superposition_1.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"height: 1px;\">\n",
    "<i>This code was authored by Alex Shvonski, Copyright 2020 MIT All Rights Reserved.</i>\n",
    "<hr style=\"height: 1px;\">\n",
    "\n",
    "<h2>Initializing the program</h2>\n",
    "\n",
    "<font size=\"3\">To initialize the visualization, you may need to click \"Run all initialization cells\" above (see button location in figure).</font>\n",
    "\n",
    "<img src=\"img/binder_initialize_button.png\" alt=\"Drawing\" style=\"width: 700px;\" align=\"left\"/>\n",
    "\n",
    "<br/>\n",
    "<br/>\n",
    "<br/>\n",
    "<br/>\n",
    "<br/>\n",
    "<br/>\n",
    "<br/>\n",
    "<font size=\"3\">You should see the visualization <i>directly below this line</i>, before the next section.</font>\n",
    "\n",
    "<br/>\n",
    "<br/>\n",
    "<hr style=\"height: 1px;\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "#This code was authored by Alex Shvonski, Copyright 2020 MIT All Rights Reserved.\n",
    "\n",
    "%matplotlib notebook\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display, clear_output\n",
    "from ipywidgets import interact, interactive, interactive_output, fixed, IntSlider, HBox, Layout, Output, VBox\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,\n",
    "                               AutoMinorLocator)\n",
    "from math import pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "init_cell": true
   },
   "outputs": [],
   "source": [
    "#Define functions\n",
    "###############################################\n",
    "###############################################\n",
    "def func1(x,t,L,polarity):\n",
    "    arg1 = (x - (t/10.)*np.ones(len(x)))\n",
    "    f1 = np.zeros(len(x))\n",
    "    for i in range(len(arg1)):\n",
    "        if arg1[i] < 0:\n",
    "            f1[i] = 0.\n",
    "        elif 0 <= arg1[i] <= 2:\n",
    "            f1[i] = 1.\n",
    "        elif 0 < arg1[i]:\n",
    "            f1[i] = 0.\n",
    "\n",
    "    x = L - x\n",
    "    arg2 = (x - (t/10.)*np.ones(len(x)))\n",
    "    f2 = np.zeros(len(x))\n",
    "    for i in range(len(arg2)):\n",
    "        if arg2[i] < 0:\n",
    "            f2[i] = 0.\n",
    "        elif 0 <= arg2[i] <= 2:\n",
    "            f2[i] = 1.\n",
    "        elif 0 < arg2[i]:\n",
    "            f2[i] = 0.\n",
    "            \n",
    "    if polarity==\"pos\":\n",
    "        result = f1+f2\n",
    "        \n",
    "    elif polarity==\"neg\":\n",
    "        result = f1-f2\n",
    "        \n",
    "    return result\n",
    "\n",
    "\n",
    "def func2(x,t,L,polarity):\n",
    "    arg1 = (x - (t/10.)*np.ones(len(x)))\n",
    "    f1 = np.zeros(len(x))\n",
    "    for i in range(len(arg1)):\n",
    "        if arg1[i] < 0:\n",
    "            f1[i] = 0.\n",
    "        elif 0 <= arg1[i] <= 1.:\n",
    "            f1[i] = arg1[i]\n",
    "        elif 1. <= arg1[i] <= 2.:\n",
    "            f1[i] = 2.-arg1[i]\n",
    "        elif 0 < arg1[i]:\n",
    "            f1[i] = 0.\n",
    "\n",
    "    x = L - x\n",
    "    arg2 = (x - (t/10.)*np.ones(len(x)))\n",
    "    f2 = np.zeros(len(x))\n",
    "    for i in range(len(arg2)):\n",
    "        if arg2[i] < 0:\n",
    "            f2[i] = 0.\n",
    "        elif 0 <= arg2[i] <= 1.:\n",
    "            f2[i] = arg2[i]\n",
    "        elif 1. <= arg2[i] <= 2.:\n",
    "            f2[i] = 2.-arg2[i]\n",
    "        elif 0 < arg2[i]:\n",
    "            f2[i] = 0.\n",
    "\n",
    "    if polarity==\"pos\":\n",
    "        result = f1+f2\n",
    "        \n",
    "    elif polarity==\"neg\":\n",
    "        result = f1-f2\n",
    "        \n",
    "    return result\n",
    "\n",
    "\n",
    "def func3(x,t,L,polarity):\n",
    "    arg1 = (x - (t/10.)*np.ones(len(x)))\n",
    "    f1 = np.zeros(len(x))\n",
    "    for i in range(len(arg1)):\n",
    "        if arg1[i] < 0:\n",
    "            f1[i] = 0.\n",
    "        elif 0 <= arg1[i] <= 2.:\n",
    "            f1[i] = np.sqrt(1-(arg1[i]-1.)**2.)\n",
    "        elif 0 < arg1[i]:\n",
    "            f1[i] = 0.\n",
    "\n",
    "    x = L - x\n",
    "    arg2 = (x - (t/10.)*np.ones(len(x)))\n",
    "    f2 = np.zeros(len(x))\n",
    "    for i in range(len(arg2)):\n",
    "        if arg2[i] < 0:\n",
    "            f2[i] = 0.\n",
    "        elif 0 <= arg2[i] <= 2.:\n",
    "            f2[i] = np.sqrt(1-(arg2[i]-1.)**2.)\n",
    "        elif 0 < arg2[i]:\n",
    "            f2[i] = 0.\n",
    "        \n",
    "    if polarity==\"pos\":\n",
    "        result = f1+f2\n",
    "        \n",
    "    elif polarity==\"neg\":\n",
    "        result = f1-f2\n",
    "        \n",
    "    return result\n",
    "\n",
    "\n",
    "def func4(x,t,L,polarity):\n",
    "    arg1 = ((x-1) - (t/10.)*np.ones(len(x)))\n",
    "    f1 = np.exp(-(2.*arg1)**2.)\n",
    "    \n",
    "    x = L - x\n",
    "    arg2 = ((x-1) - (t/10.)*np.ones(len(x)))\n",
    "    f2 = np.exp(-(2.*arg2)**2.)\n",
    "        \n",
    "    if polarity==\"pos\":\n",
    "        result = f1+f2\n",
    "        \n",
    "    elif polarity==\"neg\":\n",
    "        result = f1-f2\n",
    "        \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "init_cell": true
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   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, 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 overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "28ebb6df71e24ed4a0454f5455293b12",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(Dropdown(description='Function:', options=(('function-1', <function func1 at 0x11477db70>), ('f…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Define plot\n",
    "###############################################\n",
    "###############################################\n",
    "fig, ax = plt.subplots(1, 1, figsize=(9.5, 5))\n",
    "plt.subplots_adjust(left=0.05, bottom=None, right=1, top=None, wspace=None, hspace=1.)\n",
    "L=16\n",
    "x = np.linspace(0., L, 10000)\n",
    "polarity = \"pos\"\n",
    "func=func1\n",
    "t=0.\n",
    "\n",
    "#############################\n",
    "#plot1\n",
    "y_max = max(func(x,t,L,polarity))*3.\n",
    "\n",
    "line_1, = ax.plot(x, func(x,t,L,polarity),\n",
    "                     'r-', lw=2)\n",
    "\n",
    "\n",
    "\n",
    "#plot params\n",
    "ax.set_title('Amplitude: $A(x,t)$', fontsize=16)\n",
    "ax.set_xlabel('$x$', fontsize=16)\n",
    "ax.set_ylim(-y_max,y_max)\n",
    "ax.set_xlim(min(x),max(x))\n",
    "ax.grid(True)\n",
    "plt.setp(ax.get_xticklabels(), fontsize=14)\n",
    "plt.setp(ax.get_yticklabels(), fontsize=14)\n",
    "\n",
    "\n",
    "#Define plot updater\n",
    "###############################################\n",
    "###############################################\n",
    "def update(func,t,polarity):\n",
    "    #plot1\n",
    "    #############################\n",
    "    line_1.set_ydata(func(x,t,L,polarity))\n",
    "    \n",
    "    fig.canvas.draw_idle()\n",
    "    return\n",
    "\n",
    "\n",
    "#Define control elements\n",
    "###############################################\n",
    "###############################################\n",
    "s1=widgets.Dropdown(\n",
    "    options=[('function-1', func1),('function-2', func2),('function-3', func3),('function-4', func4)],\n",
    "    value=func1,\n",
    "    description='Function:')\n",
    "\n",
    "\n",
    "s1_1=widgets.Dropdown(\n",
    "    options=[('positive', \"pos\"),('negative', \"neg\")],\n",
    "    value=\"pos\",\n",
    "    description='Polarity:')\n",
    "\n",
    "\n",
    "s2=widgets.IntSlider(\n",
    "    min=0,\n",
    "    max=L*10,\n",
    "    step=1.,\n",
    "    value=0.,\n",
    "    layout=Layout(width='600px'),\n",
    "    description='$t$',\n",
    "    style = {'description_width': 'initial'})\n",
    "\n",
    "\n",
    "#Connect controls to plot\n",
    "###############################################\n",
    "###############################################\n",
    "out = interactive_output(update, {'func': s1, 'polarity': s1_1, 't': s2})\n",
    "\n",
    "\n",
    "#Set layout\n",
    "###############################################\n",
    "###############################################\n",
    "box_layout = Layout(display='flex', flex_flow='row', justify_content='space-between', align_items='center')\n",
    "\n",
    "\n",
    "#Display output\n",
    "###############################################\n",
    "###############################################\n",
    "d = display(HBox([s1, s1_1, s2], layout=box_layout))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"height: 1px;\">\n",
    "\n",
    "<h2>About the Visualization</h2>\n",
    "\n",
    "<font size=\"3\"><b>Plot:</b> This plot shows the superposition of identical waves traveling towards each other.</font>\n",
    "\n",
    "<br/>\n",
    "<font size=\"3\"><b>Drop-down and Sliders:</b>\n",
    "<ul>\n",
    "    <li>Function: select a function from the drop-down menu.</li>\n",
    "    <li>Polarity: choose the polarity of the counter-propagating function (positive or negative)</li>\n",
    "    <li>$t$: vary the time to display the functions advancing towards each other</li>\n",
    "</ul>\n",
    "</font>\n",
    "\n",
    "<br/>\n",
    "\n",
    "<hr style=\"height: 1px;\">\n",
    "\n",
    "<h2>Exploration</h2>\n",
    "\n",
    "<font size=\"3\">Consider the following questions and possible actions:\n",
    "<ul>\n",
    "    <li>What do you expect the superposition of different waveforms to look like?</li>\n",
    "</ul>      \n",
    "</font>\n",
    "\n",
    "<br/>\n",
    "\n",
    "<hr style=\"height: 1px;\">\n",
    "\n",
    "<h2>Viewing the Code</h2>\n",
    "<br/>\n",
    "<font size=\"3\">You are encouraged to click the button below to view the source code. You can alter the code and rerun it within this notebook, or download the notebook itself and run the code locally on your own machine.</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "init_cell": true
   },
   "outputs": [
    {
     "data": {
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       " if (code_show){\n",
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       " $('div.input').show();\n",
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       " code_show = !code_show\n",
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       "$( document ).ready(code_toggle);\n",
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     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The code in this block includes content from StackOverFlow User: harshil (CC BY-SA 4.0)\n",
    "#and can be found here: https://stackoverflow.com/questions/27934885/how-to-hide-code-from-cells-in-ipython-notebook-visualized-with-nbviewer\n",
    "###############################################\n",
    "###############################################\n",
    "#Enable hidden code\n",
    "from IPython.display import HTML\n",
    "\n",
    "HTML('''<script>\n",
    "code_show=true; \n",
    "function code_toggle() {\n",
    " if (code_show){\n",
    " $('div.input').hide();\n",
    " } else {\n",
    " $('div.input').show();\n",
    " }\n",
    " code_show = !code_show\n",
    "} \n",
    "$( document ).ready(code_toggle);\n",
    "</script>\n",
    "<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"Click here to toggle on/off the raw code.\"></form>''')\n"
   ]
  }
 ],
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