machine learning/Linear Regression - Basics.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Table of Contents\n",
    "* [Intro](#Intro)\n",
    "\t* [Regression](#Regression)\n",
    "* [Data](#Data)\n",
    "* [Residuals and Cost](#Residuals-and-Cost)\n",
    "* [Regression (Scipy)](#Regression-%28Scipy%29)\n",
    "* [Polynomial Regression](#Polynomial-Regression)\n",
    "\t* [Solve (SKlearn)](#Solve-%28SKlearn%29)\n",
    "* [Gradient Descent](#Gradient-Descent)\n",
    "\t* [Training Animation](#Training-Animation)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intro"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exploratory notebook related to the theory and concepts behind linear regression. Includes toy examples implementation and visualization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regression is a supervised learning task concerned with the prediction of continuous numerical values. It contrasts with Classification, which is instead about the prediction of classes (categorical values)."
   ]
  },
  {
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    "ExecuteTime": {
     "end_time": "2017-09-13T16:17:21.507482",
     "start_time": "2017-09-13T16:17:16.330186"
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   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt, animation, rc\n",
    "\n",
    "%matplotlib notebook\n",
    "#%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-14T09:10:08.490817",
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    "# class for generic line defined by a slope and intercept\n",
    "class Line:\n",
    "    def __init__(self, slope, intercept):\n",
    "        self.slope = slope\n",
    "        self.intercept = intercept\n",
    "        self.line_fun = lambda x : x * self.slope + self.intercept\n",
    "        \n",
    "    # get linspaces sample in the specified interval\n",
    "    def get_sample(self, n, start=0.0, stop=1.0, noise=None):\n",
    "        x = np.linspace(start, stop, n)\n",
    "        y = self.get_y(x, noise=noise)\n",
    "        return (x, y)\n",
    "    \n",
    "    # get random sample in the specified interval\n",
    "    def get_rand_sample(self, n, start=0.0, stop=1.0, noise=None):\n",
    "        x = (stop-start) * np.random.random_sample(n) + start\n",
    "        y = self.get_y(x, noise=noise)\n",
    "        return (x, y)\n",
    "    \n",
    "    def get_y(self, x, noise=None):\n",
    "        y = self.line_fun(x)\n",
    "        if noise:\n",
    "            y += ((np.random.normal(scale=0.5, size=len(y)))*noise)\n",
    "        return y"
   ]
  },
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     "end_time": "2017-09-14T09:10:10.618939",
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       "\n",
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       "\n",
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       "\n",
       "\n",
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       "    var format_dropdown = fig.format_dropdown;\n",
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       "    fig.ondownload(fig, format);\n",
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       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
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       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
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       "\n",
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       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
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       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
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       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
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       "    // Updates the figure title.\n",
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       "\n",
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       "        cursor = 'pointer';\n",
       "        break;\n",
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       "        break;\n",
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       "        cursor = 'crosshair';\n",
       "        break;\n",
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       "    fig.rubberband_canvas.style.cursor = cursor;\n",
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       "\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",
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       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
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       "    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",
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       "                    fig.imageObj.src);\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",
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       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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01fbup+qakPDhcXEfDENDRcOPLjBDW7wghvcuDYNDRTAfOLLIlJ/2WWX/VXLT/i+/xXf9x9O/JiInCkoKPiLtjaqAAAAEDnSWTDAYXzf/4ExZo3t88aYvSLS2/M8T0QGGmMWpbJdVf66sv11hRvc4AYvuMGNi8MZwDzC9/3fiMhHiR8zxrwtIkWe53kicrmIrBeRHcaY5TwJJPj1FbjBDW7wghvcuDgnT1IAISCEyx4u3OAGN3jBDW5cHAogBIZw2cOFG9zgBi+4wY2LQwGEwBAue7hwgxvc4AU3uHFxKIAQGMJlDxducIMbvOAGNy4OBRACQ7js4cINbnCDF9zgxsWhAEJgCJc9XLjBDW7wghvcuDgUQAgM4bKHCze4wQ1ecIMbF4cCCIEhXPZw4QY3uMELbnDj4lAAITCEyx4u3OAGN3jBDW5cHAogBIZw2cOFG9zgBi+4wY2LQwGEwBAue7hwgxvc4AU3uHFxKIAQGMJlDxducIMbvOAGNy4OBRACQ7js4cINbnCDF9zgxsWhAEJgCJc9XLjBDW7wghvcuDgUQAgM4bKHCze4wQ1ecIMbF4cCCIEhXPZw4QY3uMELbnDj4lAAITCEyx4u3OAGN3jBDW5cHAogBIZw2cOFG9zgBi+4uXj2Hzqp40oqdURxuY4rqdT9h07iJstDAYTAEC57uHCDG9zgBTcXz7iSSh02dkV8xpVU4ibLQwGEwBAue7hwgxvc4AU3F8+I4vJmBXBEcTlusjwUQAgM4bKHCze4wQ1ecHPxcAYw/KEAQmAIlz1cuMENbvCCm4uHawDDHwogBIZw2cOFG9zgBi+4wY2LQwGEwBAue7hwgxvc4AU3uHFxKIAQGMJlDxducIMbvOAGNy4OBRACQ7js4cINbnCDF9zgxsWhAEJgCJc9XLjBDW7wghvcuDgUQAgM4bKHCze4wQ1ecIMbF4cCCIEhXPZw4QY3uMELbnDj4lAAITCEyx4u3OAGN3jBDW5cHAogBIZw2cOFG9zgBi+4wY2LQwGEwBAue7hwgxvc4AU3uHFxKIAQGMJlDxducJNPbjL59l5R9pLpwQ1uOuom7P4AEYdw2cOFG9zkk5txJZU6bOyK+IwrqcRLFgY3uOmom7D7A0QcwmUPF25wk09uRhSXNyuAI4rL8ZKFwQ1uOuom7P4AEYdw2cOFG9zkkxvOAIYzuMFNR92E3R8g4hAue7hwg5t8csM1gOFMPrlp7xrLJzftHQogBIZw2cOFG9zgBi+4Sd+09yxzPrlp71AAITCEyx4u3OAGN3jBTfqmvdeZ5pOb9g4FEAJDuOzhwg1ucIOXbLmpOpy5h+BdGc4ApnfdhN0fIAuIyN0iskVENovIFmPMad/330+8T7du3TobY8pFZJcxZnnnzp07pbJtwmUPF25wgxu8ZMtNcQafhOPKcA1getdNZhoHOEvPnj1FRA4WFBR8I/HjxphZvu/39zzPE5GBIvJRKtsjXPZw4QY3uMFLtty0fHh02NjlOX9GkHUTzE0mOgY4jIgs9X3/lhYf/rKInPU875LG25eIyLmE21YIlz1cuMENbvCSLTctzwAOemFZzp8RZN0Ec5PufgEOY4y5QkS2tvx4jx49LhOR6sSPiUh1y7OErUG47OHCDW5wg5dsuWl5DeDwZmcD0/vC3FEZ1k1yN+nsF+A4IvKhMebWlh/v3r37N1spgMcKCwu/3tY2VVUbGi4sJuaLaWi4cODBDW5wg5cw3BQ3lsCmKS6pDH1fXXHDXHCTzn4BbvNlEam/7LLL/sryubOe532p8fYlInLGS/EhYAAAcItT5z7XiWVbdfT4Cp1YtlVPnfs87F0Cx0hnwQCH8X3/B8aYNbbPi8gc3/cHeJ7nGWNuM8bMSmW7qvx1ZfvrCje4wU3+eKk6fFKLGx+CLS6p1KrDJ3ET8uAmuZt09QtwHN/3f9Pymb3GmLdFpKjx811FZJmI7BSRCt/3u6ayXVWur7BdX4Eb3OAmf7xk8r2Qo+4mrMFNcjeZ6BqQRxAue7hwgxvc5I+X9r5LRT65CWtwk9xN2P0BIg7hsocLN7jBTf544Qyge4Ob5G7C7g8QcQiXPVy4wQ1u8sdLe9+lIp/chDW4Se4m7P4AEYdw2cOFG9zgBi9RdxNWsY2CmygPBRACQ7js4cINbnCDl6i7Ceuh7Si4ifJQACEwhMseLtzgBjd4ibqbsJ7cEgU3UR4KIASGcNnDhRvc4AYvUXfDGcDcHAogBIZw2cOFG9zgBi9Rd8M1gLk5FEAIDOGyhws3uMENXnCDGxeHAgiBIVz2cOEGN7jBC25w4+JQACEwhMseLtzgBjd4wQ1uXBwKIASGcNnDhRvc4AYvuMGNi0MBhMAQLnu4cIMb3OClrQn6JItcdhN0cJPcTdj9ASIO4bKHCze4wQ1e2pqgL7OSy26CDm6Suwm7P0DEIVz2cOEGN7jBS1sT9IWWc9lN0MFNcjdh9weIOITLHi7c4AY3eGlrOAOYucFNcjdh9weIOITLHi7c4AY3eGlruAYwc4Ob5G7C7g8QcQiXPVy4wQ1u3PMS5Xe2yLSbXBvcJHcTdn+AiEO47OHCDW5w456XKL+3babd5NrgJrmbsPsDRBzCZQ8XbnCDG/e8BH3ShWvDmsFNR92E3R8g4hAue7hwgxvcuOeFM4D5M7hJ7ibs/gARh3DZw4Ub3ODGPS9cA5g/g5vkbsLuDxBxCJc9XLjBDW7wgpvsTctyX3X4JG4sQwGEwBAue7hwgxvc4AU32ZuWD+8Xl1TixjIUQAgM4bKHCze4wQ1ecJO9ae0JPrhpfSiAEBjCZQ8XbnCDG7zgJnvDGcDUhwIIgSFc9nDhBje4wQtusjeJ1wA+P3m9vjB5vY4eX6HFOfBkn3QPBRACw4HHHi7c4AY3eMFNODOupFKHj12hI19ZqcNz4OV+0j0UQAgMBx57uHCDG9zgBTfhzIji8mYFMOov+J3uoQBCYDjw2MOFG9zgBi+4CWc4A5h8KIAQGA489nDhBje4wQtuwpn9h05qcUkl1wBahgIIgeHAYw8XbnCDG7zgBjcuDgUQAkO47OHCDW5wg5cgk8rb1uWrm1QGN8ndhN0fIOIQLnu4cIMb3OAlyLR8XbvWrmPLVzepDG6Suwm7P0DEIVz2cOEGN7jBS5Bp7Z0tcJP64Ca5m7D7A0QcwmUPF25wgxu8BJkonQFM5eFq1o07QwGEwBAue7hwgxvc4CXIROkawFTKKuvGnaEAQmAIlz1cuMENbvCSL25Sebg6X924OBRACAzhsocLN7jBDV7yxQ1nAKM1FEAIDOGyhws3uMFN7npx5Zo3V9y44sNFNy4OBTCP8H2/jzFmo4jsFpHXWvl8L2PMSRHZ3DjvprJdwmUPF25wg5vc9eLKGS8X3bgyuEnuJv1NA5yje/fuPUTkePfu3b/ped4lIlJRWFh4TeJ9RORxERnR3m0TLnu4cIMb3OSuF1eueQvTjYtn/Vxx4/pQAPME3/fv931/XNPtgoKCb3zrW9/6b4n3EZE5IrJURDYbY2YZY7qksm3CZQ8XbnCDm9z1whlAdxy46Mb1oQDmCSLyhoi8aoxZJCJbReTZVu7znoj8ovHfg0WkIpVtEy57uHCDG9zkrhdXzn6F6caVs6AuunF9KIB5gu/7k0Rkd5cuXb7m+/5XRGSJMebWZF8jImc6der01ba2rara0HBhMTFfTEPDhQMPbnCDG7zkqpvikkodPnZFfIpLKkP3cfLkeT1e16Czty3XBxa+oI8uHaP1sTOh75Nr09BAAcwLROQZ3/dfb7rt+/4QY8yEhNtf8X3/4RZfc6agoOAv2tq2AgBAXnLq3Oc6sWyrjh5foRPLtuqpc5+H+v13HD+k726cqrfOGKk3TB2sN0wdrKMWPav/8Z//kdX9igrpbRrgJMaYHxpj9vbs2fNvPM+7xBgz2/f9O1rcZ6+I9PY8zxORgcaYRalsW5W/ym1/XeEGN7jBC24yN8UllTps7FK9c8J7evMfH4+Xvr5Th+hTy17VFbs/1f/4z//ISzeprJsM1A1wERG5XUR2GGP2NJ4N/DNjzNsiUtT4+ctFZH3jfZbzJJDg11fgBje4wQtuMjM7jxzS299+Vft+eG+8+N344Qh9+9NS3X30cF67SXXdZLR0QO5DuOzhwg1ucIMX3KRvauvO6NKda/WJJcXx0nfD1MF68x+f0Dsn/FHHlqzPWzcdWTdh9weIOITLHi7c4AY3eMFN29PWM6r3VVfr5PVletfMB+Kl79bp9+mrK9/XZ0uWWb8uF9xkct2E3R8g4hAue7hwgxvc4AU3bU9rrydYV39Wy3dv0GeWj9e+U4fEi98DC1/QOdvK9XhtQ164yeS6Cbs/QMQhXPZw4QY3uMELbtqexNcTHDxugd7xhwl69+xH4qWvf9m9+trq93TTwT155yaT6ybs/gARh3DZw4Ub3OAGL7hpe14u+Ux/O/5j7f/uc3rDx1+c7Rs5/2mdsWWJVp+I5a2bTK6bsPsDRBzCZQ8XbnCDG7zgxj6Ha+p06sb5OmT2Y1+8hMvHw/SF5X/Q9VU7tL7+XN66yca6Cbs/QMQhXPZw4QY3uMELbppPff05XV+1Q8etelv7TRseL37D5z6hUzfO18M1dc3uH+Qt96LmJtvrJuz+ABGHcNnDhRvc4AYvuLkwR0/EdPrmJTpy/tPx0ndT6TB9sfwNXbNvi/VsX2tPEMk1N2Gtm7D7A0QcwmUPF25wk69ugpy1yWUvmRjX3Ww6uEdfW/2e3lL2xQs2D579iE75bI4eOF7T5tcnPkFk2NgVOqK4PGfchL1uwu4PEHEIlz1cuMFNvroJctYml71kYlx0c7y2QedsXaGjFz7f7O3Znln+e12558JLvGRjLbnoxpWhAEJgCJc9XLjBTb66CXLWJpe9ZGJccrP9cJVOXFOit04fGS9+d818UCevn677qqs7tE2uAczcugm7P0DEIVz2cOEGN/nqhjOA2Zuw3dTUndaF2yv0kcUvNXt7tieXvqLLdq3T2roz7dpeOi8fCNuNy0MBhMAQLnu4cIObfHXDNYDZm7Dc7DpyWCetm6oDZ4yKl76BM0bppHVTddeRwx3ebjr/eGDdJHcTdn+AiEO47OHCDW5wg5dcclNbd0aX7VqnTy59pdnZvocXvaQLt1doTd3pwN8jnZcPsG6Suwm7P0DEIVz2cOEGN7jBSy642Vddre+tn653zXwwXvpunT5SJ64p0W2Hq9L6vTgDmL11E3Z/gIhDuOzhwg1ucIOXqLqpqz+rK/dU6rPLX9e+U794e7bRC5/X2VtX6PHahoz8PFwDmL11E3Z/gIhDuOzhwg1ucIOXqLk5cLxGp3w2RwfPfjRe+m4pu1dfWz1ZNx7cHfrPy7pJn5uw+wNEHMJlDxducIMbvETBTX39OV2zb4uOKX9TbyodFi9+I+b9TqdvXqxHT8RC/zlZN+l3E3Z/gIhDuOzhwg1ucIMXl90cqanT0k0LdfjcJ+Olr9+04Tpu1du6vmq79e3ZojKsm+Ruwu4PEHEIlz1cuMENbvDimpv6+nO6oWqHFq96R2+eNjxe/IbNeVw/3jhfD9XUhv4zsW6y4ybs/gARh3DZw4Ub3ODm4unIRf6ueEn36xtmc81Un4jpjC1LdOT8p+Ol78bSofrCion6yd7NkT/b5/K6cXEogBAYwmUPF25wg5uLpyMv8+GKl3S/w0k21symg3t1/Or3tH/ZvfHid/fsR/SDz2Zr1bGa0Pc/TDf5PBRACAzhsocLN7jBzcXTkRf6dcVLR1+kOJNnDltzc7z2lM7dVq4PLHwhXvr6Th2izywfr+W7N2hd/dnQ10E2xpV14+JQACEwhMseLtzgBjcXT76cAUwsfYNeWKaDX1yWkTOHiW62Hz6gb6ydordOvy9e/O6a+YBOXl+me6uPhuoujIfPXVk3Lg4FEAJDuOzhwg1ucHPx5Ms1gIll8Z8fmqs3PbYgLW9v1nJq60/r2qOV+ujisc3enu2JJcW6dOdara07E/rvvKWPbFQFikAAACAASURBVD187sq6cXEogBAYwmUPF25wg5v89ZL4cPFNjy3Qf35oblrLz+6jR/TtT0v1jhmj46Xv9hn361vrPtKdRw6mvJ1snZlL53v85vK6ydZQACEwhMseLtzgBjf56yXxjNfdLy7TQS8sC1yyauvO6LJdn+pTS19t9vZsTyx/WRfsWKU1tacC7Wcmz8xxBtCtoQBCYAiXPVy4wQ1u8tdLOs+s7T92TN/bMEN/O+uheOkbUDZSJ6z5QLcd3t9uN4n7dvMTC5tdn5ipM3NcA+jWUAAhMITLHi7c4AY3eOno1NWf1VV7KvW55a/rjaVD48Vv1ILndPbW5XqstqHDbhLPxt302IJm1ye68NI2rJvsuAm7P0DEIVz2cOEGN7jBS3vn4PETOqVyjg6Z/Wi89N0y7R59tWKyVh7YlRY3idfj3f3iMr35iQVOvbg16yY7bsLuDxBxCJc9XLjBDW7wksrU15/Ttfu26ksr39KbSofFi9+Ieb/Tss2L9eiJ+rS6cfEFrVk32XcTdn+AiEO47OHCDW5wg5dkc6SmTks3LdR75j4ZL339pg3XsSsn6br921J6e7aOuHHxLe1YN9l3E3Z/gIhDuOzhwg1ucIOXllNff04/O7BTiyve0Zun3RMvfkPnPKYfbZynh47X5q0b1k123YTdHyDiEC57uHDTtpt8ORPRETdh70ss5s7vp71eXNnvxKk+cVJnblmq989/Jl76biwdqs+vmKir927q8NuzubZmXBrcJHcTdn+AiEO47OHCTdtu8uVapI64ydb3TFaWXPn9NHmpOpxasXNlv2Ox87rl0D59/ZP3dUDZiHjxGzTrYX1/wyzdf+xYJNdMVAY3yd2E3R8g4hAue7hw07abMN4dwOUJY90kK0uu/H6avBSnWOzC3u/jtad03raV+uDCF+Olr+/UIfr0std0xe71HT7b58qaicrgJrmbsPsDRBzCZQ8Xbtp249KZGhcmjHWTrCy58vtp8pJqsQtrv3ccOahvrv1Qb59+f7z43TFztL776TTdc/RozqyZqAxukrsJuz9AxCFc9nDhpm03Ll6r5YqbbH3PZGXJld9Pe88AZnO/T9Sd1sU71+hjS8bFS98NUwfr40vG6eKda7S27kzOrZmoDG6Suwm7P0DEIVz2cOEGN1Fw40rJS8VLqtcAZmP2HD2i73w6Te+YOTpe+m6ffr++ufZD3XHkYE6vmagMbpK7Cbs/QMQhXPZw4QY3uMktL3X1Z3XF7vX6u2Wvad+pQ+LF76FFY3T+9lVaU3sqb924OLhJ7ibs/gBZwvf9PsaYjSKyW0Rea/n5bt26dTbGlIvILmPM8s6dO3dKZbuEyx4u3OAmam5cPRsYupdjx/T9DTN10KyH46VvQNkIff2T93XLoX157cblwU1yN+lvGuAc3bt37yEix7t37/5Nz/MuEZGKwsLCaxLvY4yZ5ft+f8/zPBEZKCIfpbJtwmUPF24unv2HTmpxSaWOHl+hxQ4VDFcm7HXjypM+XPBSV39WV+/dpM+vmKg3lg6NF7/75z+js7Ys0+oTbqzdsNeMy4Ob5G4yUDfANXzfv9/3/XFNtwsKCr7xrW99678l3OXLInLW87xLGm9fIiLnEm5bIVz2cOHm4hlXUqnDx67Qka+s1OEOFQxXJux1E/bLp7jg5dDxWv1o4zwdOuexeOm7edo9+krFu1p5YFdKb8+Wq26iNrhJ7ia9TQOcRETeEJFXjTGLRGSriDyb+PkePXpcJiLVLb6muqCg4BttbZtw2cOFm4tnRHF5swLoSsFwZcJeN/l6BrC+/pyu279NX1r5lvYrHRYvfvfMe0qnbVqkR2rqQ3fg6ppxeXCT3E26uwY4iO/7k0Rkd5cuXb7m+/5XRGSJMebWps937979m60UwGOFhYVfb2vbqqoNDRcWE/PFNDRcOPDgpvkUtzgDWFxSGfo+JU7V4QsPUY8oLtfikkqtOnwyo1/n2rpJ18+R7smUl6Mn6nXa5kV677yn4qWvX+kwHbvyLV23f6vGYudC/9ldXzMuD26Su8lE3wDHEJFnfN9/vem27/tDjDETEu7S9BDwlxpvXyIiZ7wUHwIGSJVT5z7XiWVbdfT4Cp1YtlVPnfs87F1qxsSyrTrylZXxmVi2NaNfB+Fw4NQRfXPDB9q/7N548Rs+73Gds2eJnvv8fNi7B5AV0ts0wEmMMT80xuzt2bPn33ied4kxZrbv+3ck3kdE5vi+P6Dx/rcZY2alsm1V/rqy/XWFm+i5aXqIumlGFJdn9Oui5CbIBD2zmA4vx2pP6uyty3TUgmfjpe/G0qH63IoJunrvRq2PnQ3dE2sGN9l0k4G6AS4iIreLyA5jzJ7Gs4F/Zox5W0SKPM/zfN/vKiLLRGSniFT4vt81le2qcn2F7foK3ETPTUevgUvXtXMuuwnDazq8bDm0T1//5AMdUDYyXvx+O+shfX/DTN1/7FjoboJOrq4Z3GTeTUZLB+Q+hMseLtxEz01HXwcvXa+f57KbIBP02cXt9VJTe0rnb1+lDy0aEy99facO0aeWvaordq/P+NuzZXNcXTMuvKakq25cGAogBIZw2cOFG9zg5sJk6wzgziMH9a21H+nt0++PF787ZozWtz8t1T1Hj4TuIZ/WjAvPKHfVjQtDAYTAEC57uHCDG9xcmKBng5J5qa07o4t3rtHHl4yLl74bpg7Wxxa/rIt2fKIn6k6H/vPn45px4TUlXXXjwlAAITCEyx4u3OAGN5nzsufoUX3302l658wH4qXvtun36Rtrp+j2wwdC3+d8XzOcAXR7KIAQGMJlDxducIOb9Hqpj53VFbvX69PLXtO+U4fEi99Di17UedtW6vHaU+3etgvXquXimnHBq6tuXBgKIASGcNnDhRvc4CY9c+D4cZ2+c4HePfvheOnrX3av/v6T93Xzwb2Btu3CmSrWDG7CcBN2f4CIQ7js4cINbnDT8amrP6ur927SF1ZM1BtLh8aL333zn9EZW5Zq9YlYWr6PC9eqsWZwE4absPsDRBzCZQ8XbnCDm7an5UOFW/cd1Y82ztNhcx6Pl76bp92jE9e/r5UHdmp9/bm0fn/OAObu4Ca5m7D7A0QcwmUPF25wg5u2Z1xJpQ4du1x/+1qp9n/3Be378bB48btn7pNaummhHj1RlzEvLlyrxprBTRhuwu4PEHEIlz1cuMENbpLP0RP1etdbk/SmDx764iVcPh6qY8rf1LX7tsbP9uWbF9YMbrLhJuz+ABGHcNnDhRvc4Kb12Xhgt762erLeUnbvF+/LWzJKb39zor5YsjpvvbBmcJNNN2H3B4g4hMseLtzgBjdfzLHaBp29dbmOWvBcs7dne3LJeH18yiy9t3iF9SHYXPbCmsFNWG7C7g8QcQiXPVy4wU1rk+yas1x0s/XQfp2w5gMdUDYyXvx+O+shfW/9dN1XXc2aCbh2cGMf3CR3E3Z/gIhDuOzhwg1uWptkzzrNFTc1dad1wfYKfXjRS83P9i19RZft+lRr686wZtK0drLpJmpPmGHdJHcTdn+AiEO47OHCDW5am2SvOxd1NzuPHNI/rPtYB84YFS9+A2eM0rc/LdXdRw+zZjKwdrLpJmovmcO6Se4m7P4AEYdw2cOFG9y0Nrl2BrC27owu3blWn1hS/MUzeacO1kcXj9WFO1ZrTd1p1kwG10423UTtRbNZN8ndhN0fIOIQLnu4cIOb1iZXrgHcV12tk9dP17tmPhAvfbdOv0/fWDNFtx2uYs1kae1wBpB101E3YfcHiDiEyx4urssJ303UxnU3dfVntXz3Bn1m+XjtO3VIvPg9sPAFnbOtXI/XNuSll3xZMxxrcmcogBAYwmUPF3+Vh+8mauOqm6pjNfrBZ7P17tmPxEvfLdPu1WEfvqZDfz8j42XAVS8uDG5w01E3YfcHiDiEyx6uoG5S/Wu75XU5w8Yud/qvdA7K9qk6fFInlm114ndXX39OP9m7WV8of0NvLB0aL34j5z+tM7Ys0ZdK1mbtDw/WDG5wk343YfcHiDiEyx6uoG5SPbPX8n6DXljm9BlBDsr2KS6p1JGvrNThIf7uDtXU6scb5+uwuY/HS9/N04bruFVv64aqnfG3Z8vmEwJYM7jBTfrdhN0fIOIQLnu4grpJ9T/YlmcKhzc7G+jeM/U4KCf/nScWwGz97urrz+n6qh06btXb2m/a8HjxGz73CZ26aYEerqm76GuyeekBawY3uEm/m7D7A0QcwmUPV7bOAKbr66LkJlcn22cAj56I6fTNS3Tk/Kfjpe+m0mE6pvxNXbNvc/xsX2uTzScEsGZwg5v0uwm7P0DEIVz2cGXrGsB0fV22tstB2T7ZugZw08E9+trq9/SWsnvjxW/w7Ed0ymdz9MDxmtA9sGZwg5vMuwm7P0DEIVz2cKXTjQsvv5CuM4sclFN3k87f+/HaBp2zrVxHL3y+2duzPbv8dV25p1Lr6s+G/vOzZnCDm+y5Cbs/QMQhXPZwpdONCw/rpuuifw7KqbtJx+99++EqfWPNFL11+n3x4nfXzAd18vrpuq+6OvSfmTWDG9yE4ybs/gARh3DZw5VONy68BRNnALO/bjr6e6+pO60Ld6zWRxePbfb2bE8sKdalu9Zpbd2Z0H9W1gxucBOum7D7A0QcwmUPV2tuOvqQngtnALkGMPvrpr2/911HDuukdVN14IxR8dI3cMYonbRuqu46cjj0ny9dXhjc4Ca4m7D7A0QcwmUPV2tuOlrkXLgGMNNucnXa87vryDWAtXVndOmudfrk0leane17ZPFLumB7hdbUnQ7dAWsmOm441uTHUAAhMITLHq7W3LjwUG7Yk28H5faU/va42VddrZPXT9e7Zj4YL323Th+pE9aU6LbDVaH/3KyZaLpx4dEGV93k0lAAITCEyx6udJ4BzKXJt4Nye0p/W27q6s/qyj2V+uzy17Xv1CHx4jd64fM6Z+sKPV7bEPrPy5qJtptc+iOVdZPcTdj9ASIO4bKHK53XAObSZPqg7JrjdJwBPHC8Rqd8NkcHz34kXvpuKbtXX1v9nm48uDv032nU10yUhzOA2XOTS0MBhMAQLnu4cBOOG9f+A+voNYD19ed0zb4tOqb8Tb2pdFi8+I2Y9zudvnmxHj0RC/13mStrJsrDNYDZc5NLQwGEwBAue7hwE46bKD+EdfLkef1//+3/aOmmBTp87hPx0tdv2nB9edUkXV+1I+nbs+XqkCfc4Cb9bsLuDxBxCJc9XLgJx41rZwBTmfr6c7qhaocWV7yjN5fdEy9+w+Y+rlM3ztdDNbWh72MYk3g2amLZVq06HN2zUZkajjW46aibsPsDRBzCZQ8XbsJxE6WHsKpPxHTGlqU6cv7T8dJ3U+lQfbH8Df1k7+a8PNuXOE1lfvjYFTrylZVaHIEyn+3hWIObjroJuz9AxCFc9nDhBje22Xxwr47/5I/av+zeePG7e/YjWlI5W8/8y9m8dpM4TQ/nNxXAKD2cn60hT7jpqJuw+wNEHMJlDxducJM4x2tP6dxt5frgwhfipa/v1CH6zPLxWr57g9bVn81bN7bhDGDbw5rBTUfdhN0fIOIQLnu4cIObWOy8bj98QN9YO0Vvm35fvPjdNfMBfXd9me6tPprXbtoargFse1gzuOmom7D7A0QcwmUPF27y182JutO6aMdqfXTx2GZvz/bEkmJdunOt1tadyVs3rBnc4Cb8oQDmESLysTFmr4hsFpHNvu9fl/h53/d7GWNONn1eRN5NZbuEyx4u3OSfm91Hj+jbn5bqHTNGx0vf7TPu17fWfaQ7jxzKazesGdzgxp2hAOYRIrK/oKDgb5N8/nERGdHe7RIue7hw476bdDxjuLbujC7f9ak+tezVZm/P9vCiMTp/+yqtqT0VSTcuDV5wg5v0uwnWKiASdO3a9e9E5IyIzDPGbPN9/8mW9xGROSKyVEQ2G2NmGWO6pLJtwmUPF27cdxPkNQP3Hzumf9wwQ38766F46RtQNlInrPlAtx7aH3k3Lg1egrmJ0ksjZdtNvg4FME8Qke8aY0oLCgr+tmvXrn9pjFkhIre3uM97IvKLxn8PFpGKVLZNuOzhwo37btr7riF19Wd11Z5KfW7563pj6dB48Ru14DmdvXW5HqttyBk3Lg1egrmJ4oujZ8tNvg4FME8pLCy8XkSmJ7uPiJzp1KnTV9valqpqQ8OFxcR8MQ0NFw48uHHbTXFJpQ5vfJmR4WNXaHFJZav3O1RzQj/cOFeHzHk0XvpumXaPvrZ6sm48uCsn3bg0eAnmZkRxebN1PqK4PPT9dsVNvk5DAwUwLygsLPwHESlqui0ivzbGTG267fv+V3zffzjxa0TkTEFBwV+0tW0FiDCnzn2uE8u26ujxFTqxbKueOvd5/HN/+tOfdFf9fn1t3Tt607Rh8eJ3/8KnddH+lfr//du/hLjnAKkzsWyrjnxlZXwmlm0Ne5fAAdLbNMBJfN//kYhUXXrppX/ted6fi8jSwsLCGxPv0/gM4d6e53kiMtAYsyiVbavy15XtryvcRNPN0RN1Om3zQr1n7pPx0tevdJi+vGqSflq1TWOxc3nrhjXj3qTipurwSS1uvAawuKRSqw6fDH2/XXGTr8MZwDzC9/37RGS3MWafiDzneZ5njHm76cygiFwuIutFZIcxZjlPAgl+fQVuouOmvv6cfnZgpxZXvKM3T7snXvyGznlMP9o4Tw8dr3XOTT5d2O/imnFlcIObjrrJZOeAPIBw2cOFG/fdVJ84qTO3LNX75z8TL303lg7V51dM1NV7N2ld/Vnr12aigLXHTT5d2O/SmnFtcIObjroJuz9AxCFc9nDhxl03Ww7t099/8r4OKBsRL36DZj2s72+YpVXHjqe0jUwUsPa4ae8zmKM8LqwZVwc3uOmom7D7A0QcwmUPV9TdZOohxrDcHK89pfO2rdQHF74YL319pw7Rp5e9pit2r096tq+1yUQB4wygW2smCoMb3HTUTdj9ASIO4bKHK+puMlUwsu1mx+ED+ubaD/W26ffFi98dM0fru59O0z1HjzjlJ9+vAbT9TNlcM1HzmgvHGtyE4ybs/gARh3DZwxV1N5l6iDEbbk7UndZFOz7Rxxa/HC99N0wdrI8vGaeLd67R2rozgb9H2NcA5uLYSnU2vUTtzGq+rxncdNxN2P0BIg7hsocr6m6ieAZwz9Ej+s6n0/SOmaPjpe/26ffrm2s/1B1HDobuNB/WTZCx/dGRTS9Ru7Yy39cMbjruJuz+ABGHcNnDFXU3UbkGsK7+rK7YvV5/t+w17Tt1SLz4PbRojM7fvkprak+F7jKf1k2Q4QwgawY32XMTdn+AiEO47OHCTWbd7D92TN/fMFMHzXo4XvoGlI3Q1z/5QLcc2mf/Ooev8cr3dcM1gKwZ3GTPTdj9ASIO4bKHCzfpd1NXf1Yr9m7U51dM0BtLh37x9mwLntVZW5dp9Ym2/7N2+QwP66bjXqJW3LLpJl8HN8ndhN0fIOIQLnu4cJM+N4eO1+pHG+fp0DmPxUvfzdPu0Vcq3tXKA7va9f1dvsaLddNxLy4X+7Dd5OvgJrmbsPsDRBzCZQ8XboK5qa8/p+v2b9OxK/+g/UqHxYvfPfOe0mmbFumRmvoOfX+XiwLrpuNeXC72YbvJ18FNcjdh9weIOITLHi7cdMzN0RP1Om3zIr133lPx0tevdJi+tPItXbd/m9bXnwv0/V1+qJB103EvLhf7sN3k6+AmuZuw+wNEHMJlDxdu2uem8sAufbXiXb1l2j3x4jdkzmP6YeVcPXj8ROj7zbpx20smir3LfyywZnAT1E3Y/QEiDuGyhws3bbs5Vtugs7Yu01ELno2XvhtLh+pzKyZoxd6N7X57tqgP68YtL5k6q5jOYsmawU1H3YTdHyDiEC57uHBjd3P0zHGdsOYDHVA2Ml78fjvrIX1/w0zdf+xY6PsYphvWjTteMnVdYTqLJWsGNx11E3Z/gIhDuOzhioKbbD7EVVN7SudvX6UPLxoTL319pw7Rp5a9qst2fZqWt2eL+kRl3eSLl0ydAUxnsWTN4KajbsLuDxBxCJc9XFFw09H/4NpTHHceOahvrf1Ib59+f7z43TXrAX3701LdffRI6A5cmqism3zxkqk/kDgDmNvrJgpDAYTAEC57uKLgpqNnItr6D6y27owu2blWn1hSHC99N0wdrI8tGaeLd36i//4f/95uN1G4ID+X102Y/l32ErbLXHOTzsFNcjdh9weIOITLHq4ouOnomQhbcdxbfVTfXV+md858IF76bpt+n7659kPdcfhAIDf58DIfHXWTjXIWpv+o5ClKayYfBjfJ3YTdHyDiEC57uKLgpqPFIbEMDB27XB+bMkOfXjZe+04dEi9+Dy58UedtW6nHa091yE3LfRueUD5y9YV+XS7HYb7QclTyFKU1kw+Dm+Ruwu4PEHEIlz1cqqpVh3PzYcv9h07qCyUVescfJugtH4+Kl74BZSP09U/e1y2H9rXppq1107LUDHphGWcALZONcsYZQDcHN7jpqJuw+wNEHMJlD5eqanGOPWxZV39WV+/dpC+smKg3lg6NF7/75j+jM7cs1eoTsZTdtLVuWpaaYWOX52SZ7oiblpONcsY1gG4ObnDTUTdh9weIOITLHi5VzZn3Jz1UU6sfb5yvw+Y8Hi99N08brsWr3tHPDuxs9vZsbRWFjp4BjHp5bs+6cfEawCh6yYfBDW466ibs/gARh3DZwxX1M4D19ed0fdV2fXnVJO03bXi8+A2f+6SWblqoR2rqWv26topbR68B7GipiVI54j+s1L1E6feabTcMblJxE3Z/gIhDuOzhiuo1gEdP1GvZ5sU6Yt7v4qXvptJhOqb8TV27b2uzs32tTVtnPbN9UI7SmcR0ucm1ctSalyj9XqOwZnJxcJPcTdj9ASIO4bKHK2puNh7Yra9WTNZbpt0TL35DZj+qUyrn6MHjJ1LeTrrOAKZrovQwfLrc5Fo5as1LlH6vUVgzuTi4Se4m7P4AEYdw2cMVBTfHaht09tblOmrBc/HSd2PpUH1u+etasWej1tWfbfc203UNYLomSmUoXW5yrRxxBjDzayYXBzfJ3YTdHyDiEC57uFx2s/XQfp2w5gMdUDYyXvx+O+sh/eOGGbr/2LGccuPyw6Et963q8EnOAKa4Zlz+vYbthsFNKm7C7g8QcQiXPVyuuampO60Ltlfow4vGxEtf36lD9Kmlr+qyXeu0tu5M3roJa1oWteKSSq4BzPM1097fXT65ae/gJrmbsPsDRBzCZQ+XK252Hjmkf1j3sQ6c8cULNg+cMUonrZuqu48ezms3YU9rD9Xi5uLJpzXT3rO3+eSmvYOb5G7C7g8QcQiXPVxhuqmtO6NLd67VJ5YUx0vfDVMH66OLx+qiHau1pu503rpxaTJ1BjDXJp/WTHuv38wnN+0d3CR3E3Z/gIhDuOzhCsPNvupqnbx+ut4188F46bt1+n36xpopuv1wVehewnTj4mTqGsBcm3xaM5wBTN/gJrmbsPsDRBzCZQ9XJt0kFoeXSzbovM1r9Znlv9e+U4fEi98DC1/QudvK9XhtQ+g+sukmyoMbvHANYPoGN8ndhN0fIOIQLnu4MulmXEmlDhm3QG9/a4LeOOX+eOnrX3avjv/kj7rp4N7QHYTlJsqDG7zgBjfZchN2f4CIQ7js4cqEm/r6c7pm32YdMPl5veHjL8729fvgYZ2xZYlWn4iF/rOH5SbTk41n1kbVTaYHL7jBTfrdhN0fIOIQLnu40unmcE2dTt04X4fNffyLJ3V8NFQHvPOiDnptmr5c8lnoP3NYbrI12Xhtvai6yfTgBTe4Sb+bsPsDRBzCZQ9XUDf19ed0fdV2fXnVJO03bXi8+A2f+4S+t26OjilZE4nXecuVJzpk4901+A8LL7jBTbbchN0fIOIQLnu4Ourm6ImYTt+8REfOfzpe+m4qHaZjyt/UNfu2aH39udB/vpaT7OHRXHmpk1w5AxjFF4nmP3Lc4Cb9bsLuDxBxCJc9XO11s+ngHn1t9Xt6S9m98eI3ePYjWvLZbD1wvCb0nynZJCtHufJix7lyDWAU3yaO/8hxg5v0uwm7P0DEIVz2cKXi5nhtg87ZukJHL3y+2duzPbP897pyT6XW1Z8N/WdJZZI9PJorZwBdWjeZ+l25OvxHjhvcpN9N2P0BsoSIfGyM2Ssim0Vks+/71yV+vlu3bp2NMeUisssYs7xz586dUtku4bKHK5mbbYerdOKaEr11+sh48btr5oP63vrpuq+6OvT9b+8kO6uUK9cAurBuMv27cnX4jxw3uEm/m8y0DXAOEdlfUFDwt7bPG2Nm+b7fv/G+A0Xko1S2S7js4WrppqbutC7cXqGPLH6p2duzPbn0FV26c63W1p0JdZ+DPMTZnq/loNy+dePS7zmXvUR1cIObjrpJV78Ah+natevficgZEZlnjNnm+/6TLe7yZRE563neJY23LxGRcwm3rRAue7ia3Ow6clgnrZuqA2eMipe+gTNG6aR1U3XXkcOh72vTZOvMEAdl3OAFN7gJ3026uwY4iIh81xhTWlBQ8Lddu3b9S2PMChG5venzPXr0uExEqlt8TXVBQcE32to24Wp96urP6IZjW/TJpa80O9v3yOKXdOGO1VpTdzr0fWw52bo2LBMH5Sie1cqWm1wYvOAGN+l3k4G6Aa5TWFh4vYhMb7rdvXv3b7ZSAI8VFhZ+va1tqao2NFxYTMyFqas/oyPm/S5e+m6dPlInrinR7YerQt+3ZFNcUqnDx66IT3FJZUa+T0PDhYNyOtdNtvY905MJN7kweMENbtLvJhP9AhyjsLDwH0SkqOm2iPzaGDM14S5NDwF/qfH2JSJyxkvxIWBozr//53/oo0vH6KNLx2j5wbX6r//+b2HvUkqcOve5TizbqqPHV+jEsq166tznYe+SlZb7OvKVVTrylZXxGT2+IuxdBABwmvQ2VwDuWAAAEKlJREFUDXAS3/d/JCJVl1566V97nvfnIrK0sLDwxsT7iMgc3/cHeJ7nGWNuM8bMSmXbqvx1ZfvrCjeZc9PyjN+gF5ZxBjCHBy+4wU363WSgboCL+L5/n4jsNsbsE5HnPM/zjDFvN50Z9H2/q4gsE5GdIlLh+37XVLaryvUVtusrcJM5Ny2vVxw2djnXAObw4AU3uEm/m0x2DsgDCJc9XLjJnJsovpZdttzk4uAFN7hJv5uw+wNEHMJlDxduMucmV571mwk3uTh4wQ1u0u8m7P4AEYdw2cOFG9zgBi+4wY2LQwGEwBAue7hw0343uXpmLx1u8nnwghvcpN9N2P0BIg7hsocLN+13k6vX9qXDTUcnF0o1ecINbtLvJuz+ABGHcNnDhZv2u8nWu5G4OplYN7lQqskTbnCTfjdh9weIOITLHi7ctN9NLpSVTLnp6ORCqSZPuMFN+t2E3R8g4hAue7hw0343ufBwZabcdHRyoVSTJ9zgJv1uwu4PEHEIlz1cuMGNC25yoVSzZnCDm/S7Cbs/QMQhXPZw4QY3uMELbnDj4lAAITCEyx4u3OAGN3jBDW5cHAogBIZw2cOFG9zgBi+4wY2LQwGEwBAue7hwgxvcuOElF66DzJSbXB7cJHcTdn+AiEO47OFqr5tc/k8qqJt8GdxkxksuPBM6U25yeXCT3E3Y/QEiDuGyh6u9bnL5P6mgbvJlcJMZL7nwWoiZcpPLg5vkbsLuDxBxCJc9XO11k8v/SQV1ky+Dm8x4yeU/rlgzuOmom7D7A0QcwmUPF2cA0+cmXwY3mfGSy5dXsGZw01E3YfcHiDiEyx4urgFMn5t8GdzgBTe4yZabsPsDRBzCdfHsP3RSi0sqdfT4Ci3O4SLX0eGgjBu84AY34bsJuz9AxCFcF8+4kkodPnaFjnxlpQ7P4YdyOzoclHGDF9zgJnw3YfcHiDiE6+IZUVzerADm6pM5OjoclHGDF9zgJnw3YfcHiDiE6+LhDGDy4aCMG7zgBjfhuwm7P0DEIVwXj2vXALr25BIOyrjBC25wE76bsPsDRBzCZQ+XK25ce3kZl9y4NrjBC25wky03YfcHiDiEyx4uV9y49gLTLrlJNmGcOY2Km2wPXnCDm/S7Cbs/QMQhXPZwueKGM4DR8RYVN9kevOAGN+l3E3Z/gIhDuOzhcsUN1wB2bMI4cxoVN9kevOAGN+l3E3Z/gIhDuOzhwk203QQ5A9jR0h0VN6wZdwY3uOmom7D7A0QcwmUPF26i7SbImdOOlseouGHNuDO4wU1H3YTdHyDiEC57uHCTv246+vBxPrjpyOAFN7hJv5uw+wNEHMJlDxdu8tcNZwDTO3jBDW7S7ybs/gARh3DZw4Wb/HXDNYDpHbzgBjfpdxN2f4CIQ7js4UrFjWvP0HXJTT4ObvCCG9xky03Y/QEiDuGyhysVN669Rp9LbvJxcIMX3OAmW27C7g8QcQiXPVypuHHtXTpccpOPgxu84AY32XITdn+AiEO47OHiDGAwN/k4uMELbnCTLTdh9weIOITLHi6uAQzmJh8HN3jBDW6y5Sbs/gARh3DZw4Ub3OAGL7jBjYtDAYTAEC57uHCDG9zgBTe4cXEogBAYwmUPF25wgxu84AY3Lg4FMA8RkZdFZHLLj/u+38sYc1JENjfOu6lsj3DZw4Ub3OAGL7jBjYtDAcwzevbs+XMRibVWAEXkcREZ0d5tEi57uHCDG9zgBTe4cXEogHlE165d/05EPhWREZYCOEdElorIZmPMLGNMl1S2S7js4cINbnCDF9zgxsWhAOYRxphpvu//1Bhzm6UAviciv2j892ARqUhlu4TLHi7c4AY3eMENblwcCmCe4Pv+Xb7vj/M8z7MVwJaIyJlOnTp9ta37qao2NFxYTMwX09Bw4cDjmpuqwye1uPF1B4tLKrXq8EncODS4wQtucJMtN+noF+A4IrLUGLNdRLaIyFFjTIOIvNb0ed/3v+L7/sMtvuZMQUHBX7S1bYVIMbFsq458ZWV8JpZtDXuXAAAgBDLRN8BhbGcAjTF7RaS353meiAw0xixKZXuq/HVl++vKRTcjist1+NgV8RlRXI4bhwY3eMENbrLlJt39AhwnsQAaY94WkSLP8zwRuVxE1ovIDmPMcp4EEvz6ChfduPDew666cWFwgxfc4CZbbjLZNSAPIFz2cLnoxoX3HnbVjQuDG7zgBjfZchN2f4CIQ7js4cINbnCDF9zgxsWhAEJgCJc9XLjBDW7wghvcuDgUQAgM4bKHCze4wQ1ecIMbF4cCCIEhXPZw4QY3uMELbnDj4lAAITCEyx4u3OAGN3jBDW5cHAogBIZw2cOFG9zgBi+4wY2LQwGEwBAue7hwgxvc4AU3uHFxKIAQGMJlDxducIMbvOAGNy4OBRACQ7js4cINbnCDF9zgxsWhAEJgCJc9XLjBDW7wghvcuDgUQAgM4bKHCze4wQ1ecIMbF4cCCIEhXPZw4QY3uMELbnDj4lAAITCEyx4u3OAGN3jBDW5cHAogBIZw2cOFG9zgBi+4wY2LQwGEwBAue7hwgxvc4AU3uHFxKIAQGMJlDxducIMbvOAGNy4OBRACQ7js4cINbnCDF9zgxsWhAEJgCJc9XLjBDW7wghvcuDgUQAgM4bKHCze4wQ1ecIMbF4cCCIEhXPZw4QY3uMELbnDj4lAAITCEyx4u3OAmnW72Hzqp40oqdURxuY4rqdT9h06Gvr8ueMn3wQ1uOuom7P4AEYdw2cOFG9yk0824kkodNnZFfMaVVIa+vy54yffBDW466ibs/gARh3DZw4Ub3KTTzYji8mYFcERxeej764KXfB/c4KajbsLuDxBxCJc9XLjBTTrdcAaQNYMb3KTTTdj9ASIO4bKHCze4SacbrgFkzeAGN+l0E3Z/gIhDuOzhwg1ucIMX3ODGxaEAQmAIlz1cuMENbvCCG9y4OBRACAzhsocLN7jBDV5wgxsXhwIIgSFc9nDhBje4wQtucOPiUAAhMITLHi7c4AY3eMENblwcCiAEhnDZw4Ub3OAGL7jBjYtDAYTAEC57uHCDG9zgBTe4cXEogBAYwmUPF25wgxu84AY3Lg4FEAJDuOzhwg1ucIMX3ODGxaEAQmAIlz1cuMENbvCCG9y4OBRACAzhsocLN7jBDV5wgxsXhwIIgSFc9nDhBje4wQtucOPiUAAhMITLHi7c4AY3eMENblwcCiAEhnDZw4Ub3OAGL7jBjYtDAcxDRORlEZnc8uPdunXrbIwpF5FdxpjlnTt37pTK9giXPVy4wQ1u8IIb3Lg4FMA8o2fPnj8XkVhrBdAYM8v3/f6e53kiMlBEPkplm4TLHi7c4AY3eMENblwcCmAe0bVr178TkU9FZEQrBfDLInLW87xLGm9fIiLnEm5bIVz2cOEGN7jBC25w4+JQAPMIY8w03/d/aoy5rWUB7NGjx2UiUp34MRGpLigo+EZb2yVc9nDhBje4wQtucOPiUADzBN/37/J9f5zneV5rBbB79+7fbKUAHissLPx6W9tWVW1ouLCYmC+moeHCgQc3uMENXnCDG9emoYECmBeIyFJjzHYR2SIiR40xDSLyWsJdmh4C/lLj7UtE5IyXwkPAAAAAAOA4rZ0B9DzPE5E5vu8PaLqPMWZW9vcOAAAAANJOYgE0xrwtIkWe53m+73cVkWUislNEKnzf7xrungIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQGp06tTpq8aY2SKyS0Q2+L5f2Nr9RORlEdkhIjuMMS9mez+zie/7N4jITmPMPhF5ouXnu3Xr1tkYUy4iu4wxyzt37twpjP3MNm158X3//zbGrBWRLcaYtT169Pi/wtjPMGjLTcL9fiAi/5rNfQubttwUFBR8Q0TmN66bT3r06NE9jP0Mg7bc9OjRo7uIVDS+5uvKwsLCbmHsZ1j4vv9fjTHbe/bs+a2Wn8vX47DnJfeSz8dhaCci8mrTgaewsPBnxpi1Le/j+/5vjDGLPM/7M8/zvmyMKfd9/7ps72s26NGjx2XGmCNdu3b9O+/CC2gvE5FfJN7HGDPL9/3+nud5IjJQRD4KZWezSCpeRGRnYWHhjz3P84wx/yQiW0PZ2SyTihvP87yuXbv+pTFmjYj8Zwi7GQoprptlxpjfep7nGWMGGWNKQ9nZLJPiseYDERnc+O/hxpiSUHY2BHzf/5+Nb3jwr60VnXw8Dnte217y9TgMHUBEDiT+VSkiB1q+ZqCIXC4ilzfd9n3/dRG5J5v7mS183+8vIu8m3B5gjHkn4S5N77LS9K4ql4jIOS/H32UlBS9/JiK3N93o0qXL14wxp7K5j2GRghvP8zxPRN4QkV/nUwFsy02XLl2+JiL1CV/y57ZHIXKNVNaNiEwRkQca//2AiPwh2/sZFiLybmFh4Y+NMYdaKTp5eRz2vDa95O1xGDqAiHzuffGWcZ4x5hPf9/+n7f49evT4tojU5+pB2vf9h0TkmabbPXv2/LmILG663aNHj8taeZ/l6oKCgm9kcz+zTVteWiIib7VWgnKRVNz4vt+n6QXbReRP2d7HsGjLjTHmh8aYSmNMsYhsFZG5+fIwZyrrxhjTU0TqROS4iNQZY3pmf0/DxRhzuGXRydfjcCKteWlJPh2HIQm+7/9GRI6JSHXCrGu8HqlZATTG/NCyjR+IyFHf92/J2o5nGWPMIy0PysaYhU23u3fv/s1WDjzHCgsLv57N/cw2bXlJ4Eu+779ujPmsU6dOX83iLoZGW24a/7PacOmll/6153lePp0BbMtNYWHh/xKRPyW8g9GdIrIyjH3NNqlkyhjzSZMbEfm1MWZ7tvczbForOvl6HE6kjQKYd8dh6AAicsAY0yXxdrdu3Tq3vF/jtQR1hYWF12d3D7NLy4dhfN/v7/v+pIS7ND300FSaLxGRM16OP/SQghfP87w/N8bMEpEll1122V9leRdDoy03jaWmSkQ2N17M/ycR2ez7/n8NZ4+zR1tujDE9jTHnm243Xif5f7K9n2HQlpvOnTt3MsacTPwaEYl16dLla9ncz7CxFJ28PA4nkqQA5uVxGDqAiIxvehKI7/s/FZEtrdznu8aYk77v/yj7e5hdunfv/k1jzCHf9y/1PO+/iMiSlk94EZE5vu8P8LwL78VsjJkVys5mkVS8+L7/vjFmqpdHB2HPS81NIvn0EHCKedopIr09L/5IxepQdjbLpOimWkSu9DzPKyws/LGIHAxlZ0PEVnTy8TiciM1Lvh6HoQP07Nnzb0Rkulx4eZfKwsLCv/c8zyssLPwHEZnveRcuRDbGnE44g7HZ9/0h4e555hCRfzbGbDfG7DXGjPE8zzPGvJ3wMFVXufCMvZ0iUtHySTO5SjIvhYWFvoj8p4jsblwjW0Rks3fhmeM5T1trpsV98+YhYM9r203Pnj1FRFY2HoPWFhYW+uHucfZIwc3/EJH1xphtjc8gvzz5FnOPxCc7cBz+gta85PtxGAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAosH/D6idS5h7+DuAAAAAAElFTkSuQmCC\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "line = Line(slope=1.5, intercept=5)\n",
    "(x, y) = line.get_sample(100, noise=1)\n",
    "# plot (scatter) noisy sample\n",
    "sns.regplot(x, y, fit_reg=False, label='Noisy Sample')\n",
    "# plot line\n",
    "plt.plot(*line.get_sample(100), label='True Line')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Residuals and Cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Residuals are the differences between the true and predicted values along the sole prediction axis. Mean-squared-error is a common way to compute the quality of a prediction set compared to the true set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-07-21T15:17:00.807012",
     "start_time": "2017-07-21T15:17:00.800012"
    },
    "collapsed": true,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# mean squared error between true and predicted values\n",
    "def compute_mse(y_true, y_pred):\n",
    "    residuals = (y_pred-y_true)\n",
    "    ms = sum(residuals**2)/len(y_true)\n",
    "    return ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-07-21T15:17:01.448049",
     "start_time": "2017-07-21T15:17:01.350043"
    },
    "collapsed": false,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# Test with different slopes\n",
    "x, y_true = line.get_sample(100)\n",
    "plt.plot(x, y_true, label='true_sample')\n",
    "#sns.regplot(x, y, fit_reg=False, label=\"True\")\n",
    "for s in [-1, 0, 1, 1.5, 1.7, 2]:\n",
    "    l = Line(slope=s, intercept=5)\n",
    "    y_pred = l.get_y(x)\n",
    "    mse = compute_mse(y_true, y_pred)\n",
    "    plt.plot(x, y_pred, label=\"s={},c={:.3f}\".format(s, mse))\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-07-21T15:17:05.354272",
     "start_time": "2017-07-21T15:17:05.244266"
    },
    "collapsed": false,
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# Cost, testing with different slopes\n",
    "costs = []\n",
    "for s in np.linspace(0, 3, 20):\n",
    "    l = Line(slope=s, intercept=5)\n",
    "    y_pred = l.get_y(x)\n",
    "    mse = compute_mse(y, y_pred)\n",
    "    costs.append((s, mse))\n",
    "plt.scatter(x=[x[0] for x in costs], y=[x[1] for x in costs])\n",
    "plt.ylabel(\"cost\")\n",
    "plt.xlabel(\"slope\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "hidden": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "\n",
    "# Make data.\n",
    "slope = np.linspace(-2, 6, 20)\n",
    "intercept = np.linspace(-100, 200, 20)\n",
    "slope_s, intercept_s = np.meshgrid(slope, intercept)\n",
    "slope_m, intercept_m, x_m = np.meshgrid(slope, intercept, x)\n",
    "Y_pred = x_m * slope_m + intercept_m\n",
    "cost = np.array([compute_mse(y, Y_pred[i][j]) for i in range(20) for j in range(20)]).reshape(20, 20)\n",
    "#print(Y_pred.shape)\n",
    "#print(slope.shape)\n",
    "#print(intercept.shape)\n",
    "\n",
    "# Plot the surface.\n",
    "surf = ax.plot_surface(slope_s, intercept_s, cost, cmap=cm.coolwarm, linewidth=0, antialiased=False)\n",
    "\n",
    "# Customize the z axis.\n",
    "#ax.set_zlim(-1.01, 1.01)\n",
    "#ax.zaxis.set_major_locator(LinearLocator(10))\n",
    "#ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
    "\n",
    "# Add a color bar which maps values to colors.\n",
    "#fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression (Scipy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-14T09:13:02.925795",
     "start_time": "2017-09-14T09:13:02.884792"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope = 2.016 (r = 0.996, p = 0.00000)\n"
     ]
    }
   ],
   "source": [
    "# using scipy\n",
    "from scipy import stats\n",
    "\n",
    "line = Line(slope=2, intercept=6)\n",
    "(x, y) = line.get_rand_sample(100, 0, 10, noise=1)\n",
    "slope, intercept, r, p, _ = stats.linregress(x, y)\n",
    "print('Slope = {:.3f} (r = {:.3f}, p = {:.5f})'.format(slope, r, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using polynomial features can help to better model our data. Polynomial features can be obtained by raising to the power or by combining our original base features. Notice that the resulting polynomial function, even if not linear for the features, is a linear function of our target coefficients, so we are still dealing with a linear model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-14T09:29:22.107801",
     "start_time": "2017-09-14T09:29:22.034796"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot \n",
    "line = Line(slope=1.5, intercept=5)\n",
    "line.line_fun = lambda x : np.sin(2*np.pi*x)\n",
    "(x, y) = line.get_sample(20, noise=1)\n",
    "# plot (scatter) noisy sample\n",
    "sns.regplot(x, y, fit_reg=False, label='Noisy Sample')\n",
    "# plot line\n",
    "plt.plot(*line.get_sample(100), label='True Line')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve (SKlearn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-14T09:29:54.663663",
     "start_time": "2017-09-14T09:29:54.655662"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# create a polynomial features generator\n",
    "M = 9 # order of the polynomial\n",
    "poly = PolynomialFeatures(M)\n",
    "# generate polynomial features from original training data\n",
    "poly_x = poly.fit_transform(x.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-14T09:29:55.292699",
     "start_time": "2017-09-14T09:29:55.244696"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fir a linear regression model\n",
    "lr = LinearRegression()\n",
    "lr.fit(poly_x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-14T09:29:55.916734",
     "start_time": "2017-09-14T09:29:55.851731"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot results\n",
    "# plot training data\n",
    "sns.regplot(x, y, fit_reg=False, label='Noisy Sample')\n",
    "# plot true line\n",
    "plt.plot(*line.get_sample(100), label='True Line')\n",
    "# plot predicted line\n",
    "x_pred = np.linspace(0, 1, 40)\n",
    "y_pred = lr.predict(poly.fit_transform(x_pred.reshape(-1, 1)))\n",
    "plt.plot(x_pred, y_pred, label='Predicted Line (M={})'.format(M))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit regression line using gradient descent.\n",
    "\n",
    "[Link 1](http://aimotion.blogspot.co.uk/2011/10/machine-learning-with-python-linear.html)\n",
    "[Link 2](https://spin.atomicobject.com/2014/06/24/gradient-descent-linear-regression/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-08-31T16:13:33.390077",
     "start_time": "2017-08-31T16:13:33.377077"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Squared error cost function\n",
    "def compute_cost(X, y, theta):\n",
    "    m = len(y)\n",
    "    # compute predictions\n",
    "    pred = X.dot(theta).flatten()\n",
    "    # compute cost\n",
    "    mse = ((y - pred)** 2).sum()/(2*m)\n",
    "    return mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-08-31T16:13:33.533086",
     "start_time": "2017-08-31T16:13:33.528085"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# single gradient descent step\n",
    "def gradient_descent_step(X, y, theta, alpha):\n",
    "    # compute predictions\n",
    "    pred = X.dot(theta).flatten()\n",
    "\n",
    "    # get error\n",
    "    errors = -np.sum((y-pred)*X.T, axis=1).reshape(2,1)\n",
    "\n",
    "    # With regularization (notice bias should not be regularized) \n",
    "    #theta -= alpha * ((errors/len(y)) + (lambda*theta)/len(y))\n",
    "    theta -= alpha * (errors/len(y))\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-08-31T16:13:36.300244",
     "start_time": "2017-08-31T16:13:36.280243"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# run an entire training cycle\n",
    "def train(X, y, alpha, iters):\n",
    "    cost_history = np.zeros(shape=(iters, 1))\n",
    "    theta_history = []\n",
    "    \n",
    "    # our parameters are slope and intercepts (bias)\n",
    "    theta = np.random.randn(2, 1)\n",
    "    for i in range(iters):\n",
    "        theta = gradient_descent_step(X, y, theta, alpha)\n",
    "        \n",
    "        cost_history[i, 0] = compute_cost(X, y, theta)\n",
    "        theta_history.append(theta.copy())\n",
    "    \n",
    "    return theta_history, cost_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-08-31T16:13:54.127263",
     "start_time": "2017-08-31T16:13:54.102262"
    },
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 2)\n",
      "(100,)\n"
     ]
    }
   ],
   "source": [
    "# target line\n",
    "true_line = Line(slope=1.5, intercept=5)\n",
    "\n",
    "#training data\n",
    "(x_data, y) = true_line.get_rand_sample(100, noise=1)\n",
    "\n",
    "# train data including bias/intercept input (set to 1)\n",
    "X = np.ones(shape=(len(y), 2))\n",
    "X[:,1] = x_data\n",
    "\n",
    "print(X.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-08-01T12:05:45.588408",
     "start_time": "2017-08-01T12:05:45.559406"
    },
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "epochs = 1000\n",
    "theta_history, cost_history = train(X, y, alpha, epochs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-08-01T12:12:29.444507",
     "start_time": "2017-08-01T12:12:29.348502"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Plot history\n",
    "fig, axes = plt.subplots(2, 1)\n",
    "# plot cost\n",
    "axes[0].set_title('Cost History')\n",
    "axes[0].plot(cost_history.reshape(-1))\n",
    "axes[0].set_ylabel(\"cost\")\n",
    "# plot theta\n",
    "axes[1].set_title('Theta History')\n",
    "axes[1].plot([t[0] for t in theta_history], label='intercept')\n",
    "axes[1].plot([t[1] for t in theta_history], label='slope')\n",
    "axes[1].set_xlabel(\"epoch\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training Animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-08-31T16:26:14.174592",
     "start_time": "2017-08-31T16:26:14.092587"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.01\n",
    "epochs = 1000\n",
    "\n",
    "# Plot SGD animation\n",
    "fig, ax = sns.plt.subplots()\n",
    "#ax.set_xlim(0, 2)\n",
    "#ax.set_ylim(-10, 10)\n",
    "# plot true line\n",
    "ax.plot(*true_line.get_sample(2), label='target line')\n",
    "ax.scatter(x_data, y, label='train data')\n",
    "# initial fitted line\n",
    "theta = np.random.randn(2, 1)\n",
    "fit_line = Line(slope=theta[0], intercept=theta[1])\n",
    "# plot initial fitted line\n",
    "p_line, = ax.plot(*fit_line.get_sample(2), 'k-', label='regression line')\n",
    "epoch_text = ax.text(0, 0, \"Epoch 0\")\n",
    "\n",
    "def animate(i):\n",
    "    global X, y, theta, alpha\n",
    "    theta = gradient_descent_step(X, y, theta, alpha)\n",
    "    fit_line.intercept = theta[0]\n",
    "    fit_line.slope = theta[1]\n",
    "    l_x, l_y = fit_line.get_sample(2)\n",
    "    p_line.set_data(list(l_x), list(l_y))\n",
    "    cost = compute_cost(X, y, theta)\n",
    "    epoch_text.set_text(\"Epoch {}, Cost {:.4f}\".format(i, cost))\n",
    "    return epoch_text, p_line\n",
    "\n",
    "ani = animation.FuncAnimation(fig, animate, epochs, interval=10, repeat=False)\n",
    "plt.legend(loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:kaggle]",
   "language": "python",
   "name": "conda-env-kaggle-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700"
   },
   "moveMenuLeft": true,
   "nav_menu": {
    "height": "123px",
    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 4,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}