{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolutional Filter Factorization\n",
    "In this notebook, I want to see if we can factorize a spatial filter with large support into successive convolutions of filters with smaller spatial support. The inspiration for this comes from the fact that I often have to work with large spatial kernels, and there may be some speedup available by using successive smaller convolutions. \n",
    "\n",
    "For example lots of 5x5 kernels can be made up of 2 3x3 convolutions, using 18 multiply/adds per pixel instead of 25. Of course, there are some that cannot be made up from 2 3x3 convolutions, but perhaps we are happy to pay a small error term. \n",
    "\n",
    "Further, when viewing nvidia-prof profiling outputs, it seems that if we use 3x3 convolutions, these are done using winograd rather than fft/ifft lowlevel kernels. I wouldn't be surprised if due to the large prevalence of 3x3 kernels in the machine learning literature, that GPUs are being specifically optimized for them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:12:45.254957Z",
     "start_time": "2018-12-03T18:12:45.245953Z"
    }
   },
   "outputs": [],
   "source": [
    "# Import my plotting libraries. plotters is available at \n",
    "# https://github.com/fbcotter/plotters\n",
    "%matplotlib notebook\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['image.resample'] = False\n",
    "mpl.rcParams['image.interpolation'] = 'none'\n",
    "mpl.rcParams['image.cmap'] = 'gray'\n",
    "import matplotlib.pyplot as plt\n",
    "import plotters\n",
    "\n",
    "# Import my numeric libraries. Pytorch wavelets is a library that allows\n",
    "# the dtcwt kernels (the particular ones I want to speed up) to be done in\n",
    "# pytorch (and optionally, with a GPU). \n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn.functional as F\n",
    "import dtcwt\n",
    "from pytorch_wavelets import DTCWTForward, DTCWTInverse\n",
    "from pytorch_wavelets.dtcwt.lowlevel import q2c\n",
    "dev = torch.device('cpu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get the target filters\n",
    "This next bit of code is largely specific to my task. Any filters here would suffice. For our example, I'm looking at the synthesis filters of a single layer inverse Dual Tree Complex Wavelet Transform. They are 7x7 but have little energy in the outermost pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:24.551128Z",
     "start_time": "2018-12-03T18:05:24.447685Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"899.9999804930258\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ifm = DTCWTInverse(J=1, biort='near_sym_a', qshift='qshift_a')\n",
    "\n",
    "def yb_to_yh(yb):\n",
    "    # Converts the 6 complex bands back into the 3 LH, HH, HL bands\n",
    "    deg15, deg165 = q2c(yb[:,0])\n",
    "    deg45, deg135 = q2c(yb[:,1])\n",
    "    deg75, deg105 = q2c(yb[:,2])\n",
    "    yh = torch.stack((deg15, deg45, deg75, deg105, deg135, deg165), dim=2)\n",
    "    return yh\n",
    "\n",
    "# Create an output array to store the results\n",
    "xb = np.zeros((4,16,16))\n",
    "yl = torch.zeros(1,1,16,16)\n",
    "yb = torch.zeros(1,3,1,16,16)\n",
    "\n",
    "# Put impulses in the ll, lh, hh and hl bands\n",
    "yl[0,0,8,8] = 1\n",
    "x = ifm((yl, [yb_to_yh(yb)]))\n",
    "xb[0] = x.detach().cpu().numpy()[0,0]\n",
    "yl[0,0,8,8] = 0\n",
    "for b in range(3):\n",
    "    yb[0,b,0,8,8] = 1\n",
    "    x = ifm((yl, [yb_to_yh(yb)]))\n",
    "    xb[b+1] = x.detach().cpu().numpy()[0,0]\n",
    "    yb[0,b] = 0\n",
    "    \n",
    "# Plot the resulting outputs\n",
    "fig, ax = plt.subplots(1,4, figsize=(9,3), \n",
    "                       subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                       gridspec_kw={'top':0.95, 'bottom':0.05, 'left':0.05, \n",
    "                                    'right':0.95, 'wspace':0.05})\n",
    "for i in range(4):\n",
    "    ax[i].imshow(xb[i])\n",
    "fig.suptitle('ll, lh, hh, hl impulse responses - our 7x7 target filters');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aside 1: Convex vs Non Convex\n",
    "This is a non convex optimization problem. Consider the simple case where we want to minimize a 1x1 kernel as a convolution of 2 1x1 kernels (I know this is silly, but it makes the maths nicer). Then our output is:\n",
    "$$\n",
    "f = xy\n",
    "$$\n",
    "\n",
    "To check for convexity, we need the Hessian matrix to be positive semi definite. We know that whenever there is a cross term then the problem cannot be convex, but for simplicity sake, let us check what the Hessian matrix is anyway.\n",
    "$$\n",
    "H_{i,j} = \\frac{\\partial^2f}{\\partial x_i \\partial x_j}\n",
    "$$\n",
    "\n",
    "$$\n",
    "H = \\begin{bmatrix}\n",
    "0 & 1 \\\\\n",
    "1 & 0\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Positive semi definite means that for any $x$, $x^THx$ must be greater than or equal to zero for any x. In our above problem, our Hessian is larger than 2 by 2, but there is a nice trick in that every subset of the Hessian must also be PSD (you can set the corresponding parts of $x$ to 0 to ignore the other areas). In the above case, if $x=[-1,1]^T$ gives $x^THx = -2$.\n",
    "\n",
    "Another nice bit of info for PSD, is that if a matrix is diagonally dominant, i.e.\n",
    "$$\n",
    "h_{i,i} \\geq \\sum_{j \\neq i} |h_{i,j}|\n",
    "$$\n",
    "\n",
    "and $h_{i,i} \\geq 0$, then we have a PSD matrix. This however is sufficient and not necessary. This is often why we sometimes add a small identity matrix to a covariance matrix to make sure we are satisfying its PSD conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aside 2: check how to do alternating projections\n",
    "Non convex optimization is not trivial. A simple way of solving it is to do alternating projections. I.e. minimize w.r.t. x keeping y constant, the minimizing w.r.t. y keeping x constant.\n",
    "Let us return to the $f=xy$ problem, and try to use pytorch to alternate minimizations. This is an underdetermined set of equations, so let us also add a constraint on the norms of $x$ and $y$. I.e. minimize:\n",
    "\n",
    "$$\n",
    "L = (xy - \\alpha)^2 + \\lambda (|x| + |y|)\n",
    "$$\n",
    "\n",
    "As an example, let us try to find two numbers $x$ and $y$ that multiply to give 20, while minimising the $l_1$ norm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:24.570692Z",
     "start_time": "2018-12-03T18:05:24.552470Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step  0a: Loss = 0404.3896\tOut = -0.10 (0.04, -2.68)\n",
      "Step  0b: Loss = 0296.7857\tOut = 2.78 (-1.04, -2.68)\n",
      "Step  1a: Loss = 0284.1869\tOut = 3.15 (-1.04, -3.03)\n",
      "Step  1b: Loss = 0189.4539\tOut = 6.25 (-2.06, -3.03)\n",
      "Step  2a: Loss = 0158.8276\tOut = 7.42 (-2.06, -3.60)\n",
      "Step  2b: Loss = 0087.5617\tOut = 10.68 (-2.97, -3.60)\n",
      "Step  3a: Loss = 0059.7771\tOut = 12.31 (-2.97, -4.15)\n",
      "Step  3b: Loss = 0026.1703\tOut = 14.96 (-3.60, -4.15)\n",
      "Step  4a: Loss = 0014.7589\tOut = 16.27 (-3.60, -4.51)\n",
      "Step  4b: Loss = 0005.7598\tOut = 17.78 (-3.94, -4.51)\n",
      "Step  5a: Loss = 0003.2123\tOut = 18.47 (-3.94, -4.69)\n",
      "Step  5b: Loss = 0001.6230\tOut = 19.14 (-4.08, -4.69)\n",
      "Step  6a: Loss = 0001.2203\tOut = 19.42 (-4.08, -4.76)\n",
      "Step  6b: Loss = 0000.9932\tOut = 19.68 (-4.14, -4.76)\n",
      "Step  7a: Loss = 0000.9386\tOut = 19.78 (-4.14, -4.78)\n",
      "Step  7b: Loss = 0000.9088\tOut = 19.88 (-4.16, -4.78)\n",
      "Step  8a: Loss = 0000.9019\tOut = 19.92 (-4.16, -4.79)\n",
      "Step  8b: Loss = 0000.8980\tOut = 19.95 (-4.16, -4.79)\n",
      "Step  9a: Loss = 0000.8972\tOut = 19.96 (-4.16, -4.80)\n",
      "Step  9b: Loss = 0000.8967\tOut = 19.98 (-4.17, -4.80)\n",
      "Step 10a: Loss = 0000.8966\tOut = 19.98 (-4.17, -4.80)\n",
      "Step 10b: Loss = 0000.8965\tOut = 19.98 (-4.17, -4.80)\n",
      "Step 11a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 11b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 12a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 12b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 13a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 13b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 14a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 14b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 15a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 15b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 16a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 16b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 17a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 17b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 18a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 18b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 19a: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n",
      "Step 19b: Loss = 0000.8965\tOut = 19.99 (-4.17, -4.80)\n"
     ]
    }
   ],
   "source": [
    "# Randomly initialize x and y to be a gaussian with std 10\n",
    "x = torch.tensor(10*np.random.randn(1), dtype=torch.float32, requires_grad=True)\n",
    "y = torch.tensor(10*np.random.randn(1), dtype=torch.float32, requires_grad=True)\n",
    "\n",
    "# Set the target (α), the lagrangian multiplier (λ) and the learning rate\n",
    "α = 20\n",
    "λ = 0.1\n",
    "lr = 1e-2\n",
    "N = 20 # Number of steps\n",
    "\n",
    "# Create two optimizers, one for x and one for y\n",
    "optimx = torch.optim.SGD([x], lr=lr, momentum=0)\n",
    "optimy = torch.optim.SGD([y], lr=lr, momentum=0)\n",
    "for i in range(N):\n",
    "    # Minimize wrt x\n",
    "    optimx.zero_grad()\n",
    "    optimy.zero_grad()\n",
    "    z = x*y\n",
    "    l = (z - α)**2 + λ * (torch.abs(x) + torch.abs(y))\n",
    "    print(\"Step {:2}a: Loss = {loss:09.4f}\\tOut = {out:.2f} ({x:.2f}, {y:.2f})\".format(\n",
    "        i, loss=l.item(), out=z.item(), x=x.item(), y=y.item()))\n",
    "    l.backward()\n",
    "    optimx.step()\n",
    "    \n",
    "    # Minimize wrt y\n",
    "    optimx.zero_grad()\n",
    "    optimy.zero_grad()\n",
    "    z = x*y\n",
    "    l = (z - α)**2 + λ * (torch.abs(x) + torch.abs(y))\n",
    "    print(\"Step {:2}b: Loss = {loss:09.4f}\\tOut = {out:.2f} ({x:.2f}, {y:.2f})\".format(\n",
    "        i, loss=l.item(), out=z.item(), x=x.item(), y=y.item()))\n",
    "    l.backward()\n",
    "    optimy.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This seems to work nicely. Notice as we step from $n$a to $n$b, only one of the two parameters changes.\n",
    "\n",
    "Now onwards to the filter factorization!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define filters as convolution of 2 3x3\n",
    "Let us try match the lh, hl and hh wavelets. To make our filters admissable wavelets, we also need to impose the restriction that $\\sum_{i,j} w_{i,j} = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:24.706552Z",
     "start_time": "2018-12-03T18:05:24.571790Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step  0a: Loss = 0104.7647\tMSE: 103.354\t Reg: 000.168\tAdmiss: 001.243)\n",
      "Step  0b: Loss = 0043.8679\tMSE: 043.400\t Reg: 000.180\tAdmiss: 000.288)\n",
      "Step  1a: Loss = 0022.3645\tMSE: 021.798\t Reg: 000.226\tAdmiss: 000.341)\n",
      "Step  1b: Loss = 0009.5339\tMSE: 008.788\t Reg: 000.252\tAdmiss: 000.494)\n",
      "Step  2a: Loss = 0006.9480\tMSE: 006.337\t Reg: 000.260\tAdmiss: 000.351)\n",
      "Step  2b: Loss = 0003.7069\tMSE: 003.242\t Reg: 000.263\tAdmiss: 000.201)\n",
      "Step  3a: Loss = 0002.5059\tMSE: 002.113\t Reg: 000.263\tAdmiss: 000.129)\n",
      "Step  3b: Loss = 0001.6599\tMSE: 001.254\t Reg: 000.265\tAdmiss: 000.141)\n",
      "Step  4a: Loss = 0001.2352\tMSE: 000.890\t Reg: 000.266\tAdmiss: 000.079)\n",
      "Step  4b: Loss = 0000.9242\tMSE: 000.644\t Reg: 000.267\tAdmiss: 000.014)\n",
      "Step  5a: Loss = 0000.7898\tMSE: 000.515\t Reg: 000.265\tAdmiss: 000.009)\n",
      "Step  5b: Loss = 0000.7030\tMSE: 000.419\t Reg: 000.265\tAdmiss: 000.019)\n",
      "Step  6a: Loss = 0000.6378\tMSE: 000.362\t Reg: 000.265\tAdmiss: 000.010)\n",
      "Step  6b: Loss = 0000.5727\tMSE: 000.305\t Reg: 000.265\tAdmiss: 000.003)\n",
      "Step  7a: Loss = 0000.5402\tMSE: 000.274\t Reg: 000.264\tAdmiss: 000.002)\n",
      "Step  7b: Loss = 0000.5080\tMSE: 000.243\t Reg: 000.264\tAdmiss: 000.001)\n",
      "Step  8a: Loss = 0000.4896\tMSE: 000.225\t Reg: 000.264\tAdmiss: 000.000)\n",
      "Step  8b: Loss = 0000.4690\tMSE: 000.204\t Reg: 000.264\tAdmiss: 000.001)\n",
      "Step  9a: Loss = 0000.4556\tMSE: 000.192\t Reg: 000.264\tAdmiss: 000.000)\n",
      "Step  9b: Loss = 0000.4416\tMSE: 000.178\t Reg: 000.264\tAdmiss: 000.000)\n",
      "Step 10a: Loss = 0000.4330\tMSE: 000.169\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 10b: Loss = 0000.4227\tMSE: 000.159\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 11a: Loss = 0000.4164\tMSE: 000.153\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 11b: Loss = 0000.4086\tMSE: 000.145\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 12a: Loss = 0000.4035\tMSE: 000.140\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 12b: Loss = 0000.3980\tMSE: 000.135\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 13a: Loss = 0000.3939\tMSE: 000.131\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 13b: Loss = 0000.3890\tMSE: 000.126\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 14a: Loss = 0000.3857\tMSE: 000.123\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 14b: Loss = 0000.3818\tMSE: 000.119\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 15a: Loss = 0000.3789\tMSE: 000.116\t Reg: 000.263\tAdmiss: 000.000)\n",
      "Step 15b: Loss = 0000.3762\tMSE: 000.113\t Reg: 000.263\tAdmiss: 000.001)\n",
      "Step 16a: Loss = 0000.3738\tMSE: 000.111\t Reg: 000.262\tAdmiss: 000.001)\n",
      "Step 16b: Loss = 0000.3707\tMSE: 000.108\t Reg: 000.262\tAdmiss: 000.000)\n",
      "Step 17a: Loss = 0000.3686\tMSE: 000.106\t Reg: 000.262\tAdmiss: 000.000)\n",
      "Step 17b: Loss = 0000.3667\tMSE: 000.104\t Reg: 000.262\tAdmiss: 000.000)\n",
      "Step 18a: Loss = 0000.3649\tMSE: 000.102\t Reg: 000.262\tAdmiss: 000.000)\n",
      "Step 18b: Loss = 0000.3632\tMSE: 000.100\t Reg: 000.262\tAdmiss: 000.001)\n",
      "Step 19a: Loss = 0000.3617\tMSE: 000.099\t Reg: 000.262\tAdmiss: 000.001)\n",
      "Step 19b: Loss = 0000.3596\tMSE: 000.097\t Reg: 000.262\tAdmiss: 000.000)\n",
      "--------------------------------------------------\n",
      "Best loss was 0.3595961928367615\n"
     ]
    }
   ],
   "source": [
    "# Define our \n",
    "w1 = torch.randn(1,1,3,3, requires_grad=True)\n",
    "w2 = torch.randn(1,1,3,3, requires_grad=True)\n",
    "\n",
    "# Define the lagrangian for mse, minimum energy coefficients and admissability\n",
    "λ = 100\n",
    "λ1 = .1\n",
    "λ2 = 1\n",
    "lr = 5e-2\n",
    "N = 20\n",
    "\n",
    "# Define our target - we'll start with lh\n",
    "y = torch.tensor(xb[1], dtype=torch.float32).reshape(1,1,16,16)\n",
    "# Make it zero mean and unit std\n",
    "y = (y-y.mean())/y.std()\n",
    "\n",
    "# Define our two optimizers\n",
    "optim1 = torch.optim.SGD([w1], lr=lr, momentum=0)\n",
    "optim2 = torch.optim.SGD([w2], lr=lr, momentum=0)\n",
    "\n",
    "x = torch.zeros(1,1,16,16)\n",
    "x[0,0,8,8] = 1\n",
    "lbest = np.inf\n",
    "w1_best = w1.data.numpy()\n",
    "w2_best = w2.data.numpy()\n",
    "\n",
    "for i in range(N):\n",
    "    # Minimize wrt w1\n",
    "    optim1.zero_grad()\n",
    "    optim2.zero_grad()\n",
    "    \n",
    "    y1 = F.conv2d(x, w1, padding=1)\n",
    "    y2 = F.conv2d(y1, w2, padding=1)\n",
    "    lmse = λ * torch.mean((y - y2)**2)\n",
    "    lreg = λ1 * (torch.mean(w1**2) + torch.mean(w2**2))\n",
    "    ladmiss = λ2 * torch.abs(torch.sum(y2))\n",
    "    l = lmse + lreg + ladmiss\n",
    "        \n",
    "    print(\"Step {:2}a: Loss = {loss:09.4f}\\tMSE: {mse:07.3f}\\t \" \n",
    "          \"Reg: {reg:07.3f}\\tAdmiss: {adm:07.3f})\".format(\n",
    "              i, loss=l.item(), mse=lmse.item(), reg=lreg.item(), \n",
    "              adm=ladmiss.item()))\n",
    "    l.backward()\n",
    "    optim1.step()\n",
    "    \n",
    "    if l.item() < lbest:\n",
    "        w1_best = w1.data.numpy()\n",
    "        w2_best = w2.data.numpy()\n",
    "        lbest = l.item()\n",
    "    \n",
    "    # Minimize wrt w2\n",
    "    optim1.zero_grad()\n",
    "    optim2.zero_grad()\n",
    "    \n",
    "    y1 = F.conv2d(x, w1, padding=1)\n",
    "    y2 = F.conv2d(y1, w2, padding=1)\n",
    "    lmse = λ * torch.mean((y - y2)**2)\n",
    "    lreg = λ1 * (torch.mean(w1**2) + torch.mean(w2**2))\n",
    "    ladmiss = λ2 * torch.abs(torch.sum(y2))\n",
    "    l = lmse + lreg + ladmiss\n",
    "    \n",
    "    print(\"Step {:2}b: Loss = {loss:09.4f}\\tMSE: {mse:07.3f}\\t \"\n",
    "          \"Reg: {reg:07.3f}\\tAdmiss: {adm:07.3f})\".format(\n",
    "              i, loss=l.item(), mse=lmse.item(), reg=lreg.item(), \n",
    "              adm=ladmiss.item()))\n",
    "    l.backward()\n",
    "    optim2.step()\n",
    "    \n",
    "    if l.item() < lbest:\n",
    "        w1_best = w1.data.numpy()\n",
    "        w2_best = w2.data.numpy()\n",
    "        lbest = l.item()\n",
    "    \n",
    "print('-' * 50)\n",
    "print('Best loss was {}'.format(lbest))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:24.814317Z",
     "start_time": "2018-12-03T18:05:24.708544Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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\" width=\"899.9999804930258\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1 = F.conv2d(x, torch.tensor(w1_best, dtype=torch.float32), padding=1)\n",
    "y2 = F.conv2d(y1, torch.tensor(w2_best, dtype=torch.float32), padding=1)\n",
    "y_hat = y2.detach().cpu().numpy()[0,0]\n",
    "y_target = y.detach().cpu().numpy()[0,0]\n",
    "\n",
    "fig, ax = plt.subplots(1,3, figsize=(9,4), \n",
    "                       subplot_kw={'xticks':[], 'yticks':[]})\n",
    "ax[0].imshow(y_target, vmin=-5, vmax=5)\n",
    "ax[0].set_title('Target filter (7x7)')\n",
    "ax[1].imshow(y_hat, vmin=-5, vmax=5)\n",
    "ax[1].set_title('Learned factorization\\nwith 2 3x3 kernels')\n",
    "ax[2].imshow(y_target-y_hat, vmin=-.5, vmax=0.5)\n",
    "im = ax[2].set_title('Error\\n(scaled up by factor of 10)')\n",
    "fig.suptitle('MSE of final solution: {:.2e}'.format(\n",
    "    np.mean((y_target - y_hat)**2)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Run with different initial conditions\n",
    "This is good, but we want to run it with different random starts and find the best over these"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:24.874468Z",
     "start_time": "2018-12-03T18:05:24.815521Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_loss(x, y, net, λ, λ1, λ2):\n",
    "    y_out = net(x)\n",
    "    \n",
    "    lmse = λ*torch.mean((y - y_out)**2)\n",
    "    lreg = λ1 * net.reg_loss()\n",
    "    ladmiss = λ2 * torch.sum(y_out)**2\n",
    "    l = lmse + lreg + ladmiss\n",
    "    return l\n",
    "\n",
    "\n",
    "class MyNet(torch.nn.Module):\n",
    "    def __init__(self, k=3, n=2):\n",
    "        super().__init__()\n",
    "        self.w = torch.nn.ParameterList([\n",
    "            torch.nn.Parameter(torch.randn(1,1,k,k)) for _ in range(n)])\n",
    "        self.n = n\n",
    "        self.k = k\n",
    "        \n",
    "    def reg_loss(self):\n",
    "        loss = torch.tensor(0., dtype=torch.float)\n",
    "        for i in range(self.n):\n",
    "            loss += torch.mean(self.w[i]**2)\n",
    "        return loss\n",
    "    \n",
    "    def accept_weights(self, ws):\n",
    "        self.w = torch.nn.ParameterList([\n",
    "               torch.nn.Parameter(\n",
    "                   torch.tensor(w, dtype=torch.float32), requires_grad=False) \n",
    "            for w in ws\n",
    "        ])\n",
    "        self.n = len(ws)\n",
    "        self.k = ws[0].shape[-1]\n",
    "    \n",
    "    def forward(self, X):\n",
    "        for i in range(self.n):            \n",
    "            X = F.conv2d(X, self.w[i], padding=(self.k//2))\n",
    "        return X\n",
    "    \n",
    "        \n",
    "def find_ws(x, target, k=3, n=2, runs=50, iters=50, λ=5000, λ1=0.1, λ2=1, lr=5e-3):\n",
    "    \"\"\" Matches a target filter by convolving n smaller filters\n",
    "    \n",
    "    Args:\n",
    "        x: the impulse input\n",
    "        target: target filter\n",
    "        k: kernel size of smaller filter\n",
    "        n: number of successive smaller filters to use\n",
    "        runs: number of random starts\n",
    "        iters: number of steps per random start\n",
    "        λ: MSE lagrange multiplier\n",
    "        λ1: Regularization lagrange multiplier\n",
    "        λ2: Admissibility lagrange multiplier\n",
    "    \"\"\"\n",
    "    if np.abs(target.sum()) > 1e-6 and λ2 > 0:\n",
    "        print('Warning: the admissibility gain is non zero but the target is '\n",
    "              'itself not admissible')\n",
    "        \n",
    "    bestw = [np.zeros((1,1,k,k), dtype='float32') for _ in range(n)]    \n",
    "    \n",
    "    y = torch.tensor(target, dtype=torch.float32, device=dev)  \n",
    "    if len(y.shape) == 2:\n",
    "        y = torch.unsqueeze(torch.unsqueeze(y, dim=0), dim=0)\n",
    "    # Make the target 0 mean and unit std\n",
    "    y = (y-y.mean())/y.std()\n",
    "    \n",
    "    x = torch.tensor(x, dtype=torch.float32, device=dev)\n",
    "    if len(x.shape) == 2:\n",
    "        x = torch.unsqueeze(torch.unsqueeze(x, dim=0), dim=0)    \n",
    "    lbest = np.inf\n",
    "    \n",
    "    for N in range(runs):\n",
    "        try:\n",
    "            net = MyNet(k, n)\n",
    "            optim = [torch.optim.SGD([net.w[i]], lr=lr, momentum=0) for i in range(n)]\n",
    "\n",
    "            lbest_run = np.inf\n",
    "            bestw_run = [np.zeros((1,1,k,k), dtype='float32') for _ in range(n)]\n",
    "\n",
    "            for i in range(iters):\n",
    "                for j in range(n):\n",
    "                    [o.zero_grad() for o in optim]\n",
    "\n",
    "                    l = get_loss(x, y, net, λ, λ1, λ2)            \n",
    "                    l.backward(retain_graph=True)\n",
    "                    optim[j].step()                \n",
    "                    \n",
    "                    #if torch.isnan(net.w[j]).sum() > 0:\n",
    "                    #    raise RuntimeError                        \n",
    "                    if l.item() < lbest_run:                        \n",
    "                        for p in range(n):\n",
    "                            bestw_run[p][:] = net.w[p].detach().data.cpu().numpy()[:]\n",
    "                        lbest_run = l.item()\n",
    "                        \n",
    "            if lbest_run < lbest: \n",
    "                for p in range(n):\n",
    "                    bestw[p][:] = bestw_run[p][:]\n",
    "                lbest = lbest_run\n",
    "        except RuntimeError:\n",
    "            # Nan error raised\n",
    "            print('Nan was raised in iter {}. Continuing...'.format(N))\n",
    "            continue\n",
    "            \n",
    "    return lbest, bestw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:30.194392Z",
     "start_time": "2018-12-03T18:05:24.875539Z"
    }
   },
   "outputs": [],
   "source": [
    "impulse16 = torch.zeros((1,1,16,16))\n",
    "impulse16[0,0,8,8] = 1\n",
    "lbest, bestw = find_ws(x=impulse16, \n",
    "                       target=xb[1], \n",
    "                       k=3, \n",
    "                       n=2, \n",
    "                       iters=100, \n",
    "                       λ=100, λ1=0.1, λ2=1, lr=5e-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:30.244550Z",
     "start_time": "2018-12-03T18:05:30.195561Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
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     "output_type": "display_data"
    },
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\" width=\"899.9999804930258\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the output by passing impulse to network\n",
    "net = MyNet()\n",
    "net.accept_weights(bestw)\n",
    "y_hat = net(impulse16).detach().cpu().numpy()[0,0]\n",
    "y_target = torch.tensor(xb[1], dtype=torch.float32, device=dev)  \n",
    "y_target = ((y_target-y_target.mean())/y_target.std()).cpu().numpy()\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(1,3, figsize=(9,4),\n",
    "                       subplot_kw={'xticks':[], 'yticks':[]})\n",
    "ax[0].imshow(y_target, vmin=-5, vmax=5)\n",
    "ax[1].imshow(y_hat, vmin=-5, vmax=5)\n",
    "ax[2].imshow(y_target-y_hat, vmin=-.5, vmax=0.5)\n",
    "fig.suptitle('MSE of final solution: {:.2e}'.format(\n",
    "    np.mean((y_target - y_hat)**2)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare to parameterization as 1 5x5\n",
    "We know this should be pretty much perfect, so how does the above compare to a 5x5?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:31.966610Z",
     "start_time": "2018-12-03T18:05:30.245880Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\" width=\"899.9999804930258\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lbest, bestw_1_5x5_lh = find_ws(impulse16, xb[1], k=5, n=1, iters=100)\n",
    "\n",
    "# Get the output by passing impulse to network\n",
    "x = torch.zeros(1,1,16,16)\n",
    "x[0,0,8,8] = 1\n",
    "for w in bestw_1_5x5_lh:\n",
    "    x = F.conv2d(x, torch.tensor(w), padding=w.shape[-1]//2)\n",
    "y_hat = x.detach().cpu().numpy()[0,0]\n",
    "\n",
    "fig, ax = plt.subplots(1,3, figsize=(9,4),\n",
    "                       subplot_kw={'xticks':[], 'yticks':[]})\n",
    "ax[0].imshow(y_target, vmin=-5, vmax=5)\n",
    "ax[1].imshow(y_hat, vmin=-5, vmax=5)\n",
    "ax[2].imshow(y_target-y_hat, vmin=-.5, vmax=0.5)\n",
    "\n",
    "fig.suptitle('MSE of final solution: {:.2e}'.format(\n",
    "    np.mean((y_target - y_hat)**2)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare to 3 3x3 kernels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:43.061409Z",
     "start_time": "2018-12-03T18:05:31.968662Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\" width=\"899.9999804930258\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lbest, bestw_3_3x3_lh = find_ws(impulse16, xb[1], k=3, n=3, iters=100, λ=500)\n",
    "\n",
    "# Get the output by passing impulse to network\n",
    "net = MyNet()\n",
    "net.accept_weights(bestw_3_3x3_lh)\n",
    "y_hat = net(impulse16).detach().cpu().numpy()[0,0]\n",
    "y_target = torch.tensor(xb[1], dtype=torch.float32, device=dev)  \n",
    "y_target = ((y_target-y_target.mean())/y_target.std()).cpu().numpy()\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(1,3, figsize=(9,4),\n",
    "                       subplot_kw={'xticks':[], 'yticks':[]})\n",
    "ax[0].imshow(y_target, vmin=-5, vmax=5)\n",
    "ax[1].imshow(y_hat, vmin=-5, vmax=5)\n",
    "ax[2].imshow(y_target-y_hat, vmin=-.5, vmax=0.5)\n",
    "fig.suptitle('MSE of final solution: {:.2e}'.format(\n",
    "    np.mean((y_target - y_hat)**2)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Try a different filter\n",
    "For finality, let us also try the ll filter. Again we'll go back to the design with 2 3x3 filters instead of 1 5x5 or 3 3x3's"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-03T18:05:48.118412Z",
     "start_time": "2018-12-03T18:05:43.062595Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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   ],
   "source": [
    "lbest, bestw_2_3x3_ll = find_ws(impulse16, xb[0], k=3, n=2, iters=100, λ=1000, λ2=0)\n",
    "\n",
    "# Get the output by passing impulse to network\n",
    "net = MyNet()\n",
    "net.accept_weights(bestw_2_3x3_ll)\n",
    "y_hat = net(impulse16).detach().cpu().numpy()[0,0]\n",
    "y_target = torch.tensor(xb[0], dtype=torch.float32, device=dev)  \n",
    "y_target = ((y_target-y_target.mean())/y_target.std()).cpu().numpy()\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots(1,3, figsize=(9,4),\n",
    "                       subplot_kw={'xticks':[], 'yticks':[]})\n",
    "ax[0].imshow(y_target, vmin=-5, vmax=5)\n",
    "ax[1].imshow(y_hat, vmin=-5, vmax=5)\n",
    "ax[2].imshow(y_target-y_hat, vmin=-.5, vmax=0.5)\n",
    "fig.suptitle('MSE of final solution: {:.2e}'.format(\n",
    "    np.mean((y_target - y_hat)**2)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "We have shown how it is possible to factorize some larger filters as convolutions of smaller filters. Note that we haven't discussed a lot of the hyperparameter search done for the different weight factors between MSE loss, l2 loss and admissibility as well as the learning rate. These are not necessarily easy to find, and some optimization may need to be done if repeating on your own filters."
   ]
  }
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