Tuto-GUDHI-Barycenters-of-persistence-diagrams.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Barycenters of persistence diagrams"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Theo Lacombe\n",
    "\n",
    "https://tlacombe.github.io/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A statistical descriptor in the persistence diagram space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorial presents the concept of barycenter, or __Fréchet mean__, of a family of persistence diagrams. Fréchet means, in the context of persistence diagrams, were initially introduced in the seminal papers:\n",
    "- Probability measures on the space of persistence diagrams, by Mileyko, Mukherjee, and Harer. https://math.hawaii.edu/~yury/papers/probpers.pdf ,\n",
    "- Fréchet means for distributions of persistence diagrams, by Turner, Mileyko, Mukherjee and Harer, https://arxiv.org/pdf/1206.2790.pdf \n",
    "and later studied in https://arxiv.org/pdf/1901.03048.pdf (theoretical viewpoint) and https://arxiv.org/pdf/1805.08331.pdf (computational viewpoint).\n",
    "\n",
    "## Motivation and mathematical formulation\n",
    "\n",
    "Recall that given an object $X$, say a point cloud embedded in the Euclidean space $\\mathbb{R}^d$, one can compute its persistence diagram $\\mathrm{Dgm}(X)$ which is a point cloud supported on a half-plane $\\Omega \\subset \\mathbb{R}^2$ (see this tutorial https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-persistence-diagrams.ipynb for an introduction to persistence diagrams).\n",
    "\n",
    "Now, consider that instead of building one diagram $\\mathrm{Dgm}(X)$ from one object $X$, you observe a collection of objects $X_1 \\dots X_n$ and compute their respective diagrams, let's call them $\\mu_1 \\dots \\mu_n$. How can you build a statistical summary of this information? \n",
    "\n",
    "Fréchet means is one way to do so. It mimics the notion of arithmetic mean in metric spaces. First, recall that the space of persistence diagrams, equipped with either the bottleneck (https://gudhi.inria.fr/python/latest/bottleneck_distance_user.html) or the Wasserstein (https://gudhi.inria.fr/python/latest/wasserstein_distance_user.html) metrics is **not** a linear space. Therefore, the notion of arithmetic mean cannot be faithfully transposed to the context of persistence diagrams.\n",
    "\n",
    "To overcome this limitation, one relies on _Fréchet means_. In Euclidean spaces, one of the characterization of the arithmetic mean \n",
    "$$ \\overline{x} = \\frac{1}{n} \\sum_{i=1}^n x_i $$\n",
    "of a sample $x_1 \\dots x_n \\in \\mathbb{R}^d$ is that it minimizes the _variance_ of the sample, that is the map\n",
    "$$\\mathcal{E} : x \\mapsto \\sum_{i=1}^n \\|x - x_i \\|_2^2 $$\n",
    "has a unique minimizer, that turns out to be $\\overline{x}$.\n",
    "\n",
    "Although the former formula does not make sense in general metric spaces, the map $\\mathcal{E}$ can still be defined, in particular in the context of persistence diagrams. Therefore, a _Fréchet mean_ of $\\mu_1 \\dots \\mu_n$ is any minimizer, should it exist, of the map\n",
    "$$ \\mathcal{E} : \\mu \\mapsto \\sum_{i=1}^n d_2(\\mu, \\mu_i)^2, $$\n",
    "where $d_2$ denotes the so-called Wasserstein-2 distance between persistence diagrams.\n",
    "\n",
    "It has been proved that Fréchet means of persistence diagrams always exist in the context of averaging finitely many diagrams. Their computation remains however challenging."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Lagrangian algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We showcase here one of the algorithm used to _estimate_ barycenters of a (finite) family of persistence diagrams (note that their exact computation is intractable in general). This algorithm was introduced by Turner et al. (https://arxiv.org/pdf/1206.2790.pdf) and adopts a _lagrangian_ perspective. Roughly speaking (see details in their paper), this algorithm consists in iterating the following: \n",
    "\n",
    "- Let $\\mu$ be a current estimation of the barycenter of $\\mu_1 \\dots \\mu_n$.\n",
    "- (1) Compute $\\sigma_i$ ($1 \\leq i \\leq n$) the optimal (partial) matching between $\\mu$ and $\\mu_i$.\n",
    "- (2) For each point $x$ of the diagram $\\mu$, apply $x \\mapsto \\mathrm{mean}((\\sigma_i(x))_i)$, where $\\mathrm{mean}$ is the arithemtic mean in $\\mathbb{R}^2$.\n",
    "- (3) If $\\mu$ didn't change, return $\\mu$. Otherwise, go back to (1).\n",
    "\n",
    "This algorithm is proved to converge ($\\mathcal{E}$ decreases at each iteration) to a _local_ minimum of the map $\\mathcal{E}$. Indeed, the map $\\mathcal{E}$ is **not convex**, which can unfortunately lead to arbritrary bad local minima. Furthermore, its combinatorial aspect (one must compute $n$ optimal partial matching at each iteration step), makes it too computationally expensive when dealing with a large number of large diagrams. It is however a fairly decent attempt when dealing with few diagrams with few points.\n",
    "\n",
    "The solution $\\mu^*$ returned by the algorithm is a persistence diagram with the following property:\n",
    "each point $x \\in \\mu^*$ is the mean of one point (or the diagonal) $\\sigma_i(x)$ in each of the $\\mu_i$s. These are called _groupings_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** This algorithm is said to be based on a _Lagrangian_ approach by opposition to _Eulerian_ , from fluid dynamics formalism (https://en.wikipedia.org/wiki/Lagrangian_and_Eulerian_specification_of_the_flow_field). Roughly speaking, Lagrangian models track the position of each particule individually (here, the points in the barycenter estimate), while Eulerian models instead measure the quantity of mass that is present in each location of the space. We will present in a next version of this tutorial an Eulerian approach to solve (approximately) this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Illustration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports and preliminary tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current gudhi version: 3.2.0\n",
      "Version >= 3.2.0 is required for this tutorial\n"
     ]
    }
   ],
   "source": [
    "import gudhi\n",
    "print(\"Current gudhi version:\", gudhi.__version__)\n",
    "print(\"Version >= 3.2.0 is required for this tutorial\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gudhi.wasserstein.barycenter import lagrangian_barycenter as bary\n",
    "from gudhi.persistence_graphical_tools import plot_persistence_diagram\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us consider three persistence diagrams."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "diag1 = np.array([[0., 1.], [0, 2], [1, 2], [1.32, 1.87], [0.7, 1.2]])\n",
    "diag2 = np.array([[0, 1.5], [0.5, 2], [1.2, 2], [1.3, 1.8], [0.4, 0.8]])\n",
    "diag3 = np.array([[0.2, 1.1], [0.1, 2.2], [1.3, 2.1], [0.5, 0.9], [0.6, 1.1]])\n",
    "\n",
    "diags = [diag1, diag2, diag3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"625\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Set of 3 persistence diagrams')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "colors=['r', 'b', 'g']\n",
    "for diag, c in zip(diags, colors):\n",
    "    plot_persistence_diagram(diag, axes=ax, colormap=c)\n",
    "ax.set_title(\"Set of 3 persistence diagrams\", fontsize=22)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let us compute (more precisely, estimate) a barycenter of `diags`.\n",
    "\n",
    "Using the verbose option, we can get access to a `log` (dictionary) that contains complementary informations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "b, log = bary(diags, \n",
    "         init=0,\n",
    "         verbose=True)  # we initialize our estimation on the first diagram (the red one.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy reached by this estimation of the barycenter: E=0.47.\n",
      "Convergenced made after 2 steps.\n"
     ]
    }
   ],
   "source": [
    "print(\"Energy reached by this estimation of the barycenter: E=%.2f.\" %log['energy'])\n",
    "print(\"Convergenced made after %s steps.\" %log['nb_iter'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `groupings` provided in logs, we can have a better visibility on what is happening."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = log[\"groupings\"]\n",
    "\n",
    "def proj_on_diag(x):\n",
    "    return ((x[1] + x[0]) / 2, (x[1] + x[0]) / 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "colors = ['r', 'b', 'g']\n",
    "\n",
    "for diag, c in zip(diags, colors):\n",
    "    plot_persistence_diagram(diag, axes=ax, colormap=c)\n",
    "\n",
    "def plot_bary(b, diags, groupings, axes):\n",
    "    # n_y = len(Y.points)\n",
    "    for i in range(len(diags)):\n",
    "        indices = G[i]\n",
    "        n_i = len(diags[i])\n",
    "\n",
    "        for (y_j, x_i_j) in indices:\n",
    "            y = b[y_j]\n",
    "            if y[0] != y[1]:\n",
    "                if x_i_j >= 0:  # not mapped with the diag\n",
    "                    x = diags[i][x_i_j]\n",
    "                else:  # y_j is matched to the diagonal\n",
    "                    x = proj_on_diag(y)\n",
    "                ax.plot([y[0], x[0]], [y[1], x[1]], c='black',\n",
    "                        linestyle=\"dashed\")\n",
    "\n",
    "    ax.scatter(b[:,0], b[:,1], color='purple', marker='d', label=\"barycenter (estim)\")\n",
    "    ax.legend()\n",
    "    ax.set_title(\"Set of diagrams and their barycenter\", fontsize=22)\n",
    "\n",
    "plot_bary(b, diags, G, axes=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that, as the problem is not convex, the output (and its quality, i.e. energy) might depend on optimization.\n",
    "\n",
    "Energy: lower is better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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width=\"1363\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 3)\n",
    "\n",
    "colors = ['r', 'b', 'g']\n",
    "\n",
    "for i, ax in enumerate(axs):\n",
    "    for diag, c in zip(diags, colors):\n",
    "        plot_persistence_diagram(diag, axes=ax, colormap=c)\n",
    "\n",
    "    b, log = bary(diags, init=i, verbose=True)\n",
    "    e = log[\"energy\"]\n",
    "    G = log[\"groupings\"]\n",
    "    # print(G)\n",
    "    plot_bary(b, diags, groupings=G, axes=ax)\n",
    "    ax.set_title(\"Barycenter estim with init=%s. Energy: %.2f\" %(i, e))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}