AM18_ex3.ipynb

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    "# Example 3: Rutherford Scattering\n",
    "\n",
    "With this example we want to illustrate Rutherford experiment, i.e. the scattering of charged particles at Coulomb potential. We consider the original setup of scattering Helium nuclei off a gold target. The corresponding repulsive potential reads $$V_{\\rm RF}(r)=\\frac{\\alpha}{r}\\,,\\quad \\text{with}\\quad \\alpha=\\frac{Z_{\\rm He}Z_{\\rm Au}e^2}{4\\pi\\epsilon_0}\\,,$$\n",
    "\n",
    "with $Z_{\\rm He}=2$ and $Z_{\\rm Au}=79$ the respective charge numbers, $e$ the elementary charge and $\\epsilon_0$ the electric field constant. In the lecture we have derived the relation between the impact parameter $b$ and the scattering angle $\\theta$, under which the projectiles get observed in a detector, i.e. $$b=\\left(\\frac{\\alpha}{2E}\\right)\\cot\\left(\\frac{\\theta}{2}\\right)=\\left(\\frac{\\alpha}{2E}\\right)\\tan^{-1}\\left(\\frac{\\theta}{2}\\right)\\,,$$ with $E$ the kinetic energy of the Helium nuclei. Furthermore, we derived the dependence of the differential scattering cross section on the angle $\\theta$: $$\\frac{d\\sigma_{\\rm RF}}{d\\Omega}=\\left(\\frac{\\alpha}{4E}\\right)^2\\frac{1}{\\sin^4\\left(\\frac{\\theta}{2}\\right)}\\,.$$ For the initial energy of the $\\alpha$-particles we assume $3.6$ MeV.\n",
    "\n",
    "\n",
    "To gain some first insight into the relation between the scattering angle and the impact parameter, we generate values for $\\theta$ at random, following the distribution \n",
    "\n",
    "$$P(\\theta>\\theta_{\\rm min})\\propto\\frac{1}{\\sin^4\\left(\\frac{\\theta}{2}\\right)}$$ \n",
    "\n",
    "This is based on a simple hit-or-miss Monte Carlo method, that is implemented in the function `genTheta` below. The resulting distribution can be seen in Fig. 2. In Fig. 3 we present the distribution of the corresponding impact parameters, note the microscopic scale!\n"
   ]
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    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random as ran\n",
    "\n",
    "## physical input parameters\n",
    "e = 1.602e-19\n",
    "epsilon0 = 8.854e-12\n",
    "Z1 =  2 # charge number He\n",
    "Z2 = 79 # charge number Au\n",
    "alpha = Z1*Z2*e*e/(4*np.pi*epsilon0)\n",
    "\n",
    "## energy of the incoming He nuclei (3.6 MeV)\n",
    "E = 3.6e6*e \n",
    "\n",
    "## generate theta according to 1/sin^4(theta/2)\n",
    "def genTheta(xmiss,ymiss,xhit,yhit):\n",
    "    hit=False\n",
    "    theta=0\n",
    "    thetamin=0.1\n",
    "    max=1./pow(np.sin(thetamin/2.),4)\n",
    "    while hit==False:\n",
    "        theta=(np.pi-thetamin)*ran.random()+thetamin        \n",
    "        ftheta=(max*(np.pi-theta+0.05))*ran.random()\n",
    "        func=pow(np.sin(theta/2.),-4)\n",
    "        if ftheta<func:\n",
    "            hit=True\n",
    "            xhit.append(theta)\n",
    "            yhit.append(ftheta)\n",
    "            return theta\n",
    "        else:\n",
    "            xmiss.append(theta)\n",
    "            ymiss.append(ftheta)\n",
    "            \n",
    "\n",
    "## calculate impact parameter from theta\n",
    "def calcb(theta):\n",
    "    b=(alpha/(2.*E))*1./np.tan(theta/2.)\n",
    "    return b\n",
    "\n",
    "## calculate theta from impact parameter\n",
    "def calcTheta( b ):\n",
    "    arg = (2.*E*b)/alpha\n",
    "    theta = 2.*np.arctan(1./arg)\n",
    "    return theta"
   ]
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   "cell_type": "markdown",
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   "source": [
    "# Monte Carlo Hit-or-Miss generation of $\\theta$ values"
   ]
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  {
   "cell_type": "code",
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       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
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       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
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       "\n",
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       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
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       "\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",
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       "    if (!this.waiting) {\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",
       "}\n",
       "\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",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
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       "    y1 = Math.floor(y1) + 0.5;\n",
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       "    var min_y = Math.min(y0, y1);\n",
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       "    var height = Math.abs(y1 - y0);\n",
       "\n",
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       "\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",
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       "        cursor = 'pointer';\n",
       "        break;\n",
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       "        break;\n",
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       "\n",
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       "    fig.message.textContent = msg['message'];\n",
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       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
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       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
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       "\n",
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       "    // 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",
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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",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(*args, **kw)>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xmiss = []\n",
    "ymiss = []\n",
    "xhit = []\n",
    "yhit = []\n",
    "\n",
    "for i in range(0,50):\n",
    "    theta=genTheta(xmiss,ymiss,xhit,yhit)\n",
    "  \n",
    "# scatter plot of accepted and rejected points\n",
    "fig = plt.figure(1)\n",
    "plt.scatter(xmiss, ymiss, marker='x',s=0.5,c='r',label='rejected')\n",
    "plt.scatter(xhit, yhit, marker='x',s=0.5,c='b',label='accepted')\n",
    "\n",
    "plt.legend()\n",
    "plt.title('hit-or-miss Monte Carlo', fontsize=20)\n",
    "plt.xlabel('$\\\\theta$')\n",
    "plt.ylabel('f($\\\\theta$)')\n",
    "\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# event loop: generate $\\theta$ and calculate $b$ and plot results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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kWVZSk1NrfG5cF+RGWyRpKamyrKC/9JzbbwqgKNGjQp5ufLycvuyw4cPr/K57du36//9v/8X9n1y00031bj+yrOyZs2aWo/7xRdfDPiq1GCp/lZCkjtzVSHU4qz8IpG6pPpSDfdnf+qpp9br9qr/G624f2644YaQtxeOxx57zL6dlStXhrzs3//+93qfNw4ePKihQ4cGfKV2x44d9fvf/z7oq57rUwDPOeecWi9blwJYXl4e8rpGjRplX7b69xFJBfDWW28N+3uq/POeN29e2MdaWSS9lyJqx08pDkRiAczJyan1uIMVwGnTptm30aZNGz333HNaunSpdu7cWeXps8qPQlQXqQVw9OjRIS8XqgBWfrXsr3/9a33wwQfasGGD9u3bV+Wp/YpHcgP9HOvy5r/ffPONXf6OO+44jR07VosWLdL27durPNU7YcKEkNfpVwHs27evLMtSVlZWwFeXBsuePXuqXE+4P/sOHTrIso49tV2X26v+NHm49084KhfA6m9zU52TAljh66+/1kMPPaQePXrUeES6SZMm+te//lXja+pTAGs7d0l1K4DVH9WrLhoLYG3fEwUw/vBTigORWACdPAU8aNAgWZalZs2ahXxKqeL3UQKdjGLtKeCysjL7F++vv/76kNdR8apcpwXw/vvvl2Ude2VuqPdbHDt2bEQUwIpXAKekpNQ6e6GE+7OveAXwySefXO/bktwtgJWXvJdPAQeyf/9+TZ06VUOGDLFfmNCoUaMar1yPhALo5Cngikc9A/2ObWUVb7cTTU8BUwBjCz+lOBCJBdCyQr8I5NChQ/arFfv06VPlc6eddpos69gbl4Zy1llnBT0ZXXrppbKsY7/wXJ8XgVT8PpnfLwJ555137MtWfpuK4uJi++OhXqX3zTff2JdzWgAvvvhiWdaxt60JpaKwmy6AlYto9Uc46iLcn33F/4AkJCTU6xXbFdwsgHPmzLHvg9peBFLx83WrAFY2btw4+7qrv/VN5SJSG68KYG0vAqk4B7Vv377G59LT02VZod/l4OjRo/aL3AId+4YNG1wpgHV5EUjFr0iEehEIBTC28FOKA5FaAEO9V9Rbb71lX+6JJ56o8rlf/OIXsqzQrw5evHix/fWBTkb/+Mc/7M8FerVybYYPHy7LCu93GcNR+VgXL14c9HIVJ+mkpKQqj5zMmzfP/vpQrw6+6667XCuA/fr1k2WFfpXrDz/8YP9JLtMFcOXKlfajM9dcc03I2wol3J995Tfzre13O0NxswCWl5fb/2N1xhlnBH3V//fff1/lKVu3C+CSJUvs667+XoSPP/64/bnafm/NqwJ46aWXBr2eBQsW2Je7/fbba3y+4n0Cu3XrFvQ6Pv74Y/s6Ah37li1b7M///e9/D/l9hfs2MBdddFHQ69i4caP9DEKot4GhAMYWfkpxIFILYMOGDTVr1qwal9m8ebP9NhJpaWk1XhVZ+S1cVq9eXePrt23bVuWvXgQ6Ge3fv18tW7a0b+Pzzz8P+v2UlpbW+FjF02OJiYlh/e3Z2lQ+1s6dO9f4vTOp6v/NV/4TWtKxv3BRUW769esXcLF/8MEH9jJwowD+9re/te+DOXPm1Pj83r17a7wS1mQBlP77fnvhPAK2bt26gG8GXJeffdeuXe3C/uabb4a87NKlSwM+eutmAZSku+++274P/vznP9f4/KFDh+y3BKnPeWP79u364IMPQr6lVOVHY6v/D8v//d//2Z+r/LeCA/GqAFqWFfDntXv3bp155pn2z7/6e01K0p133inLOvbIb6A/gbh582a1adMmZAE8dOiQXcBDvepdqtsbQb/00ks1Pn/gwAH17t3bvkyoN4KmAMYWfkpxIBILYHZ2tvLz85WamqrRo0dr1qxZWrBggZ599tkqf7My0JKu/F54ubm5+tvf/qY5c+Zozpw5Gjt2rHJycpSQkKDu3buHPBlV/lNwDRo00JAhQ/T+++9r0aJF+vLLLzVx4kRdeeWVSk5OrvG1U6dOta/7uuuu09y5c7V69Wo7dVW5/FmWpV/84heaNGmSiouL9dlnn+m2226z/1pE06ZNA/4cK79v24UXXqh3331XxcXFKioq0s0336ykpCS1a9dO2dnZrhTAyo+EZGZm6tFHH9XMmTM1f/58Pffcc2rXrp0s69ifD4yUArh9+/Yqy7dnz5568cUXNXfuXC1evFhTp07Vk08+qQsvvFCJiYk1irZUt5/9mjVrqrxN0SWXXKJXXnlF8+fPt382jz76qP0GuiNHjqz3/ROunTt32r8Da1mWrr32Wn3yySdatGiRXn/9dftPwFXMYl3PGxU/g1atWunuu+/Wm2++qXnz5qm4uFgffvihbrnlFnuWW7ZsWeOv3qxevdq+3T59+mjmzJlatWqVff9WfqGXVwWwc+fOSkpK0u23367p06eruLhYEydOtF/YY1mWfvvb3wa8neXLl9vnlWbNmumpp57SwoULNWfOHD3xxBM64YQT1KJFC/vfR7Bjr/h306JFC7322mtasWKFfR9UfiP02gpgaWmp/ahvYmKi/ud//kdTp05VcXGxXnnllSp/7/vqq68OeCwUwNjETykORGIBzM/P18KFC0P+UfFQTxFX/BJ2oCQlJemvf/1rWCejKVOm2CfHUKnuyJEj9tIO5/K1qXyfhXqLm/T09KCPVn733Xf2I6eBkpeXp6+//jrkz7EuBVCq+kKBQBk5cmSt1+lnAZSOPQJz7rnn1voztyxLQ4YMqfH1df3Zf/vtt/bvjNWWRx55pN73T10sX7485Ps23nTTTfU+b1T+GYRKTk5O0L96U/mR2uqpfCxeFcB169apdevWQY/hiiuuCPinBitU/h3H6mnevLm++OKLWo/9o48+Cvg2OtX/DdRWAKVjvxJT+X+sA+Xyyy8P+mbaFMDYxE8pDkRqAZSOlZY777xTJ598slJTU9WiRQv169cv4NMQ1f3zn//Uueeeq6ZNmyolJUX5+fn6zW9+Y79xb7gnox07dth/nL5FixZKSkpSenq6fvWrX2nEiBFasGBBwK/btWuXHnroIXXq1ElNmjSpcrKuq+r32ZQpUzRgwAAdf/zxSk5OVqtWrXT77bcHfDq6sp9++kn33nuv2rdvr5SUFGVkZKhTp04qLCzUzz//LCn0z7GuBVA69vtMffr0UbNmzZScnKwTTzxRl19+uf7973+HdZ1+F8AKH330ka6//nq1adNGaWlpatiwof13rkeOHBnw71RXqOvP/vDhw3rttdd0xRVXKC8vT40aNVJycrJycnJ03nnn6aGHHgr6oigvCqB07NHQ++67T+3atVNKSoqysrJ0/vnn20971/e8cfToUS1YsEB/+MMf1KdPH3Xo0EGZmZlq0KCBsrKy1LNnT40dO1ZlZWVBj+3gwYN64okn1LVrV2VkZNiPGPpVAKVjf9XmgQce0CmnnKK0tDRlZGSoZ8+eeuWVV2q9LenYv+G+ffuqWbNmSklJUevWrVVQUGD/ZZlwjn369OkaOHCgcnNzq/xpvroWQOnY09ePPfaYzjrrLGVmZio5OVm5ubm6/PLLQ75wLNxjlSiA0YafEnzl9tunxIpwyg0AAG6hAMJXFMDAKIAAAD9RAOErCmBgFEAAgJ8ogPAVBTAwCiAAwE8UQPiKAhgYBRAA4CcKIHxFAQyMAggA8BMFEAAAIM5QAAEAAOIMBdCBI0eOqLS0VDt37lRZWRkhhBBCoiA7d+5UaWmpjhw5YrpKGEMBdKC0tDSsP3lECCGEkMhLbX9dKZZRAB3YuXOnPUCm/2+GEEIIIeGl4gGcnTt3mq4SxlAAHSgrK5NlWSorC/43LQEAQGRhf1MAHWGAAACIPuxvCqAjDBAAANGH/U0BdIQBAgAg+rC/KYCOMEAAAEQf9jcF0BEGCACA6MP+pgA6wgABABB92N8UQEcYIAAAog/7mwLoCAMEAED0YX9TAB1hgAAAiD7sbwqgIwwQAADRh/1NAXSEAQIAIPqwvymAjjBAAABEH/Y3BdARBggAgOjD/qYAOsIAAQAQfdjfFEBHGCAAAOon//6Pao1X2N8UQEcYIAAA6ocCaBYF0AEGCACA+qEAmkUBdIABAgCgfiiAZlEAHWCAAACoHwqgWRRABxggAADqhwJoFgXQAQYIAID6oQCaRQF0gAECAKB+KIBmUQAdYIAAAKgfCqBZFEAHGCAAAOqHAmgWBdABBggAgPqhAJpFAXSAAQIAoH4ogGZRAB1ggAAAqB8KoFkUQAcYIAAA6ocCaBYF0AEGCACA+qEAmkUBdIABAgCgpnDKHQXQLAqgAwwQAAA1UQAjHwXQAQYIAICaKICRjwLoAAMEAEBNFMDIRwF0gAECAKAmCmDkowA6wAABAFATBTDyUQAdYIAAAKiJAhj5KIAOMEAAgHjjVrmjAJpFAXSAAQIAxBsKYGygADrAAAEA4g0FMDZQAB1ggAAA8YYCGBsogA4wQACAeEMBjA0UQAcYIABALPGz3FEAzaIAOsAAAQBiienCRwH0DwXQAQYIABBLTBc+CqB/orIAjhkzRp07d1aTJk2UnZ2tgQMHauXKlVUu06tXL1mWVSW33nprlcts3LhR/fv3V6NGjZSdna177rlHhw4dCvs4GCAAQCwxXfgogP6JygLYt29fTZo0ScuXL9dXX32l/v37Ky8vT3v27LEv06tXLw0bNkybN2+2U/kHffjwYZ122mm68MILVVJSoqKiImVlZWn06NFhHwcDBACIJaYLHwXQP1FZAKvbtm2bLMvSzJkz7Y/16tVLd911V9CvKSoqUmJiorZs2WJ/7Pnnn1d6eroOHDgQ1u0yQACAWGK68FEA/RMTBXD16tWyLEvLli2zP9arVy9lZWWpRYsW6tixo0aNGqW9e/fan3/44YfVqVOnKtezbt06WZalxYsXh3W7DBAAIJaYLnwUQP9EfQE8cuSIBgwYoLPPPrvKx8ePH68pU6Zo6dKleuWVV9SyZUtddtll9ueHDRumPn36VPmavXv3yrIsFRUVBbyt8vJylZWV2SktLY37AQIAxA7ThY8C6J+oL4DDhw9Xfn6+SktLQ17us88+k2VZWrNmjaT6FcDCwsIaLyyJ9wECAMQO04WPAuifqC6ABQUFOvHEE7Vu3bpaL7tnzx5ZlqUpU6ZIqt9TwDwCCACIZaYLHwXQP1FZAI8ePaqCggLl5uZq1apVYX3N7NmzZVmWlixZIum/LwLZunWrfZnx48crPT1d5eXlYV0nAwQAiCWmCx8F0D9RWQBvu+02ZWRk6PPPP6/yNi/79u2TJK1Zs0Z//OMfVVxcrPXr1+v9999XmzZt1LNnT/s6Kt4Gpk+fPvrqq680ZcoUZWdn8zYwAIC4ZbrwUQD9E5UFMNDv4VmWpUmTJkmSvvvuO/Xs2VPNmzdXSkqK2rZtq3vvvbfGD3rDhg266KKL1KhRI2VlZWnkyJG8ETQAIG6ZLnwUQP9EZQGMFAwQACCWmC58FED/UAAdYIAAALHEdOGjAPqHAugAAwQAiCWmCx8F0D8UQAcYIABALDFd+CiA/qEAOsAAAQBiienCRwH0DwXQAQYIABAtTJc5CmBkoQA6wAABAKKF6TJHAYwsFEAHGCAAQLQwXeYogJGFAugAAwQAiBamyxwFMLJQAB1ggAAA0cJ0maMARhYKoAMMEAAgWpgucxTAyEIBdIABAgBEC9NljgIYWSiADjBAAIBoYbrMUQAjCwXQAQYIABAtTJc5CmBkoQA6wAABAKKF6TJHAYwsFEAHGCAAQLQwXeYogJGFAugAAwQA8JpbRcl0maMARhYKoAMMEADAaxRA97G/KYCOMEAAAK9RAN3H/qYAOsIAAQC8RgF0H/ubAugIAwQA8BoF0H3sbwqgIwwQAMBrFED3sb8pgI4wQAAAr1EA3cf+pgA6wgABALxGAXQf+5sC6AgDBADwGgXQfexvCqAjDBAAwGsUQPexvymAjjBAAACvUQDdx/6mADrCAAEAvEYBdB/7mwLoCAMEAPCa6RJGAYxNFAbRBoEAACAASURBVEAHGCAAgNdMlzAKYGyiADrAAAEAvGa6hFEAYxMF0AEGCADgNdMljAIYmyiADjBAAACvmS5hFMDYRAF0gAECAHjNdAmjAMYmCqADDBAAwGumSxgFMDZRAB1ggAAAXjNdwiiAsYkC6AADBADwmukSRgGMTRRABxggAIDXTJcwCmBsogA6wAABALxmuoRRAGMTBdABBggAEIxbBcd0CaMAxiYKoAMMEAAgGAogBTCSUQAdYIAAAMFQACmAkYwC6AADBAAIhgJIAYxkFEAHGCAAQDAUQApgJKMAOsAAAQCCoQBSACMZBdABBggAEAwFkAIYySiADjBAAIBgKIAUwEhGAXSAAQIABEMBpABGMgqgAwwQACAYCiAFMJJRAB1ggAAAwVAAKYCRjALoAAMEAAjGdHmKhXiF/U0BdIQBAgAEY7o8xUK8wv6mADrCAAEAgjFdnmIhXmF/UwAdYYAAAMGYLk+xEK+wv6O0AI4ZM0adO3dWkyZNlJ2drYEDB2rlypVVLrN//37dfvvtat68uRo3bqzLL79cW7ZsqXKZjRs3qn///mrUqJGys7N1zz336NChQ2EfBwMEAAjGdHmKhXiF/R2lBbBv376aNGmSli9frq+++kr9+/dXXl6e9uzZY19m+PDhOumkk/TZZ5+puLhY3bp1U48ePezPHz58WKeddpouvPBClZSUqKioSFlZWRo9enTYx8EAAQCCMV2eYiFeYX9HaQGsbtu2bbIsSzNnzpQk7dy5Uw0bNtTbb79tX+abb76RZVmaO3euJKmoqEiJiYlVHhV8/vnnlZ6ergMHDoR1uwwQACAY0+UpFuIV9neMFMDVq1fLsiwtW7ZMkvTZZ5/Jsizt2LGjyuXy8vI0btw4SdLDDz+sTp06Vfn8unXrZFmWFi9eHPB2ysvLVVZWZqe0tDTuBwgAEJjp8hQL8QoFMAYK4JEjRzRgwACdffbZ9sdeffVVJScn17hsly5ddN9990mShg0bpj59+lT5/N69e2VZloqKigLeVmFhoSzLqpF4HiAAQGCmy1MsxCsUwBgogMOHD1d+fr5KS0vtj3lVAHkEEAAQLtPlKRbiFQpglBfAgoICnXjiiVq3bl2Vj3v1FHB1DBAAIBjT5SkW4hX2d5QWwKNHj6qgoEC5ublatWpVjc9XvAjknXfesT+2cuXKgC8C2bp1q32Z8ePHKz09XeXl5WEdBwMEAAjGdHmKhXiF/R2lBfC2225TRkaGPv/8c23evNnOvn377MsMHz5ceXl5mj59uoqLi9W9e3d1797d/nzF28D06dNHX331laZMmaLs7GzeBgYA4ArT5SkW4hX2d5QWwEAvxLAsS5MmTbIvU/FG0M2aNVNaWpouu+wybd68ucr1bNiwQRdddJEaNWqkrKwsjRw5kjeCBgC4wnR5ioV4hf0dpQUwUjBAAIBgTJenWIhX2N8UQEcYIABAMKbLUyzEK+xvCqAjDBAAIBjT5SkW4hX2NwXQEQYIABCM6fIUC/EK+5sC6AgDBAAIxnR5ioV4hf1NAXSEAQIABGO6PMVCvML+pgA6wgABAIIxXZ5iIV5hf1MAHWGAAADBmC5PsRCvsL8pgI4wQACAYEyXp1iIV9jfFEBHGCAAQDCmy1MsxCvsbwqgIwwQACAY0+UpFuIV9jcF0BEGCAAQjOnyFAvxCvubAugIAwQACMZ0eYqFeIX9TQF0hAECgNjjVjExXZ5iIV5hf1MAHWGAACD2UAAjJ15hf1MAHWGAACD2UAAjJ15hf1MAHWGAACD2mC49hALoBwqgAwwQAMQe06WHUAD9QAF0gAECgNhjuvQQCqAfKIAOMEAAEHtMlx5CAfQDBdABBggAYo/p0kMogH6gADrAAAFA7DFdeggF0A8UQAcYIACIPaZLD6EA+oEC6AADBACxx3TpIRRAP1AAHWCAACD2mC49hALoBwqgAwwQAMQe06WHUAD9QAF0gAECgNhjuvQQCqAfKIAOMEAAEHtMlx5CAfQDBdABBggAYo/p0kMogH6gADrAAAFA7DFdeggF0A8UQAcYIADwh59lwXTpIRRAP1AAHWCAAMAfbpUF04WGUAAjBQXQAQYIAPxBAYzPeIX9TQF0hAECAH9QAOMzXmF/UwAdYYAAwB8UwPiMV9jfFEBHGCAA8AcFMD7jFfY3BdARBggA/EEBjM94hf1NAXSEAQIAf1AA4zNeYX9TAB1hgADAHxTA+IxX2N8UQEcYIABwzs+yYLrQEApgpKAAOsAAAYBzFEBCAfQfBdABBggAnKMAEgqg/yiADjBAAOAcBZBQAP3nawH87rvvVFpaav/3/Pnzddddd2n8+PF+HoZrGCAAcI4CSCiA/vO1AJ5zzjl6+eWXJUmbN29Wenq6unfvrqysLD3yyCN+HoorGCAAcM50ySCRG6+wv30ugJmZmVq5cqUk6emnn1aPHj0kSZ9++qlat27t56G4ggECAOdMlwwSufEK+9vnAti4cWOtX79eknTJJZfo8ccflyRt3LhRqampfh6KKxggAHDOdMkgkRuvsL99LoBdu3bV/fffry+++EKpqan66quvJElz585Vy5Yt/TwUVzBAAOCc6ZJBIjdeYX/7XABnzJihzMxMJSYmasiQIfbHR48ercsuu8zPQ3EFAwQAzpkuGSRy4xX2t4G3gTl8+LB+/vnnKh9bv369tm3b5vehOMYAAYBzpksGidx4hf3tcwE8//zztWPHjhofLysr0/nnn+/nobiCAQIA50yXDBK58Qr72+cCmJCQoK1bt9b4+NatW9WgQQM/D8UVDBAAOGe6ZJDIjVfY3z4VwCVLlmjJkiVKSEjQjBkz7P9esmSJFi9erDFjxig/P9+PQ3EVAwQAzpkuGSRy4xX2t08FMCEhQYmJiUpMTFRCQkKNpKWlacKECWFf38yZM3XxxRcrJydHlmVp8uTJVT4/ePBgWZZVJX379q1yme3bt+u6665T06ZNlZGRoaFDh2r37t11+r4YIABwznTJIJEbr7C/fSqAGzZs0Pr165WQkKCFCxdqw4YNdn744QcdPny4TtdXVFSkBx98UO+9917QAtivXz9t3rzZTvUXnvTr10+dOnXSvHnzNGvWLLVt21bXXnttnY6DAQIA50yXDBK58Qr728CrgN0WrAAOHDgw6NesWLFClmVp4cKF9sc++eQTJSQkaNOmTWHfNgMEAM6ZLhkkcuMV9reBArhq1SqNHz9ef/rTn/TII49USX0EK4AZGRnKzs5W+/btNXz4cP3000/25ydMmKDMzMwqX3Po0CElJSXpvffeC/u2GSAAcM50ySCRG6+wv30ugC+88IKSkpJ0/PHHq1OnTjrjjDPsnHnmmfW6zkAF8PXXX9f777+vpUuXavLkyTrllFPUpUsX+6nmRx99VO3bt69xXdnZ2XruueeC3lZ5ebnKysrslJaWxv0AAYBTpksGidx4hQLocwHMy8uz//6vWwIVwOrWrl0ry7I0bdo0SfUvgIWFhTVeXBLvAwQATpkuGSRy4xUKoM8FsGnTplq7dq2r1xlOAZSkrKws/f3vf5dU/6eAeQQQANxnumSQyI1XKIA+F8ChQ4fq+eefd/U6wymApaWlSkhI0Pvvvy/pvy8CKS4uti/z6aef8iIQADDAdMkgkRuvsL99LoBjxoxRVlaWBg8erCeffFJPP/10lYRr9+7dKikpUUlJiSzL0rhx41RSUqKNGzdq9+7duueeezR37lytX79e06ZN069+9Su1a9dO5eXl9nX069dPZ555pubPn6/Zs2erXbt2vA0MABhgumSQyI1X2N8+F8BWrVoFTevWrcO+nhkzZgT8XbzBgwdr37596tOnj7Kzs9WwYUPl5+dr2LBh2rJlS5Xr2L59u6699lo1adJE6enpGjJkCG8EDQAGmC4ZJHLjFfZ3DLwPoEkMEAA4Z7pkkMiNV9jfFEBHGCAAcM50ySCRG6+wv30ugEOGDAmZaMMAAYBzpksGidx4hf3tcwH89a9/XSUDBgxQfn6+MjIydNlll/l5KK5ggADAOdMlg0RuvML+joCngI8cOaJbbrlFf/7zn00fSp0xQADgnOmSQSI3XmF/R0ABlKSVK1fqhBNOMH0YdcYAAYBzpksGidx4hf0dIQXw448/VlZWlunDqDMGCACcM10ySOTGK+xvnwvg7373uyoZMWKEBg0apCZNmqigoMDPQ3EFAwQAzpkuGSRy4xX2t88F8LzzzquSCy64QIMGDdL48eN16NAhPw/FFQwQADhnumSQyI1X2N8R8hRwtGKAAMA50yWDRG68wv42VAC3bdumWbNmadasWdq2bZuJQ3AFAwQAzpkuGSRy4xX2t88FcM+ePRoyZIiSkpKUkJCghIQENWjQQEOHDtXevXv9PBRXMEAA4JzpkkEiN15hf/tcAG+55Ra1adNGRUVFKisrU1lZmT7++GOdfPLJGj58uJ+H4goGCACcM10ySOTGK+xvnwtgixYtNGPGjBofnz59Om8DAwBxynTJIJEbr7C/fS6AjRo10ooVK2p8fPny5UpLS/PzUFzBAAFAaKYLBInueIX97XMBvOCCC3TVVVdp//799sf27dunq666Sr179/bzUFzBAAGIZ6bLAYn9eIX97XMBXLp0qXJzc9WiRQtdcMEFuuCCC9SiRQvl5uZq+fLlfh6KKxggAPHMdDkgsR+vsL8NvA3M3r179cILL+juu+/W3XffrX/84x/at2+f34fhCgYIQDwzXQ5I7Mcr7G+fC+CYMWM0YcKEGh+fMGGCHn/8cT8PxRUMEIB4ZrockNiPV9jfPhfA/Px8zZkzp8bH582bp1atWvl5KK5ggADEM9PlgMR+vML+9rkApqSkaN26dTU+vnbtWqWkpPh5KK5ggADEM9PlgMR+vML+9rkAtm3bVv/85z9rfPzll19W69at/TwUVzBAAOKZ6XJAYj9eYX/7XAD//Oc/q0WLFpo4caI2bNigDRs2aMKECWrRooXGjBnj56G4ggECEM9MlwMS+/EK+9vnAnj06FHdd999Sk1NVWJiohITE5WWlqZHHnnEz8NwDQMEIJ6ZLgck9uMV9reBt4GRpN27d2vBggVatmyZysvLTRyCKxggAPHMdDkgsR+vsL8NFcBYwQABiGemywGJ/XiF/U0BdIQBAhDPTJcDEvvxCvubAugIAwQgnpkuByT24xX2NwXQEQYIgFtMLsP6Ml0OSOzHK+xvCqAjDBAAt5hchvVluhyQ2I9X2N8UQEcYIABucWsZ+nk9hHgdr7C/KYCOMEAA3OLWMvTzegjxOl5hf1MAHWGAALjFrWXo5/UQ4nW8wv6mADrCAAFwi1vL0M/rIcTreIX9TQF0hAEC4Ba3lqGf10OI1/EK+5sC6AgDBMAtbi1DP6+HEK/jFfY3BdARBgiAW9xahn5eDyFexyvsbwqgIwwQALe4tQz9vB5CvI5X2N8UQEcYIABucWsZ+nk9hHgdr7C/KYCOMEAA3OLWMvTzegjxOl5hf1MAHWGAALjFrWVoemET4ma8wv6mADrCAAFwi1vL0PTCJsTNeIX9TQF0hAEC4Ba3lqHphU2Im/EK+5sC6AgDBMAtbi1D0wubEDfjFfY3BdARBgiAW9xahqYXNiFuxivsbwqgIwwQALe4tQxNL2xC3IxX2N8UQEcYIABucWsZml7YhLgZr7C/KYCOMEAA3OLWMjS9sAlxM15hf1MAHWGAALjFrWVoemET4ma8wv6mADrCAAFwi1vL0PTCJsTNeIX9TQF0hAEC4Ba3lqHphU2Im/EK+5sC6AgDBMAtbi1D0wubEDfjFfY3BdARBgiAW9xahqYXNiFuxivsbwqgIwwQALe4tQxNL2xC3IxX2N9RWgBnzpypiy++WDk5ObIsS5MnT67y+aNHj+rhhx/WCSecoNTUVPXu3VurVq2qcpnt27fruuuuU9OmTZWRkaGhQ4dq9+7ddToOBgiAW9xahqYXNiFuxivs7ygtgEVFRXrwwQf13nvvBSyAjz/+uDIyMvSvf/1LS5Ys0aWXXqrWrVtr//799mX69eunTp06ad68eZo1a5batm2ra6+9tk7HwQABcItby9D0wibEzXiF/R2lBbCy6gXw6NGjOuGEEzR27Fj7Yzt37lRKSopef/11SdKKFStkWZYWLlxoX+aTTz5RQkKCNm3aFPZtM0AA3OLWMjS9sAlxM15hf8dgAVy7dq0sy1JJSUmVy/Xs2VN33nmnJGnChAnKzMys8vlDhw4pKSlJ7733XtDbKi8vV1lZmZ3S0tK4HyAA7nBrGZpe2IS4Ga9QAGOwAM6ZM0eWZemHH36ocrmrrrpKV199tSTp0UcfVfv27WtcV3Z2tp577rmgt1VYWCjLsmokngcIgDvcWoamFzYhbsYrFEAKYBW1FUAeAQTgFbeWoemFTYib8QoFMAYLoJdPAVfHAAFwi1vL0PTCJsTNeIX9HYMFsOJFIE8++aT9sbKysoAvAikuLrYv8+mnn/IiEADGuLUMTS9sQtyMV9jfUVoAd+/erZKSEpWUlMiyLI0bN04lJSXauHGjpGNvA5OZman3339fS5cu1cCBAwO+DcyZZ56p+fPna/bs2WrXrh1vAwPAGLeWoemFTYib8Qr7O0oL4IwZMwK+GGPw4MGS/vtG0Mcff7xSUlLUu3dvffvtt1WuY/v27br22mvVpEkTpaena8iQIbwRNABj3FqGphc2IW7GK+zvKC2AkYIBAuAWt5ah6YVNiJvxCvubAugIAwTALW4tQ9MLmxA34xX2NwXQEQYIgFtML1pCIjFeYX9TAB1hgAC4xfSiJSQS4xX2NwXQEQYIgFtML1pCIjFeYX9TAB1hgAC4xfSiJSQS4xX2NwXQEQYIgFtML1pCIjFeYX9TAB1hgAC4xfSiJSQS4xX2NwXQEQYIgFtML1pCIjFeYX9TAB1hgACEw/QSJSRa4xX2NwXQEQYIQDhML1FCojVeYX9TAB1hgIDY5taCMr1ECYnWeIX9TQF0hAECYptbC8r0EiUkWuMV9jcF0BEGCIhtbi0o00uUkGiNV9jfFEBHGCAgtrm1oEwvUUKiNV5hf1MAHWGAgNjm1oIyvUQJidZ4hf1NAXSEAQJim1sLyvQSJSRa4xX2NwXQEQYIiG1uLSjTS5SQaI1X2N8UQEcYICC2mV5+hMR7vML+pgA6wgABsc308iMk3uMV9jcF0BEGCIhtppcfIfEer7C/KYCOMEBAbDO9/AiJ93iF/U0BdIQBAmKb6eVHSLzHK+xvCqAjDBAQ20wvP0LiPV5hf1MAHWGAgNhmevkREu/xCvubAugIAwTENtPLj5B4j1fY3xRARxggILaZXn6ExHu8wv6mADrCAAHRy/RiI4TUHq+wvymAjjBAQPQyvdgIIbXHK+xvCqAjDBAQvUwvNkJI7fEK+5sC6AgDBEQv04uNEFJ7vML+pgA6wgAB0cv0YiOE1B6vsL8pgI4wQED0Mr3YCCG1xyvsbwqgIwwQEL1MLzZCSO3xCvubAugIAwREL9OLjRBSe7zC/qYAOsIAAdHL9GIjhNQer7C/KYCOMECA/9xaGqYXGyGk9niF/U0BdIQBAvzn1tIwvdgIIbXHK+xvCqAjDBDgP7eWhunFRgipPV5hf1MAHWGAAP+5tTRMLzZCSO3xCvubAugIAwT4z/RCIoT4F6+wvymAjjBAgP9MLyRCiH/xCvubAugIAwSEz62TvemFRAjxL15hf1MAHWGAgPC5dbI3vZAIIf7FK+xvCqAjDBAQPrdO9qYXEiHEv3iF/U0BdIQBAsLn1sne9EIihPgXr7C/KYCOMEBA+Nw62ZteSIQQ/+IV9jcF0BEGCAifWyd70wuJEOJfvML+pgA6wgAB4XPrZG96IRFC/ItX2N8UQEcYICB8bp3sTS8kQoh/8Qr7mwLoCAMEHOPnyd70QiKE+BevsL8pgI4wQMAxfp7sTS8kQoh/8Qr7mwLoCAMEHOPnyd70QiKE+BevsL9juAAWFhbKsqwq6dChg/35/fv36/bbb1fz5s3VuHFjXX755dqyZUudboMBAo7x82RveiERQvyLV9jfMV4AO3bsqM2bN9v58ccf7c8PHz5cJ510kj777DMVFxerW7du6tGjR51ugwECjvHzZG96IRFC/ItX2N8xXgA7deoU8HM7d+5Uw4YN9fbbb9sf++abb2RZlubOnRv2bTBAwDF+nuxNLyRCiH/xCvs7xgtgWlqacnJy1Lp1a1133XXauHGjJOmzzz6TZVnasWNHla/Jy8vTuHHjwr4NBgg4xs+TvemFRAjxL15hf8dwASwqKtJbb72lJUuWaMqUKerevbvy8vK0a9cuvfrqq0pOTq7xNV26dNF9990X9DrLy8tVVlZmp7S0NO4HCJAogIQQb+IVCmAMF8DqduzYofT0dL344ov1LoCBXlgS7wMESBRAQog38QoFMI4KoCR17txZo0aNqvdTwDwCCATm58ne9EIihPgXr1AA46gA7t69W82aNdPTTz9tvwjknXfesT+/cuVKXgQC1JOfJ3vTC4kQ4l+8wv6O4QI4cuRIff7551q/fr3mzJmjCy+8UFlZWdq2bZukY28Dk5eXp+nTp6u4uFjdu3dX9+7d63QbDBBwjJ8ne9MLiRDiX7zC/o7hAjho0CDl5OQoOTlZLVu21KBBg7RmzRr78xVvBN2sWTOlpaXpsssu0+bNm+t0GwwQcIyfJ3vTC4kQ4l+8wv6O4QLoBwYIOMbPk73phUQI8S9eYX9TAB1hgIBj/DzZm15IhBD/4hX2NwXQEQYIOMb0kiCExGa8wv6mADrCAAHHmF4ShJDYjFfY3xRARxgg4BjTS4IQEpvxCvubAugIAwQcY3pJEEJiM15hf1MAHWGAgGNMLwlCSGzGK+xvCqAjDBBwjOklQQiJzXiF/U0BdIQBAo4xvSQIIbEZr7C/KYCOMECIB6YXACEkfuMV9jcF0BEGCJHM9ImbEEKcxivsbwqgIwwQIpnpEzchhDiNV9jfFEBHGCBEMtMnbkIIcRqvsL8pgI4wQIhkpk/chBDiNF5hf1MAHWGAEMlMn7gJIcRpvML+pgA6wgAhkpk+cRNCiNN4hf1NAXSEAUIkM33iJoQQp/EK+5sC6AgDhEhm+sRNCCFO4xX2NwXQEQYIkcz0iZsQQpzGK+xvCqAjDBBMMX1SJoQQP+IV9jcF0BEGCKaYPikTQogf8Qr7mwLoCAMEL5g+4RJCSKTEK+xvCqAjDBC8YPqESwghkRKvsL8pgI4wQPCC6RMuIYRESrzC/qYAOsIAwQumT7iEEBIp8Qr7mwLoCAMEL5g+4RJCSKTEK+xvCqAjDBAqc+tkZvqESwghkRKvsL8pgI4wQKjMrZOZ6RMuIYRESrzC/qYAOsIAoTK3TmamT7iEEBIp8Qr7mwLoCAOEytw6mZk+4RJCSKTEK+xvCqAjDBAqc+tkZvqESwghkRKvsL8pgI4wQKjMrZOZ6RMuIYRESrzC/qYAOsIAoTLTJ0pCCIm1eIX9TQF0hAGKH6ZPgoQQEo/xCvubAugIAxQ/TJ8ECSEkHuMV9jcF0BEGKH6YPgkSQkg8xivsbwqgIwxQ/DB9EiSEkHiMV9jfFEBHGKD4YfokSAgh8RivsL8pgI4wQPHD9EmQEELiMV5hf1MAHWGAYoPpExwhhJDA8Qr7mwLoCAMUG0yf4AghhASOV9jfFEBHGKDYYPoERwghJHC8wv6mADrCAMUG0yc4QgghgeMV9jcF0BEGKDaYPsERQggJHK+wvymAjjBAZpk+MRFCCPE2XmF/UwAdYYDMMn1iIoQQ4m28wv6mADrCAJll+sRECCHE23iF/U0BdIQBqh+3/tGbPjERQgjxNl5hf1MAHYm3AXLrH6uf10MIISR645V429+BUAAdiLcBcusfq5/XQwghJHrjlXjb34FQAB2ItwFy6x+rn9dDCCEkeuOVeNvfgVAAHfB6gEz+4/DyeEyfUAghhERHvEIBpAA6QgGs3/GYPqEQQgiJjniFAkgBdCQSCqCf/4BMnwgIIYTEV7xCAaQA6tlnn1V+fr5SUlLUtWtXzZ8/P+yvpQASQggh3sUrFMA4L4BvvPGGkpOTNXHiRH399dcaNmyYMjMztXXr1rC+ngJICCGEeBevUADjvAB27dpVBQUF9n8fOXJEubm5euyxx8L6egogIYQQ4l28QgGM4wJ44MABJSUlafLkyVU+fuONN+rSSy8N+DXl5eUqKyuz891338myLJWWllb5uFs5acRbhBBCSNzGi91aVlam0tJSWZalnTt3+lE5IlLcFsBNmzbJsix9+eWXVT5+7733qmvXrgG/prCwUJZlEUIIISQGUlpa6kfliEgUwDoUwOqPAO7YsUNr167Vzp07Pfk/E68eWYz2cP9w33D/cN9w/0ROovG+2blzp0pLS3XkyBE/KkdEitsCWJ+ngP1SVsbvJoTC/RMc901o3D/Bcd+Exv0THPdNdIrbAigdexHIHXfcYf/3kSNH1LJly7BfBOIV/jGFxv0THPdNaNw/wXHfhMb9Exz3TXSK6wL4xhtvKCUlRS+99JJWrFihW265RZmZmdqyZYvR4+IfU2jcP8Fx34TG/RMc901o3D/Bcd9Ep7gugJL0zDPPKC8vT8nJyeratavmzZtn+pBUXl6uwsJClZeXmz6UiMT9Exz3TWjcP8Fx34TG/RMc9010ivsCCAAAEG8ogAAAAHGGAggAABBnKIAAAABxhgIIAAAQZyiAEejZZ59Vfn6+UlJS1LVrV82fP9/0IUWEmTNn6uKLL1ZOTo4sy6rxJt7xbMyYMercubOaNGmi7OxsDRw4UCtXrjR9WBHhueee0+mnn66mTZuqadOm6tatm4qKikwfVkR67LHHZFmW7rrrLtOHEhEC/fnPDh06mD6siPL999/r+uuvV/PmzZWamqrTTjtNCxcuNH1YCAMFMMK88cYbSk5O1sSJE/X1119r2LBhyftrDgAACUpJREFUyszM1NatW00fmnFFRUV68MEH9d5771EAq+nbt68mTZqk5cuX66uvvlL//v2Vl5enPXv2mD404z744AN9/PHHWrVqlb799ls98MADatiwoZYvX2760CLKggUL1KpVK/3yl7+kAP5HYWGhOnbsqM2bN9v58ccfTR9WxPj555+Vn5+vm266SfPnz9e6dev06aefas2aNaYPDWGgAEaYrl27qqCgwP7vI0eOKDc31/hfJ4k0FMDQtm3bJsuyNHPmTNOHEpGaNWumF1980fRhRIzdu3erXbt2mjp1qnr16kUB/I/CwkJ16tTJ9GFErPvvv1/nnHOO6cNAPVEAI0gk/33iSEMBDG316tWyLEvLli0zfSgR5fDhw3r99deVnJysr7/+2vThRIwbb7xRI0aMkCQKYCWFhYVKS0tTTk6OWrdureuuu04bN240fVgR45RTTtGIESN05ZVXKjs7W2eccYZeeOEF04eFMFEAI8imTZtkWZa+/PLLKh+/99571bVrV0NHFZkogMEdOXJEAwYM0Nlnn236UCLG0qVL1bhxYyUlJSkjI0Mff/yx6UOKGK+//rpOO+007d+/XxIFsLKioiK99dZbWrJkiaZMmaLu3bsrLy9Pu3btMn1oESElJUUpKSkaPXq0Fi9erPHjxys1NVUvvfSS6UNDGCiAEYQCGD4KYHDDhw9Xfn6+SktLTR9KxDhw4IBWr16t4uJijRo1SllZWTwCKOm7777TcccdpyVLltgfowAGt2PHDqWnp/PrA//RsGFDde/evcrHfvvb36pbt26Gjgh1QQGMIDwFHD4KYGAFBQU68cQTtW7dOtOHEtF69+6tW265xfRhGDd58mRZlqWkpCQ7lmUpISFBSUlJOnz4sOlDjDidO3fWqFGjTB9GRMjLy9PNN99c5WPPPfeccnNzDR0R6oICGGG6du2qO+64w/7vI0eOqGXLlrwIpBoKYFVHjx5VQUGBcnNztWrVKtOHE/HOP/98DR482PRhGLdr1y4tW7asSjp37qwbbriB3x8NYPfu3WrWrJmefvpp04cSEa699toaLwIZMWJEjUcFEZkogBHmjTfeUEpKil566SWtWLFCt9xyizIzM7VlyxbTh2bc7t27VVJSopKSElmWpXHjxqmkpIRfypZ02223KSMjQ59//nmVt6zYt2+f6UMzbtSoUZo5c6bWr1+vpUuXatSoUUpISNC///1v04cWkXgK+L9Gjhypzz//XOvXr9ecOXN04YUXKisrS9u2bTN9aBFhwYIFatCggR599FGtXr1ar776qtLS0vTKK6+YPjSEgQIYgZ555hnl5eUpOTlZXbt21bx580wfUkSYMWNGjTdltSyLR3KkgPeLZVmaNGmS6UMzbujQocrPz1dycrKys7PVu3dvyl8IFMD/GjRokHJycpScnKyWLVtq0KBBvMddNR9++KFOO+00paSk6Be/+AWvAo4iFEAAAIA4QwEEAACIMxRAAACAOEMBBAAAiDMUQAAAgDhDAQQAAIgzFEAAAIA4QwEEAACIMxRAAADgyMyZM3XxxRcrJyfHlz/VGc7tFRYWqkOHDkpLS1NmZqZ69+7NH1aohAIIAAAcKSoq0oMPPqj33nvPlwIYzu29+uqrmjp1qtauXavly5fr5ptvVnp6On/K7z8ogABi1v33368BAwaEfflevXrZf0avpKTE0W0PHjzYvi6vlyEQSQLNfHl5uUaOHKnc3FylpaWpa9eumjFjhme3F0hZWZksy9K0adNcud1oRwEEELP69u2rBx54IOzL9+rVS8OGDdPmzZt16NAhR7e9c+dObd68mQKIuBNo5v/nf/5HPXr00BdffKE1a9Zo7NixSklJ0apVqzy5veoOHDigsWPHKiMjQz/++KPj24wFFEAAMev444/XG2+8Efble/XqpbvuusvVY6AAIt5Un/mNGzcqKSlJmzZtqnK53r17a/To0a7fXmUffvihGjdurISEBOXm5mrBggWOby9WUAABxKSKR99effVVnXvuuWrUqJE6d+6spUuXBv2aQAWwV69euuOOO3TXXXcpMzNTxx13nF544QXt2bNHN910k5o0aaKTTz5ZRUVFAa+TAoh4U33mP/roI1mWpcaNG1dJgwYNdPXVV0uSvvnmG/tXJoLl/vvvD+v2KtuzZ49Wr16tuXPnaujQoWrVqpW2bt3q/jcdhSiAAGLSJ598Isuy1KVLF82ePVtff/21zjvvPHXs2DHo1wQrgE2bNtWf/vQnrVq1Sn/605+UlJSkiy66SC+88IJWrVql2267TS1atNDevXtrXCcFEPGm+sy/8cYbSkpK0sqVK7V69eoq2bx5s6RjT9F+8803IRPsxRt1+TfWtm1bjRkzxvk3GQMogABi0mOPPabU1NQqTzvNmTNHlmUF/R2gYAXwnHPOsf/78OHDaty4sX7zm9/YH6t4tHHu3Lk1rpMCiHhTfea//fZbWZalL774wpfbC6VNmzYqLCz05DiiDQUQQEwaNGiQbrzxxiofW7FihSzLCvoUULACePvtt1f5WF5enp544gn7v48ePSrLsvT+++/XuE4KIOLB7t27VVJSopKSElmWpXHjxqmkpEQbN26UJF1//fVq1aqV3n33Xa1bt07z58/XmDFj9NFHH3lye3v27NHo0aM1d+5cbdiwQcXFxRoyZIhSUlK0fPly177vaEYBBBCTOnTooHHjxlX52MSJE9WyZcugXxOsAFb/WH5+vp566qkqHwtW9CiAiAczZswI+Ht7gwcPliQdPHhQv//979WqVSs1bNhQOTk5uuyyy0L+Tq6T29u/f78uu+wy5ebmKjk5WTk5Obr00kt5EUglFEAAMWfv3r1KTEzU2LFj7Y8dOXJEnTp10oMPPhj06yiAAOIFBRBAzJk7d64aNmyoU089VQsWLNDKlSt1xRVXqH379tq1a1fQr6MAAogXFEAAMef5559Xx44d9eabb6ply5Zq3LixrrnmGv30008hv44CCCBeUAAB4D94I2gA8YICCAD/0atXLzVs2FCNGzeu9y+nV7j11lvVuHFjCiCAiEQBBID/+P777+03qD1w4ICj69q6dat9XXv27HHpCAHAHRRAAACAOEMBBAAAiDMUQAAAgDhDAQQAAIgzFEAAAIA4QwEEAACIMxRAAACAOEMBBAAAiDP/H2Y/OD6pNRpAAAAAAElFTkSuQmCC\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ThetaVals = []\n",
    "bVals = []\n",
    "\n",
    "# number of scattering events\n",
    "noEvents = 5000\n",
    "\n",
    "# generate angle theta and calculate b \n",
    "for i in range(0,noEvents):\n",
    "    theta=genTheta(xmiss,ymiss,xhit,yhit)\n",
    "    b=calcb(theta)\n",
    "    ThetaVals.append(theta)\n",
    "    bVals.append(b)\n",
    "  \n",
    "\n",
    "# generate and plot histograms of theta and b values\n",
    "\n",
    "NBins = 50\n",
    "fig = plt.figure(2)\n",
    "\n",
    "# theta distribution\n",
    "n,bins,patches = plt.hist(ThetaVals,NBins,density=False, histtype='stepfilled')\n",
    "plt.title(\"scattering angle distribution\", fontsize=20)\n",
    "plt.xlabel('$\\\\theta$')\n",
    "plt.ylabel('counts')\n",
    "\n",
    "fig = plt.figure(3)\n",
    "\n",
    "# impact parameter distribution\n",
    "n,bins,patches = plt.hist(bVals,NBins,density=False, histtype='stepfilled')\n",
    "plt.title(\"impact parameter distribution\", fontsize=20)\n",
    "plt.xlabel('$b$ [m]')\n",
    "plt.ylabel('counts')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# illustration of selected particle trajectories\n",
    "\n",
    "As another illustration we want to consider the explicte trajectories for a set of scattering angles. For the repulsive\n",
    "Coulomb interaction the trajectory in polar coordinates is given by $$r(\\varphi)=\\frac{p}{e\\cos\\varphi-1}\\,,$$ this is implemented in function `Trajectory` below. Note, in order to have for the various scattering angles considered all incoming particles approach from $x\\to -\\infty$, we rotate the coordinate system accordingly. To specify the trajectory we have to use the corresponding relations of the parameters $p$ and $e$ to the scattering angle $\\theta$, i.e. the impact parameter $b=b(\\theta):\n",
    "\n",
    "$$p=\\frac{2b^2E}{\\alpha}\\,,\\quad e = \\sqrt{1+\\left(\\frac{2bE}{\\alpha}\\right)^2}\\,.$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
    {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# polar coordinate presentation of the hyperbola for the repulsive case\n",
    "def Trajectory(phi,theta,p,e):\n",
    "    r=p/(e*np.cos(phi)-1)\n",
    "    x=np.cos(phi+np.pi)*r\n",
    "    y=np.sin(phi+np.pi)*r\n",
    "    # rotate to new x' axis\n",
    "    angle = (theta-np.pi)/2.\n",
    "    xp=x*np.cos(angle)-y*np.sin(angle)\n",
    "    yp=x*np.sin(angle)+y*np.cos(angle)\n",
    "    return xp,yp \n",
    "\n",
    "# routine to plot an individual trajectory\n",
    "def plotTrajectory(theta):\n",
    "    b=calcb(theta)\n",
    "    e=np.sqrt(1+(4.*b*b*E*E)/alpha**2)\n",
    "    p=2.*b*b*E/alpha\n",
    "    dphi = (np.pi-theta)/2\n",
    "    plt.plot(*Trajectory(np.linspace(-0.999*dphi,0.999*dphi, 10000),theta=theta,p=p,e=e),label='$\\\\theta=$ %.2f' %theta)\n",
    "    return True;\n",
    "\n",
    "fig = plt.figure(4)\n",
    "\n",
    "# loop of set of scattering angles\n",
    "for val in [0.05,0.1,0.2,0.6,1.2,1.8]:\n",
    "    plotTrajectory(val)\n",
    "\n",
    "plt.xlabel('x [m]')\n",
    "plt.ylabel('y [m]')\n",
    "plt.xlim(-5.*10**-12, 5.*10**-12)\n",
    "plt.ylim(-5*10**-13, 3.*10**-12)\n",
    "plt.title(\"projectile trajectories\", fontsize=20)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# suggestions for further studies:\n",
    "\n",
    "- compile the actual differential cross section with respect to $\\theta$\n",
    "- study the dependence on the energy of the $\\alpha$-particles\n",
    "- consider the case of an attractive interaction and compare the trajectories\n",
    "- ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}