ex4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.io import loadmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(x):  \n",
    "    return math.exp(-np.logaddexp(0, -x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Setup the parameters you will use for this exercise\n",
    "input_layer_size  = 400   # 20x20 Input Images of Digits\n",
    "hidden_layer_size = 25   # 25 hidden units\n",
    "num_labels = 10          # 10 labels, from 1 to 10   \n",
    "                         # (note that we have mapped \"0\" to label 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# =========== Part 1: Loading and Visualizing Data =============\n",
    "#  We start the exercise by first loading and visualizing the dataset. \n",
    "#  You will be working with a dataset that contains handwritten digits.\n",
    "ex4data1 = loadmat('ex4data1.mat')\n",
    "X = ex4data1['X']\n",
    "y = ex4data1['y']\n",
    "m = len(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def showGreymaps(greymap):\n",
    "    arr = np.asarray(np.reshape(greymap, (-1, 20)).T)\n",
    "    plt.figure()\n",
    "    plt.imshow(arr, cmap='gray')\n",
    "    plt.show()\n",
    "    \n",
    "choices = np.random.choice(len(X), 20)\n",
    "showGreymaps(X[choices])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ================ Part 2: Loading Parameters ================\n",
    "# In this part of the exercise, we load some pre-initialized \n",
    "# neural network parameters.\n",
    "ex4weights = loadmat('ex4weights.mat')\n",
    "Theta1 = ex4weights['Theta1']\n",
    "Theta2 = ex4weights['Theta2']\n",
    "nn_params = (Theta1, Theta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at parameters (loaded from ex4weights): None\n",
      "(this value should be about 0.287629)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# ================ Part 3: Compute Cost (Feedforward) ================\n",
    "#  To the neural network, you should first start by implementing the\n",
    "#  feedforward part of the neural network that returns the cost only. You\n",
    "#  should complete the code in nnCostFunction.m to return cost. After\n",
    "#  implementing the feedforward to compute the cost, you can verify that\n",
    "#  your implementation is correct by verifying that you get the same cost\n",
    "#  as us for the fixed debugging parameters.\n",
    "#\n",
    "#  We suggest implementing the feedforward cost *without* regularization\n",
    "#  first so that it will be easier for you to debug. Later, in part 4, you\n",
    "#  will get to implement the regularized cost.\n",
    "\n",
    "def nnCostFunction(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lamb):\n",
    "    pass\n",
    "\n",
    "lamb = 0\n",
    "J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lamb)\n",
    "\n",
    "print('Cost at parameters (loaded from ex4weights): ' + str(J) + '\\n(this value should be about 0.287629)\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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