FR_cosine.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do `Kernel -> Restart & Run All` in top menu to run the notebook and enable the interactive widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import pi\n",
    "from IPython.display import display\n",
    "from ipywidgets import widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def set_stem_plot(handle, x, y):\n",
    "    ml, sl, _ = handle\n",
    "    ml.set_data(x, y)\n",
    "    for i_l, l in enumerate(sl):\n",
    "        l.set_data(np.stack((x,x)).T[i_l], \n",
    "                   np.stack((np.zeros(x.shape), y)).T[i_l])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9d061a4b19554075aab09cf1b5916b92"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.plot_cos_spectrum>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_axis = np.linspace(-0.005,0.005,1000)\n",
    "k_lim = 2\n",
    "k_axis = np.arange(-k_lim,k_lim+1)\n",
    "\n",
    "# cosine frequency\n",
    "f = 1000\n",
    "\n",
    "# setting up the plots\n",
    "fig, ax = plt.subplots(2,2)\n",
    "ax[0,0].set_xlim([-0.005,0.005])\n",
    "ax[0,0].set_ylim([-20,20])\n",
    "ax[0,0].set_xlabel('t [s]')\n",
    "ax[0,1].set_xlim([-k_lim-1,k_lim+1])\n",
    "ax[0,1].set_ylim([0,8])\n",
    "ax[0,1].set_xlabel('k')\n",
    "ax[0,1].set_title('$|c_k|$')\n",
    "ax[1,1].set_xlabel('k')\n",
    "ax[1,1].set_title('$arg\\ c_k$')\n",
    "ax[1,1].set_xlim([-k_lim-1,k_lim+1])\n",
    "ax[1,1].set_ylim([-10,10])\n",
    "ax[1,0].axis('off')\n",
    "spec_zeros = np.zeros(k_axis.shape)\n",
    "sig_plot, = ax[0,0].plot(t_axis,t_axis)\n",
    "magspec_plot = ax[0,1].stem(k_axis, spec_zeros, basefmt = ' ')\n",
    "argspec_plot = ax[1,1].stem(k_axis, spec_zeros, basefmt = ' ')\n",
    "plt.tight_layout()\n",
    "\n",
    "# wrapper for interactive mode\n",
    "def plot_cos_spectrum(a = 10, ph = 0, k = 0):\n",
    "    # cosine in time\n",
    "    cos_t = a * np.cos(2 * pi * f * t_axis + ph) + k\n",
    "    # magnitude spectrum\n",
    "    mag_spec = np.zeros(k_axis.shape)\n",
    "    arg_spec = np.zeros(k_axis.shape)\n",
    "    mag_spec[k_lim+1] = a / 2\n",
    "    mag_spec[k_lim-1] = a / 2\n",
    "    mag_spec[k_lim] = np.abs(k)\n",
    "    # argument of spectrum\n",
    "    arg_spec[k_lim+1] = ph\n",
    "    arg_spec[k_lim-1] = -ph\n",
    "    arg_spec[k_lim] = 0 if k >= 0 else pi\n",
    "    # updating the plots\n",
    "    ax[0,0].set_title(f'${a:.2f}\\ cos(2000\\pi t{ph:+.2f}){k:+.2f}$', fontsize=10)\n",
    "    sig_plot.set_data(t_axis, cos_t)\n",
    "    set_stem_plot(magspec_plot, k_axis, mag_spec)\n",
    "    set_stem_plot(argspec_plot, k_axis, arg_spec)\n",
    "    plt.draw()\n",
    "    \n",
    "widgets.interact(plot_cos_spectrum, \n",
    "                 a = (0.1,15,0.1), \n",
    "                 ph = (-8.0,8.0,0.2), \n",
    "                 k = (-8,8,0.2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}