lab2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "from math import log\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.matrix('0 0 0 0; 0.5 0 0 0; 0 0.5 0 0; 0 0 1 0')\n",
    "a = np.matrix('0; 0.5; 0.5; 1')\n",
    "v = 1/6\n",
    "b = np.matrix([[v], [2*v], [2*v], [v]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(u,t):\n",
    "    return u+t**2+1\n",
    "u0 = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simple_solver(f, u0, t):\n",
    "    u = np.array([u0]*len(t))\n",
    "    for i,ui in enumerate(u[:-1]):\n",
    "        tau = t[i+1] - t[i]\n",
    "        w1 = f(ui,t[i])\n",
    "        w2 = f(ui + tau*w1/2, t[i] + tau/2)\n",
    "        w3 = f(ui + tau*w2/2, t[i] + tau/2)\n",
    "        w4 = f(ui + tau*w3, t[i] + tau)\n",
    "        u[i+1] = ui + tau * (w1 + 2*w2 +2*w3 + w4)/6\n",
    "    return u,t\n",
    "def effective_p(U2,U1,U0,r):\n",
    "    return np.log((U2-U1)/(U1-U0))/np.log(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "answers = [ simple_solver(f, u0, np.linspace(0, 1, 2**i+1)) for i in range(8)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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=\"720\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x27408970160>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "effective_p_in_1 = [effective_p(answers[i][0][-1], answers[i-1][0][-1], answers[i-2][0][-1], 1/2) for i in range(2, len(answers))]\n",
    "plt.plot(range(2,len(answers)), effective_p_in_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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=\"720\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2740b786e80>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import sin, cos, pi\n",
    "def f1(u, t):\n",
    "    om = [sin(t), cos(t), sin(t+pi/4)]\n",
    "    Omega = np.matrix([[0, -om[2], om[1]], [om[2], 0, -om[0]],[-om[1], om[0], 0]])\n",
    "    return Omega*u\n",
    "answers1 = [ simple_solver(f1, np.matrix('1; -0.5; 0.6'), np.linspace(0, 1, 2**i + 1)) for i in range(8) ]\n",
    "plt.figure()\n",
    "plt.plot(answers1[-1][1], [t.item(0,0)for t in answers1[-1][0]])\n",
    "plt.plot(answers1[-1][1], [t.item(1,0)for t in answers1[-1][0]])\n",
    "plt.plot(answers1[-1][1], [t.item(2,0)for t in answers1[-1][0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для реализации на компьютере в системе MATLAB удобнее записать в векторной форме"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\t\\begin{split}\n",
    "\t\t\\mathbf{u}_{n+1} = \\mathbf{u}_n + \\tau_n \\boldsymbol{\\omega} \\mathbf{b}^T,\n",
    "\t\\qquad\n",
    "\t\t\\tau_n = t_{n+1} - t_n; \\\\\n",
    "\t\t\\boldsymbol{\\omega}_k = \\mathbf{f} \\left( \\mathbf{u}_n + \\tau_n \\boldsymbol{\\omega} \\boldsymbol{\\alpha}^T_k, t_n + \\tau_n a_k \\right),\n",
    "\t\\qquad\n",
    "\t\t1 \\le k \\le s,\n",
    "\t\\end{split}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "где $\\boldsymbol{\\omega}_k$ - $k$-тая строка матрицы промежуточных результатов $\\boldsymbol{\\omega}$, первоначально полагаемой нулевой, $\\mathbf{b}$ - вектор-строка коэффициентов $b$ и $\\boldsymbol{\\alpha}_k$ - $k$-тая строка матрицы Бутчера. Верхний индекс $T$ означает транспонирование."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "butcher = [ np.array([0, 0, 0, 0, 0, 0, 0]), np.array([4/7, 0, 0, 0, 0, 0, 0]), np.array([115/112, -5/16, 0, 0, 0, 0, 0]), np.array([589/630, 5/18, -16/45, 0, 0, 0, 0]),\n",
    "np.array([229/1200-29/6000*5**0.5, 119/240-187/1200*5**0.5, -14/75+34/375*5**0.5, -3/100*5**0.5, 0, 0, 0]),\n",
    "np.array([71/2400-587/12000*5**0.5, 187/480-391/2400*5**0.5, -38/75+26/375*5**0.5, 27/80-3/400*5**0.5, (1+5**0.5)/4, 0, 0]),\n",
    "np.array([-49/480+43/160*5**0.5, -425/96+51/32*5**0.5, 52/15-4/5*5**0.5, -27/16+3/16*5**0.5, 5/4-3/4*5**0.5, 5/2-0.5*5**0.5, 0]) ]\n",
    "a = np.array([0, 4/7, 5/7, 6/7, (5-5**0.5)/10, (5+5**0.5)/10, 1]);\n",
    "b = np.array([1/12, 0, 0, 0, 5/12, 5/12, 1/12]);\n",
    "u0 = np.array([1, -0.5, 0.6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mult(vect,list_):\n",
    "    res = np.matrix(np.zeros(vect[0].shape))\n",
    "    for v,l in zip(vect,list_):\n",
    "        res+= v*l\n",
    "    return res\n",
    "def universal_runge_kutta(f ,u0, t, butcher, a, b):\n",
    "    u = np.array([u0] * len(t))\n",
    "    w = [np.matrix(np.zeros(u0.shape))] * len(butcher)\n",
    "    for i,ui in enumerate(u[:-1]):\n",
    "        tau = t[i+1] - t[i]\n",
    "        for j,wj in enumerate(w):\n",
    "            w[j] = f(ui + tau * mult(w, butcher[j]),t[i] + tau * a[j])\n",
    "        u[i+1] = ui + tau * mult(w,b)\n",
    "    return u, t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2740b7c9940>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "answers2 = [ universal_runge_kutta(f, np.matrix([[0.5]]),np.linspace(0, 1, 2**i + 1), butcher, a, b) for i in range(8)]\n",
    "effective_p_in_1_2 = [effective_p(answers2[i][0][-1], answers2[i-1][0][-1], answers2[i-2][0][-1], 1/2) for i in range(2, len(answers2))]\n",
    "plt.plot(range(2,len(answers2)), [t[0][0] for t in effective_p_in_1_2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        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\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\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=\"720\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2740b2f9550>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "answers3 = [ universal_runge_kutta(f1, np.matrix('1; -0.5; 0.6'), np.linspace(0, 1, 2**i + 1), butcher, a, b) for i in range(15) ]\n",
    "plt.figure()\n",
    "plt.plot(answers1[-1][1], [t.item(0,0)for t in answers1[-1][0]])\n",
    "plt.plot(answers1[-1][1], [t.item(1,0)for t in answers1[-1][0]])\n",
    "plt.plot(answers1[-1][1], [t.item(2,0)for t in answers1[-1][0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
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