week_5_intep_approx.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I. Linear least squares approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a function $y = f(x)$ which is defined by a set of values $y_0, y_1, \\cdots, y_n$ at points $x_0, x_1, \\cdots, x_n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "x = np.array([-1, -0.7, -0.43, -0.14, -0.14, 0.43, 0.71, 1, 1.29, 1.57, 1.86, 2.14, 2.43, 2.71, 3])\n",
    "y = np.array([-2.25, -0.77, 0.21, 0.44, 0.64, 0.03, -0.22, -0.84, -1.2, -1.03, -0.37, 0.61, 2.67, 5.04, 8.90])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.I. Find a best fit polynomial\n",
    "\n",
    "$$\n",
    "P_m(x) = a_0 + a_1 x + \\cdots + a_m x^m\n",
    "$$\n",
    "\n",
    "using the linear least squares approach. To this end\n",
    "\n",
    "1. implement a function which constructs the design matrix using $1, x, \\cdots, x^m$ as the basis functions.\n",
    "\n",
    "2. construct explicitly the normal system of equations of the linear least squares problem at fixed $m$.\n",
    "\n",
    "3. Solve the normal equations to find the coefficients of $P_m(x)$ for $m = 0, 1, 2, \\dots$. For the linear algebra problem, you can either use library functions (`numpy.linalg.solve`) or your LU factorization code from week 1.\n",
    "\n",
    "(20% of the total grade)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Design matrix is\n",
    "$$\n",
    "A_{jk} = \\phi_{k}(x_j) = x_j^k\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_design_a(x, m):\n",
    "    a = np.zeros((x.shape[0], m+1))\n",
    "    a[:,0] = 1\n",
    "    \n",
    "    vec = x.copy()\n",
    "    a[:, 1] = vec\n",
    "    \n",
    "    for j in range(2, m+1):\n",
    "        vec = vec * x\n",
    "        a[:, j] = vec\n",
    "    \n",
    "    return a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To minimize system we have to solution next system:\n",
    "$$\n",
    "A^{T}A \\,\\mathbf{a} = A^{T} \\mathbf{y}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_system(A, y):\n",
    "    return A.T @ A , A.T @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_best_pol(x, y, m):\n",
    "    A = get_design_a(x, m)\n",
    "    sys = get_system(A, y)\n",
    "    a = np.linalg.solve(sys[0],sys[1])\n",
    "    return a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.II \n",
    "\n",
    "To find the optimal value of m, use the following criterion: take $m=0, 1, 2, \\dots$, for each value of $m$ compute \n",
    "\n",
    "$$\n",
    "\\sigma_m^2 = \\frac{1}{n - m} \\sum_{k=0}^n \\left( P_m(x_k) - y_k \\right)^2\n",
    "$$\n",
    "\n",
    "And take the value of $m$, at which $\\sigma_m$ stabilizes or starts increasing.\n",
    "\n",
    "(20% of the total grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sigma(x, y, N=5):\n",
    "    sigma = np.zeros(N+1)\n",
    "    n = y.shape[0]\n",
    "    sigma[0] = (np.mean(y) - y) @ (np.mean(y) - y) / n\n",
    "    for m in range(1, N+1):\n",
    "        A = get_design_a(x, m)\n",
    "        a = find_best_pol(x, y, m)\n",
    "        sigma[m] = 1/(n-m) * (A @ a - y) @ (A @ a - y)\n",
    "    return sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
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       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
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       "\n",
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       "\n",
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       "\n",
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       "             * 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",
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       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib notebook\n",
    "plt.figure()\n",
    "plt.title(r'Error of approximation')\n",
    "plt.xlabel('m')\n",
    "plt.ylabel(r'$\\sigma$')\n",
    "plt.grid()\n",
    "plt.plot(get_sigma(x, y, N=x.shape[0]-1), 'o')\n",
    "#plt.yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot your polynomials $P_m(x)$ on one plot, together with the datapoints. Visually compare best-fit polynomials of different degrees. Is the visual comparison consistent with the optimal value of $m$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "plt.figure()\n",
    "plt.title(r'Data and aprroximation')\n",
    "x_view = np.linspace(x.min(), x.max(), 500)\n",
    "N = 4\n",
    "plt.plot(x, y, '.', label='Original data')\n",
    "for m in range(1, N+1):\n",
    "    A = get_design_a(x, m)\n",
    "    a = find_best_pol(x, y, m)\n",
    "    y_view = get_design_a(x_view, m) @ a\n",
    "    plt.plot(x_view, y_view, label=f'm={m}')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I.III. Linear least-squares using the QR factorization.\n",
    "\n",
    "For the optimal value of $m$ from the previous part, solve the LLS problem using the QR factorization, withou ever forming the normal equations explicitly. For linear algebra, you can use standard library functions (look up `numpy.linalg.solve`, `numpy.linalg.qr` etc) or your code from previous weeks.\n",
    "\n",
    "Compare the results with the results of solving the normal system of equations.\n",
    "\n",
    "(20% of the grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.linalg import solve_triangular\n",
    "def find_byqr(x, y, m):\n",
    "    A = get_design_a(x, m)\n",
    "    q,r = np.linalg.qr(A)\n",
    "    f = (q.T @ y)\n",
    "    a = solve_triangular(r, f)\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" 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      "text/plain": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "plt.figure()\n",
    "plt.title(r'Comparing QR and normal system')\n",
    "x_view = np.linspace(x.min(), x.max(), 500)\n",
    "m = 3\n",
    "plt.plot(x, y, '.', label='Original data')\n",
    "\n",
    "A = get_design_a(x, m)\n",
    "\n",
    "a = find_best_pol(x, y, m)\n",
    "y_view = get_design_a(x_view, m) @ a\n",
    "plt.plot(x_view, y_view, label=f'By normal, m={m}')\n",
    "\n",
    "a = find_byqr(x, y, m)\n",
    "y_view = get_design_a(x_view, m) @ a\n",
    "plt.plot(x_view, y_view, label=f'By QR, m={m}')\n",
    "\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.85407245e-14  1.70974346e-14 -4.44089210e-14  1.33226763e-14]\n"
     ]
    }
   ],
   "source": [
    "print(find_best_pol(x, y, m)-find_byqr(x, y, m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# II. Lagrange interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.1 \n",
    "\n",
    "Consider the function, $f(x) = x^2 \\cos{x}$. On the interval $x\\in [\\pi/2, \\pi]$, interpolate the function using the Lagrange interpolating polynomial of degree $m$ with $m=1, 2, 3, 4, 5$. Use the uniform mesh. Plot the resulting interpolants together with $f(x)$.\n",
    "\n",
    "(20% of the total grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lagrange(x_new, roots, value):\n",
    "    n = roots.shape[0]\n",
    "    p = 0\n",
    "    for i in range(n):\n",
    "        li=1\n",
    "        ri = roots[i]\n",
    "        for root in roots:\n",
    "            li = li * (x_new - root) / (ri - root) if root != ri else li\n",
    "        p += value[i] * li\n",
    "    return p\n",
    "lg =  np.vectorize(lagrange, signature='(n),(m),(m)->(n)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xa29a058c>"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "plt.plot()\n",
    "plt.grid()\n",
    "plt.title('Uniform mesh')\n",
    "N = 3\n",
    "x_view = np.linspace(np.pi/4, np.pi*1.5, 700)\n",
    "y = x_view*x_view*np.cos(x_view)\n",
    "plt.plot(x_view , y, label=r'$f(x) = x^2\\, \\cos x$')\n",
    "\n",
    "for m in range(1, 6):\n",
    "    roots = np.linspace(np.pi/2, np.pi, m+1)\n",
    "    value = roots*roots*np.cos(roots)\n",
    "    #plt.plot(roots, value,'.')\n",
    "\n",
    "\n",
    "    y_view = lg(x_view, roots, value)\n",
    "\n",
    "    plt.plot(x_view , y_view, label=f'm = {m}')\n",
    "\n",
    "\n",
    "plt.xticks(np.linspace(np.pi/3,np.pi*7/6,6), \n",
    "          (r'$\\frac{\\pi}{6}$' , r'$\\frac{\\pi}{2}$',r'$\\frac{2\\pi}{3}$',r'$\\frac{5\\pi}{6}$',r'$\\pi$',r'$\\frac{7\\pi}{6}$'))\n",
    "plt.vlines(np.pi, -12, 1.5, colors='r', linestyles='--')\n",
    "plt.vlines(np.pi/2, -12, 1.5, colors='r', linestyles='--')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### II.2. \n",
    "\n",
    "Repeat the previous task using the Chebyshev nodes. Compare the quality of interpolation on a uniform mesh and Chebyshev nodes for $m=3$.\n",
    "\n",
    "(20% of the total grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_roots(a, b, n):\n",
    "    df = np.pi / n\n",
    "    phase = [np.pi / 2 / n]\n",
    "    for _ in range(n-1):\n",
    "        phase.append(phase[-1]+df)\n",
    "    phase = np.array(phase)\n",
    "    roots = (a+b)/2 + (b-a)/2*np.cos(phase)\n",
    "    return roots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"633\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xa3a29f6c>"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "plt.plot()\n",
    "plt.grid()\n",
    "plt.title('Chebyshev`s roots mesh')\n",
    "N = 3\n",
    "x_view = np.linspace(np.pi/4, np.pi*1.5, 700)\n",
    "y = x_view*x_view*np.cos(x_view)\n",
    "plt.plot(x_view , y, label=r'$f(x) = x^2\\, \\cos x$')\n",
    "\n",
    "for m in range(1, 6):\n",
    "    roots = get_roots(np.pi/2, np.pi, m+1)\n",
    "    value = roots*roots*np.cos(roots)\n",
    "    #plt.plot(roots, value,'.')\n",
    "\n",
    "\n",
    "    y_view = lg(x_view, roots, value)\n",
    "\n",
    "    plt.plot(x_view , y_view, label=f'm = {m}')\n",
    "\n",
    "plt.xticks(np.linspace(np.pi/3,np.pi*7/6,6), \n",
    "          (r'$\\frac{\\pi}{6}$' , r'$\\frac{\\pi}{2}$',r'$\\frac{2\\pi}{3}$',r'$\\frac{5\\pi}{6}$',r'$\\pi$',r'$\\frac{7\\pi}{6}$'))\n",
    "plt.vlines(np.pi, -12, 1.5, colors='r', linestyles='--')\n",
    "plt.vlines(np.pi/2, -12, 1.5, colors='r', linestyles='--')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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nmlpaTh58iSMRqMmr282m3Hr1i3eKUgS1hMwGo04efIk0tLScv1MxQyhNQZVyVRsMr0tXJoym2E6cwabv/kGpvR0rWejC+xPufRWz5ygmteiXuQsFpjT0pB0/XqJDlYyMaja72kVM4TWGFQlU7HJ9LZwaYonU0nH/pRLb/XUNKhmZQEREUBEBMyZmcX/+jrEoMqg6igGVclUbDK9LVyaYlCVjv0pl97qyaCqLwyqDKqOYlCVTMUm09vCpSkGVenYn3LprZ4MqvrCoMqg6igGVclUbDK9LVyaYlCVjv0pl97qyaCqrUuXLiE0NBS1a9dG/fr1sXz58gd6PgZVBlVHMahKpmKT6W3h0hSDqnTsT7n0Vk8GVW3FxcXhyJEjAIBr166hYsWKSHmAa0gzqDKoOopBVTIVm0xvC5emGFSlY3/Kpbd66iWozpkzByEhIXBzc0OPHj0QHByMmJiYQv/+W2+9hRkzZjzQHGSoX78+Ll26dN+/z6DKoOooBlXJVGuyxbtj0Gb2Djw7YT1az9qB1rN3otWsHdbRcmb2f9t++Tfaz9uNTt/sRbfv9+P9JRHo+9MhDPn1CMaHH8f0309h/vazWLb/ItYfvYLtp6/j8MWbuJhohDGjBL3TwKAqnd6Cldb0Vk89BNXjx4/D3d0dGzZsQFxcHIYMGYL33nvPoec4evQoypYtq+naEhERgbp16z7QczCoMqg6ikFVMtWabOqmKIR8vKHIR51xmxA67S90+Ho3PvzxIMLWnsCCHeew6Xgcjl9OQpJRH4sm0tOR1acPzrdpA9OdO1rPRhf0Fqy0prd6ahpUzWZYLlxA+pkzMGdl3ffTTJ48GU2aNAEApKamokyZMtizZ4/Dz/PUU09h3rx59z2PB5GYmIjatWtj9+7dD/Q8DKoMqo5iUJVMtSY7e/0Otp64gs8WrcWfkXHYcfo6dp7JHn+fScCu6AT8fSYBf0Vdw6bj8Vj7zxUsj7iEH/ddwMJd5/H19rOY/vspjA8/jiG/HEGvxQfw9vw9aD17J5757E/UHLux0GG2XtjvaD17J/r8cBAzNp/C2n+u4GTcbaSZ7n8B0ILegoDWWE+59FZPTYMqHjxYPf744xBCWIefnx+CgoJyPW7ZsmXw8vLC5cuXrd/r1asX6tevj6SkJACAwWDA888/f39/SD4K87rp6el4/vnnsXTp0nyfx2w2Y8qUKXj88cfh6emJypUrY9KkSdafp6enY8CAAQgODoaXlxeeffZZHDhwwPrzFStWoF69evD29kbZsmXx0ksv2RwLW5h5OgsGVccwqEqmYpMV5cJlsVhwJz0T5xNSsP/8DWw4GodFu85jyqYo9F92GG/M2YVGE7faDbBVR25A8+nb8P6SCMzYchpbIq/i6m1tFqXC0FsQ0BrrKZfe6pnXom6xWGDMyCyWcSctA3HXEnEnLQPGjExYLBaH5n/t2jU89thjmD59OuLj4/Hee++hdevWuR5nsVjQoEED9OvXD0B2KK1UqZJNMNu4cSO8vLyQnsdd8SZPngxfX1+7Y+fOnQ6/rsViQadOnRAWFmb37xwxYgQCAwOxePFinD17Fn///Te+/fZb688HDhyIChUqYMOGDdi7dy+6deuGwMBA3LhxA3FxcXB3d8fMmTMRExODY8eOYe7cubhz16dWhamPs2BQdQyDqmQqNpkKC1dqRhbOXE3Gn1FX8d3f5zFy1VG8NW83Ghg25xtg/zNpK3ouOoAZW05j26lrSE5TYOG1WGC6cgUblyyBKSND69noggr9qSd6q2dei7oxI7NYDmnKazh6TL7RaISrqyv27t0LAHjjjTfyPT51/fr18PLywqRJkxAYGIgTJ07Y/Pzo0aMQQuDChQu5fvfGjRuIjo62O1JTUx1+3b///hsuLi5o2LChdRw7dszm95OTk+Hl5WUTTO+WkpICDw8P/PTTT9Z3qNPT01GhQgVMmzYNhw4dyvfvcqQ+zoJB1TEMqpKp2GQqL1wWiwXXktOw+2wCFu06j6HL/0GrWTtQdWTe77y2mb0TYWtPYP3RK9q868qTqaRTuT+dkd7q6exBde/evXB1dbV+jN2yZUv07ds338c/+eST8PT0xPbt23P97MyZMxBC4OTJkw7NoTDsvW5B9u/fDyEEzp8/n+fP7w7Ydx9K0a5dO/Ts2RNZWVl46aWX4O/vjw4dOmDBggW4efOm9HmqgkHVMQyqkqnYZM64cKVmZOHghZtYvDsGQ349guen/pXnovHC59sQtvYE/oy6ipT0Yrj6AIOqdM7YnyrTWz01/eg/NR3GvQdg3HsAd4xp9/XR/9dff40aNWpYv+7SpQs6d+6c52M3bdoEHx8fuLm5ISoqKtfP9+3bByEEEhIScv3sfj/6L8zrFuTYsWMPFFSB7H/TXbt2Yfz48ahfvz6Cg4NzPd+DzlMVDKqOYVCVTMUm08vCdfV2GtYfvYKwtSfQZvZOPHrPu67VRv+Gjt/swZy/ohEVf9vhBaVQGFSl00t/qkJv9XT2y1P17t0bb7/9tvXr6dOno2HDhrked+jQIfj7+2Pp0qV45ZVX0KFDh1yP+e6771CpUqU8X+d+P/ovzOsWJC0tDT4+PnY/+vf09Mz10X/FihUxffr0XI/PyspCxYoVba4bK2OeqmBQdQyDqmQqNpneFq4cSakmbDoeh1Grj+HZKX/merf1+al/YeL6SOw/fwNZZkmhlUFVOr32p1b0Vk9nD6pNmjTB5MmTrV8fO3YM7u7uNh9tx8TEoHz58tbHHTx4EC4uLjh06JDNc3Xv3t3h66/aU9jXLQyDwYDAwEAsWbIEZ8+exd69e/Hdd99Zfz5o0CBUqFABv/32m83JVDdv3sS+ffswefJkRERE4OLFi1i+fDk8PT2xceNG6fNUAYOqYxhUJVOxyfS2cOXFYrEgJiEFS/fE4L1FB1B9jO1ls56asAUjVhzF9tPXkZn1ANfvY1CVriT0Z3HSWz2dOaiazWaUKlUKGzZssPl+06ZNMX/+fADZ74TWrFkTvXv3tnnM66+/jlatWlm/TktLQ0BAgPWkrAdV2NctLLPZjEmTJiEkJAQeHh6oUqUKPv30U+vP09LSMGDAAAQFBeW6PNXJkyfRqlUr66WratSoga+++qpI5qkCBlXHMKhKpmKT6W3hKoyU9ExsOh6HIb8cQf2w321Ca6OJWxC29gQOX7zp+OEBDKrSlcT+LEp6q6czB9X8/Pbbb6hdu7ZD12adM2cOWrRoIW0OWuEF/xlUHcWgKpmKTaa3hctRpiwzdkUnYMyaY3hywhab0PrfaX9hxuZTiElIKfiJAAbVIlDS+1M2vdVTj0EVAGbPno1Lly4V+vHffPMNTp06JXUOWmBQZVB1FIOqZCo2mdMuXBYLEBcH7NgBLF0KTJwIvP8+8OqrwLPPAvXqAZUqAaVLAwEBtuORR4BatYAmTYCWLYGuXYExY5A1bx7++WYZJn++CvXG2B7T2umbvQg/chnpmXbulJWeDnPXrrj4wgu8haokTtufitJbPTW/her580g/deqBbqFK/2JQZVB1FINqPubOnYtHH30UXl5eeOqpp/K9rMe9VGwyp1m4YmOBn38GBg0CXngBCAqyvnuZMzLcBM6XEThQQWBjNYElDQVmNRWY9ozA5OcFPgkVGPeCwMT/CsxsKvBNI4EfGgj8Vl3gcHmBq74CZpfs57J4eeFWzbrY3aw1PmveAx26TEGNj1bhiU82Y8L6SERfS85zmk5TTyfBesqlt3o6+y1UyRbryaDqKAbVPPzyyy/w8PDAt99+i5MnT2LQoEHw9fXFxYsXC/xdFZtM2YUrMRH46Sfg3XeBKlVsAmmKh8DuygJfNnHBh50D0GJQIKqO8YOrwQXCIB5ouI0XqDLEBS3fFRjQRmBuY4G/HhW47SWQ6eqGI4/UwHf/eQM9OoSh6xd/YvOJeJurBihbTyfFesqlt3oyqOoL68mg6igG1Tw8/fTT6NOnj833atWqhZEjRxb4uyo2mVILV0wMMGUK0KwZ4OpqDaZXfQV+qeeC3j2CUHdsWbuB1GuiFyrPrIwn5z+JFktboOOKjui+pjt6re2FPuv7oN9v/fDBug/QZVUXvPHzG3h56ct4cv6TeHj6w3Cx87wuYQK1+wl0b5cdXiODBdLc3LAz5AnMebUPVvz0B+6kmWC6dBJ7vjfAlBCjdTV1Qan+1AG91VPToGqxwJyZiVs3bpToYCUTgyqDqqMYVO+RkZEBNzc3rF692ub7AwcOxH//+98Cf1/FJtN84UpIAL74Amja1BpMzS4C+yoKjOocjHrjg/IMjo98/gjaLmuL0X+MxqIji7Dzwk7EJcc90IX8M82ZuJJ8Bbsu7sL3h7/H8C3D8dqy1xAyKyTPOVT4SKBbO4GlDQSu+QrEhVaAZVwAEBYAi6EMcGiJxEKVTJr3p87orZ56PZmqpGJQZVB1FIPqPa5cuQIhBHbv3m3z/cmTJ9vcBi9Heno6bt++bR2xsbEQQiAxMREmk0mJYTQaER4eDqPRWHyvm5GBzD/+gLlTJ1g8PbOPCRUC+ysK9H+/Ih6ZUDpXKGwwrwEG/jYQK0+sxMWbF4u9TpdvXUb4yXCM+WMMXlr8ErwnedvMz3W8wPNhbpgV5oULYX7ZYTWsNEzn/tH839iZhyb9qeOht3omJycjMjISRqMRZrO5eEdmpjWoZplMxf/6OhxZWVm4desWsrKyNJ+LVsNoNCIyMhLJycm5+j0xMZFB9R4MqvdwNKiGhYVBCJFrLFu2DOHh4SVurF2xAocGDMDtu445jfcTGPd6IKqOsQ2nPhN88OzsZzFk4RAsXblU87nfO5avXo5PfvgEb817C49NfSxXsG4c5oqvwrwRX9sTp5s9j10TJiB8zRrN583BoaexYcMGHDx4ENeuXcOtW7eKd9y4YQ2qt27cKP7X59DluHbtGg4ePIgNGzbk6vdly5YxqN6DQfUejn70z3dU/zdu3EDWtGmwVKpkffd0d3VvdB7+ODw+cf83nE7yQcflHbH25FrcSb2jeW0cGdHnd2GWwQehYW5wDfs3sHqME3izo8C6GgJ3atVC5jffIPZqNHbH7kZsUqzm81Z96O0dQK2H3urJd1T1NfiOKt9RdRSDah6efvppfPjhhzbfq127Nk+myktqKjB1KhAYaD32NLxpGTT+pJLNu4/NvmuG7w9/j9vp6tTlvuxZAIzzx9UwP8wy+KDe9Mo2f2eVwQLvvxeIBgvrot7iemiwuAFWnVml9ayVVqT9WQLprZ48RlVfzGYeo8pjVB3DoJqHnMtTff/99zh58iQGDx4MX19fXLhwocDfVbHJimThyswEFiwAKlQAhECWi8CvLz+C+pMq2pyd3zO8Jw5eOSjvdbWWkgL4uwAhbjBdOgkAOHr1KN5b0x8+E0rDfaI76i7KDqk5o8GieoiPPqzxxNWlt2ClNb3Vk0FVXxhUGVQdxaCaj7lz5yIkJASenp546qmnsGPHjkL9nopNJn3h2rABqFHD+hH/2ueCUXtyBWtA9f/UH6P+GIXrKdflvJ5K7NxCNdWUikGbxtiE1JyxqHkA8OGHQCGuxVvS6C1YaU1v9WRQzRYaGopBgwZpOgcZzGYzOnfujNdff13rqWiGQdUxDKqSqdhk0hau8+eB11+3BrWIOqUROvFxa0AtM6UMDNsMuJl6U87EVZSWBnP79rj8zDMwJee+c1V8SjwaLGlgE1LrLqoL94nueKG7wJbqbrD0/RC4elWDyatJb8FKa3qrp+a3UI2ORkZU1H3dQjW/cLlmzRoI4djye+PGDSTftc8JCQnBrFmzHJ6T1hhUGVQdxaAqmYpN9sALV1oaMGEC4O0NCIErZdzwztja1oDqPckbo/8YjaS0JLkTV1RB9Vx1ZpU1rNZf3ACPzf4vXMJcrfUK7SGwu7oPMHFi9ju0JZzegpXW9FZPZ74zlcygei8GVefFoOoYBlXJVGyyB1q4DhwAate2Hoc6553q8J/kaw1dXVd3xcWkkvVxdmHqGZ8SjwPxB/rasEMAACAASURBVBCfEg+z2YKv/96Pcp+0g+v4f6+A8HongeN1g4Hvvsv+iLGE0luw0pre6lkSgmpYWBgaNmyIpUuXIiQkBAEBAejYsaPNO6h3P1doaGiuSyKmpKTA398fK1assHmtdevWoVSpUjbPde8c+/fvj0GDBqFMmTIoV64cvvnmG6SkpKBHjx7w8/PDY489ho0bN9r8XmRkJNq0aQNfX1+UK1cO7777LhISEqw/X7FiBerVqwdvb2+ULVsWL730ElJSUmyC6vTp01G+fHmULVsWffv21U3PFoRB1TEMqpKp2GT3tXClpwNjxgBuboAQOFKnLBpP+fdj/ibfNtHXSVIOuN8gkJKeidFr/0LAuJZwCXOx3ra1WzuBK03rAvdcu7ek0Fuw0pre6pnnom6xZH8aUQzDnJyMW5cvw5ycnP09B+6M50hQ9fPzQ/v27XH8+HHs3LkT5cuXx+jRo/N8rhs3bqBSpUqYMGEC4uPjER8fDwD44IMP8Morr9i81ptvvolu3brZnaO/vz8mTpyIM2fOYOLEiXB1dUWbNm2wYMECnDlzBh9++CEeeughGI1GAEBcXByCgoIwatQoREVF4fDhw2jRogVeeOEF68/d3d0xc+ZMxMTE4NixY5g7dy7u3LljDaoBAQHo06cPoqKisH79epQqVQoLFiwodG2dGYOqYxhUJVOxyRxeuI4cAerXB4RAhpvA6AF14PaJG4RBIOCzAMw7MA9Z5hL6DqCdk6kK69INIzovXAm/Mc2swd93tMBnzwmk9+wGXLsmedJq01uw0pre6pnnon7Xdljsw4HDdRwJqve+6zl8+HA0adIk3+fK66P//fv3w83NDXFxcQCA69evw8PDA9u3b7c7x+eee876dVZWFnx9fdG1a1fr9+Lj4yGEwN69ewEA48aNQ8uWLW2eJ+ca4qdPn8ahQ4cghMjzSjk5QTUkJARZd32S9Pbbb6Njx475zlNPGFQdw6AqmYpNVuiFy2IB5swB/nfL08jqZfDklKrWMPX28rdxJflK8UxaVRKCao49ZxPRaOrX8B1T3VrjxwcKrH3KF5Y5c0rM4QB6C1Za01s9S0pQrVOnjs1jZs6ciapVq+b7XPkdo9qgQQN89tln1ud4/PHHYbHzLnBoaCj69u1r870qVapg2rRp1q8tFguEEFi7di0A4JVXXoGHhwd8fX1thhACGzduRFZWFl566SX4+/ujQ4cOWLBgAW7ezD7JNieotmnTxuY1Bw4caH1HVu8YVB3DoCqZik1WqIXr1i3grbesF+3/olc9eE/Mvtd92allsSJyRf6/W5JIDKoAkJ6ZhdlbT+HhsUPhPTbAGljbvCMQ88ITQGSkhEmrTW/BSmt6q6emH/3fvg3s3Ans3AlzUpLDH/2/9tpr6NGjR67vL1q0CAEBAdavc45RvdusWbMQEhJi/bqwQfXLL79EzZo1AQD169fHpEmT7M4xrzCd13MLIbBmzRoAQOvWrdG+fXtER0fnGin/C/IWiwW7du3C+PHjUb9+fQQHB+P8+fP5nkw1aNAghIaG2p2rXjCoOoZBVTIVm6zAhSsiAqhaFRACCQHuaD2pljUwtf6xNeKS44p3wiqTHFRzxCSkoOOCP1F6dHu4jc++QkCp0QIznnND5gQDoJPQkRe9BSut6a2eznwd1eHDh6NevXq53tHs168fGjdubP36foJq9erV8fnnn+d6zZs3b8Lb2xtffPEFXF1dERsba3eO9xNUR48ejZo1ayKzkDXJyspCxYoVMWPGDAZVMKg6ikFVMhWbzO7CtXCh9aP+ff95BJWnPGy95NSc/XPsfmRUIhVRUAWy34FY988V1J2wEP6ja1r/Z6HR/wkcDq0BHNbn3a30Fqy0prd6OnNQjYmJgY+PD/r27Yt//vkHp0+fxpw5c+Dl5YXly5dbH3c/QbVFixZ4/fXXcfnyZZuz7QGgS5cu8PT0ROvWrQuc4/0E1StXriA4OBgdOnTA/v37ce7cOWzevBk9e/ZEVlYW9u3bh8mTJyMiIgIXL17E8uXL4enpiY0bNzKogkHVUQyqkqnYZHkuXJmZwJAh1rtLzXm/ATwmeEAYBKp/WR3Hrh7TbsIqK8KgmuOWMQODfz6EsqP6w2usF4RBwG28wMgWLkj/ZHz2v52O6C1YaU1v9XTmoAoABw8eRKtWrVCuXDkEBATgP//5D37++Webx9xPUN27dy8aNGgALy+vXNdk/fPPPyGEsAnD+bmfoAoAZ86cwZtvvokyZcrAx8cHtWrVwuDBg2GxWHDy5Em0atUKwcHB8PLyQo0aNfDVV18ByP86qgyq2VTMEFpjUJVMxSbLtXDdvAm0bAkIgVR3gS5h9a3v3r3161u4na7O3JVTDEE1x9bIq3hi4q8oM6qJ9d+nQR+Bf1o2AM6dK9LXLk56C1Za01s9nT2oauHHH3/EQw89hIyMDK2nksuDXJdWLxhUHcOgKpmKTWazcEVHA9WrA0IgPtgHT0+tlv2O3SdumLlnJj/qL0haGsxt2iC+UaM8b6EqW5LRhCG/HkHwqNHwGeMDYRDwGCfw6YueyFz4nUMndqhKb8FKa3qrp+a3UD1zBqbIyPu6hWpxMxqNOHHiBOrWrWtzDVaVMKgyqDqKQVUyFZssZ+HK3L0bCA4GhMDRJx5B5anlrWf1b4/J/zp7ZEuLIPBn1FU8MXE5yo580vruatNeAme7tAYSE4ttHkVBb8FKa3qrpzPfmaq4hYWFwd3dHS+++CLu3Lmj9XTy5Ez1LCoMqo5hUJVMxSYzmUzYM3YsLKVKAUJgfZvH4Tc5+zaoNb+qiegb0VpP0aloFQRupmTggyUHEDRqELzGZh9P7D9KYFloWeB/F+J2RnoLVlrTWz0ZVPWF9WRQdRSDqmQqNlnmt9/C7OoKCIFvutaB6yfZlz96aclLuJl6U+vpOR0tg4DFYsHP+y/i8bFLEDjyMeu7q73ecIFx5lSnPBRAb8FKa3qrJ4OqvrCeDKqOYlCVTLkmmzzZemb/xAENrcHm/bXvw5Slj4WsWKWkwFKqFDK9vIr8ZCp7zl2/g1e+2Iagke3hEpb9b1qnr8Dxzi9l37zBiegtWGlNb/XU+mQqy6FDsBw86FQnU6mMQZVB1VEMqpIp12SzZsHsItC9fzVrSB331zieNHW/ivGs/4JkZJoxZVMUHh41CX6jS2Vf/3aMwIJWQbAcPKjp3Byht2ClNb3VU+ug6oxn/auMQZVB1VEMqpKp1mSmLBO6fN3CGlJn752t9ZScm0JBNceu6AQ0mPArgkf8e5OAXu1ckbboW62nVih6C1Za01s9GVT1hUGVQdVRDKqSqdZkXVZ1gTAIuBpcsejwIq2n4/wUDKoAcPV2Gjp8vQvlR3SE6/jssPqfDwQuDnlP+RsE6C1YaU1v9WRQ1RcGVQZVRzGoSqZak22L2YbAKYEYu2SsbhYuTSkaVAEgM+t/hwKM/ASlRntCGASChgv81f5JpS9hpbdgpTW91ZNBVV/sBVWLxYIvvvgC+/fv12BmxYdB1TEMqpKp2GSJdxJ1tXBpSuGgmuPPqKuoZViCoBEPZ7+bPl5getuysBxT87a4egtWWtNbPUtCUL339qT3I69bocqU121e70dB76ju2LEDISEhiI+Pf+DXUhWDqmMYVCVTscn0tnBpygmCKgDE3jTi1S//QIVhT1uPW+36tjvSV6/Qemq5sD/l0ls9nT2oxsfHo3///qhatSo8PT1RqVIltG3bFn/88Yf1MQyqtn755Rc0b94cWYreDexBa82g6hgGVclUbDK9LVyaSk2F+b//RULdujAp9G+clzRTFob8cgQVh3WH2/+OW33mPYFrMyYodb1V9qdcequn5rdQjYqC6cSJ+7qFakxMDCpUqIA6depg5cqVOH36NE6cOIEZM2agZs2a1scxqBa9jIwMac/FoFq8GFQlU7HJ9LZwac2Z6mmxWLBo13lUHDUBpUa7QxgEHh0kcHxQZ2VOsnKmejoDvdXTmS/436ZNG1SsWBEpKSm5fnbrrk9khBD49ttv0a5dO/j4+KBatWpYu3atzeMjIyPRpk0b+Pr6oly5cnj33XeRkJBg/XloaCj69euHfv36oXTp0ihbtizGjBljvRThJ598grp16+aax1NPPYWxY8cCALZt24bGjRujVKlSKF26NJ555hlcuHABwL9BdenSpQgJCUFAQAA6duyI5ORk63NZLBZMmTIFVatWhbe3Nxo0aIAVK1ZY61ixYkXMmTPHpp6HDx+GEALnzp2zW0uLxYKwsDBUrlwZnp6eeOSRRzBgwIB8H58z3++//x5Vq1aFi4sLLBYL0tPTMWDAAAQHB8PLywvPPvssDhw4YPO727dvR+PGjeHp6Yny5cvj448/Rub/9pfdu3eHEMJmxMTE4ObNm+jSpQuCgoLg7e2NatWqYeHChXnOjUHVMQyqkqnYZHpbuLTmjPXcczYRtQ3f4aERAdZbr/7WpTGgwP3AnbGeKtNbPfNa1C0WC1IyUoplJKcl4/L1y0hOS0ZKRkqhr0F948YNuLi44NNPPy3wsUIIVKpUCcuWLUN0dDQGDhwIPz8/3LhxAwAQFxeHoKAgjBo1ClFRUTh8+DBatGiBF154wfocoaGh8PPzw6BBg3Dq1Cn8+OOPKFWqFBYsWAAAiI2Nhaurq00oO3r0KFxcXHDu3DlkZmaidOnSGDZsGM6ePYuTJ09i8eLFuHjxIoDs4Ofn54f27dvj+PHj2LlzJ8qXL4/Ro0dbn2/06NGoVasWfv/9d5w7dw6LFi2Cl5cXtm/fDgAYNmwYnnvuOZugOnToUDRr1qzAGq1YsQIBAQHYuHEjLl68iP3791v/tryEhYXB19cXrVq1wuHDh3H06FFYLBYMHDgQFSpUwMaNGxEZGYnu3bsjMDDQWuvLly+jVKlS6Nu3L6KiorBmzRoEBQUhLCwMAJCUlIRmzZrhgw8+QHx8POLj45GVlYV+/frhiSeeQEREBGJiYrB161asW7cuz7kxqDqGQVUyFZtMbwuX1py1nrE3jXh51npUGFrFepLVF+0rApcvazovZ62nqvRWz7wW9ZSMFOux18U9UjJyvzual/3790MIgdWrVxf4WCGE9V1NAEhJSYEQAps2bQIAjBs3Di1btrT5ndjYWAghcPr0aQDZQbV27do2Qfrjjz9G7dq1rV+3adMGH374ofXrwYMHo3nz5gCyg7UQwhoq7xUWFoZSpUrZvIM6fPhwNGnSxDpnb29v7Nmzx+b3evXqhc6dOwMAjhw5AhcXFxw7dgxms9nmXdaCzJgxAzVq1Ch0X4eFhcHDwwPXr1+3fi8lJQUeHh746aefrN8zmUyoUKECpk2bBiA7bNesWdOmjnPnzoWfn581XOf10f9rr72Gnj17FmpuDKqOYVCVTMUm09vCpamUFFiCgpAeEKD0yVT5Sc3IQp8f9yHkoybWhXdYez+YTxzXbE7sT7n0Vk9nDar79u1zKKguX77c5nsBAQFYsmQJAOCVV16Bh4cHfH19bYYQAhs3bgSQHZ7uDUrh4eFwd3e3npS0evVqlClTBmlpaTCZTAgKCsLSpUutj+/Rowe8vLzQtm1bzJ49G3FxcdafhYWFoU6dOjbPP3PmTFStWhUAcODAAQghcs3Rw8MDTz/9tPV36tSpg/Hjx8NsNuOvv/6Cu7u7zSEM+bl06RIqV66MSpUq4f3338fq1autH8fnJSwsDNWqVbP53tGjRyGEsB7OkKNdu3bW2r355pvo0aOHzc//+ecfCCGs7y7nFVQ3btwIHx8fNGzYEMOHD8fu3bvznRuDqmMYVCVTscn0tnBpyknO+rfHbLZg+u9RCBn6lnXx7dLJExm7dmgyH/anXHqrp6Yf/afeRsrenUjZuxPJxqQi/ej/3pOpSpcujUWLFgEAWrdujfbt2yM6OjrXyDn+tTBBNTMzEw8//DCWLVuGVatWISAgAKmpqTa/c/jwYXz66ado1qwZ/Pz8sHfvXgB5n0w1a9YshISEAPg3mG/fvj3XHC9dumT9nUmTJqFOnTowm814//338eqrrxZYnxypqalYt24dBgwYgPLly6NZs2b59nle8y3KoAoA169fx+LFi/HOO+/A29sbQ4cOzXNuDKqOYVCVTMUm09vCpSkdBNUcKw/GourwvtYrArzUwxW31xX/5avYn3LprZ7OfHmq1q1bF/pkKntBNefjaHvvIIaGhuZ6x3PkyJE2H/0DwIgRI9CiRQu0bdsW//d//2d3/k2bNrWesFRQUE1OToaXl5fNO7R5OXfuHFxcXHDgwAGUKVMGP//8s93H5+fUqVMQQuDQoUN5/jyv+aakpMDT0zPXR/8VK1bE9OnTAeT/0b+/v7/1o/8WLVqgf//+duc3f/58+Pv75/kzBlXHMKhKpmKT6W3h0pSOgioA7DuXiJpjDfAZ4wphEGjYR+DK97OLdQ7sT7n0Vk9nDqrnzp1D+fLlrZenOnPmDE6ePIkvvvgCtWrVsj6uoKB65coVBAcHo0OHDti/fz/OnTuHzZs3o2fPntZ3S3NOphoyZAhOnTqFZcuWwdfXF/Pnz7d53jNnzsDNzQ1ubm7Yt2+f9fvnz5/HyJEjsWfPHly4cAGbN29G2bJlMW/ePAAFB1UAGDNmDB566CEsXrwYZ8+exeHDhzFnzhwsXrzY+hiz2YwmTZqgYcOG8Pf3h9FoLFQtFy1ahO+++w7Hjx/HuXPnMGbMGPj4+CAxn7vu5Xc5rUGDBqFChQrYtGmTzclUN2/eBPDvyVT9+vVDVFQUwsPDbU6mAoAPPvgAjRs3RkxMDBISEmA2mzFu3DiEh4cjOjoaJ06cQNu2bW0Oebgbg6pjGFQlU7HJ9LZwaUpnQRUAziekoPGn81BmZPZtV6sMFjg5dVixvT77Uy691dOZgyqQfcZ+v379EBISAk9PT1SsWBGvv/46tm3bZn1MQUEVyA6Yb775JsqUKQMfHx/UqlULgwcPtr7zFxoair59+6JPnz4ICAhAYGAgRo4cmeehCs8//3yuS1VdvXoV7dq1wyOPPAJPT0+EhIRYjyUFChdULRYLZs+ejZo1a8LDwwPBwcFo1aoVduz497Ais9mMzz//HEIIdOvWrdB1XLNmDZo0aYKAgAD4+vqiadOmNjdNuFd+QTUtLQ0DBgxAUFDQfV2eCgBOnz6Npk2bwsfHx3p5qokTJ6J27drw8fFB2bJl8cYbb+D8+fN5zo1B1TEMqpKp2GR6W7g0pcOgCgA3UzLwypfL8fAwPwiDwEMjBA5+3LVYbgzA/pRLb/V09qCqGovFgho1amDGjBmavL5WF/xXCYOqYxhUJVOxyfS2cGlKp0EVyL6TVbdFf6DiR0EQBoGAkQI7B74BFPGCwv6US2/1ZFCV59q1a/j888/h6+tr/ai7uDGoMqg6ikFVMhWbTG8Ll6ZSU2Fu1Ag3q1VT/haq9yPLbMHwlXtR+aOKEAYBnzECm/q0yF6wiwj7Uy691VPzW6hGRiLz2LH7uoWqaoQQCAoKsjmZqLgxqDKoOopBVTIVm0xvC5fW9F5Pi8WCGVuOIWRIVQiDgMc4geW9ngGK6O/Vez2Lm97q6cy3UKXcWE8GVUcxqEqmYpPpbeHSWkmp50/7zuKxwbWsd7Fa2P0JID1d+uuUlHoWF73Vk0FVX1hPBlVHMahKpmKT6W3h0lpJqueWyCuoMfhJ640BZnetCRTycjKFVZLqWRz0Vk8GVX1hPRlUHcWgKpmKTaa3hUtTRiMsISEwBgfDlJSk9WyKxb7zCag7+BlrWJ3R5fHsk8okYX/Kpbd65izq995BqVhkZcFy9CiyjhzRxclUKmBQzb7DFoNq4TGoSqZik+lt4dKUjs/6t+dY7C3U++hFa1id9s7j0t5ZZX/Kpbd6ZmVl4eTJk/le2L2IX1xXZ/2rgEEVSExMxMmTJ603a7ibihlCawyqkqnYZHpbuDRVQoMqAJyOv40Gw1pYw+qUdx6TElbZn3LpsZ5xcXHWsJqamoq0tLTiGSkpSIuIQFpEBIx37hTf6+p4GI1GXLt2DUajUfO5FPdITU21htS4uLg8e13FDKE1BlXJVGwyPS5cminBQRUALiSk4Klhraxh9dN3Hwce8CNZ9qdceqynxWKxhtViHSdO4OSmTTi5aRMiT5wo/tfX4YiMjMTBgwcRGRmp+Vy0GnFxcXneMQxQM0NojUFVMhWbTI8Ll2ZKeFAFgCu3jGg8vLU1rE7o+jiQdv8nurA/5dJzPbOysor3XbAbN5AWEoK0kBAkX7um+TtyehjJycnYsGEDkpOTNZ+LFiOvj/vvpmKG0BqDqmQqNpmeF65ix6AKAEi4k45nRrSxhtVPulW777DK/pSL9ZSI27t07E/7VMwQWmNQlUzFJuOOQSIuXFZJRhOeuyusTnm35n1dZ5X9KRfrKRG3d+nYn/apmCG0xqAqmYpNxh2DREYjLLVr43blyiXm8lT2JKWa8PyI1nddZ7W+w3ewYn/KxXpKxO1dOvanfSpmCK0xqEqmYpNxxyAX62nrljEDzT7OvnSVS5jA1+81ARy49AzrKRfrKRfrKRfraZ+KGUJrDKqSqdhk3DHIxXrmlpSagSbDm/17u9UPXwTyOav1XqynXKynXKynXKynfSpmCK0xqEqmYpNxxyAX65m3W6npaDw0+3ar7uMEfhzyRqF+j/WUi/WUi/WUi/W0T8UMoTUGVclUbDLuGCTiMWt23TSm4T8f1YYwCHiNFVg++t0Cf4f9KRfrKRG3d+nYn/apmCG0xqAqmYpNxh2DRDwLuEA3Uox4avBjEAYBnzEC6yb3s/t49qdcrKdE3N6lY3/ap2KG0BqD6l1iYmLw3nvv4dFHH4W3tzcee+wxjB8/HhkZGYV+DhWbjDsGibhwFcq15DtoOKgihEGg9EiBHV+Mz/ex7E+5WE+JuL1Lx/60T8UMoTUG1bts2rQJPXr0wObNm3Hu3DmsXbsW5cqVw9ChQwv9HCo2GXcMEnHhKrTYmzdRa/BDEAaB8kMFti7+DPvj9iM+Jd7mcexPuVhPibi9S8f+tE/FDKE1BtUCTJs2DVWrVi3041VsMu4YJOLC5ZDT8Zfx6Ed+CPw8EHUX1UW9xfXQYEkDrDqzyvoY9qdcrKdE3N6lY3/ap2KG0BqDagHGjBmDRo0aFfrxKjYZdwwSceFy2JZTe6whNWc0WNLA+s4q+1Mu1lMibu/SsT/tUzFDaI1B1Y6zZ88iICAA3377bb6PSU9Px+3bt60jNjYWQggkJibCZDIpMYxGI8LDw2E0GjWfi9OPW7esC5fx+nXt5+MEY3fsbpuQmjP2xO6BycT+lD1YT4mD27v0wf60PxITExlU71EigmpYWBiEEHZHRESEze9cuXIF1apVQ69eve7ruZctW4bw8HAOnY31v/4KY3AwjMHBWP/rr5rPxxnGktVLUH9xfduguqguvl/0leZz4+CwN7i9cxT3WLZsGYPqPUpEUE1ISEBUVJTdkZaWZn38lStXUKNGDXTt2hXmAm4FyXdUS95gPR0fy6OWo8GSBqi3uB7qLqqLwM8D8da7gTAm3mA9JQ/Wk/VUebCe9gffUc2tRARVR1y+fBnVq1dHp06dkJWV5fDvq3h8icnEY4JkYj3vT3xKPA7EH8DkH8fBdbyAMAj06VIFGVejseuHT2FKvKD1FHWB/SkX6ykX62mfihlCawyqd7l8+TKqVauGl156CZcvX0Z8fLx1FJaKTcYdg1ys54MbPacfhCE7rC4Y7w2EBcBiKAMcWqL11Jwe+1Mu1lMu1tM+FTOE1hhU77Jo0aJ8j2EtLBWbjDsGiVJTYW7UCDerVYNJoX9jZ9Rz0ssQBgG3MIGNYT5AWABgCASSLms9NafG7V0ibu/SsT/tUzFDaI1BVTIVm4w7Bol4uRppLOe2o1uYB4RBwDdM4GCYb3ZYPb9T66k5NW7vEnF7l479aZ+KGUJrDKqSqdhk3DFIxIVLnqTLyDCUxsthbhAGgYfDXHA+zJ/vqD4gbu8ScXuXjv1pn4oZQmsMqpKp2GTcMUjEhUuuQ0twy1AG9cNcIQwCNYe54O9Nm7WelVPj9i4Rt3fp2J/2qZghtMagKpmKTcYdg0RcuKQzJV7AqvlDUX6EO4RB4OkPPHHqWJTW03Ja3N4l4vYuHfvTPhUzhNYYVCVTscm4Y5CIC5d0Of2599Bm+I9ygTAItOrmj6tXb2g9NafE7V0ibu/SsT/tUzFDaI1BVTIVm4w7Bom4cEl3d3+Gb/4WHuOyL1vVtXNlGNMytJ6e0+H2LhG3d+nYn/apmCG0xqAqmYpNxh2DRCkpsAQFIT0ggAuXJPf25+yFQ63XWB36bjNkZtm/OxzZ4vYuEbd36dif9qmYIbTGoCqZik3GHYNcrKdcedWz75Q2EAYBj3ECkwZ2h8Vi0XCGzoX9KRfrKRfraZ+KGUJrDKqSqdhk3DHIxXrKlVc9zRYzWo2qAWEQKDtCYP7nn2s4Q+fC/pSL9ZSL9bRPxQyhNQZVyVRsMu4Y5GI95cqvnsaMFDQYWhrCIFB9gCtWr9mk0QydC/tTLtZTLtbTPhUzhNYYVCVTscm4Y5AoNRXm//4XCXXr8paKktjrz7jr5/DI8OzLVj3Tywt7Dp/WYIbOhdu7RNzepWN/2qdihtAag6pkKjYZdwwS8Sxg6Qrqz0NHt8B3dPZlq15/Jwjn41h3e7i9S8TtXTr2p30qZgitMahKpmKTcccgERcu6QrTn6vWzYBLWPaVALp3aYAkI3s5P9zeJeL2Lh370z4VM4TWGFQlU7HJuGOQiAuXdIXtz0lfvgNhEHAJExjQuwNMvGxVnri9S8TtXTr2p30qZgitMahKpmKTcccgERcu6QrbnxaLBV3HPAlhEPAfJTDBMIGXrcoDt3eJuL1Lx/60T8UMoTUGVclUbDLuGCTiwiWdI/2ZkZmOph89BGEQeGygCxb9tLYYZuhcuL1LxO1dOvanfSpmpzdu5QAAIABJREFUCK0xqEqmYpNxxyARFy7pHO3P64kXUWm4B4RB4LmeXvjzwKkinqFz4fYuEbd36dif9qmYIbTGoCqZik3GHYNEKSmwlCqFTC8vLlyS3E9/Hj62GaXGZJ9c9XbHR3DqSlIRztC5cHuXiNu7dOxP+1TMEFpjUJVMxSbjjkEu1lOu+63nstWTIQzZYbVX52eRcCe9iGboXNifcrGecrGe9qmYIbTGoCqZik3GHYNcrKdcD1LPEdNfhTAIeI0V6NevLzIyeSUA9qdcrKdcrKd9KmYIrTGoSqZik3HHIBfrKdeD1NNsMaPNx49CGAQeGSpgmPldib8SAPtTLtZTLtbTPhUzhNYYVCVTscm4Y5AoLQ3mNm0Q36gRTMnJWs9GFx60P2/fSUTNoT4QBoEnentgye8HJM/QuXB7l4jbu3TsT/tUzBBaY1CVTMUm445BIp4FLJ2M/jwbvR9lRmbfZrXVuw9h7+mrEmfoXLi9S8TtXTr2p30qZgitMahKpmKTcccgERcu6WT155bf58FtfPbJVZ07P4XLt1IlzdC5cHuXiNu7dOxP+1TMEFpjUJVMxSbjjkEiLlzSyezPaV92gTAIuI8T6N27J1IzsiTM0Llwe5eI27t07E/7VMwQWmNQlUzFJuOOQSIuXNLJ7E+LxYK3RtWAMAg8PExg9GfzStzJVdzeJeL2Lh370z4VM4TWGFQlU7HJuGOQiAuXdLL7M8WYhNrDfCEMAo3+zwPfrtsn5XmdBbd3ibi9S8f+tE/FDKE1BlXJVGwy7hgk4sIlXVH0Z/S5CJQelX1y1RudymF7VMk5uYrbu0Tc3qVjf9qnYobQGoOqZCo2GXcMEnHhkq6o+nPdb7Osd656t9NziElIkfr8quL2LhG3d+nYn/apmCG0xqAqmYpNxh2DXKynXEVZz7EzXoMwCHiPEejRbzCMGZnSX0M17E+5WE+5WE/7VMwQWmNQlUzFJuOOQS7WU66irKfZYkarEZUgDAJVBrtg+KyfdX9yFftTLtZTLtbTPhUzhNYYVCVTscm4Y5CL9ZSrqOt581Ycqg7zhDAIPPNeKSz640SRvI4q2J9ysZ5ysZ72qZghtMagKpmKTcYdg0RpaTC3b4/LzzzDWypKUhz9efTwJviMyT5etV3nxxERc6PIXktr3N4l4vYuHfvTPhUzhNYYVCVTscm4Y5CIJ1dIV1z9+cOPI6wnV3Xu/gauJacV6etphdu7RNzepWN/2qdihtAag6pkKjYZdwwSceGSrjj7s19YEwiDQOmRAu+PngpTlrnIX7O4cXuXiNu7dOxP+1TMEFpjUJVMxSbjjkEiLlzSFWd/mkzpaPpRGQiDQN0P3fHZT38V+WsWN27vEnF7l479aZ+KGUJrDKqSqdhk3DFIxIVLuuLuz9iLxxH0sSuEQaBtlyBsOHK5WF63uHB7l4jbu3TsT/tUzBBaY1CVTMUm445BIi5c0mnRn5s3z4NLWPbxqu90fA7R1/Rzogy3d4m4vUvH/rRPxQyhNQZVyVRsMu4YJOLCJZ1W/TnufzcDKDVaoGv/EbiTro+bAXB7l4jbu3TsT/tUzBBaY1CVTMUm445BIi5c0mnVn1nmLLw4ojyEQaD6AFcMmbNWFzcD4PYuEbd36dif9qmYIbTGoCqZik3GHYNEFgtMt25h/S+/wJSRofVsdEHL/rx2PQaPjHCHMAi83LUMlu6MLvY5yMbtXSJu79KxP+1TMUNojUFVMhWbjDsGuVhPubSu5987foDb+OzjVd/u2BjHYpM0mYcsWtdTb1hPuVhP+1TMEFpjUJVMxSbjjkEu1lMuFeo5/avOEAYBz7ECnfsMwO005/23VaGeesJ6ysV62qdihtAag6pkKjYZdwwSpafD3LUrLr7wAkx37mg9G11QoT8tFgteHxECYRCoMtgFA2ctd9rjVVWop25we5eO/WmfihlCawyqkqnYZNwxSMSTK6RTpT9v3YxD1WEeEAaB53r64/ttpzSdz/1SpZ66wO1dOvanfSpmCK0xqEqmYpNxxyARFy7pVOrPQ/vWwGts9vGqb3aujyOXnO/fWKV6Oj1u79KxP+1TMUNojUFVMhWbjDsGibhwSadaf349/30Ig4DbeIFO/9cbt4zOdba3avV0atzepWN/2qdihtAag6pkKjYZdwwSceGSTrX+tFgs6PhxdQiDQKUhLuj/+TKnOl5VtXo6NW7v0rE/7VMxQ2iNQVUyFZuMOwaJuHBJp2J/3r59HY8N84QwCDTv7ocFf0RpPaVCU7GeTovbu3TsT/tUzBBaY1CVTMUm445BIi5c0qnan4ci1sHzf8erdvx/DXHwwk2tp1QoqtbTKXF7l479aZ+KGUJrDKr5SE9PR8OGDSGEwJEjRwr9eyo2GXcMEnHhkk7l/vzim17/Xl/1//o7xfGqKtfT6XB7l479aZ+KGUJrDKr5GDhwINq0acOgSrYsFpiuXMHGJUt4S0VJVO5Pi8WC10dWhTAIPDrIFQNmr1T+eFWV6+l0uL1Lx/60T8UMoTUG1Txs3LgRtWrVQmRkJIMq5cJ6yqV6PW/cvILKw7Ovr/pStzJYujNa6ynZpXo9nQ3rKRfraZ+KGUJrDKr3uHr1KipWrIiIiAjExMQUGFTT09Nx+/Zt64iNjYUQAomJiTCZTEoMo9GI8PBwGI1Gzeeih8F6lrx67ti2FG7js49XfbtzMxy7dEPzOTlzPZ1psJ6sZ3GOxMREBtV7MKjexWKxoHXr1pg4cSIAFCqohoWFQQiRayxbtgzh4eEcOhvrVqzA+TZtcL5NG6xbsULz+XAU3xgw/BkIg4D3GIH2vYfg11Xaz4mjaAe3d47iHsuWLWNQvUeJCKr5hcm7R0REBL744gs8++yzyMrKAlC4oMp3VEvYuHXLenKF8fp17eejg+Es/ZmenoaXh5WHMAjU6O+Gkd9t0nxOzlxPpxjc3qUP9qf9wXdUcysRQTUhIQFRUVF2R1paGt544w24urrCzc3NOoQQcHNzQ7du3Qr1WioeX2Iy8ZggaXgWsHTO1J/Xrp5D+RFuEAaBlu8GY92Ry1pPKRdnqqfyuL1Lx/60T8UMobUSEVQL6+LFizh+/Lh1bN68GUIIrFy5ErGxsYV6DhWbjDsGibhwSeds/fnX5vlwCcs+XrXDuy/j0g2j1lOy4Wz1VBq3d+nYn/apmCG0xqBqR2E++r+Xik3GHYNEXLikc8b+HPdpKwiDgN8oge6jPoMpy6z1lKycsZ7K4vYuHfvTPhUzhNYYVO1gUKVcuHBJ54z9mZWViec/KgthEKj3oQemrtyr9ZSsnLGeyuL2Lh370z4VM4TWGFQlU7HJuGOQiAuXdM7an5cvHEfZkS4QBoHXOlfB32cStJ4SAOetp5K4vUvH/rRPxQyhNQZVyVRsMu4YJOLCJZ0z92f4yskQhuzjVbt0fxsJd9K1npJT11M53N6lY3/ap2KG0BqDqmQqNhl3DBKZzTCdOYPN33wDU7r2oUQPnL0/e4f9B8IgUG6YQN9J38Fs1vYWq85eT6Vwe5eO/WmfihlCawyqkqnYZNwxyMV6yuXs9TSmJaP2sFIQBoHne5bCwj+jNJ2Ps9dTNaynXKynfSpmCK0xqEqmYpNxxyAX6ymXHup57OgWeI3NPgSgY8eGiIrXbvvXQz1VwnrKxXrap2KG0BqDqmQqNhl3DBJlZCDro49wpl07mFJStJ6NLuilP7/8pheEQcBzrECP/kORZsrSZB56qacSuL1Lx/60T8UMoTUGVclUbDLuGCTiyRXS6aU/LRYLXhlRBcIgUG2AKyYu3arJPPRSTyVwe5eO/WmfihlCawyqkqnYZNwxSMSFSzo99WfC9QvWW6y+8k45bIu6Wuxz0FM9NcftXTr2p30qZgitMahKpmKTcccgERcu6fTWn39s/tp6i9UuXV9BYjFfskpv9dQUt3fp2J/2qZghtMagKpmKTcYdg0RcuKTTY38OndwcwiAQ+LHAgElzYLEU3yWr9FhPzXB7l479aZ+KGUJrDKqSqdhk3DFIxIVLOj32Z4YpDU995A9hEGj8gTd+2BZZbK+tx3pqhtu7dOxP+1TMEFpjUJVMxSbjjkEiLlzS6bU/o0/tgd/o7EMA3uxcG9HXkovldfVaT01we5eO/WmfihlCawyqkqnYZNwxSMSFSzo99+eiRUMgDAJu4wV69O+H9Myiv2SVnutZ7Li9S8f+tE/FDKE1BlXJVGwy7hgkMpthOnIEf375JW+pKIme+9NiseD/fVwdwiBQZbArPluyschfU8/1LHbc3qVjf9qnYobQGoOqZCo2GXcMcrGecum9nreTruHRoR4QBoGXu5bF7jPXi/T19F7P4sZ6ysV62qdihtAag6pkKjYZdwxysZ5ylYR67t7+A1zHZx+v+m7XlrhlzCiy1yoJ9SxOrKdcrKd9KmYIrTGoSqZik3HHIFFGBrLGjkVUx468paIkJaU/x3zWCsLw/9u78/goq7N94CdhR0AWRSsKLhRFNitqXepWra9a6v5arbYuqFUrKosgW/Ig7qg/UKvWYnGNKKJRKO6ooLwKCLIoiopCgAhJIIGEJJPMXL8/oqNsD1mu5Nwzc30/n+cPMZk5vbzPeS7SyYzD7rc6DLnjoXp7y6pUybNBaL/TaT7DWewQvqmoklkcMh0MRPrlCrpUmc9IRTmOGLQ7XOBw1FXNMPWjZfXzPCmSZ4PQfqfTfIaz2CF8U1ElszhkOhiIdOOiS6X5/Prrj7Hbj29ZdfGfD8GajVvoz5FKedY77Xc6zWc4ix3CNxVVMotDpoOBSDcuulSbz8efuhkucGgy2uHGmwYiGuW+BCDV8qxX2u90ms9wFjuEbyqqZBaHTAcDkW5cdKk2n7FYDP1uPRAucOh2QzqeyJ5FffxUy7Neab/TaT7DWewQvqmoklkcMh0MRLpx0aXifOYV5GDvoY3gAoezLt4Ly3N550Uq5llvtN/pNJ/hLHYI31RUySwOmQ4GIt246FJ1Pt948xG4oOr1qn/vfz7KK6KUx03VPOuF9jud5jOcxQ7hm4oqmcUh08FApBsXXSrP53VjjoULHPYc4nD/45Mpj5nKedJpv9NpPsNZ7BC+qaiSWRwyHQxElZWomDMH748bh0hpqe/VJIVUns/S8hIcMrglXOBwwuW7Yd7yH+r8mKmcJ532O53mM5zFDuGbiiqZxSHTwcClPLlSPc9Fn72JpqOqXgLwt0uPRnFZRZ0eL9XzZFOeXMoznMUO4ZuKKpnFIdPBwKU8uZQncNeDf4ELHFqMdMi84946PZby5FKeXMoznMUO4ZuKKpnFIdPBQFRejsq77sLSyy7TRyqSaD6BaCyKEwZ1hAscel/bGO/O/bLWj6U8ibTf6TSf4Sx2CN9UVMksDpkOBiL9cgWd5rPK6pzP0fbWNLjA4YK/HIiC4vJaPY7yJNJ+p9N8hrPYIXxTUSWzOGQ6GIh046LTfP4sa3IGXOCQlukwaPB1iMVq/qlVypNI+51O8xnOYofwTUWVzOKQ6WAg0o2LTvO5tYuGHQoXOOw3MA0vTn+/xt+vPIm03+k0n+EsdgjfVFTJLA6ZDgYi3bjoNJ9b27QpH10GN4ELHE77W3us3lBSo+9XnkTa73Saz3AWO4RvKqpkFodMBwORblx0ms/tzXrvGaRnVL1l1XVX90M0Wv2XAChPIu13Os1nOIsdwjcVVTKLQ6aDgUg3LjrN544NHnsqXODQfqjDxElZ1f4+5Umk/U6n+QxnsUP4pqJKZnHIdDAQ6cZFp/ncsUhFOXoNbAUXOPzuyhb4Oie/et+nPHm03+k0n+EsdgjfVFTJLA6ZDgaiykpUvP02Zo8dq49UJNF87tzSJTPRfGTVSwCu/uuRqKiM7vJ7lCeR9jud5jOcxQ7hm4oqmcUh08HApTy5lGe4Ox/6K1zg0HKEw8P3jdvl1ytPLuXJpTzDWewQvqmoklkcMh0MXMqTS3mGi8aiOHbQXnCBw2F/b4zPl60I/XrlyaU8uZRnOIsdwjcVVTKLQ6aDgSgSQeWECVh0zTWIlNTsbYNkxzSfu7Zy9edoM7zqU6suv/gglFfs/CUAypNI+51O8xnOYofwTUWVzOKQ6WAg0i9X0Gk+q+ex50bABQ6NMhzuHzVop1+nPIm03+k0n+EsdgjfVFTJLA6ZDgYi3bjoNJ/VE4vFcMbQX8MFDr++IR3zP1mww69TnkTa73Saz3AWO4RvKqpkFodMBwORblx0ms/qKyjMRcehjeECh//9y14oLa/Y7muUJ5H2O53mM5zFDuGbiiqZxSHTwUCkGxed5rNmps54BC6oesuq22++ZLt/rzyJtN/pNJ/hLHYI31RUySwOmQ4GIt246DSfNfeXkUfCBQ77DHKY/eY7W/075Umk/U6n+QxnsUP4pqJKZnHIdDAQ6cZFp/msueLSTThgcHO4wOHMv7ZBScnPb0avPIm03+k0n+EsdgjfVFTJLA6ZDgYi3bjoNJ+1M3POVDTKqHoJwIi//0/8z5UnkfY7neYznMUO4ZuKKpnFIdPBQFRRgYrsbPzfqFGIbNniezVJQfNZe9fffgZc4NB2mMMbL04GoDyptN/pNJ/hLHYI31RUySwOmQ4GLuXJpTxrL1JRjh4D28AFDr+7sjk2FmxUnmTKk0t5hrPYIXxTUSWzOGQ6GLiUJ5fyrJtPl85C85FVLwG46fIjlCeZ8uRSnuEsdgjfVFTJLA6ZDgaiSAQVEyfi0wED9JGKJJrPuhs9/nK4wKH5SIeXH87Eh8/ciUj+976Xlfi03+m038NZ7BC+qajuwPTp03HUUUehefPm6NChA84999xqf6/FIdPBQKRfrqDTfNZdNBbFb2/eCy5wOCIzHZHM1ogFbYFPn/K9tMSm/U6n/R7OYofwTUV1Gy+99BLatWuHRx99FF999RW+/PJLTJkypdrfb3HIdDAQ6cZFp/nk+OaL99Eus+olABmZTYHMNkDQDihc7XtpiUv7nU77PZzFDuGbiuovVFRUoFOnTpg4cWKtH8PikOlgINKNi07zSbLiAzyf2QIucGiU6fBxZsuqsrpilu+VJS7tdzrt93AWO4RvKqq/8Mknn8A5h//85z847LDDsPfee+P000/HkiVLdvo9ZWVlKCoqil85OTlwziE/Px+RSMTEVVJSguzsbJSUlHhfS8JfGzfGb1wl69f7X08SXJpP0pX/PWJBW1yU2RgucPh1Zjo2B7sjkv+9/7Ul6qX9Tr+038Ov/Px8FdVtqKj+wvPPPw/nHDp37oyXXnoJ8+fPx8UXX4wOHTqgoKBgh9+TmZkJ59x2V1ZWFrKzs3Ul2TVt8uT4jWva5Mne16NL1y+vBU8MRF5mG3TKTIMLHC69bne88vIr3teVqJf2u66GvrKyslRUt5ESRXVnZfKX17x58/Dcc8/BOYd//etf8e8tKyvDHnvsgccee2yHj62fqKbYpZ+w0C/NJ/fa8sPXuOf2c+GCqterPjTicu9rSthL+51+ab+HX/qJ6vZSoqjm5eVh2bJloVdpaSlmzpwJ5xxmz5691fcfddRRGDFiRLWey+LrSyIRvSaIRq9Zo9N8cv2U57lDDocLHPYe7PDVxx/5XlZi0n6n034PZ7FD+JYSRbW6ioqK0KxZs61+mSoSiaBjx45b/ZR1V49hbch0MBBVVKAiKwtzb7lFH6lIovnk+inP/MJ87D+wGVzgcObluyOmfGtO+51O+z2cxQ7hm4rqNm666SZ06tQJb775Jr788kv0798fHTt2xIYNG6r1/RaHTAcDl/LkUp5cv8wz+53n0Sij6iUAdw/s53tpCUnzyaU8w1nsEL6pqG4jEolg8ODB6NixI1q3bo1TTz0VS5curfb3WxwyHQxcypNLeXJtm+ffRp0KFzh0GNkYz756P3KLcz2vMLFoPrmUZziLHcI3FVUyi0Omg4FI/1cgneaTa9s8S8vLcOiYX6HHpB7o+WRP9H6yN6Yun+p5lQlC+51O+z2cxQ7hm4oqmcUh08FApF+uoNN8cm2bZ25xLno92Qs9n+wZv3o/1Vs/Wa0O7Xc67fdwFjuEbyqqZBaHTAcDkW5cdJpPrm3z/GTtJ1uV1J+uublzPa80AWi/02m/h7PYIXxTUSWzOGQ6GIh046LTfHLt6CeqvZ/qvXVRndQDK3O+8LzSBKD9Tqf9Hs5ih/BNRZXM4pDpYCDSjYtO88m1ozynLp8aL6s9JvVAu/vaYUD/7h5XmSC03+m038NZ7BC+qaiSWRwyHQxEunHRaT65dpZnbnEu5ubOxY0TroELHBplOLz+6G2eVpkgtN/ptN/DWewQvqmoklkcMh0MRLpx0Wk+uXaVZzQaxXEDusAFDt0GpGPT99808AoTiPY7nfZ7OIsdwjcVVTKLQ6aDgUg3LjrNJ1d18ly6agX2uKURXOBwxeWdgFisAVeYQLTf6bTfw1nsEL6pqJJZHDIdDESRCComTsSnAwYgUlLiezVJQfPJVd08b594B1xQ9alVL9x1fQOtLsFov9Npv4ez2CF8U1ElszhkOhi4lCeX8uSqbp6xWAyn3tQTLnDoNCgN6xbPb6AVJhbNJ5fyDGexQ/imokpmcch0MHApTy7lyVWTPFesX4d9BzWFCxzOu7wdUFHRACtMLJpPLuUZzmKH8E1FlczikOlgIKqoQEV2Nv5v1Ch9pCKJ5pOrpnlOeGEi0jOqXgLw7+Hn1/PqEoz2O532eziLHcI3FVUyi0Omg4FIv1xBp/nkqk2efxp8PFzg0GGow/ezXq/H1SUY7Xc67fdwFjuEbyqqZBaHTAcDkW5cdJpPrtrkmVu4CV1v2g0ucDi1f0vE9NPDKtrvdNrv4Sx2CN9UVMksDpkOBiLduOg0n1y1zfOJ17PRbFTVSwDG3Xhi/Swu0Wi/02m/h7PYIXxTUSWzOGQ6GIh046LTfHLVJc8LRpwDFzjsNsLh8+wn62F1CUb7nU77PZzFDuGbiiqZxSHTwUCkGxed5pOrLnluKC5DjwHt4QKH3/69CSoL8uthhQlE+51O+z2cxQ7hm4oqmcUh08FApBsXneaTq655vjB7NloNT4MLHEZe04u8ugSj/U6n/R7OYofwTUWVzOKQ6WAg0o2LTvPJxcjz0tuuggscmox2+Pg/dxNXl2C03+m038NZ7BC+qaiSWRwyHQxEkQgqJ0zAomuu0Ucqkmg+uRh5Fm0px+H/2BcucDj0H+koXbWCuMIEov1Op/0ezmKH8E1FlczikOlg4FKeXMqTi5Xn9AWL0X5oI7jA4YYrOgOxGGmFiUXzyaU8w1nsEL6pqJJZHDIdDFzKk0t5cjHzvHrccLjAIS3T4c0HbiasLvFoPrmUZziLHcI3FVUyi0Omg4GoshIVb7+N2WPHIlJa6ns1SUHzycXMs7isAkf/4xC4wKHLzQ5Fny8grDCBaL/Tab+Hs9ghfFNRJbM4ZDoYiPTLFXSaTy52nu9+sQK/GtwELnC45IoOQEUF5XETgvY7nfZ7OIsdwjcVVTKLQ6aDgUg3LjrNJ1d95HnjIw8gLbPqU6teyLyY9rjmab/Tab+Hs9ghfFNRJbM4ZDoYiHTjotN8ctVHnqWRShx/42/hAoc9b3FY99FbtMc2TfudTvs9nMUO4ZuKKpnFIdPBQKQbF53mk6u+8vz427XocnNLuMDhj1fuhlgqvF2T9jud9ns4ix3CNxVVMotDpoOBSDcuOs0nV33mOfSpp9BkdNVLAB4b9Hv645uj/U6n/R7OYofwTUWVzOKQ6WAg0o2LTvPJVZ95llVU4uRBp8MFDq2HO6yY9gz9OUzRfqfTfg9nsUP4pqJKZnHIdDAQ6cZFp/nkqu88P1tVgG4D2sEFDr+7pikqC/Lr5XlM0H6n034PZ7FD+KaiSmZxyHQwEJWXo/Kuu7D0sssQKS72vZqkoPnkaog8M6a8hpYj0uACh7uuPazensc77Xc67fdwFjuEbyqqZBaHTAcDl/LkUp5cDZFnpDKKU4deAhc4NB3lsPipcfX2XL5pPrmUZziLHcI3FVUyi0Omg4FLeXIpT66GynPZ2iL0/Mc+cIFD7+vTUb7qu3p9Pl80n1zKM5zFDuGbiiqZxSHTwUBUWYmKOXPw/rhx+khFEs0nV0Pmefd/P0DbYelwgcMtV+4PxGL1/pwNSvudTvs9nMUO4ZuKKpnFIdPBQKRfrqDTfHI1ZJ4VlVGcPupGuMAhPcPhw/GD6/05G5T2O532eziLHcI3FVUyi0Omg4FINy46zSdXQ+f5zfrNOOz6X8MFDgfelIbNSxc0yPM2CO13Ou33cBY7hG8qqmQWh0wHA5FuXHSaTy4feU54ZwE6DmkCFzhcdfmeQEVFgz13vdJ+p9N+D2exQ/imokpmcch0MBDpxkWn+eTykWc0GsOfxo6BC6o+tWpacEmDPXe90n6n034PZ7FD+KaiSmZxyHQwEOnGRaf55PKV5/f5xeh7fV+4wGHvwQ55H73doM9fL7Tf6bTfw1nsEL6pqJJZHDIdDES6cdFpPrl85jlx1hfYb2ALuMDhvCtaIVZS0uBroNJ+p9N+D2exQ/imokpmcch0MBDpxkWn+eTymWc0GsO59z2ExqOrXgLw1OA/NPgaqLTf6bTfw1nsEL6pqJJZHDIdDETl5agcNQrL/vxnfaQiieaTy3eeqzduwRE3nAIXOOx+q8Oqac96WQeF9jud7/m0zmKH8E1FlczikOlg4FKeXMqTy0KeWR+vwEE3toULHH5/VVNEC/K9raWuLOSZTJRnOIsdwjcVVTKLQ6aDgUt5cilPLgt5xmIxXPjQM2g+Mg0ucBh/3eHe1lJXFvJMJsoznMUO4ZuKKpnFIdPBQBSNIrJwId598EFEysp8ryYpaD65rOT5Q1EpjrzpArjAoflIhy+eut/rempF+53OynxaZbFD+KaiSmZxyHQwEOmXK+g0n1yW8nz50xwccsPecIHD4dc1QmTVd76XVDPa73SW5tMiix3CNxVVMovotCsaAAAgAElEQVRDpoOBSDcuOs0nl6U8Y7EYLn38VbS5NR0ucBh95QFANOp7WdWn/U5naT4tstghfFNRJbM4ZDoYiHTjotN8clnLM29zGY4cfA1c4NAow+GTcTf7XlL1ab/TWZtPayx2CN9UVMksDpkOBiLduOg0n1wW8/zv4rU49B9d4QKHbgPSULLgE99Lqh7tdzqL82mJxQ7hm4oqmcUh08FApBsXneaTy2qeVz89Ex2GNoELHP5xSXugtNT3knZN+53O6nxaYbFD+Kaiuo2vvvoKZ511Fjp06IDWrVvj2GOPxcyZM6v9/RaHTAcDkW5cdJpPLqt5FpZEcMTIUXBB1adWvTX4HN9L2jXtdzqr82mFxQ7hm4rqNrp27YozzzwTixYtwvLly3H99dejZcuWyM3Nrdb3WxwyHQxEunHRaT65LOf54dd5OHjAkXCBQ6dBDhv++5LvJYXTfqezPJ8WWOwQvqmo/kJeXh6cc5g1a1b8zzZt2gTnHN55551qPYbFIdPBQFRejspBg7D8nHP0kYokmk8u63mOenU+9h6yG1zgcNElzYG8PN9L2jntdzrr8+mbxQ7hm4rqL8RiMXTv3h1XXXUViouLUVFRgXHjxmGvvfbCxp38bbqsrAxFRUXxKycnB8455OfnIxKJmLhKSkqQnZ2NkpIS72tJhkt5Kk/Ll/U8N5eU4tg7J6BRRtVLALIu64tIebn3dSVqnol2Kc/wKz8/X0V1Gyqq21i9ejX69u2LtLQ0NGrUCPvssw8WLly406/PzMyEc267KysrC9nZ2bp06dKla5vrn89lo+vN/wMXOLQb5vDmgMu9r0mXLgtXVlaWiuo2UqKo7qxM/vKaN28eYrEYzjrrLJxxxhn48MMP8emnn+K6665Dp06dsHbt2h0+tn6immJXWRm2fPEF3vzXv1CyebP/9STBpflMzTwffGcp9hncAS5wOO1v6ShfutT7mra7tN/pV6LMp69LP1HdXkoU1by8PCxbtiz0Ki0txTvvvIP09PTtBqRr16646667qvVcFl9fEonoNUE0+uUKOs0nV6LkWRmN4YwHn0XTUWlwgcODF3QGrK1Z+50uUebTF4sdwreUKKrV9dprryE9PR2bN2/e6s+7deuGO+64o1qPYXHIdDAQ6cZFp/nkSqQ8czaUoNvQS+ECh+YjHZaO+rvvJW1N+50ukebTB4sdwjcV1V/Iy8tDhw4dcN555+Gzzz7DV199hSFDhqBJkyb47LPPqvUYFodMBwORblx0mk+uRMtz6qersN+gA+ECh97XOpR98K7vJf1M+50u0eazoVnsEL6pqG5j3rx5OO2009C+fXu0bt0aRx99NGbMmFHt77c4ZDoYiHTjotN8ciVanrFYDJc/9SZaD6/61KqBF7QBCgt9L6uK9jtdos1nQ7PYIXxTUSWzOGQ6GIh046LTfHIlYp4bS8rRa/TI+KdWvX31Kb6XVEX7nS4R57MhWewQvqmoklkcMh0MRLpx0Wk+uRI1z9nL83DAzcfABQ6/GuyQ/+zjvpek/V4PEnU+G4rFDuGbiiqZxSHTwUCkGxed5pMrkfMckT0PHYe0gQsczrmkMWLff+93QdrvdIk8nw3BYofwTUWVzOKQ6WAgKitD5bXXYsUZZyCyzbtDSO1oPrkSOc/SSCWOvvtRNB5d9RKAxy/qBlRW+luQ9jtdIs9nQ7DYIXxTUSWzOGQ6GLiUJ5fy5Er0PD9fU4SDBv8vXODQcoTDV3cO9rqeRM/TGuUZzmKH8E1FlczikOlg4FKeXMqTKxnyfHzWN+g8cF+4wOGIa9IQmfuxt7UkQ56WKM9wFjuEbyqqZBaHTAcDUSyGyJo1mPHUU4iUl/teTVLQfHIlQ56xWAwX/Os1tBreGC5wGH5Be8DH//Wu/U6XDPNZnyx2CN9UVMksDpkOBiL9cgWd5pMrWfJcv6kMPUYOgQsc0jIdPrj2jIZfhPY7XbLMZ32x2CF8U1ElszhkOhiIdOOi03xyJVOe7325DvsP7AsXOOw30GHjsxMbdgHa73TJNJ/1wWKH8E1FlczikOlgINKNi07zyZVseY54ZS72GNoKLnD480WNEfv224Z7cu13umSbTzaLHcI3FVUyi0Omg4FINy46zSdXsuVZVlGJY+/9JxplVL1l1dPnHgQ01P827Xe6ZJtPNosdwjcVVTKLQ6aDgUg3LjrNJ1cy5vn1uk044JZz4QKH1sMdVoz8R8M8sfY7XTLOJ5PFDuGbiiqZxSHTwUCkGxed5pMrWfN85v9WYO8hVW9ZdeyVDhXvvl3/T6r9Tpes88lisUP4pqJKZnHIdDAQ6cZFp/nkStY8Y7EY/vLEa2gxsuotq4J+rYG8vPp9Uu13umSdTxaLHcI3FVUyi0Omg4GorAzRv/4VK08+WR+pSKL55ErmPDeWlOOQzMFwgUOjDIcPLz4OiMXq7wm13+mSeT4ZLHYI31RUySwOmQ4GLuXJpTy5kj3POd/kY58hR8AFDp1vdtjw0Lh6fb5kz7OhKc9wFjuEbyqqZBaHTAcDl/LkUp5cqZDn2P/OR/thbeACh/MvSkds0aJ6e65UyLMhKc9wFjuEbyqqZBaHTAcDUSyGyMaNmDZ5sj5SkUTzyZUKeVZURvH78RPRKCMNLnB4tN+vgJIS/hNpv9OlwnzWhcUO4ZuKKpnFIdPBQKRfrqDTfHKlSp5rNm7BgcMvhQscmo90WHrDhfwn0X6nS5X5rC2LHcI3FVUyi0Omg4FINy46zSdXKuX59hdr8ashXeECh57XOWyZksV9Au13ulSaz9qw2CF8U1ElszhkOhiIdOOi03xypVqew7NnofXwZnCBw3XnNgNWreI9uPY7XarNZ01Z7BC+qaiSWRwyHQxEunHRaT65Ui3PSGUUv7vvXrig6iNWp57bHaio4Dy49jtdqs1nTVnsEL6pqJJZHDIdDES6cdFpPrlSMc9VBSU4cNjpcIFDu2EOq0YN4Dyw9jtdKs5nTVjsEL6pqJJZHDIdDES6cdFpPrlSNc9pi1ei4y17wwUOx1/hUPnWG3V/UO13ulSdz+qy2CF8U1ElszhkOhiIdOOi03xypXKeA16cgeYjG8EFDpln7gbk5tbtAbXf6VJ5PqvDYofwTUWVzOKQ6WAgKi1F9LzzsPrYYxHZtMn3apKC5pMrlfMsr4jiyLuHwwUO6RkO759zOFBZWfsH1H6nS+X5rA6LHcI3FVUyi0Omg4FLeXIpT65Uz3Nlfgn2HXYMXOCw30CHgmBYnR4v1fNkU57hLHYI31RUySwOmQ4GLuXJpTy5lCcwdcFytL21LVzgcO6fHWIzZ9b6sZQnl/IMZ7FD+KaiSmZxyHQwcClPLuXJpTyrXP/ilPhHrD70+zbAunW1ehzlyaU8w1nsEL6pqJJZHDIdDET65Qo6zSeX8qxSURnF4fdcCxc4NBvlMP/so4FotGYPov1Op/kMZ7FD+KaiSmZxyHQwEOnGRaf55FKeP8stLMGvRvSGCxx+PcCh6I7Mmj2A9jud5jOcxQ7hm4oqmcUh08FApBsXneaTS3lu7c0vlqP18FZwgcNFF6QhNmtW9b9Z+51O8xnOYofwTUWVzOKQ6WAg0o2LTvPJpTy3N+zVF5GeUfURq//8/e5Afn71vlH7nU7zGc5ih/BNRZXM4pDpYCDSjYtO88mlPLcXi8Vw3P1/j79edd55x1Xv9ara73Saz3AWO4RvKqpkFodMBwORblx0mk8u5bljhVvKsO/IXnCBQ7cbHArvHbvrb9J+p9N8hrPYIXxTUSWzOGQ6GIh046LTfHIpz537vxXfoc2Pr1e94JIm+PitJ5BbHPIxq9rvdJrPcBY7hG8qqmQWh0wHA1FpKaJnnIHcvn31kYokmk8u5RnuzrdfRvtx7dBjUg/0fLInej/ZG1OXT93xF2u/02k+w1nsEL6pqJJZHDIdDFzKk0t5cinPcLnFueg5qSd6Pvnz1fup3jv9yary5FKe4Sx2CN9UVMksDpkOBi7lyaU8uZRnuE/WfrJVSf3pmps7d4dfrzy5lGc4ix3CNxVVMotDpoOBS3lyKU8u5RkutzgXvZ/qvXVR/U8PrM5+bodfrzy5lGc4ix3CNxVVMotDpoOBqLgYsZYtUdGsmX65gkTzyaU8d23q8qnxstpjUg+0u68dHjmmBfD991t/ofY7neYznMUO4ZuKKpnFIdPBQKTfAqbTfHIpz+rJLc7F3Ny5uDjrBrjAoflIh1nHHQyUlf38RdrvdJrPcBY7hG8qqmQWh0wHA5FuXHSaTy7lWTPRWBQ97jkSLnD49QCHFZdf9vO/1H6n03yGs9ghfFNRJbM4ZDoYiHTjotN8cinPmvth83q0zWgLFzicd6FD4cQnq/6F9jud5jOcxQ7hm4oqmcUh08FApBsXneaTS3nWzrvffoRGGelwgcNdv2uMss8Wa7/XA81nOIsdwjcVVTKLQ6aDgUg3LjrNJ5fyrL0x79wHFzg0ynB4ue/eiOXmar+TaT7DWewQvqmoklkcMh0MRCqqdJpPLuVZe7FYDKf/qx9c4LD3YIdZfzhZ+51M8xnOYofwTUWVzOKQ6WAg2rIF0RNOQF6PHogY+m+cyDSfXMqzborLi7H/7fvBBQ4nXO6w+Ld9UXjSQYis/tL30pKC5jOcxQ7hm4oqmcUh08HApTy5lCeX8qy7L/O+RMuMpnCBw5CMJkBmG8SCtsCnT/leWsLTfIaz2CF8S6mievvtt+OYY45BixYtsPvuu+/wa1auXIl+/fqhZcuW6NChAwYMGIDy8vJqP4fFIdPBwKU8uZQnl/LkeOGTR+ECBxc4TM1sAWS2AYJ2QOFq30tLaJrPcBY7hG8pVVQzMjLwwAMPYNCgQTssqpWVlejZsydOPvlkLFiwAG+//Tb22Wcf3HDDDdV+DotDpoOBS3lyKU8u5Umy4gMMyqz6qWrrTIevMnerKqsrZvleWULTfIaz2CF8S6mi+pNJkybtsKjOmDED6enpWLNmTfzPnn/+eTRr1qzaQ2NxyHQwEBUXI7bHHihr00a/XEGi+eRSniSFqxEJdsfvMhvBBQ69MtNRnNEakQ2rfK8soWk+w1nsEL6pqP7C6NGj0bt3763+bMOGDXDOYebMmdV6bItDpoOBSL/1T6f55FKeRHMex5rRu2GvzDS4wOGv/dPwwjUjEYvFfK8sYWk+w1nsEL6pqP7C1VdfjT/84Q/b/XnTpk2RlZW1w8cqKytDUVFR/MrJyYFzDvn5+YhEIiaukpISZGdno6SkxPtaEv7auDFeVEvWr/e/niS4NJ/K0+y1cSPQOg3v/TYd6T+W1QlHpeOZB573v7YEvTSf4Vd+fr6K6jYSvqhmZmbCORd6zZs3b6vvYRbVnT1/VlYWsrOzdSXZNW3y5HhRnTZ5svf16NKlq/6uX+73yx++GC5waDzaIfvg1rjt3ie9r09X8l1ZWVkqqttI+KKal5eHZcuWhV6lpaVbfQ/z//rXT1RT7NJPVOmX5lN5mr1+sd+L163DBc+eAxc47DXEYdrB3fDWgu/9rzHBLs1n+KWfqG4v4Ytqbezql6lyc3PjfzZ58mT9MpX8TK9RpdN8cilPom32e3F5MXr9v25wgcNvr3J44rd/xKIcnQM1ofkMZ7FD+JZSRXXlypVYuHAhxowZg1atWmHhwoVYuHAhNm/eDODnt6c65ZRTsGDBArzzzjvYd9999fZU8jMVVTrNJ5fyJNrBfv+m4Bu0G9sKLnDof5bD6POGYEVeseeFJg7NZziLHcK3lCqql1122Q5fT/ree+/Fv2blypX44x//iBYtWqB9+/YYMGAAysrKqv0cFodMBwPRli2I9u2LDV276iNUSTSfXMqTaCf7/Y2v30BaZtWHATx0ZDquuu5h5BaWhjyQ/ETzGc5ih/AtpYpqQ7A4ZDoYuJQnl/LkUp5cO8vzrll3wgUOTUY7TOvWGhdmTEFBcfU/xTBVaT7DWewQvqmoklkcMh0MXMqTS3lyKU+uneUZi8Xwv1nnwgUOew92eOvAA3D+/e9gc1mFp5UmBs1nOIsdwjcVVTKLQ6aDgUt5cilPLuXJFZbn5vLN6Dm+6perju7v8GLP43HRY3NQGqn0sNLEoPkMZ7FD+KaiSmZxyHQwEJWUINalC0r23BORwkLfq0kKmk8u5UlUjf3+TcE3aHt71S9XXf0nh7tPvAz9n5yHispoAy82MWg+w1nsEL6pqJJZHDIdDET6rX86zSeX8iSq5n5//evXkRZUfXLVI30drjx/NG58fgEqo/qo1W1pPsNZ7BC+qaiSWRwyHQxEKqp0mk8u5UlUg/1+54+/XNV4tMPrXZvi1Cv/iYEvLFRZ3YbmM5zFDuGbiiqZxSHTwUCkokqn+eRSnkQ12O+xWAwXvXghXODQYajDrM57oM+NWbhlymeIqqzGaT7DWewQvqmoklkcMh0MRCqqdJpPLuVJVMP9viWyBUc8chhc4NDjeoe3uvbAQUOycevURSqrP9J8hrPYIXxTUSWzOGQ6GIhUVOk0n1zKk6gW+3110Wr86u494QKHfhc7PP2b09Fl6DSMfGUxYjGVVc1nOIsdwjcVVTKLQ6aDgUhFlU7zyaU8iWq53z9Z/Qmaj2kKFzgMPdXhtt9fhS7DpiMje0nKl1XNZziLHcI3FVUyi0Omg4GopASx7t1RtN9+ensqEs0nl/IkqsN+z1qcBRdUfczqpMMcrj5vFLoMm45hLy1K6V+w0nyGs9ghfFNRJbM4ZDoYuJQnl/LkUp5cdclz5Dsj4AKHpqMcPjioKf50+Xh0GTYdNz6/AJEUfZ9VzWc4ix3CNxVVMotDpoOBS3lyKU8u5clVlzyjsSjOzTobLnDoOMThqwP2wHH/eApdhk3HVU/NQ1lF6n2CleYznMUO4ZuKKpnFIdPBwKU8uZQnl/Lkqmuem8s3o8/DPeEChz7XOqzteQgOG/ISugybjksnfowt5alVVjWf4Sx2CN9UVMksDpkOBiK9RpVO88mlPIlI+/37jd+j490d4AKHsy9yWH/Sqegxcjq6DJuO/310DjaVps5/K81nOIsdwjcVVTKLQ6aDgUi/9U+n+eRSnkTE/f7Rqo/Q7LaqdwIY+D8OP1x+DXpmvoEuw6bj9PGz8ENRKWnRtmk+w1nsEL6pqJJZHDIdDEQqqnSaTy7lSUTe788veT7+TgAPH+mwZuy96Dv2bXQZNh3H3vUuvl63ibBo2zSf4Sx2CN9UVMksDpkOBiIVVTrNJ5fyJKqH/X7HrDvgAof0DIfpB6dh/XNTcPK499Bl2HT0Dt7EvO8KKM9jleYznMUO4ZuKKpnFIdPBQKSiSqf55FKeRPWw32OxGK7MvgIucNhthMOCLs1QOHMWzvnnh+gybDq6jZyB15fkUp7LIs1nOIsdwjcVVTKLQ6aDgUhFlU7zyaU8ieppv0cqIzjlyd/DBQ77DHLI6dwWpUu+QP8n56HLsOnY/9bpeOz9b5LyU6w0n+EsdgjfVFTJLA6ZDgYiFVU6zSeX8iSqx/2+sXQjDn3okPjbVm3q2hkVq9dgxMuL0WVY1TsCDHrhs6R7r1XNZziLHcI3FVUyi0Omg4GopASxLl1QsueeensqEs0nl/Ikquf9/t3G77DXPXvCBQ6nX+JQcfhhiBUVYdKHK3DArVVl9dx/foh1m5LnHQE0n+EsdgjfVFTJLA6ZDgYu5cmlPLmUJ1d95zl39Vy0GNscLnD4ez+H2Gl/AMrLMWv5evT68e2rjrnzHSxZnRx/MdZ8hrPYIXxTUSWzOGQ6GLiUJ5fy5FKeXA2R5yvLXkFakAYXOIw9wQF//SsQi+Hb9Zvj7whw8KgZmDI/p97W0FA0n+EsdgjfVFTJLA6ZDgYu5cmlPLmUJ1dD5fngxw/G32P134c7YPhwAEBhSQR/feKT+OtWh05ZhNJI4r5uVfMZzmKH8E1FlczikOlgINqyBdG+fbGha1dEDP03TmSaTy7lSdTA+334O8Pj77H6WjcHTJgAAKiMxjD+7eXY/8fXrZ4+fhZW5BXX+3rqg+YznMUO4ZuKKpnFIdPBQKTf+qfTfHIpT6IG3u+xWAyXvXIZXODQYqTDnH0d8PTT8X8/e3keDr/tLXQZNh09Mt7A9EVr631NbJrPcBY7hG8qqmQWh0wHA5GKKp3mk0t5EnnY75HKCM589ky4wKH9UIdlHdOBV1+N//vcwlJc8OhHW72F1abSxPlvrfkMZ7FD+KaiSmZxyHQwEKmo0mk+uZQnkaf9XlxejKMePwoucOh8s8OaDk2B996L//tIZRT3vL4s/hZWx939Lj5ZkRgfvar5DGexQ/imokpmcch0MBCpqNJpPrmUJ5HH/Z5XkoduD3aDCxx6XeewcY9WwLx5W33N3O8KcNzd78Y/zequGcvM/6KV5jOcxQ7hm4oqmcUh08FApKJKp/nkUp5Envf7ig0rsPe4veEChxMvd9jSsT3wxRdbfc2m0giGvPhZ/KUAJ417D3O+yW/wtVaX5jOcxQ7hm4oqmcUh08FApKJKp/nkUp5EBvb7wtyFaH1na7jA4U8XO0T26wR8//12X/fG0lwcefvbW72N1caScg8rDqf5DGexQ/imokpmcch0MBAVFyO2xx4oa9NGRZVE88mlPImM7Pf3v3sfzX/89Kq/nOcQ/XVXYO32v/FfVBrByFcWx8tq37Fv4YW5q1AZjXlY9Y5pPsNZ7BC+qaiSWRwyHQxcypNLeXIpTy4reU7/ajoaj2kMFzhc+0eH2KHdgXXrdvi1874rwKn3vx8vrGdOmIWPv7XxcgAreVplsUP4pqJKZnHIdDBwKU8u5cmlPLks5Tl5yeT4R60OO9UBvXoB+TsuoOUVUfx71rfomflGvLBe+8x8fLt+cwOvemuW8rTIYofwTUWVzOKQ6WDgUp5cypNLeXJZy/Px+Y/HP2r1zt854De/ATZs2OnX528uw8hXFsffyuqAW6dj4AsL8Z2nT7aylqc1FjuEbyqqZBaHTAcD0ZYtiJ5wAvJ69NBHqJJoPrmUJ5HR/T7uo3HxsvrwkQ446ihgF+v7MncT+j85N/7T1QOH/xeDX/yswX/CqvkMZ7FD+KaiSmZxyHQwEBn4LeBko/nkUp5Ehvf7qHdHxcvqU30ccOyxwOZdl85FORtxxaSfC2uXYdNx5aS5+PDrPMRi9f9LV5rPcBY7hG8qqmQWh0wHA5HhG1ei0nxyKU8iw/s9FothwIwBcIFDeobDc70ccMIJVWuuhoWrNqL/k3Ox/60/F9bTHvgAT8xegYLi+ntbK81nOIsdwjcVVTKLQ6aDgcjwjStRaT65lCeR8f0ejUVx1atXxcvq5B4OOPnkapdVAFiRV4yM7CXoPvr1eGHtOuK/+PvT8/HG0lz6J11pPsNZ7BC+qaiSWRwyHQxExm9ciUjzyaU8iRJgv0djUVyRfQVc4NAow2HKoQ44/nhg06YaPU5hSQRPfvQd/vjgrK1eFnDIqNfx96fn4+UFOVi/qazO69V8hrPYIXxTUSWzOGQ6GIgS4MaVaDSfXMqTKEH2e2W0En975W9wgUPj0Q4vH+KAY44BCgtr9XhfrC3CbdM+x7F3vbtVae0ybDpOvf99jHplCV79bA2+Wb+5xh8moPkMZ7FD+KaiSmZxyHQwECXIjSuRaD65lCdRAu33ymglLn350nhZffVgBxx5ZOhbV+1KLBbDktWFuO/NL3H6+FnbldaffuJ69sMfYuDkhbjvzS+R9clKzFy2DvO+K8AXa4uwqqAEazZuwff5xfh63WYsXlWA+5/ORsGmEuL/+uRhsUP4pqJKZnHIdOMiKi5GrGVLVDRrZv7GlSg0n1zKkyjB9ntltBIXv3QxXODQZLTDtG4OOOwwIC+P8vgbisvx+pJcZL66FGc9/CEOHjVjh+W1OteHy3+grCnZWOwQvqmoklkcMt24uJQnl/LkUp5ciZZnRbQCF065EC5waDra4bVuP36C1U4+brUuKqMxfL1uM6YtWoNH3vsGI19ZjCsmzcUZ42fhhHtnou/Yt3DwqBn49YgZ6D76dfQO3kTfsW/hiMxpmP2ViuqOWOwQvqmoklkcskQ7aK1TnlzKk0t5ciVinpHKCC548YL4ywCmHOqAgw8GVq70vbSEzLMhWewQvqmoklkcMh0MXMqTS3lyKU+uRM2zIlqBv0z9S/ytq57p7YD99gOWLfO6rkTNs6FY7BC+qaiSWRwyHQxEpaWInnEGcvv2RaSGb/8iO6b55FKeRAm+3yujlbgy+0q4wCEt0+Hfhztgjz2A+fO9rUnzGc5ih/BNRZXM4pDpYCBKoN8CThSaTy7lSZQE+z0ai+L66dfHP271waMc0Lo18N57Xtaj+QxnsUP4pqJKZnHIdDAQJcGNyxrNJ5fyJEqS/R6LxTD4zcHxsnrPcQ5o1gx49dUGX4vmM5zFDuFbShXV22+/HccccwxatGiB3Xfffbt//9lnn+Giiy7Cvvvui+bNm+OQQw7B+PHja/QcFodMBwNRkty4LNF8cilPoiTa77FYDKNnjo6X1eGnOMQapQOTJjXoOjSf4Sx2CN9SqqhmZGTggQcewKBBg3ZYVJ944gnceOONeP/99/Htt9/imWeeQYsWLfDQQw9V+zksDpkOBqIkunFZofnkUp5ESbjf75p9V7ys9j/LoSLdAWPGALGafcJUbWk+w1nsEL6lVFH9yaRJk3ZYVHfk+uuvx8knn1ztx7Y4ZDoYiJLwxuWb5pNLeRIl6X7/96f/RvqYdLjA4Zw/O2xp7IArrwQaYGY0n+EsdgjfVFR34ZJLLsH5559f7ce2OGQ6GIiS9Mblk+aTS3kSJfF+f/mLl9FsbDO4wOGEKxwKmzngtNOAer53aT7DWewQvqmohpgzZw6aNGmCt956a6dfU1ZWhqKioviVk5MD5xzy8/MRiURMXCUlJcjOzkZJSYn3tST8tXFj/MZVsn69//UkwaX5VJ5mryTf729//Tba3NUGLnDoc10a1hrYhZUAAA3ESURBVLZyiPXqhch339Xbc2o+w6/8/HwV1W0kfFHNzMyEcy70mjdv3lbfU52iunTpUuy5554YO3ZsrZ4/KysL2dnZunTp0qVLl9nrgawH0Pb2tnCBw/4D07G8vcOWDh0wc/x472tLxSsrK0tFdRsJX1Tz8vKwbNmy0Ku0tHSr79lVUf3888/RsWNHjBgxYpfPr5+opt6lPJWn5Ut5Ks+aXsvWLcOB4w+ECxzaD0/HrM4OsVatUPHSS8qzgS/9RHV7CV9UayOsqC5duhQdO3bELbfcUqvHtvj6kkhErwliUp5cypNLeXKlSp4/bP4BR/37KLjAoWlGGp7t5YC0NOCOO6jvCJAqedaWxQ7hW0oV1ZUrV2LhwoUYM2YMWrVqhYULF2LhwoXYvHkzAGDJkiXYc889cemllyI3Nzd+rV+/vtrPYXHIdDBwKU8u5cmlPLlSKc+SSAnOe+G8+NtXjTnRIeYccPHFwJYtlOdIpTxrw2KH8C2liupll122w9eTvvfjR8nt7PWmXbp0qfZzWBwyHQxcypNLeXIpT65UyzMai+KWt26Jl9W/nZeG8kYO6NsXWL26zo+fannWlMUO4VtKFdWGYHHIdDBwKU8u5cmlPLlSNc/H5j2GRmMawQUOJ17VGPktHLD33sDs2XV63FTNs7osdgjfVFTJLA6ZDgYu5cmlPLmUJ1cq5/nG12+g9Z2t4QKHA4Y0weKODmjUCLj//lq/bjWV86wOix3CNxVVMotDpoOBS3lyKU8u5cmV6nkuWbcEB06oekeA3TIa46XuVe8ri/PPr9WHA6R6nrtisUP4pqJKZnHIdDBwKU8u5cmlPLmUJ1CwpQCnPn1q/HWrI09NRzTNAd26AUuW1OixlGc4ix3CNxVVMotDpoOBS3lyKU8u5cmlPKtURCsw+M3B8bLa78rmVR+72rIlMGlStV8KoDzDWewQvqmoklkcMh0MXMqTS3lyKU8u5bm1ZxY9g+a3N4cLHLoOa4nP9vrxpQAXXQRs3LjL71ee4Sx2CN9UVMksDpkOBi7lyaU8uZQnl/Lc3vw189H5/3WGCxyaBY3xryPTq95vtUuXXb4rgPIMZ7FD+KaiSmZxyHQwcClPLuXJpTy5lOeOFWwpQL+sfvGXAvzlslbY3NQB6elAZiZQUbHD71Oe4Sx2CN9UVMksDpkOBi7lyaU8uZQnl/LcuWgsins+vCf+fquHjNgdSzr++FKAY44Bvvpqu+9RnuEsdgjfVFTJLA6ZDgYu5cmlPLmUJ5fy3LXZK2ej0/2d4AKH5mOa4OHjm1e9FKB5c+C++4DKyvjXKs9wFjuEbyqqZBaHTAcDl/LkUp5cypNLeVbP+uL1OP3Z0+MvBTj9pg5Y2+rHn64efTSwbBkA5bkrFjuEbyqqZBaHTAcDl/LkUp5cypNLeVZfNBbFhI8nxN8VoMNtrfDy4S2qymqzZsA99yCyZYvyDGGxQ/imokpmcch00HIpTy7lyaU8uZRnzX2+/nMc9thh8Z+uXnF9J2xqWvXT1dhvfoP37rtPee6ExQ7hm4oqmcUh00HLpTy5lCeX8uRSnrVTXlmOYW8PQ1qQBhc4dB7bAW/02a2qrKano2LiRN9LNMlih/BNRZXM4pDpoOVSnlzKk0t5cinPuvng+w9wwPgD4j9dvfzmA7CubXNEvvvO99JMstghfFNRJbM4ZDpouZQnl/LkUp5cyrPuisuLcdPrN8V/utrutt3x+lev+16WSRY7hG8qqmQWh0wHLZfy5FKeXMqTS3nyfLjyQ3R7sBvSg3R89P1HvpdjksUO4ZuKKpnFIdNBy6U8uZQnl/LkUp5cm7ZswqinRynPnbDYIXxTUSWzOGQ6aLmUJ5fy5FKeXMqTS3mGs9ghfFNRJbM4ZDoYuJQnl/LkUp5cypNLeYaz2CF8U1ElszhkOhi4lCeX8uRSnlzKk0t5hrPYIXxTUSWzOGQ6GLiUJ5fy5FKeXMqTS3mGs9ghfFNRJbM4ZDoYuJQnl/LkUp5cypNLeYaz2CF8U1ElszhkOhi4lCeX8uRSnlzKk0t5hrPYIXxTUSWzOGQ6GLiUJ5fy5FKeXMqTS3mGs9ghfFNRJbM4ZDoYuJQnl/LkUp5cypNLeYaz2CF8U1ElszhkOhi4lCeX8uRSnlzKk0t5hrPYIXxTUSWzOGQ6GLiUJ5fy5FKeXMqTS3mGs9ghfFNRJbM4ZDoYuJQnl/LkUp5cypNLeYaz2CF8U1ElszhkOhi4lCeX8uRSnlzKk0t5hrPYIXxTUSWzOGQ6GLiUJ5fy5FKeXMqTS3mGs9ghfFNRJbM4ZDoYuJQnl/LkUp5cypNLeYaz2CF8U1ElszhkOhi4lCeX8uRSnlzKk0t5hrPYIXxTUSUrLCyEcw45OTkoKioyceXn5yMrKwv5+fne15IMl/JUnpYv5ak8LV/KM/zKycmBcw6FhYW+64wZKqpkPw2ZLl26dOnSpUtXba6cnBzfdcYMFVWyaDSKnJwcFBYWev+b2bZ/Q7P0U95EvpSn8rR8KU/laflSnuFXYWEhcnJyEI1GfdcZM1RUU0BRkV7zwqQ8uZQnl/LkUp5cylNqSkU1Behg4FKeXMqTS3lyKU8u5Sk1paKaAnQwcClPLuXJpTy5lCeX8pSaUlFNAWVlZcjMzERZWZnvpSQF5cmlPLmUJ5fy5FKeUlMqqiIiIiJikoqqiIiIiJikoioiIiIiJqmoioiIiIhJKqoiIiIiYpKKqog0mFWrVuHEE09E9+7d0atXL7z44ou+l5TwGjVqhD59+qBPnz7o37+/7+WIxH355Zfx2ezTpw+aN2+OV155xfeyJMGoqCapZcuWoV27djjwwAPRp08f7LbbbjjxxBN9LyuhKdO6W7t2LRYuXAgAWLduHTp16oTi4mLPq0psHTp08L0EkV3avHkzOnTooP0uNaaimsROO+00LF68GABw0EEHobS01POKEp8y5erVqxdWrVqlvwTUwY6KqvKsu0MOOQTOuR1eEyZM8L28hPPcc8/hwgsvBKD5lJpRUU1i+++/P8rLy7Fp0yZ069bN93KSgjLlmTdvHnr06BH/Z/0loHaaNGmCww8/HMcddxzee++9+J8rz7r5/PPP4ZzDu+++i9zcXKxatQqNGzfGlClT9Gb1tXD22Wdj6tSp8X/WfEp1qagmqcLCQnTv3h0AMGfOHJxzzjmeV5T4lClPfn4+unfvjo8++ij+Z/pLQO2sWbMGALBkyRJ07twZhYWFAJRnXc2cORONGzeOl9KFCxfCOYcffvjB88oST1FREfbcc8+tyqjmU6pLRTVJzZkzB+effz4A4IknnsDQoUM9ryjxKVOOsrIyHH/88Xj66afjf6a/BHCcfvrpmDdvnvIkmDBhAg499ND4P0+aNAkdO3b0uKLE9fTTT+OSSy6J/7PmU2pCRTVJTZw4ERkZGQCAyZMno1evXigoKPC8qsSmTOsuFovhoosuQmZm5lZ/rr8E1M6GDRviP/HLyclB586dUVBQoDwJ+vfvjz//+c/xf77ppptwyimneFxR4urXrx9ee+21+D9rPqUmVFRFpMHMnj0baWlpW71lzeLFi/WXgFr66KOP0LNnT/Tu3Rt9+vSJv/WP8qy7I488EnfccUf8n0888UQMHDjQ44oSU2FhITp27Ijy8vL4n2k+pSZUVEVERH4hGo2iZcuWmDZtWvzP9ttvP4wfP97jqkRSk4pqktrZ26r8dEnNKVOR1LB8+XI457By5cr4n/Xr1w9t27bFBx984HFlIqlHd9cktmLFCpx00kno3r07evbsqTdariN9qlLd7ars6y8BNaM8xTLNpzBoIpLYCSecgFmzZgEACgoKUFFR4XlFiU2fqsS1adMmHHHEEejTpw969uyJxx9/3PeSEp7+ciqWaT6lNlRUk9TSpUv1G6r17KdPVZLaqaysRElJCQCgpKQEBxxwAPLz8z2vKrHpL6dimeZTakNFNUm98sorOPvss9GvXz/85je/2eq3V6Xutv1UJambgoICdO7cGXl5eb6XkrD0l1OxTPMptaWimqSmTJmC9u3bY9WqVSgrK8NJJ52Et956y/eyksKOPlVJamfjxo3o3bs3WrRogYcfftj3chKa/nIqlmk+pbZUVJPUnDlzcNppp8X/+d5778W9997rcUXJYUefqiR198MPP+DYY4/Vx1PWgf5yKpZpPqW2VFSTVEVFBQ477DBs2LAB0WgU/fr12+o9AaXmdvapSsJx3XXX6Z0U6kB/ORXLNJ9SWyqqSWzGjBno2bMnevTooU9UIdjZpypJ7fzwww8oKioCABQVFeHQQw/FokWLPK8qcekvp2KZ5lNqS0VVRLyYP38++vTpg969e6NXr1545JFHfC8p4ekvp2KZ5lNqQ0VVRERERExSURURERERk1RURURERMQkFVURERERMUlFVURERERMUlEVEREREZNUVEVERETEJBVVERERETFJRVVERERETFJRFRERERGTVFRFRERExCQVVRERERExSUVVRERERExSURURERERk1RURURERMQkFVURERERMUlFVURERERMUlEVEREREZNUVEVERETEJBVVERERETFJRVVERERETFJRFRERERGTVFRFRERExCQVVRERERExSUVVRERERExSURURERERk1RURURERMQkFVURERERMUlFVURERERMUlEVEREREZNUVEVERETEJBVVERERETHp/wPLGxHwseCOzwAAAABJRU5ErkJggg==\" width=\"682\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xa3a543cc>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "plt.plot()\n",
    "plt.grid()\n",
    "plt.title(r'Comparing meshs, $m=3$')\n",
    "N = 3\n",
    "x_view = np.linspace(np.pi/3, np.pi*7/6, 700)\n",
    "y = x_view*x_view*np.cos(x_view)\n",
    "plt.plot(x_view , y, label=r'$f(x) = x^2\\, \\cos x$')\n",
    "\n",
    "for m in range(3, 4):\n",
    "    roots = np.linspace(np.pi/2, np.pi, m+1)\n",
    "    value = roots*roots*np.cos(roots)\n",
    "    \n",
    "    y_view = lg(x_view, roots, value)\n",
    "\n",
    "    plt.plot(x_view , y_view,'r-', label='Unity mesh')\n",
    "    plt.plot(roots, value,'.')\n",
    "\n",
    "for m in range(3, 4):\n",
    "    roots = get_roots(np.pi/2, np.pi, m+1)\n",
    "    value = roots*roots*np.cos(roots)\n",
    "    \n",
    "    y_view = lg(x_view, roots, value)\n",
    "\n",
    "    plt.plot(x_view , y_view,'g-',label='Chebyshev`s roots')\n",
    "    plt.plot(roots, value,'.')\n",
    "\n",
    "plt.xticks(np.linspace(np.pi/3,np.pi*7/6,6), \n",
    "          (r'$\\frac{\\pi}{6}$' , r'$\\frac{\\pi}{2}$',r'$\\frac{2\\pi}{3}$',r'$\\frac{5\\pi}{6}$',r'$\\pi$',r'$\\frac{7\\pi}{6}$'))\n",
    "plt.vlines(np.pi, -12, 1.5, colors='r', linestyles='--')\n",
    "plt.vlines(np.pi/2, -12, 1.5, colors='r', linestyles='--')\n",
    "\n",
    "plt.legend()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xa5fe240c>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "plt.plot()\n",
    "plt.grid()\n",
    "plt.title(r'Comparing meshs, $m = 3$')\n",
    "N = 3\n",
    "x_view = np.linspace(np.pi/3, np.pi*7/6, 700)\n",
    "y = x_view*x_view*np.cos(x_view)\n",
    "#plt.plot(x_view , y, label=r'$f(x) = x^2\\, \\cos x$')\n",
    "\n",
    "for m in range(3, 4):\n",
    "    roots = np.linspace(np.pi/2, np.pi, m+1)\n",
    "    value = roots*roots*np.cos(roots)\n",
    "    \n",
    "    y_view = lg(x_view, roots, value)\n",
    "\n",
    "    plt.plot(x_view , y_view-y, label='Unity mesh')\n",
    "    plt.plot(roots, np.zeros_like(roots),'.')\n",
    "\n",
    "for m in range(3, 4):\n",
    "    roots = get_roots(np.pi/2, np.pi, m+1)\n",
    "    value = roots*roots*np.cos(roots)\n",
    "    \n",
    "    y_view = lg(x_view, roots, value)\n",
    "\n",
    "    plt.plot(x_view , y_view-y, label='Chebyshev`s roots')\n",
    "    plt.plot(roots, np.zeros_like(roots),'.')\n",
    "\n",
    "plt.xticks(np.linspace(np.pi/3,np.pi*7/6,6), \n",
    "          (r'$\\frac{\\pi}{6}$' , r'$\\frac{\\pi}{2}$',r'$\\frac{2\\pi}{3}$',r'$\\frac{5\\pi}{6}$',r'$\\pi$',r'$\\frac{7\\pi}{6}$'))\n",
    "plt.vlines(np.pi, -1, 1.5, colors='r', linestyles='--')\n",
    "plt.vlines(np.pi/2, -1, 1.5, colors='r', linestyles='--')\n",
    "plt.hlines(0, np.pi/3,np.pi*7/6, colors='black', linestyles='-')\n",
    "\n",
    "plt.legend(title = r'Error of intrepolation:')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, Chebyshev's roots gets less derivation from zerow, but in some changes we need to reduce $L_2$ norm:\n",
    "$$\n",
    "\\| L_2(g(x))\\| = \\int g^2 \\text{d}x\n",
    "$$\n",
    "Let compute this norm in our cases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "chebyshev`s roots:\n",
      "m= 1 e= 2.40e-01\n",
      "m= 2 e= 2.90e-02\n",
      "m= 3 e= 8.70e-04\n",
      "m= 4 e= 9.35e-07\n",
      "m= 5 e= 1.05e-07\n"
     ]
    }
   ],
   "source": [
    "x_view = np.linspace(np.pi/2, np.pi, 700)\n",
    "y = x_view*x_view*np.cos(x_view)\n",
    "dx = x_view[1] - x_view[0]\n",
    "print('chebyshev`s roots:')\n",
    "for m in range(1, 6):\n",
    "    roots = get_roots(np.pi/2, np.pi, m+1)\n",
    "    value = roots*roots*np.cos(roots)\n",
    "    y_view = lg(x_view, roots, value)\n",
    "    err = (y-y_view) @ (y-y_view) * dx \n",
    "    print( 'm=',m,'e=' ,'%.2e' % err) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "unity roots:\n",
      "m= 1 e= 8.61e-01\n",
      "m= 2 e= 7.20e-02\n",
      "m= 3 e= 1.66e-03\n",
      "m= 4 e= 1.93e-06\n",
      "m= 5 e= 2.17e-07\n"
     ]
    }
   ],
   "source": [
    "x_view = np.linspace(np.pi/2, np.pi, 700)\n",
    "y = x_view*x_view*np.cos(x_view)\n",
    "dx = x_view[1] - x_view[0]\n",
    "print('unity roots:')\n",
    "for m in range(1, 6):\n",
    "    roots = np.linspace(np.pi/2, np.pi, m+1)\n",
    "    value = roots*roots*np.cos(roots)\n",
    "    y_view = lg(x_view, roots, value)\n",
    "    err = (y-y_view) @ (y-y_view) * dx \n",
    "    print( 'm=',m,'e=' ,'%.2e' % err) \n"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "As u will see, chevyshev wins here too"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the conclusion I would like to notice that If we definde mesure 'goodness' of intrepolation as\n",
    "\n",
    "$$\n",
    "G_f[P_m](\\varepsilon) = \\mu^*(x : |f(x) - P_m(x)|>\\varepsilon), \\text{ where } \\mu^* \\text{- Lebeg's measure}\n",
    "$$\n",
    "we can observe fact, that chevyshev wins here too."
   ]
  }
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