+wDhWLxG0drdKHsK0f+/+ipEsk/Wudbf5f2THuqLPdgu5trujHPAYLhSIw1BQKEb/4WGWZePouEZtWx9K1m2Ofkyu/N3GXURPi3qeWpzIVFrE+MvOQl4e8fGTmIS8PefnIzENe+UGhCKRrX5U+YJfU2ObFkh7v3maVpJelNJeZKl3JuEONbRaIQhGA69Hrk1cn/u2S6OwqxJcvuzexqLzwjrmpTYVFrI/MPOTlIS8fmXnIy0NePjLzkFd+UCgC6TpVpQ/YfnW2G1W23aEpzeXMsmO8v8Y2C0ShCMDRsSXivL0qy8Tz9oro2BLjp8xOLCi/8av7omuQvzexHItYH5l5yMtDXj4y85CXh7x8ZOYhr/ygUATS1XO783pJL62z3f4qfRBPSGku55cd4701tlkgCkUAjr9dmrw68dHr4+55y2L4Nt+buN8pt8WK9VtSnQ6LWB+ZecjLQ14+MvOQl4e8fGTmIa/8oFAE0rVMxQ/Xw71st71KH8Q/pDSXv3fvv13Sv9TYZkH3Nk+rOOd1Kj5QZr6kayV9VtKLUppfDwpFYKjYtLr4XYnlZeJlB8eKdZtj31Mqvzdx19ETY+b8FalPiUWsj8w85OUhLx+ZecjLQ14+MvOQV35QKALp+QeVPlwT+rD9+u5t701hLp8sm8tNdbZbULZdrXGXpDcPYC479TL2EYUiMDTcdkLi6sTC/Lvi21fMTCwkfz51XkOmxCLWR2Ye8vKQl4/MPOTlIS8fmXnIKz8oFIH0vE6lD9c1fdh+Sfe2swZ5Hq9RqSjslLR3nW3nSPqLpB9I+qikvSQdKGm0pIUq/TyPS9qun/PprbDcOigUgSa2elHESa+vLBR/9+W48p75iUXk1375t1S/N7Eci1gfmXnIy0NePjLzkJeHvHxk5iGv/KBQBNKzs0ofrqv6sH1PYTdvEOfwEkmTyubR1sv2r67z2qskTS7b1/h+zolCEWgF13+/skxs2z6eevyBeMtxN1csIN974pRYsnZTw6bFItZHZh7y8pCXj8w85OUhLx+ZecgrPygUgfQ0wxWKl5bN4SYVC8aB2E7SCpUeNPPyfuyDW56BoW7xoxHHb1dRKHbc8H/x8bOnJhaQdzy5pKFTYxHrIzMPeXnIy0dmHvLykJePzDzklR8UikB6sv4OxZ+VHX+6pH8cpP1eVLbfDw7SPsvxUBag2f3mc5VXJ578xjj12jsTi8cTb3qs4VNjEesjMw95ecjLR2Ye8vKQl4/MPOSVHxSKQLqWK5unPI8s298Dqv1U5/74Qdm+jxjE/fagUASa2VN3Jh7EMufa4xILx38/b3ps7uhs+PRYxPrIzENeHvLykZmHvDzk5SMzD3nlB4UikK7pKt0e/NI62+2v0gfxhAEe8/tl+3pc0g4D3F+9/VMoAnnS1RXx8wMqysTO03eP/Y6/oWLR+LYxk2Le0nWZTJFFrI/MPOTlIS8fmXnIy0NePjLzkFd+UCgC6TpVpQ/YfnW2G1W23aEDON7XJRW69/OUpDcNYF+1XKjSXD+Uwv4pFIFm9fdrE1cnXjZ+bGLReO2MhZlNkUWsj8w85OUhLx+ZecjLQ14+MvOQV35QKALp2lelD9glNbZ5sYpXEoakVZJe1s9j/aekzu79PCtpeD/3U892Kt3GvUHSK1I4BoUi0IzaN0WM37OiTFx5+nti15F/qVgwfv+3D0ShUMhsmixifWTmIS8PefnIzENeHvLykZmHvPKDQhFIX89tzx0q3tq8raNV+hC2VXl9RC+vS8WrGrd0b7NE0h79mOe/qf6DW/5Z0uSyuZzfj2P0BYUi0IzuOi9xdeKRY06qWCzuf+ptsXpje6bTZBHrIzMPeXnIy0dmHvLykJePzDzklR8UikD69pa0UcUP2TpJoyV9QNJBki5V6QM4W9Krqrx/hOoXih9Q8WrBkNQu6SuS9uxlvLrKfqZKWiHpF5K+KekASXtJ+mj3nJ8pm8eTkl7Tp5/eR6EINJsNKyJ+tnNFmfjISR+MYSNv2rpQHD5qQtwzb3nWM2UR2w9k5iEvD3n5yMxDXh7y8pGZh7zyg0IRaIzDJa1R6cO27Zgtafca7x2h+oViW5391hojquxnah/fO1XSm3v9ifuPQhFoNrccm7g68dOjzq1YKJ484bGsZxkRLGL7g8w85OUhLx+ZecjLQ14+MvOQV35QKAKNM0zSeBXLww0qfl/iTEnHSHplnfeNUGMKxX0kjZR0g6QnJC1T8TbtNd3/fYWkwyS9qNefdGAoFIFmsnJ+xIk7VJSJN445tGKReOj4abGpvTPrmUYEi9j+IDMPeXnIy0dmHvLykJePzDzklR8UigCaDYUi0Ez++O2KMrH9+NfEh0f9ausCcfdjJ8Zjz63JepZbsYj1kZmHvDzk5SMzD3l5yMtHZh7yyg8KRQDNhkIRaBbPPZi41flXx32hYoF48Z3zsp5lBRaxPjLzkJeHvHxk5iEvD3n5yMxDXvlBoQig2VAoAs2gUIi4/JMVZeKacTvGe0b+fuvi8PM/vzs6uwpZz7QCi1gfmXnIy0NePjLzkJeHvHxk5iGv/KBQBNBsKBSBZjB7cuLqxJ8de+TWheE7xk6KhSs2ZD3LBBaxPjLzkJeHvHxk5iEvD3n5yMxDXvlBoQig2VAoAlnr6oy4cL+KMnHRuF3irSP/vHVheO3MhVnPsioWsT4y85CXh7x8ZOYhLw95+cjMQ175QaEIoNlQKAJZe+CqxNWJPxp9zNZF4XeunBmFQnPd6tyDRayPzDzk5SEvH5l5yMtDXj4y85BXflAoAmg2FIpAlrasjzhrj4oy8bGx74pdRt4Yw0ZOiPecMDmWrN2U9SxrYhHrIzMPeXnIy0dmHvLykJePzDzklR8UigCaDYUikKVpZySuTvza6FO3LghveGhR1jOsi0Wsj8w85OUhLx+ZecjLQ14+MvOQV35QKAJoNhSKQFbWLY045c0VZeK0MR/auhj8bhPf6tyDRayPzDzk5SEvH5l5yMtDXj4y85BXflAoAmg2FIpAVib8pKJM7Bq3XXxi1IUxbOSEeHdbc9/q3INFrI/MPOTlIS8fmXnIy0NePjLzkFd+UCgCaDYUikAWls2NOOE1FYXiH8d8cutC8PoHm/tW5x4sYn1k5iEvD3n5yMxDXh7y8pGZh7zyg0IRQLOhUASycM3XKsrEzeNeG/uPvCKGjWzupzpvi0Wsj8w85OUhLx+ZecjLQ14+MvOQV35QKAJoNhSKQKM987fEg1guPu6rpVud1zT/rc49WMT6yMxDXh7y8pGZh7w85OUjMw955QeFIoBmQ6EINFKhEPHLQyrKxJXj3hTvGnltDBs5If784ND6HLKI9ZGZh7w85OUjMw95ecjLR2Ye8soPCkUAzYZCEWikx29MXJ14wrE/iGEjJ8S3rxg6tzr3YBHrIzMPeXnIy0dmHvLykJePzDzklR8UigCaDYUi0Cid7RHn7V1RJi4Yu3vsPvKG2PP4W2LxELrVuQeLWB+ZecjLQ14+MvOQl4e8fGTmIa/8oFAE0GwoFIFGue+yxNWJPxh9XAwbOSF+d98zWc+uX1jE+sjMQ14e8vKRmYe8POTlIzMPeeUHhSKAZkOhCDTC5rURp+9aUSY+NHavGD7yxjjiknuiq2to3ercg0Wsj8w85OUhLx+ZecjLQ14+MvOQV35QKAJoNhSKQCPcflLi6sQvjDoz3nLczTFv6bqsZ9dvLGJ9ZOYhLw95+cjMQ14e8vKRmYe88oNCEUCzoVAE0rbm+YiT3lBRJk4Zc2AMGzkhLrh9TtazGxAWsT4y85CXh7x8ZOYhLw95+cjMQ175QaEIoNlQKAJp+8sPK8rEznHbxcdGXRKHnTMttnR0ZT27AWER6yMzD3l5yMtHZh7y8pCXj8w85JUfFIoAmg2FIpCmJY9Hoe3VFYXib4/7TAwfNSEefGZl1rMbMBaxPjLzkJeHvHxk5iEvD3n5yMxDXvlBoQig2VAoAmm6+oiKMnHDuNfFPiN/E203Ppr1zAYFi1gfmXnIy0NePjLzkJeHvHxk5iGv/KBQBNBsKBSBtDw9LfEglnOPGxEf/NntsX5zR9azGxQsYn1k5iEvD3n5yMxDXh7y8pGZh7zyg0IRQLOhUATS0NUVcelHK8rEpeN2ineMvC7ueGJJ1rMbNCxifWTmIS8PefnIzENeHvLykZmHvPKDQhFAs6FQBNLwyHWJqxOPPfao+MFvH8h6ZoOKRayPzDzk5SEvH5l5yMtDXj4y85BXflAoAmg2FIrAYOvYHIVz9qwoE+eN3SPeM25CLF6zKevZDSoWsT4y85CXh7x8ZOYhLw95+cjMQ175QaEIoNlQKAKD7Z4LE1cnfnf08fHru57OemaDjkWsj8w85OUhLx+ZecjLQ14+MvOQV35QKAJoNhSKwGDauDK6Tv3XijLxvrHvj0+cMy06Oruynt2gYxHrIzMPeXnIy0dmHvLykJePzDzklR8UigCaDYUiMJgmj0lcnfjZ0efEg8+szHpmqWAR6yMzD3l5yMtHZh7y8pCXj8w85JUfFIoAmg2FIjBYVj0TnSfsUFEmThjz8Rj950eynllqWMT6yMxDXh7y8pGZh7w85OUjMw955QeFIoBmQ6EIDJKO675TUSa2j9s+PnPClbF6Q3vWU0sNi1gfmXnIy0NePjLzkJeHvHxk5iGv/KBQBNBsKBSBwfD8w4lbnX993BFx3f2t/bliEesjMw95ecjLR2Ye8vKQl4/MPOSVHxSKAJoNhSIwUIVCbPjFv1eUiWvHvSG+ddHNUSgUsp5dqljE+sjMQ14e8vKRmYe8POTlIzMPeeUHhSKAZkOhCAxQYc6UxNWJZx333Zi9eG3WU0sdi1gfmXnIy0NePjLzkJeHvHxk5iGv/KBQBNBsKBSBgejqjLXj319RJj4/bniccdODWc+sIVjE+sjMQ14e8vKRmYe8POTlIzMPeeUHhSKAZkOhCAxA+8yrElcnnnji6Fi/uSPrqTUEi1gfmXnIy0NePjLzkJeHvHxk5iGv/KBQBNBsKBSB/mrfGOtO2b2iTHx87DvjhgefyXpmDcMi1kdmHvLykJePzDzk5SEvH5l5yCs/KBQBNBsKRaCf1kw+LXF14knnnNfyD2IpxyLWR2Ye8vKQl4/MPOTlIS8fmXnIKz8oFAE0GwpFoD/WL4uNJ+xYUSb+dez+MevZVVnPrKFYxPrIzENeHvLykZmHvDzk5SMzD3nlB4UigGZDoQj0wwu//9/E1YkXXH1d1tNqOBaxPjLzkJeHvHxk5iEvD3n5yMxDXvlBoQig2VAoAqaOpXOj4/jtK8rECcd/Mlas35L11BqORayPzDzk5SEvH5l5yMtDXj4y85BXflAoAmg2FIqAaf7Fn68oEzePe0388fa7s55WJljE+sjMQ14e8vKRmYe8POTlIzMPeeUHhSKAZkOhCBjWzLkncavzdad+Mzo6u7KeWiZYxPrIzENeHvLykZmHvDzk5SMzD3nlB4UigGZDoQj0VaEQ8884oKJMXDXujXHfY09lPbPMsIj1kZmHvDzk5SMzD3l5yMtHZh7yyg8KRQDNhkIR6KNF916XuDrxjxeOzHpamWIR6yMzD3l5yMtHZh7y8pCXj8w85JUfFIoAmg2FItAXnR3x3EnvrCgTnx23WyxatirrmWWKRayPzDzk5SEvH5l5yMtDXj4y85BXflAoAmg2FIpAH8y+6ZzE1YkTrz4362lljkWsj8w85OUhLx+ZecjLQ14+MvOQV35QKAKNM0zS2ZKelLRB0kpJMyUdLemVg3icL0uaImmxpM2SnpF0taT9jX3sIOlESY9IWts9Hun+s9cO4lyroVAEetGxYXWsbNu5okx8rG3vWL9pS9ZTyxyLWB+ZecjLQ14+MvOQl4e8fGTmIa/8oI0dy4YAABGbSURBVFAEGuNwSWtU+rBtO2ZL2n2Ax/hHSRPrHKNL0vF92M9+kl6os5/nJe07wLnWQ6EIbGPtpvaYs3htPLRwVcxZvDYeuOLoxNWJd9z8x6yn2RRYxPrIzENeHvLykZmHvDzk5SMzD3nlB4UikL69JW1U8UO2TtKxKl4teLCky1RZKr5qAMf5fdm+7pD0GUnvl/QtSfPKXjuyzj52lrS0e7sOSadL+nD3OL37z0LSEqX3FwaFIhARhUIh7p63LP7nN/fHrqMnbl2Q7TPyN7Fh3OsqysT7Tjo4OrsKWU+5KbCI9ZGZh7w85OUjMw95ecjLR2Ye8soPCkUgfdNVKuiq3XZ8tEofwrZ+HuPgsn3cKOkl27y+g4q3PoekVZK2r7Gfq8r2c0SV179Q9voV/ZxrbygUkXuzFq2OQ8ZPTSzGho2cEL897rMVZWLnuO3ixim3Zj3lpsEi1kdmHvLykJePzDzk5SEvH5l5yCs/KBSBdO2r0gfskhrbvFjS4yqVfS/rx3FuVqm0rPVB/lLZXI6u8vqOKt4WHZJuqXOsW1S6hXrHfsy1NxSKyLXpc5bG28dOqlomHjzq0ugct11Fofj74z4dbx87KabPWZr11JsCi1gfmXnIy0NePjLzkJeHvHxk5iGv/KBQBNJ1qkofsP3qbDeqbLtDzWO8StKW7vdOqrPdy1X6Hsd7qrx+ZNkcvlhnP+XFZL3bp/uLQhG5NWvR6ppl4rCRE2LKmIMqysSN43aIfUdeFcNGToi3j50UsxatzvpHyByLWB+ZecjLQ14+MvOQl4e8fGTmIa/8oFAE0tVzu/N6SS+ts93+Kn0QTzCPUX6786hetp2s0pWM214JWX67c70rD99Ytt2V5lz7gkIRuVQoFGre5jxs5IQ4YtSZiQexnH/cNyq2OXT8tCgU8v1diixifWTmIS8PefnIzENeHvLykZmHvPKDQhFI1zIVP1wP97Ld9ip9EP9gHuOHZe/9bC/bnle27Tu2ee3+7j9f3Ydj9lzpOMOaad9QKCKX7p63rGaZOGzkTfHQ2L0qysRl43aKd478Q2Lbe+Ytz/pHyRSLWB+ZecjLQ14+MvOQl4e8fGTmIa/8oFAE0vMPKn24JvRh+/Xd295rHue0suPs08u2Py3b9rBtXlvc/eeP9uGYj3Zv+4I1074Z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width=\"650\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot discrete result and continuous-time counterpart\n",
    "fh = plt.figure(figsize=(6.5,2.5));\n",
    "plt.plot(tvp,yvp);  plt.stem(tv,yv);  plt.plot(tv,yv);  plt.xlabel('t');  plt.ylabel('y(t)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximate impulse input\n",
    "\n",
    "We cannot formally sample a signal containing an impulse.  However, recall the working definition of the impulse as\n",
    "$$\\delta(t) = \\lim_{A \\to 0} \\frac{1}{A} p_A(t),$$\n",
    "where $p_A(t)$ is unit pulse with total width $A$ centered on $t=0$.  If we sample the signal with a spacing $T$, and let $T$ become small, then this leads to the approximation\n",
    "$$\\delta(t) \\approx \\frac{1}{T} p_T(t).$$\n",
    "\n",
    "The code below demonstrates this concept by using discrete convolution to find the approximate output of the previous system when the input is an impulse at the origin:  $x(t) = \\delta(t)$.  The red curve in the first plot shows the finite approximation to the input, along with the samples $x[n] = x(nT)$ starting at $n=0$.  The second plot contains the sample points for the discrete convolution output, along with the linear interpolation of these points (red).  Also shown is the actual impulse response of the system (green), which for this case represents the actual or ideal output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "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"
    },
    {
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       "<IPython.core.display.HTML object>"
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "# Approximation to x(t)=delta(t)\n",
    "xvip = 1/T*np.where(abs(tvp)<=T/2, 1, 0);\n",
    "\n",
    "# Explicit discrete convolution sum\n",
    "xvi = np.zeros(xv.shape);  xvi[0] = 1/T;\n",
    "yvi = np.zeros(nv.shape);\n",
    "for n in nv:\n",
    "    for k in nv:\n",
    "        xcurr = 0 if n-k<0 else xvi[n-k];\n",
    "        yvi[n] += hv[k]*xcurr;\n",
    "yvi *= T;\n",
    "\n",
    "# Plots\n",
    "fh = plt.figure();\n",
    "plt.subplot(211);  plt.plot(tvp,xvip,'r-');  plt.stem(tv,xvi);  plt.ylabel('Approx $\\delta(t)$');\n",
    "plt.subplot(212);  plt.plot(tv,yvi,'r-',label=\"Approximate\");  plt.stem(tv,yvi);  \n",
    "plt.plot(tvp,hvp,'g-',label=\"Actual\");  plt.ylabel('h(t)');  plt.xlabel('t');  plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tasks\n",
    "\n",
    "These tasks involve writing code, or modifying existing code, to meet the objectives described.\n",
    "\n",
    "1.  The previous code snippets use samples with spacing $T = 0.5$ to approximate the output $y(t)$ from a system with impulse response $h(t) = e^{-t} u(t)$ when the input is $x(t) = u(t)$.  Repeat this with a spacing of $T=0.1$ in the discretisation.  Generate a plot that shows the approximate output $y(t)$ using linear interpolation for this case, and on the same set of axes include the actual output calculated analytically.  The domain of your plot should span $t=-1$ to $t=5$.<br><br>\n",
    "\n",
    "2.  Repeat the previous task but using a system with the highpass impulse response $h(t) = \\delta(t) - e^{-t} u(t)$.<br><br>\n",
    "\n",
    "3.  An underdamped second-order system with transfer function\n",
    "$$\n",
    "H(s) = \\frac{K \\omega_n^2}{s^2 + 2 \\zeta \\omega_n s + \\omega_n^2}\n",
    "$$\n",
    "has impulse response\n",
    "$$\n",
    "h(t) = \\frac{\\omega_n}{\\sqrt{1-\\zeta^2}} e^{-\\zeta \\omega_n t} \n",
    "\\sin(\\omega_n \\sqrt{1-\\zeta^2} t) u(t)\n",
    "$$\n",
    "when $\\zeta<1$.  Here $K$ is the *gain*, $\\zeta$ is called the *damping ratio*, and $\\omega_n$ is the *natural frequency* of the system.  On one set of axes make a plot of this impulse response for $K=1$, $\\omega_n = 3$ and the three cases $\\zeta = 0.25, 0.5, 0.99$.  Your plot should span the domain $t=-1$ to $t=10$.  Then, using discrete-time convolution with $T=0.1$, find the approximate step responses for each of the three cases.  Plot these responses on one set of coordinate axes over the same domain $t=-1$ to $t=10$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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