Animated Sinc and FT example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def rect(x, B):\n",
    "    \"\"\"\n",
    "    create a rectangle function\n",
    "    returns a numpy array that is 1 if |x| < w and 0 if |x| > w\n",
    "    B is the rectangle width centered at 0\n",
    "    x is the number of points in the array\n",
    "    \"\"\"\n",
    "    \n",
    "    B = int(B)\n",
    "    x = int(x)\n",
    "    \n",
    "    high = np.ones(B)\n",
    "    low1 = np.zeros(int(x/2 - B/2))    \n",
    "    x1 = np.append(low1, high)\n",
    "    rect = np.append(x1, low1)\n",
    "    \n",
    "    if x > len(rect):\n",
    "        rect = np.append(rect, 0)\n",
    "    elif x < len(rect):\n",
    "        rect = rect[:-1]\n",
    "\n",
    "    return rect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\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",
       "            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 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);\n",
       "        canvas.attr('height', height);\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'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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;\n",
       "    var y = canvas_pos.y;\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",
       "    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 + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "\n",
    "# constants and x array\n",
    "pi = np.pi\n",
    "length = 2000\n",
    "x = np.linspace(-1, 1, length)\n",
    "\n",
    "# create figure and axes \n",
    "fig, (ax1, ax2) = plt.subplots(2, figsize=(12, 6))\n",
    "\n",
    "# creating our line objects for the plots\n",
    "sinc, = ax1.plot(x, np.sin(x), '-b')\n",
    "box, = ax2.plot(x, np.sin(x), '-r')\n",
    "\n",
    "def animate(B):\n",
    "    \"\"\"\n",
    "    this function gets called by FuncAnimation\n",
    "    each time called, it will replot with a different width \"B\"\n",
    "    \n",
    "    B: rect width\n",
    "    \n",
    "    return:\n",
    "        sinc: ydata\n",
    "        box: ydata\n",
    "    \"\"\"\n",
    "    \n",
    "    # create our rect object\n",
    "    f = rect(len(x), B)\n",
    "    box.set_ydata(f)\n",
    "    \n",
    "    # create our sinc object\n",
    "    F = (B / length) * np.sin(x * B / 2) / (x * B / 2)\n",
    "    sinc.set_ydata(F)\n",
    "    \n",
    "    # adjust the sinc plot height in a loop\n",
    "    ax1.set_ylim(np.min(F), np.max(F))\n",
    "    \n",
    "    # format the ax1 yticks\n",
    "    plt.setp(ax1, xticks=[-0.25, 0.25], xticklabels=['-1/4', '1/4'],\n",
    "             yticks=[0, np.max(F)], yticklabels=['0', 'B={:.2f}'.format((B / length))])\n",
    "    \n",
    "    # format the ax2 xticks to move with the box\n",
    "    plt.setp(ax2, yticks=[0, 1], \n",
    "             xticks=[-1, -1 * B / length, 1 * B / length, 1], xticklabels=['-1', '-B/2', 'B/2', '1'])\n",
    "    \n",
    "def init():\n",
    "    \"\"\"\n",
    "    initialize the figure\n",
    "    \"\"\"\n",
    "    \n",
    "    ax2.set_ylim(-0.2, 1.1)\n",
    "    ax1.set_xlim(-0.25, 0.25)\n",
    "    ax2.set_xlim(-1, 1)\n",
    "    ax1.axhline(0, color='black', lw=1)\n",
    "    ax2.axhline(0, color='black', lw=1)\n",
    "    plt.rcParams.update({'font.size':14})\n",
    "    \n",
    "    return sinc, box,\n",
    "\n",
    "# the FuncAnimation function iterates through our animate function using the steps array\n",
    "step = 10\n",
    "steps = np.append(np.arange(10, 1000, step), np.arange(1000, 10, -1 * step))\n",
    "ani = FuncAnimation(fig, animate, steps, init_func=init, interval=50, blit=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n"
   ]
  }
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