2D_benchmark.ipynb

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    "# An Introduction to the Immersed Boundary Method\n",
    "\n",
    "In this notebook, we introduce + demonstrate a simple 2D immersed boundary method. We simulate the *fluid-structure interaction* for an elastic fiber immersed in an incompressible fluid. \n",
    "\n",
    "## The Fluid\n",
    "In general, we can model a fluid via the incompressible Navier Stokes equations:\n",
    "\n",
    "$ \\rho(\\partial_t + \\vec{u}\\cdot\\vec{\\nabla})\\vec{u} = \\mu\\nabla^2 \\vec{u} - \\vec{\\nabla} P + \\rho\\vec{f}$\n",
    "\n",
    "$\\vec{\\nabla}\\cdot\\vec{u}=0$\n",
    "\n",
    "with density $\\rho$ and velocity $u$, viscosity $\\mu$, pressure $P$, and where $f$ is an external force density. \n",
    "\n",
    "We can easily solve these equations on a grid using any fluid solver - in this code, we use fast fourier transforms (fft's). The original code was written for periodic boundary conditions, but can (in certain circumstances) be generalized to allow Dirichlet or Neumann boundary conditions by taking the edges as ghost cells, which we update between iterations. \n",
    "\n",
    "## The Solid\n",
    "NS are difficult to solve for complex boundary conditions, so modeling the flow around a strangely shaped obstacle - especially a deformable obstacle - is difficult. This is where the Immersed Boundary Method comes in. \n",
    "\n",
    "We treat the boundary as a set of Lagrangian points $X$ which move at the fluid velocity $U$ (i.e. no-slip) and are connected by springs of stiffness $K$. Then, to model the fluid-structure interaction, the elastic force felt at each boundary point is then exerted locally onto the fluid. Since the only effect of the boundary on the fluid is to exert an external force, NS can be solved for a fluid without the geometry of the boundary. \n",
    "\n",
    "Crucially, the fluid $u$ is modeled on an *eulerian* grid, while the *lagrangian* boundary points $X$ are generally off-grid. A *discrete dirac-delta function* can be used to transform from the eulerian grid to the lagrangian boundary, and vice versa. In particular, to calculate the Lagrangian boundary velocity $U$ , we can *interpolate* the nearby Eulerian velocities $u$; and likewise, we can *spread* the elastic Lagrangian force $F$ onto the nearby eulerian gridpoints to exert a force density $f$. \n",
    "\n",
    "Here, we use the four-point dirac-delta function constructed by Peskin - which effectively means we interpolate to / spread from the nearest 4x4(x4) Eulerian points, with the appropriate weights. \n",
    "\n",
    "## Implementation\n",
    "\n",
    " The immersed boundary method generally proceeds as follows:\n",
    "\n",
    "- At each timestep, we interpolate the local fluid velocity $u(t)$ to find the boundary velocity $U(t)$ and then estimate the new boundary position $X$\n",
    "\n",
    "\n",
    "- The elastic force at the new boundary point $X_k$ is $F_k \\approx K(X_{k+1}-X_k) + K(X_k-X_{k-1})$. At each boundary point, we spread this force to the fluid and then solve Navier Stokes with the resulting external force density $f$ to compute the new fluid velocity $u$\n",
    "\n",
    "\n",
    "To properly model the time evolution of the system, we must calculate both the velocity of the fluid $u^{n+1}$ and the position of the immersed boundary $X^{n+1}$ at each timestep. Since the boundary motion is determined by the fluid velocity, and force exerted on the fluid is determined by the boundary position, calculating both of these simultaneously is tricky. Consequently, we *iterate* the system by first computing the boundary position at a *half* timestep $X^{n+1/2}$, and use the resulting 'midpoint' force $F^{n+1/2}$ to compute both the updated fluid velocity $u^{n+1}$, and the 'midpoint' fluid velocity $u^{n+1/2}$ used to compute the updated boundary position $X^{n+1}$. Explicitly,\n",
    "\n",
    "- We first compute the *midpoint* boundary position  $XX = X(t+\\frac{dt}{2} \\approx X(t)+\\frac{dt}{2}U(t)$, and then compute the force density $ff$ at the midpoint. \n",
    "- We then solve Navier Stokes subject to $ff$ to find both the updated fluid velocity $u(t+dt)$; and the midpoint fluid velocity $uu\\equiv u(t+\\frac{dt}{2})$\n",
    "- Finally, we interpolate $uu$ to find the midpoint boundary velocity $UU \\equiv U(t+\\frac{dt}{2})$, and the updated boundary $X(t+dt) = X(t) + UUdt$\n"
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    "# Benchmarking the Fluid Solver: Poisseuille Flow\n",
    "\n",
    "To start, let's simulate a flow through a channel by setting $u_x=1, u_y=0$ at the top and the bottom:"
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       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"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\";/* global mpl */\n",
       "\n",
       "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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "plt.rcParams['animation.writer'] = animation.writers['pillow']\n",
    "ani_path = 'tutorial_figures/'\n",
    "%matplotlib notebook \n",
    "\n",
    "from ib2 import IB2\n",
    "from fluid2 import FLUID    #### Generic fluid solver\n",
    "    \n",
    "import warnings; warnings.simplefilter('ignore')\n",
    "\n",
    "########  Simulate pressure-driven flow in no-slip channel    #############\n",
    "\n",
    "#### Initialization of Fluid+Boundary Conditions\n",
    "fluid = FLUID(L=2.)\n",
    "\n",
    "def channel(u):\n",
    "    u[0][:, 0] = 0.\n",
    "    u[0][:,-1] = 0.\n",
    "\n",
    "    u[1][:, 0] = 0.\n",
    "    u[1][:,-1] = 0.\n",
    "    \n",
    "fluid.boundary = channel    ## No-slip channel\n",
    "\n",
    "inlet_pressure = 0*fluid.u\n",
    "inlet_pressure[0][0, :] = 1.    ## External force density is pressure-driven flow at inlet\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "# Velocity Profile\n",
    "ax = fig.add_subplot(1,2,1)\n",
    "plt.title('Velocity Profile at x=N/2')\n",
    "plt.xlabel('y')\n",
    "plt.ylabel('vx')\n",
    "\n",
    "cmap = plt.get_cmap('tab10')\n",
    "y = np.linspace(0, fluid.L, fluid.N)\n",
    "u_theo = -1.*y*(y-fluid.L)\n",
    "profile_theo = ax.plot(u_theo, color=cmap(1))\n",
    "\n",
    "#### Vorticity Map\n",
    "ax2 = fig.add_subplot(1, 2, 2)\n",
    "plt.xlim([0, fluid.L])\n",
    "plt.ylim([0, fluid.L])\n",
    "\n",
    "ims = []\n",
    "for i in range(2000):\n",
    "    fluid.t += fluid.dt\n",
    "    uu = fluid.step_u(inlet_pressure)\n",
    "    if i%20==0:\n",
    "        #Velocity Profile\n",
    "        im = ax.plot(fluid.u[0][int(fluid.N/2), :], color=cmap(0))  ## ax.plot returns a list of 2DLines (e.g. list of artists)\n",
    "        im.extend(profile_theo)\n",
    "\n",
    "        # Vorticity Map\n",
    "        im.append(fluid.show_vorticity(ax2))     #### show_vorticity returns output from plt.imshow(), which is an artist\n",
    "        im.append(ax2.set_title('t={}'.format(1*fluid.t)))\n",
    "        ims.append(im)\n",
    "\n",
    "ani = animation.ArtistAnimation(fig, ims, interval=50, repeat_delay=100)\n",
    "ani.save(ani_path+'2D_pois_vanilla.gif', writer='pillow')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "u_pois = fluid.u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we see that we get a poisseuille flow profile, as expected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reynolds Number\n",
    "\n",
    "In the specific case of flow through a pipe, the flow profile has the analytic form $v_x = \\frac{Gy^2}{4\\mu}$, where $y$ is the distance from the center of the pipe, and $G\\equiv\\Delta P/L$ is dependent on the pressure gradient.\n",
    "\n",
    "Plugging in our boundary condition that the walls are moving at $u_0$ at a $y=L_y/2$, we have \n",
    "\n",
    "$u_0 = \\frac{G(L/2)^2}{4\\mu}$, and $v_x = u_0\\big(\\frac{2y}{L_y}\\big)^2$\n",
    "\n",
    "This allows us to quantify Reynolds number and the scale of the inlet flow $G$ in terms of system parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2D Elastic Boundaries\n",
    "Next, we simulate an actual immersed boundary. We take the poisseuille flow we established in the previous simulation, and put two elastic, circular boundaries in it. The boundary points are off-grid, move at the local fluid velocity, and are connected to each other by simple springs. \n",
    "\n",
    "We write a (commented-out) method which shows explicitly how the midpoint-method time-iteration works, but in general it is easier to use the built-in functions. ib2 has step_XX and step_X to update $XX$ and $X$ respectively, and $ib2.ff$ returns the midpoint force Force(XX) spread to the fluid at the points XX. Likewise, fluid.step_u updates the fluid velocity u and returns the midpoint velocity uu. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "#### Iterate fluids and immersed solids using built-in functions\n",
    "def iterate(fluid, solids, ext=None):\n",
    "    dt = fluid.dt\n",
    "    fluid.t += dt\n",
    "    \n",
    "    ff = 0.          ## Force density on fluid\n",
    "    for solid in solids:\n",
    "#         solid.XX=solid.X+(dt/2)*solid.interp(fluid.u,solid.X)  # Euler step to midpoint\n",
    "#         F = solid.Force(solid.XX)\n",
    "#         ff += solid.vec_spread(F,solid.XX) # Force at midpoint # Force at midpoint \n",
    "        solid.step_XX(fluid.u)                                   # equivalent built-in functions\n",
    "        ff += solid.ff \n",
    "    if ext is not None:   ## External force on fluid.    **NOTE: add this after the solid forces (not before), otherwise numpy gets cranky\n",
    "        ff += ext\n",
    "    uu=fluid.step_u(ff) # Step Fluid Velocity\n",
    "    for solid in solids:\n",
    "#         solid.X+=dt*solid.interp(uu,solid.XX) # full step using midpoint velocity         \n",
    "        solid.step_X(uu)                        # built-in function            \n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we illustrate a general procedure for modeling a system:\n",
    "1) Initialize the fluid and fluid parameters (L, $\\rho$, $\\eta$, etc) and fields (i.e. $\\vec{u}$)\n",
    "\n",
    "2) Initialize the immersed boundary(ies) and specify relevant parameters (i.e. $K$)\n",
    "\n",
    "3) Iterate the system in time\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    var resizeObserver = new ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"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\";/* global mpl */\n",
       "\n",
       "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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Return a Nbx2 array corresponding to a circle of radius RAD centered at position POS\n",
    "def CIRCLE(Nb, RAD, POS):  \n",
    "    theta = np.linspace(0, 2*np.pi, Nb)\n",
    "    return np.array(POS)[None, :] + RAD*np.vstack([np.cos(theta), np.sin(theta)]).transpose()\n",
    "    \n",
    "fluid = FLUID(L=2.)\n",
    "fluid.u = u_pois\n",
    "fluid.boundary = channel\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "fig.figsize=(8, 8)\n",
    "fluid.show_streamlines(ax, cmap='coolwarm')\n",
    "plt.title('Initial Velocity Profile')\n",
    "plt.show()\n",
    "\n",
    "circle1 = CIRCLE(100, 0.2, (0.1, 0.3))*fluid.L\n",
    "circle2 = CIRCLE(100, 0.1, (0.1, 0.8))*fluid.L\n",
    "\n",
    "solid1 = IB2(circle1, fluid.N, fluid.h, fluid.dt)\n",
    "solid2 = IB2(circle2, fluid.N, fluid.h, fluid.dt)\n",
    "solids = [solid1, solid2]\n",
    "\n",
    "ext = fluid.u*0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we iterate the system forward in time. Let's also briefly discuss how we're creating the corresponding animations. \n",
    "\n",
    "A common way to create animations via matplotlib is using the function plt.animation.FuncAnimation, in which the *data* for a matplotlib object (for example, the y-values of a scatterplot) are specified for each frame in an animation. Here, we use slightly-heavier but still useful the ArtistAnimation function, in which the *artists* are specified on each frame of the animation. *Artists* are matplotlib objects responsible for displaying lines, points, and other visuals in a figure. Many of matplotlib's functions actually return either an artist or a list of artists - for example, plt.imshow() returns an artist corresponding to the output image to be drawn; and plt.plot() returns a list of artists, corresponding to each of the lines to be plotted. \n",
    "\n",
    "ArtistAnimation takes as input a list of lists of artists. Each frame corresponds to a particular list of artists to be displayed, while other lists of artists remain hidden. Conceptually, FuncAnimation is like saying \"plot *this line* with *different y-values* at each frame\", whereas ArtistAnimation is like saying \"plot a *different line* at each frame\". "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    var resizeObserver = new ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"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\";/* global mpl */\n",
       "\n",
       "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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Animation\n",
    "fig, ax = plt.subplots()\n",
    "fig.figsize=(12, 8)\n",
    "plt.xlim([0, fluid.L])\n",
    "plt.ylim([0, fluid.L])\n",
    "\n",
    "cmap = plt.get_cmap('tab10')\n",
    "ims = []\n",
    "\n",
    "for i in range(500):\n",
    "    iterate(fluid, solids, ext=inlet_pressure)\n",
    "    if i%10==0:\n",
    "        im = [fluid.show_vorticity(ax)]\n",
    "#         lines, arrows = fluid.show_streamlines(ax)\n",
    "#         im.append(lines)\n",
    "#         im.append(arrows)\n",
    "        for i, solid in enumerate(solids):\n",
    "            im.append(plt.scatter(solid.X[:, 0]%fluid.L, solid.X[:, 1]%fluid.L, color=cmap(2*i)))\n",
    "            im.append(plt.scatter([solid.X[0, 0]%fluid.L], [solid.X[0, 1]%fluid.L], color=cmap(2*i+1)))\n",
    "        im.append(plt.title('t={}'.format(1*fluid.t)))\n",
    "        ims.append(im)\n",
    "        \n",
    "ani = animation.ArtistAnimation(fig, ims, interval=50, repeat_delay=100)\n",
    "ani.save(ani_path+'2D_pois_circles.gif', writer='pillow')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Another Example: Shear Flow\n",
    "\n",
    "An interesting aspect of this simulation is that the elastic bodies elastically repel each other without imposing any repulsive forces. In general, an elastic membrane will not \"topologically\" cross itself, since boundary points move at the fluid velocity and the fluid is incompressible. Likewise, multiple immersed bodies will preserve their own topologies in the same manner, and consequently will not 'penetrate' each other under moderate conditions. \n",
    "\n",
    "Likewise, boundaries which are initialized as 'overlapping' will remain overlapped, and 'overlapping' boundaries typically correspond to a system which is not physical."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "fluid = FLUID(L=2.)\n",
    "\n",
    "def shear(u):\n",
    "    u[0][:, 0] = 1.\n",
    "    u[0][:,-1] = -1.\n",
    "    u[1][:, 0] = 0.\n",
    "    u[1][:,-1] = 0.\n",
    "\n",
    "fluid.boundary = shear\n",
    "\n",
    "for i in range(1000):\n",
    "    fluid.t += fluid.dt\n",
    "    uu = fluid.step_u(0.)\n",
    "\n",
    "u_shear = fluid.u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    var resizeObserver = new ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"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\";/* global mpl */\n",
       "\n",
       "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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div id='2d3e428c-31d0-48d5-a648-040ce322b33c'></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    var resizeObserver = new ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"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\";/* global mpl */\n",
       "\n",
       "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 = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div id='cfda1bcc-9935-4e13-8ab4-d0427e5070d7'></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fluid = FLUID(L=2.)\n",
    "fluid.u = u_shear\n",
    "fluid.boundary = shear\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "fig.figsize=(8, 8)\n",
    "fluid.show_streamlines(ax, cmap='coolwarm')\n",
    "plt.title('Initial Velocity Profile')\n",
    "plt.show()\n",
    "\n",
    "circle1 = CIRCLE(100, 0.18, (0.1, 0.25))*fluid.L\n",
    "circle2 = CIRCLE(100, 0.18, (0.5, 0.5))*fluid.L\n",
    "circle3 = CIRCLE(100, 0.18, (0.9, 0.75))*fluid.L\n",
    "\n",
    "solid1 = IB2(circle1, fluid.N, fluid.h, fluid.dt)\n",
    "solid2 = IB2(circle2, fluid.N, fluid.h, fluid.dt)\n",
    "solid3 = IB2(circle3, fluid.N, fluid.h, fluid.dt)\n",
    "solids = [solid1, solid2, solid3]\n",
    "\n",
    "\n",
    "#### Animation\n",
    "fig, ax = plt.subplots()\n",
    "fig.figsize=(12, 8)\n",
    "plt.xlim([0, fluid.L])\n",
    "plt.ylim([0, fluid.L])\n",
    "\n",
    "cmap = plt.get_cmap('tab10')\n",
    "ims = []\n",
    "\n",
    "for i in range(700):\n",
    "    iterate(fluid, solids, ext=ext)\n",
    "    if i%10==0:\n",
    "        im = [fluid.show_vorticity(ax)]\n",
    "#         im.append(fluid.show_streamlines())\n",
    "        for i, solid in enumerate(solids):\n",
    "            im.append(ax.scatter(solid.X[:,0]%fluid.L, solid.X[:,1]%fluid.L, color=cmap(2*i)))\n",
    "            im.append(ax.scatter([solid.X[0,0]%fluid.L], [solid.X[0, 1]%fluid.L], color=cmap(2*i+1)))\n",
    "#             im.append(plt.scatter(solid.XX[0], solid.XX[1], color=cmap(2*i+1)))\n",
    "        im.append(plt.title('t={}'.format(1*fluid.t)))\n",
    "        ims.append(im)\n",
    "        \n",
    "ani = animation.ArtistAnimation(fig, ims, interval=50, repeat_delay=100)\n",
    "ani.save(ani_path+'circle_in_init_shear.gif')\n",
    "\n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Several Circles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'u_shear' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-21-73951edaebb7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mfluid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFLUID\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mfluid\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mu\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mu_shear\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mfluid\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mboundary\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mshear\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'u_shear' is not defined"
     ]
    }
   ],
   "source": [
    "fluid = FLUID(L=2.)\n",
    "fluid.u = u_shear\n",
    "fluid.boundary = shear\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "fluid.show_streamlines(cmap='coolwarm')\n",
    "plt.title('Initial Velocity Profile')\n",
    "plt.show()\n",
    "\n",
    "R = 0.025\n",
    "solids = []\n",
    "for i in range(30):\n",
    "    solids.append(IB2(CIRCLE(25, R, (0.8*np.random.random(size=2)+0.1))*fluid.L, fluid.N, fluid.h, fluid.dt))\n",
    "\n",
    "#### Animation\n",
    "fig = plt.figure()\n",
    "fig.figsize=(12, 8)\n",
    "plt.xlim([0, fluid.L])\n",
    "plt.ylim([0, fluid.L])\n",
    "\n",
    "cmap = plt.get_cmap('tab10')\n",
    "ims = []\n",
    "\n",
    "for i in range(500):\n",
    "    iterate(fluid, solids, ext=ext)\n",
    "    if i%10==0:\n",
    "        im = [fluid.show_vorticity()]\n",
    "#         im.append(fluid.show_streamlines())\n",
    "        for i, solid in enumerate(solids):\n",
    "            im.append(plt.scatter(solid.X[0]%fluid.L, solid.X[1]%fluid.L, color=cmap(2*i)))\n",
    "            im.append(plt.scatter([solid.X[0][0]]%fluid.L, [solid.X[1][0]]%fluid.L, color=cmap(2*i+1)))\n",
    "#             im.append(plt.scatter(solid.XX[0], solid.XX[1], color=cmap(2*i+1)))\n",
    "        im.append(plt.title('t={}'.format(1*fluid.t)))\n",
    "        ims.append(im)\n",
    "        plt.show()\n",
    "        \n",
    "ani = animation.ArtistAnimation(fig, ims, interval=50, repeat_delay=100)\n",
    "# # ani.save('circle_in_init_shear.mp4')\n",
    "\n",
    "# writer = animation.FFMpegWriter(\n",
    "#     fps=15, metadata=dict(artist='Me'), bitrate=1800)\n",
    "# ani.save(\"movie.mp4\", writer=writer)\n",
    "\n",
    "plt.show()        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# *DEPRECATED* \n",
    "# Two Circles in a Uniform Flow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at a different configuration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "fluid = FLUID(L=2.)\n",
    "fluid.u[1] += 1.\n",
    "plt.figure(figsize=(8, 8))\n",
    "fluid.show_streamlines(cmap='autumn')\n",
    "plt.title('Initial Velocity Profile')\n",
    "plt.show()\n",
    "\n",
    "circle = CIRCLE(100, 0.15, (0.3, 0.1))*fluid.L\n",
    "solids = IB2(circle, fluid.N, fluid.h, fluid.dt)\n",
    "solids = [solids]\n",
    "\n",
    "\n",
    "\n",
    "#### Animation\n",
    "fig = plt.figure()\n",
    "fig.figsize=(12, 8)\n",
    "plt.xlim([0, fluid.L])\n",
    "plt.ylim([0, fluid.L])\n",
    "\n",
    "cmap = plt.get_cmap('tab10')\n",
    "ims = []\n",
    "\n",
    "for i in range(600):\n",
    "    iterate(fluid, solids)\n",
    "    if i%10==0:\n",
    "        im = [fluid.show_vorticity()]\n",
    "#         fluid.show_streamlines()\n",
    "        for i, solid in enumerate(solids):\n",
    "            im.append(plt.scatter(solid.X[0], solid.X[1], color=cmap(2*i)))\n",
    "            im.append(plt.scatter(solid.XX[0], solid.XX[1], color=cmap(2*i+1)))\n",
    "        im.append(plt.title('t={}'.format(1*fluid.t)))\n",
    "        ims.append(im)\n",
    "        \n",
    "ani = animation.ArtistAnimation(fig, ims, interval=50, blit=True, repeat_delay=100)\n",
    "# ani.save('dynamic_images.mp4')\n",
    "plt.show()     \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's try two circles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "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 / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"800\">"
      ],
      "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 / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" 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 / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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VHPX9HRpyR3S6hzptbHSmsnVPRih6//WxvwmABqhgQA0m8b2toUa4NjjRjVHhXN6mRm9qg+gOVXv/uO9Zgl6DWF+EwCN0EAAggrngIVgt7G3jYpEmZwHcPZ51aeraeqVQGrua8FQFw7mNwHQCA0ExKCGwluofxLeKNNq6nkAa4c2kyuBtOLgFinMbwKgERoIaKUaC3Hv50qrJ0trHpPe/13gfU25MD1FNaVC3cMWzn0xHtoiiflNADRCAwEtIFiYCxbiam5b/NPqS0VFe8BTsVmNfact1L8T1qKO+U0ANEIDASGqHeIa2wNX975lv5am9oj+0Kdip6b3rD44JtwrgRDcYgrzmwBohAZCzDP9Phwfq1KRrBm9pOUPhH8lEAIc6mB+EwCN0EBoNZpydYW6f9Z9DMGNas6ani4tvSO0Xo3CaUIQ25jfBEAjNBCaJNy9aqcakAQ1qiWr9l64cK8Ewp44tBLMbwKgERoojviqqgfYmseDH3gQyvfZCGtUNKv2d9+aciUQ9sIhhjC/CYBGaCCL+APc5OpLDK2eJG2Y+6+AtmHuvy4/VPe+//mV9Hi36A9wKv6qob1t4QQ49rgB9TC/CYBGaKAW1mCIy5Fe+6X06u3Sq7+of/uLw6TJZ0V/mFPxVaEesNDQbYQ2oNkwvwmARmigJgoIcjXBrXYFCXEvDJUmdY7+UKfip2oOUgj3yGfCG9DqMb8JgEbivoFOGeSCFEGOauma9j3pzQmhXQmEAAfEhbif34qxADhv3jylp6fL7XbL6/WqsLCwwWUzMjLkOE69Gj58eMjri8kGOlFZPSD/NFLK+09p/g+lF/6j+s+av+f9p/T7IQQ5quWrJsw1diWQmtsIcgAaEJPzO0wxEwDz8/Plcrk0f/58bd++XWPHjpXH49GBAweCLv/VV19p//79/tq2bZsSExOVl5cX8jqta6ATldL6udILg6XZF0ozz5dmnS/NvVya93+kqRydSjVzTU+XltwR3pHT7JUDEGHWze9mEDMB0Ov1avz48f6ffT6funfvrmnTpoX0+KeeekqdOnXS0aNHQ15nq2sgX5W0653qj1pnXyhN6ylNO0eaeo406czoD3/K3mrq9+EIcABaoVY3v6MgJgJgZWWlEhMTtXTp0oDbx4wZo8zMzJCe48ILL9TYsWPDWm/UGshXJe1cLc2/ofqi93wUS9VUOFdXCOWE0wQ3ADGIABgjAXDfvn1yHEcFBQUBt0+YMEFer/eUjy8sLJTjOI1+Z1CSKioqVF5e7q+SkpKWaaBvy6Tnr5MmnRH9gEFFPqyZXgmEoAYAYSEAEgAlSePGjdNFF110yuVycnKCHjjSLA30bZn0zDXRDylUYE1NlfJ/1vQrgRDWACDqCIAxEgBNPgI+evSokpOTNWfOnFOup8X2AOakRT/oxGo93kV66frwrgTCEaUAEFMIgDESAKXqg0Cys7P9P/t8PqWmpp7yIJC8vDy53W59+eWXYa+zWRoo2gHJlnrsTGnxT0O7Esirv6g+V+HutQQ4AAABUDEUAPPz8+V2u7VgwQIVFxdr3Lhx8ng8Ki0tlSSNHj1aEydOrPe4q6++Wv/1X//VpHVGvIGiHaqiFeReHHrqK4HU3E6QAwAYIgDGUACUpNzcXKWlpcnlcsnr9Wrjxo3++zIyMpSVlRWw/I4dO+Q4jlatWtWk9UW0gfZ8FP0w1ixhLlgR5AAA0UMAjLEA2NIi2kDRDm/BapJHmveD4FcCeeXnhDkAgJUIgARAI9YHwCe6B14J5HeXS7ne6mC3cw2BDgAQkwiABEAjVgTAx7pUXwlkaro0vZf0/CBpw5zqy8IBABCHCIAEQCOtPgBO6mz+ugAAiDEEQAKgkVYfAAmBAADUQwAkABqJaAMV/bX5QuChz8xfHwAAMYIASAA0Ys15AJ84OzKvDwCAGEAAJAAasedKIJ7IvT4AACxHACQAGmm2BmIPIAAAzYYASAA00qwNVLKd7wACANAMCIAEQCMt0kBffc5RwAAARBABkABopMUb6NBnhD8AAAwRAAmARqLaQL4q6W8Lgge/x7rwsS8AAA0gABIAjdBAAADYh/lNADRCAwEAYB/mNwHQCA0EAIB9mN8EQCM0EAAA9mF+EwCN0EAAANiH+U0ANEIDAQBgH+Y3AdAIDQQAgH2Y3wRAIzQQAAD2YX4TAI3QQAAA2If5TQA0QgMBAGAf5jcB0AgNBACAfZjfBEAjNBAAAPZhfhMAjdBAAADYh/lNADRCAwEAYB/mNwHQCA0EAIB9mN8EQCM0EAAA9mF+EwCN0EAAANiH+U0ANEIDAQBgH+Y3AdAIDQQAgH2Y3wRAIzQQAAD2YX4TAI3QQAAA2If5TQA0QgMBAGAf5jcB0AgNBACAfZjfBEAjNBAAAPZhfhMAjdBAAADYh/lNADRCAwEAYB/mNwHQCA0EAIB9mN8EQCM0EAAA9mF+EwCN0EAAANiH+U0ANEIDAQBgH+Y3AdAIDQQAgH2Y3wRAIzQQAAD2YX4TAI3QQAAA2If5TQA0QgMBAGAf5jcB0AgNBACAfZjfBEAjNBAAAPZhfsdYAJw3b57S09Pldrvl9XpVWFjY6PKHDx/WXXfdpW7dusnlcqlv37568803Q14fDQQAgH2Y3zEUAPPz8+VyuTR//nxt375dY8eOlcfj0YEDB4IuX1lZqX/7t3/T8OHDtWHDBu3du1fr1q3Txx9/HPI6aSAAAOzD/I6hAOj1ejV+/Hj/zz6fT927d9e0adOCLv/ss8+qV69eOn78eJPXSQMBAGAf5neMBMDKykolJiZq6dKlAbePGTNGmZmZQR9z/fXX66c//anGjh2rLl266IILLtCUKVNUVVXV4HoqKipUXl7ur5KSkrhvIAAAbEMAjJEAuG/fPjmOo4KCgoDbJ0yYIK/XG/Qx/fr1k9vt1u23366PPvpI+fn56ty5syZNmtTgenJycuQ4Tr2K5wYCAMA2BMA4DoB9+/bV9773vYA9frNnz1a3bt0aXA97AAEAsB8BMEYCYFM+Ar7mmms0aNCggNuWL18ux3FUWVkZ0nppIAAA7MP8jpEAKFUfBJKdne3/2efzKTU1tcGDQB588EGlp6fL5/P5b5szZ47OPvvskNdJAwEAYB/mdwwFwPz8fLndbi1YsEDFxcUaN26cPB6PSktLJUmjR4/WxIkT/cv/85//VKdOnZSdna1PP/1Uy5YtU5cuXfTEE0+EvE4aCAAA+zC/YygASlJubq7S0tLkcrnk9Xq1ceNG/30ZGRnKysoKWL6goEBXXHGF3G63evXqdcqjgOuigQAAsA/zO8YCYEujgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zO8YC4Lx585Seni632y2v16vCwsIGl83Ly5PjOAHldrvDWh8NBACAfZjfMRQA8/Pz5XK5NH/+fG3fvl1jx46Vx+PRgQMHgi6fl5en5ORk7d+/31+lpaVhrZMGAgDAPszvGAqAXq9X48eP9//s8/nUvXt3TZs2LejyeXl5SklJMVonDQQAgH2Y3zESACsrK5WYmKilS5cG3D5mzBhlZmYGfUxeXp4SExOVlpamHj16KDMzU9u2bWt0PRUVFSovL/dXSUlJ3DcQAAC2IQDGSADct2+fHMdRQUFBwO0TJkyQ1+sN+piCggK9/PLLKioq0rp16/TDH/5QycnJKikpaXA9OTk59b43GO8NBACAbQiAcRwA6zp+/Lh69+6thx9+uMFl2AMIAID9CIAxEgCb8hFwMLfccotGjhwZ8vI0EAAA9mF+x0gAlKoPAsnOzvb/7PP5lJqa2uBBIHVVVVWpX79+uu+++0JeJw0EAIB9mN8xFADz8/Pldru1YMECFRcXa9y4cfJ4PP5Tu4wePVoTJ070Lz958mStXLlSe/bs0aZNmzRy5Ei1b99e27dvD3mdNBAAAPZhfsdQAJSk3NxcpaWlyeVyyev1auPGjf77MjIylJWV5f/53nvv9S/btWtXDR8+XJs3bw5rfTQQAAD2YX7HWABsaTQQAAD2YX4TAI3QQAAA2If5TQA0QgMBAGAf5jcB0AgNBACAfZjfBEAjNBAAAPZhfhMAjdBAAADYh/lNADRCAwEAYB/mNwHQCA0EAIB9mN8EQCM0EAAA9mF+EwCN0EAAANiH+U0ANEIDAQBgH+Y3AdAIDQQAgH2Y3wRAIzQQAAD2YX5HOQCOGTNG7777bjRfghEaCAAA+zC/oxwAR4wYoXbt2qlPnz6aMmWKPv/882i+nLDRQAAA2If53Qo+Aj548KBmz56t/v37q23btho2bJheffVVHT9+PNov7ZRoIAAA7MP8bgUBsLZNmzYpOztb7du315lnnql7771XO3fujPbLahANBACAfZjfrSgAfvHFF5o+fbr69eunjh07asyYMRo0aJDatm2rJ598MtovLygaCAAA+zC/oxwAjx8/rtdee0033HCD2rVrp8suu0zPPvtswAZZsmSJPB5PFF9lw2ggAADsw/yOcgA844wzdPrpp+uuu+5SUVFR0GUOHz6snj17tvArCw0NBACAfZjfUQ6ACxcu1LFjx6L5EozQQAAA2If53Yq+A2gjGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zO8YC4Lx585Seni632y2v16vCwsKQHrd48WI5jqMRI0aEtT4aCAAA+zC/YygA5ufny+Vyaf78+dq+fbvGjh0rj8ejAwcONPq4vXv3KjU1VQMHDiQAAgAQB5jfMRQAvV6vxo8f7//Z5/Ope/fumjZtWoOPqaqq0lVXXaUXX3xRWVlZBEAAAOIA8ztGAmBlZaUSExO1dOnSgNvHjBmjzMzMBh/36KOP6sYbb5QkAiAAAHGC+R0jAXDfvn1yHEcFBQUBt0+YMEFerzfoY9avX6/U1FQdOnRIUmgBsKKiQuXl5f4qKSmJ+wYCAMA2BMA4DYDffPONevbsqeXLl/tvCyUA5uTkyHGcehXPDQQAgG0IgDESAMP9CLioqEiO4ygxMdFfCQkJSkhIUGJionbv3h10PewBBADAfgTAGAmAUvVBINnZ2f6ffT6fUguO4mYAABi/SURBVFNTgx4EcuzYMW3dujWgRowYoeuuu05bt25VZWVlSOukgQAAsA/zO4YCYH5+vtxutxYsWKDi4mKNGzdOHo9HpaWlkqTRo0dr4sSJDT6eg0AAAIgPzO8YCoCSlJubq7S0NLlcLnm9Xm3cuNF/X0ZGhrKyshp8LAEQAID4wPyOsQDY0mggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/yOsQA4b948paeny+12y+v1qrCwsMFl/+d//keXXXaZUlJSlJSUpAEDBmjhwoVhrY8GAgDAPszvGAqA+fn5crlcmj9/vrZv366xY8fK4/HowIEDQZdfu3atlixZouLiYu3evVtz5sxRYmKi3nrrrZDXSQMBAGAf5ncMBUCv16vx48f7f/b5fOrevbumTZsW8nNccsklevjhh0NengYCAMA+zO8YCYCVlZVKTEzU0qVLA24fM2aMMjMzT/n4kydPas2aNUpKStKqVatCXi8NBACAfZjfMRIA9+3bJ8dxVFBQEHD7hAkT5PV6G3xcWVmZOnbsqLZt28rtduull15qdD0VFRUqLy/3V0lJSdw3EAAAtiEAxnkA9Pl82rVrl4qKijRr1iylpKRo7dq1DS6fk5Mjx3HqVTw3EAAAtiEAxkgANP0IuMYvfvELDRkypMH72QMIAID9CIAxEgCl6oNAsrOz/T/7fD6lpqaGdRDIz3/+c2VkZIS8PA0EAIB9mN8xFADz8/Pldru1YMECFRcXa9y4cfJ4PCotLZUkjR49WhMnTvQvP3XqVK1atUp79uxRcXGxZs2apbZt2+qFF14IeZ00EAAA9mF+x1AAlKTc3FylpaXJ5XLJ6/Vq48aN/vsyMjKUlZXl//mhhx5Snz591L59e51++um68sorlZ+fH9b6aCAAAOzD/I6xANjSaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGiEBgIAwD7MbwKgERoIAAD7ML8JgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAgMiq8p1Uwe4v9XrR5yrY/aWqfCcjvg7mNwHQCA0EAEDkrNj6hS5/fKXSH1jmr8sfX6kVW7+I6HqY3wRAIzQQAACRsWLrFwHBr25FMgQyvwmARmggAADMVflOqu9DyxsNgH0fWh6xj4OZ3wRAIzQQAADm1hUfaDT81dS64gMRWR/zmwBohAYCAMBMle+khj25NqQAeN4jyyOyTuY3AdAIDQQAQHC1j+bdsOuQNuw8FPD3JZs/1//9c5H657wVUvirqSPHThi/NuY3AdAIDQQAiEUNhbeC3V+q8oQv4DQttX+uWfaxN7bpksdWhhXsQq3bXiwwfn/MbwKgERoIANBa1D1/XihBLdh9c1Z/qiumrG4wgJ0zsfGfm7vOf9j8Y2DmNwHQCA0EADDVWHBrLKjVvi9YaAsnqLV0iDMKgI+sMP6dM78JgEZoIACIT6f6fltjf68d5IJ9VBorQa256rb5hcbbj/lNADRCAwGAHYIFtiWbP9eL7+3Rkk0lYYW4SHy/jSDX9OIgkMggABqggQCgZdUEuWDhrea21z4qCbjvyVU7NGBS8xyQQLVs/fB370akj5jfBEAjNBAAhCecAEeQo2rXNb99O2J9yPwmABqhgQDEk1DCW2O3EeCoplTvB9/Ukk2fR7SXmd8EQCM0EIDWLpST8Tb2Pbia+yf9ZWuzndeNotIfWKYBk1bq/j8XafqKYt2zeLNmrCjWhp2HInb939qY3wRAIzQQgObS2N62UAMce9yo5qhwTi9z6WOrNPmNbafs3YLdXzZL0GsI85sAaIQGAhBM3fBW97tsp/rIlL1tVCTK5DyAP5i6RnNW72zylUBq7mvJUBcO5jcB0AgNBMSehsJbqH8S3ijTaup5AGuHNpMrgbTm4BYpzG8CoBEaCGidGgtxv393j2as+Lt++9bf9ft3dwfc15QL01NUU6pukKv5qLSpVwKJh9AWScxvAqARGghofsHCXLAQV3PbrxZ+qAseXR71AU/FfjX2/bZQrwRCeIsO5jcB0AgNBISmdohrbA9c3fsefX2LLsxZEfVBT8VODZi8Uk+t+tToSiCENvsxvwmARmggxDrT78PxsSrVXDVg0kr93z8XhXQlEEIb6mJ+EwCN0EBobRq73umpwlrdQUpwo5qzQglwBDk0F+Y3AdAIDQQToe5dC2VAsqeNaqm69LFVmvTGtiZdCYQAh9aC+U0ANEIDxZdQD0bgaFOqNVbt77415Uog0ThZL9BcmN8EQCM0kF2qfCe1YdchzXxrh3771t/13Lrd/oD23Lrd/ssPTV9RHHAfByNQ0aqG9raFE+DY4wbUx/wmABqhgVpesBBXE9zu/tMm3f2nTf4AV/v2cS//Td9/6M2oD3Qqfqp2eAv3SiDsbQOaF/ObAGiEBmq6miD327f+HhDeGgtxP3pmg3o3chZ8iopk1RykEO6Rz4Q3oPVjfhMAjdBApw5ywYogR7VkXZTzlh59fWtI380kwAHxgfkdYwFw3rx5Sk9Pl9vtltfrVWFhYYPL/v73v9fVV18tj8cjj8ejQYMGNbp8MLHYQLUD3d1/2qyfPF+gm55er588X6CRz73v//t///Ej/ejp9Y1el5KiIl01Ya6xK4HU3EaQA9CQWJzf4YqZAJifny+Xy6X58+dr+/btGjt2rDwejw4cOBB0+VGjRunpp59WUVGR/v73v+u2225TSkqKPv/885DXaVsDVflO6r1PD+ruP23W4NlrddXU1bpy6ioNmvm2rn9qna54nAvYU81bAyat1P1/Lgr7yGnCHIBIsm1+N4eYCYBer1fjx4/3/+zz+dS9e3dNmzYtpMdXVVWpU6dOevnll0NeZ2tsoMoTPj27dpcGz16riyev1CWTVujinOU696HoD3/K3mrq9+EIcABao9Y4v1taTATAyspKJSYmaunSpQG3jxkzRpmZmSE9xzfffKP27dvrr3/9a8jrjWYDfVdZpQde+0QXT16pPg8u0zmtICRQraeCXe803CuBENwAxCoCYIwEwH379slxHBUUFATcPmHCBHm93pCe484771SvXr107NixBpepqKhQeXm5v0pKSlqkgb6rrNKEVz/WhY+uIOjFYJ1q71qoVwIhsAFAaAiABEBJ0rRp03T66afrk08+aXS5nJwcOY5Tr5qjgY4cO6FRv/8g6uGECl6NHYzA0aYA0LoRAGMkAJp8BDxz5kylpKToww8/POV6WmoP4DVPRD/gxHpd8OgK3ZdfFPKVQAhtABA7CIAxEgCl6oNAsrOz/T/7fD6lpqY2ehDIjBkzlJycrA8++KBJ62yOBop2MLKp+j20XPflF4V0JZDpK4o5NQgAQBIBUIqhAJifny+3260FCxaouLhY48aNk8fjUWlpqSRp9OjRmjhxon/56dOny+Vy6bXXXtP+/fv9deTIkZDXGekGinagilb1/c2buuWZDae8EkhNzVhRrA07DxHiAABNQgCMoQAoSbm5uUpLS5PL5ZLX69XGjRv992VkZCgrK8v/c3p6etDv8+Xk5IS8vkg20JbPyqIexCJR1816J6SrgRDkAADRQgCMsQDY0iLZQNEObg1V7weX6d9nvhP0SiD//cdNGvV8gX654G/6/bu7VXnCF4HfKgAAzYsASAA0YnsA7PnAMl08+S3/lUAGzXpb/zH7HY187n1NW76dvXMAgJhEACQAGrEhAPZ5cJkuzlmu/jkrdMnkFbpu5tv67z9+pPd2HCTcAQDiEgGQAGiktQfAXg8ui8C7BAAgthAACYBGWnsArPkOHwAA+BcCIAHQSCQb6M3CkmYLgZ8d+jYC7xYAgNhAACQAGrHlPIDnPbw8Iq8PAIBYQAAkABqx5UogPR/gY2AAAGoQAAmARpqrgdgDCABA8yEAEgCNNGcDRfLKIHwHEACAfyEAEgCNtEQD/ePAUY4CBgAgggiABEAjLd1Au/YfIfwBAGCIAEgANBLNBjpy7IRunbs6aPDr95s3+dgXAIAGEAAJgEZoIAAA7MP8JgAaoYEAALAP85sAaIQGAgDAPsxvAqARGggAAPswvwmARmggAADsw/wmABqhgQAAsA/zmwBohAYCAMA+zG8CoBEaCAAA+zC/CYBGaCAAAOzD/CYAGqGBAACwD/ObAGikrKxMjuOopKRE5eXlFEVRFEVZUCUlJXIcR2VlZdGOElFDADRQ00AURVEURdlXJSUl0Y4SUUMANODz+VRSUqKysrKg/2fBnsHWV2yb1l1sn9ZdbJ/WW2yb8KqsrEwlJSXy+XzRjhJRQwBsBuXlfLegtWLbtG5sn9aN7dN6sW0QLgJgM+AfYuvFtmnd2D6tG9un9WLbIFwEwGbAP8TWi23TurF9Wje2T+vFtkG4CIDNoKKiQjk5OaqoqIj2S0EdbJvWje3TurF9Wi+2DcJFAAQAAIgzBEAAAIA4QwAEAACIMwRAAACAOEMABAAAiDMEwCDmzZun9PR0ud1ueb1eFRYWhvS4xYsXy3EcjRgxIuD20tJSZWVl6eyzz1aHDh00dOhQ7dy503//3r17G7xMzSuvvBLR92a7lt42krR//3797Gc/U9euXZWUlKRLLrlEr732WsTeUyyJxvbZvXu3brzxRp155pnq1KmTbr31VpWWlkbsPcWScLZPXl5evf8eud3ugGVOnjypRx55RN26dVP79u01aNCgetvnq6++0qhRo9SpUyelpKTo9ttv15EjR5rl/dksGtvmiSee0JVXXqkOHTooJSWlWd4XWi8CYB35+flyuVyaP3++tm/frrFjx8rj8ejAgQONPm7v3r1KTU3VwIEDA4bYyZMn9YMf/EADBw7U3/72N+3YsUPjxo1TWlqajh49KkmqqqrS/v37A2ry5Mk67bTT+A9lLdHYNpI0ePBgXX755SosLNSePXv0+OOPq02bNtq8eXOzvVcbRWP7HD16VL169dJNN92kLVu2aMuWLRoxYoQuv/zyuL7EUzDhbp+8vDwlJycH/HepbrCePn26UlJS9Prrr+uTTz5RZmamzjnnHB07dsy/zLBhwzRgwABt3LhR69evV58+ffSTn/ykWd+rbaK1bR599FE9+eSTuv/++wmAcYgAWIfX69X48eP9P/t8PnXv3l3Tpk1r8DFVVVW66qqr9OKLLyorKytgiH366adyHEfbtm0LeM6zzjpLL7zwQoPPefHFF+v22283fDexJVrbpmPHjlq4cGHA83bu3LnR7RePorF9Vq5cqTZt2gSc/LasrEwJCQlavXp1JN+e9cLdPnl5eY2GgpMnT6pbt26aOXOm/7aysjK53W4tXrxYklRcXCzHcfThhx/6l1mxYoUSEhK0b98+07cUM6KxbcJ5PsQmAmAtlZWVSkxM1NKlSwNuHzNmjDIzMxt83KOPPqobb7xRkuoNsS1btshxHO3evTvgMT169FBWVlbQ5/voo4/kOI7ef//9Jr6T2BPNbTN48GDdcMMN+uqrr+Tz+bR48WIlJSVp165dEXhnsSFa2+eNN95QYmJiwMlvKyoqlJiYqJycHMN3FTuasn3y8vKUmJiotLQ09ejRQ5mZmQFhfM+ePXIcR0VFRQGPu+aaa3T33XdLkl566SV5PJ6A+0+cOKHExEQtWbIkEm/NetHaNnWfjwAYfwiAtezbt0+O46igoCDg9gkTJsjr9QZ9zPr165WamqpDhw5Jqj/Ejh8/rrS0NN166636+uuvVVlZqenTp8txHA0ZMiToc955550677zzIvSuYkM0t83hw4c1ZMgQOY6jtm3bKjk5WStXrmyGd2mvaG2fgwcPKjk5Wffcc4++/fZbHT16VNnZ2XIcR+PGjWumd2ufpmyfgoICvfzyyyoqKtK6dev0wx/+UMnJySopKZEkvf/++3IcR1988UXA42699Vb9+Mc/liRNmTJF3//+9+s991lnnaVnnnkmEm/NetHaNrURAOMTAbCWcP8hfvPNN+rZs6eWL1/uv63uEJOq9+gNGDBAjuMoMTFRQ4cO1fXXX69hw4bVe87vvvtOKSkpmjVrVoTeVWyI5rbJzs6W1+vVmjVr9PHHH2vSpElKSUnRli1bIvwu7RXN7bNy5Ur16tVLCQkJSkxM1M9+9jNdeumluuOOOyL8Lu3VlJBR1/Hjx9W7d289/PDDkgiAkRKtbVMbATA+EQBrCXdXfFFRkX8w1VRCQoJ/ENX96KqsrEwHDx6UVP2dj7vuuqvecy5cuFDt2rXzL4dq0do2u3fvrvc9NEkaNGiQfvWrX0XyLVqtNfzbOXTokA4fPixJ6tq1q377299G6u1Zr6kf0dd1yy23aOTIkZL4CDhSorVtaiMAxicCYB1er1fZ2dn+n30+n1JTU4N+GffYsWPaunVrQI0YMULXXXedtm7dqsrKyqDr2Llzp9q0aRP0Y8SMjAz96Ec/itwbiiHR2DY130MrLi4OWG7IkCEaO3ZsBN+d/aL9b6fG22+/rYSEBO3YscP8TcWQcLZPMFVVVerXr5/uu+8+Sf860KD2pxXl5eVBDwL56KOP/MusXLmSg0DqiMa2qY0AGJ8IgHXk5+fL7XZrwYIFKi4u1rhx4+TxePyH2I8ePVoTJ05s8PHBPsZ65ZVXtHbtWu3Zs0evv/660tPTdfPNN9d77K5du5SQkKAVK1ZE9k3FiGhsm+PHj6tPnz4aOHCgCgsLtXv3bs2aNUsJCQl68803m+eNWipa/3bmz5+vDz74QLt379aiRYvUuXNn3X///ZF/g5YLd/tMnjxZK1eu1J49e7Rp0yaNHDlS7du31/bt2/3LTJ8+XR6PR3/5y1/8p+AJdhqYSy65RIWFhdqwYYP69u3LaWDqiNa2+eyzz1RUVOQ/7VhRUZGKioo4/VicIAAGkZubq7S0NLlcLnm9Xm3cuNF/X0ZGRoNH70rBh9jcuXPVo0cPtWvXTmlpaXr44YeD7uF48MEH9b3vfY/zlzUiGttm586duvnmm9WlSxclJSWpf//+9U4Lg2rR2D4PPPCAunbtqnbt2qlv376aPXu2Tp48GdH3FSvC2T733nuvf9muXbtq+PDh9c59WXOy4a5du8rtdmvQoEH69NNPA5b56quv9JOf/ESnnXaakpOT9fOf/5yAEUQ0tk1WVlbQCxCsXbu2Od8qWgkCIAAAQJwhAAIAAMQZAiAAAECcIQACAADEGQIgAABAnCEAAgAAxBkCIAAAQJwhAAIAAMQZAiAAAECcIQACAADEGQIgAABAnCEAAsD/OnjwoLp27aopU6b4b3v//ffVrl07rVmzJoqvDAAiiwAIALW8+eabateunT788EN988036tWrl+67775ovywAiCgCIADUcdddd+n73/++Ro0apYsuukgVFRXRfkkAEFEEQACo47vvvlOvXr3Url07bdmyJdovBwAijgAIAHVs3bpV7du3V2Jiot54441ovxwAiDgCIADUUllZqQEDBigrK0tTp05Vly5ddODAgWi/LACIKAIgANTy61//Wj179lR5ebl8Pp+uvvpq3XDDDdF+WQAQUQRAAPhfa9euVdu2bbV+/Xr/bXv37lVycrKeeeaZKL4yAIgsAiAAAECcIQACAADEGQIgAABAnCEAAgAAxBkCIAAAQJwhAAIAAMQZAiAAAECcIQACAADEGQIgAABAnCEAAgAAxBkCIAAAQJwhAAIAAMQZAiAAAECc+f81ZmECIKffEAAAAABJRU5ErkJggg==\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fluid = FLUID()\n",
    "fluid.u = PLANE_WAVE(fluid.N)\n",
    "plt.figure(figsize=(8, 8))\n",
    "fluid.show_streamlines(cmap='autumn')\n",
    "plt.title('Initial Velocity Profile')\n",
    "plt.show()\n",
    "\n",
    "circles = [CIRCLE(100, 0.15, (0.5, 0.5+DY))*fluid.L for DY in [-0.25, 0.25]] \n",
    "solids = [IB2(circle, fluid.N, fluid.h, fluid.dt) for circle in circles]\n",
    "\n",
    "# solids = TWO_CIRCLES(sim.N, sim.h, SEPARATION=.5)\n",
    "# solids = [CIRCLE(100, sim.N, sim.h, R=.15, R0=(.5, .5))]\n",
    "# solids = [CIRCLE(100, sim.N, sim.h, R=.25, R0=(.5, .5))]\n",
    "# for i in range(200):\n",
    "#     iterate(sim, solids, ext)\n",
    "\n",
    "    \n",
    "#### Run the experiment\n",
    "X1 = []\n",
    "X2 = []\n",
    "\n",
    "#### Animation\n",
    "fig = plt.figure()\n",
    "fig.figsize=(12, 8)\n",
    "plt.xlim([0, fluid.L])\n",
    "plt.ylim([0, fluid.L])\n",
    "\n",
    "cmap = plt.get_cmap('tab10')\n",
    "ims = []\n",
    "\n",
    "for i in range(600):\n",
    "    iterate(fluid, solids)\n",
    "    if i%10==0:\n",
    "        im = [fluid.show_vorticity()]\n",
    "#         fluid.show_streamlines()\n",
    "        for i, solid in enumerate(solids):\n",
    "            im.append(plt.scatter(solid.X[0], solid.X[1], color=cmap(2*i)))\n",
    "            im.append(plt.scatter(solid.XX[0], solid.XX[1], color=cmap(2*i+1)))\n",
    "        im.append(plt.title('t={}'.format(1*fluid.t)))\n",
    "        ims.append(im)\n",
    "    X1.append(np.sum(solids[0].X, axis=1)/solids[0].Nb)\n",
    "    X2.append(np.sum(solids[1].X, axis=1)/solids[1].Nb)        \n",
    "ani = animation.ArtistAnimation(fig, ims, interval=50, blit=True, repeat_delay=100)\n",
    "# ani.save('dynamic_images.mp4')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#### Results\n",
    "plt.figure()\n",
    "X1 = np.array(X1)\n",
    "X2 = np.array(X2)\n",
    "plt.scatter(X1[:,0], X1[:,1])\n",
    "plt.scatter(X2[:,0], X2[:,1])\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Particle Trajectories')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some notes about notation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We translate the pibm described here https://math.nyu.edu/faculty/peskin/ib_lecture_notes/KimPeskin_rigid.pdf into python. One aspect of this is vectorizing the matrix operations described in the paper into an efficient numpy formulation. As an illustrative example, take Eq. 19, where we compute the moment of inertia of the rigid body:\n",
    "\n",
    "$I_0 = \\sum_{k=1}^{N_b}m_k(C_K^TC_KI_3 - C_kC_k^T)\\Delta q\\Delta r\\Delta s$\n",
    "\n",
    "In this case, $C_k$ and $m_k$ describe the coordinates (in rigid body COM frame) and the mass anof each rigid body point $k$; $\\Delta q\\Delta r\\Delta s$ is a scalar factor associated with rigid body point spacing; and $I_3$ is the 3x3 identity matrix. In particular, we'd like to translate this quantity\n",
    "\n",
    "$\\sum_{k=1}^{N_b}C_K^TC_KI_2 - C_kC_k^T$\n",
    "\n",
    "into python. (Note that we switch to $I_2$ because we're working in 2D). This can of course be computed using loops, but we show that these expressions can be equivalently expressed using inner and outer products:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 100)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def CIRCLE(Nb, RAD, POS):  \n",
    "    theta = np.linspace(0, 2*np.pi, Nb)\n",
    "    return np.array(POS)[:, np.newaxis] + RAD*np.array([np.cos(theta), np.sin(theta)])\n",
    "\n",
    "circle = CIRCLE(100, 0.2, (0.5, 0.5))\n",
    "circle -= np.mean(circle, axis=1)[:, np.newaxis]\n",
    "print(np.shape(circle))\n",
    "plt.scatter(circle[0], circle[1])\n",
    "plt.title('Coordinates C_k for a circle')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Sums:\n",
      "Sum of First Terms\n",
      "[[216.8   0. ]\n",
      " [  0.  216.8]]\n",
      "\n",
      "Sum of Second Terms\n",
      "[[108.88 100.4 ]\n",
      " [100.4  107.92]]\n",
      "\n",
      "Total sum:\n",
      "[[ 107.92 -100.4 ]\n",
      " [-100.4   108.88]]\n",
      "\n",
      "\n",
      "Vectorized:\n",
      "Sum of first terms (i.e. norm):\n",
      "[[216.8   0. ]\n",
      " [  0.  216.8]]\n",
      "\n",
      "Sum of second terms (i.e. inner product):\n",
      "[[108.88 100.4 ]\n",
      " [100.4  107.92]]\n",
      "\n",
      "Total sum:\n",
      "[[ 107.92 -100.4 ]\n",
      " [-100.4   108.88]]\n"
     ]
    }
   ],
   "source": [
    "#### First, let's calculate the sum explicitly using loops:\n",
    "\n",
    "print('Using Sums:')\n",
    "TERM1 = [np.inner(circle[:,i], circle[:,i]) for i in range(circle.shape[1])]\n",
    "TERM1 = sum([val*np.eye(2) for val in TERM1])\n",
    "print('Sum of First Terms')\n",
    "print(TERM1)\n",
    "print()\n",
    "\n",
    "TERM2 = [np.outer(circle[:,i], circle[:,i]) for i in range(circle.shape[1])]\n",
    "TERM2 = sum(TERM2)\n",
    "print('Sum of Second Terms')\n",
    "print(TERM2)\n",
    "print()\n",
    "\n",
    "print('Total sum:')\n",
    "print(TERM1 - TERM2)\n",
    "print()\n",
    "print()\n",
    "\n",
    "#### Now, let's compute the equivalent, vectorized code. We note that the first term is simply the sum of |C_k|^2,\n",
    "#### and the second term is a sum of outer products, which is equivalent to an inner product (or contraction) of \n",
    "####   the TENSOR C of all C_k's with itself:\n",
    "print('Vectorized:')\n",
    "\n",
    "TERM1 = sum(np.linalg.norm(circle, axis=0)**2)*np.eye(2)\n",
    "print('Sum of first terms (i.e. norm):')\n",
    "print(TERM1)\n",
    "print()\n",
    "\n",
    "TERM2 = np.inner(circle, circle)\n",
    "print('Sum of second terms (i.e. inner product):')\n",
    "print(TERM2)\n",
    "print()\n",
    "\n",
    "print('Total sum:')\n",
    "print(TERM1 - TERM2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4 5 6]\n",
      " [8 3 3]\n",
      " [6 0 8]]\n",
      "[[6 9 7]\n",
      " [8 1 2]\n",
      " [1 3 4]]\n",
      "[[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "A = (10*np.random.random([3, 3])).astype(int)\n",
    "B = (10*np.random.random([3, 3])).astype(int)\n",
    "I3 = np.eye(3)\n",
    "print(A)\n",
    "print(B)\n",
    "print(I3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[70 59 62]\n",
      " [75 84 74]\n",
      " [44 78 74]]\n",
      "\n",
      "[[70 59 62]\n",
      " [75 84 74]\n",
      " [44 78 74]]\n",
      "\n",
      "[[138  57 119]\n",
      " [ 52  43  67]\n",
      " [ 52  14  47]]\n",
      "\n",
      "[[138  52  52]\n",
      " [ 57  43  14]\n",
      " [119  67  47]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(np.matmul(A, B))\n",
    "print()\n",
    "print(A.dot(B))\n",
    "print()\n",
    "print(B.dot(A))\n",
    "print()\n",
    "print(A.transpose().dot(B.transpose()))\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 77  65  72]\n",
      " [ 65  82  72]\n",
      " [ 72  72 100]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(A.dot(A.transpose()))\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def rot(ax, theta, X): return np.cos(theta)*X + (1-np.cos(theta))*np.dot(ax, X)*ax + np.sin(theta)*np.cross(ax, X)\n",
    "\n",
    "\n",
    "I2 = np.eye(2)\n",
    "\n",
    "X = np.linspace(5, 9, 10)\n",
    "Y = np.linspace(4, 3, 10)\n",
    "R = np.vstack([X, Y])\n",
    "RCM = np.array([4, 4])\n",
    "theta = np.linspace(0, 2*np.pi, 100)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(RCM[0]+np.cos(theta), RCM[1]+np.sin(theta), linestyle='--')\n",
    "plt.scatter(R[0], R[1])\n",
    "plt.xlim([-10, 10])\n",
    "plt.ylim([-10, 10])\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 0.]\n",
      "(2, 10)\n",
      "[[5.         5.44444444 5.88888889 6.33333333 6.77777778 7.22222222\n",
      "  7.66666667 8.11111111 8.55555556 9.        ]\n",
      " [4.         3.88888889 3.77777778 3.66666667 3.55555556 3.44444444\n",
      "  3.33333333 3.22222222 3.11111111 3.        ]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(RCM[0]+np.cos(theta), RCM[1]+np.sin(theta), linestyle='--')\n",
    "plt.scatter(R[0], R[1])\n",
    "plt.xlim([-10, 10])\n",
    "plt.ylim([-10, 10])\n",
    "\n",
    "\n",
    "\n",
    "ax = R[:, 0]-RCM\n",
    "print(ax)\n",
    "theta = np.pi/4\n",
    "\n",
    "Rr = [rot(ax, theta, R[:,i]) for i in range(R.shape[1])]\n",
    "Rr = np.vstack(Rr).transpose()\n",
    "Rr = [rot(ax, theta, Rr[:,i]) for i in range(Rr.shape[1])]\n",
    "Rr = np.vstack(Rr).transpose()\n",
    "print(np.shape(Rr))\n",
    "print(R)\n",
    "plt.scatter(Rr[0], Rr[1])\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 0.]\n",
      "(2, 10)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rot(ax, theta, X): \n",
    "    out = np.cos(theta)*X \n",
    "    out += (1-np.cos(theta))*np.dot(ax, X) \n",
    "    out += np.sin(theta)*np.cross(ax, X, axisb=0)\n",
    "    return out\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(RCM[0]+np.cos(theta), RCM[1]+np.sin(theta), linestyle='--')\n",
    "plt.scatter(R[0], R[1])\n",
    "plt.xlim([-10, 10])\n",
    "plt.ylim([-10, 10])\n",
    "\n",
    "\n",
    "\n",
    "ax = R[:, 0]-RCM\n",
    "print(ax)\n",
    "# theta = np.pi/4\n",
    "theta=np.pi/2\n",
    "\n",
    "print(np.shape(R))\n",
    "Rr = rot(ax, theta, R)\n",
    "# Rr = rot(ax, theta, Rr)\n",
    "# Rr = rot(ax, theta, Rr)\n",
    "# Rr = rot(ax, theta, Rr)\n",
    "\n",
    "plt.scatter(Rr[0], Rr[1])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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