MinMax/nacl.ipynb

{
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   "cell_type": "markdown",
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    "# Finding optima of molecular simulations\n",
    "\n",
    "Here we investigate the potential\n",
    "\n",
    "$$\n",
    "V\\left(r_{i j}\\right)=\\left\\{\\begin{array}{l}{-\\frac{e^{2}}{4 \\pi \\epsilon_{0} r_{i j}}+\\alpha e^{-r_{i j} / \\rho}+b\\left(\\frac{c}{r_{i j}}\\right)^{12}} (\\mathrm{+ -})\\\\ {+\\frac{e^{2}}{4 \\pi \\epsilon_{0} r_{i j}}+b\\left(\\frac{c}{r_{i j}}\\right)^{12}} (\\mathrm{++ or --}) \\end{array}\\right.\n",
    "$$\n",
    "\n",
    "where the Coulomb force has constant:\n",
    "\n",
    "$$ke^2 = e^2/4\\pi\\epsilon_0 = 1.44\\; \\mathrm{eV-nm}$$\n",
    "\n",
    "with Pauli exclusion term:\n",
    "\n",
    "$$\\alpha = 1.09e3\\;\\mathrm{eV}$$\n",
    "\n",
    "and a term to stabilize (or \"regularize\") the computation at small distances with:\n",
    "\n",
    "$$b = 1.0\\;\\mathrm{eV}$$\n",
    "\n",
    "$$c = 0.01\\;\\mathrm{nm}$$\n",
    "\n",
    "\n",
    "\n",
    "The solution chosen is to use `numpy` arrays to fully vectorize the calculation. Granted, for small numbers of Na and Cl ions, this is a bit of overkill, but it's mostly for demonstration. "
   ]
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  {
   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import itertools\n",
    "import scipy.optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Physical constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ke2 = 197 / 137 # eV-nm   Coulomb force charge\n",
    "alpha = 1.09e3  # eV      parameter of model\n",
    "rho = 0.0321    # nm      parameter of model\n",
    "b = 1.0         # eV      regular\n",
    "c = 0.01        # nm"
   ]
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   "source": [
    "## Class to implement the potential calculation\n",
    "\n",
    "This is fully vectorized!\n",
    "\n",
    "- `init`: Inputs the positions of the Na and Cl ions as `ndarray`s with sizes `(N,3)`, with the second dimension representing 3-space. This will create a list of all of the combinations, and store their relative distances `rij` and potentials `Vij`. The positions are stored in \"human readable\" format in `positions`. \n",
    "- `Vij`: computes the vector of potentials `Vij_` from the positions (updated per iteration) and charges (static throughout) using the `combs` list of combinations (static throughout)\n",
    "- `V`: computes the sum of `Vij()` (updated per iteration)\n",
    "- `get_vals`: returns the flattened version of `positions`. \n",
    "- `set_vals`: inputs the flattened version of `positions` and reshapes correctly. \n",
    "- `__call__`: accepts the flattened positions, calls `set_vals` and then returns `V`. This is used by `scipi.optimize.minimize`. "
   ]
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   "execution_count": 3,
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   "source": [
    "\n",
    "#Helpful solution to convert itertools combinations to numpy arrays here:\n",
    "## https://stackoverflow.com/questions/33282369/convert-itertools-array-into-numpy-array\n",
    "def cp(l):\n",
    "    return np.fromiter(itertools.chain(*itertools.combinations(l,2)),dtype=int).reshape(-1,2)\n",
    "\n",
    "class Cluster:\n",
    "    def __init__(self, r_na, r_cl):\n",
    "        '''\n",
    "        Inputs the list of Na and Cl positions. Na has charge +1, Cl has -1.\n",
    "        The array of ions itself does not change throughout the calculation, and\n",
    "        neither do the charges. As such, we can just compute the combinations one time\n",
    "        and refer to it throughout the calculation. \n",
    "        '''\n",
    "        self.positions = np.concatenate( (r_na,r_cl))\n",
    "        self.charges = np.concatenate( [np.ones(r_na.shape[0]), np.full(r_cl.shape[0], -1)] )\n",
    "        self.combs = cp(np.arange(self.charges.size))\n",
    "        self.chargeprods = self.charges[self.combs][:,0] * self.charges[self.combs][:,1]\n",
    "        self.rij = np.linalg.norm(self.positions[self.combs][:,0] - self.positions[self.combs][:,1], axis=1)\n",
    "\n",
    "    def Vij(self):\n",
    "        '''Calculate a numpy vector of all of the potentials of the combinations'''\n",
    "        self.Vij_ = np.zeros_like(self.rij)\n",
    "        pos = self.chargeprods>0\n",
    "        neg = ~pos\n",
    "        self.Vij_[pos] = ke2 / self.rij[pos] + b*(c/self.rij[pos])**12\n",
    "        self.Vij_[neg] =-ke2 / self.rij[neg] + alpha*np.exp(-self.rij[neg]/rho) + b*(c/self.rij[neg])**12\n",
    "        return self.Vij_\n",
    "    \n",
    "    def V(self):\n",
    "        '''Total potential, which is a sum of the Vij vector'''\n",
    "        return np.sum(self.Vij())\n",
    "    \n",
    "    def get_vals(self):\n",
    "        '''Positions interpreted as a flat shape'''\n",
    "        return np.reshape(self.positions, -1)\n",
    "        \n",
    "    def set_vals(self, vals ):        \n",
    "        '''Inputs flat shape of positions, used by __call__'''\n",
    "        self.positions = vals.reshape(self.positions.shape)\n",
    "        self.rij = np.linalg.norm(self.positions[self.combs][:,0] - self.positions[self.combs][:,1], axis=1)\n",
    "\n",
    "    \n",
    "    def __call__(self, vals):\n",
    "        '''Function that  scipy.optimize.minimize will call'''\n",
    "        self.set_vals(vals)\n",
    "        return self.V()"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the simulation for a simple box"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial Na positions:\n",
      " [[0.  0.  0. ]\n",
      " [0.2 0.2 0. ]]\n",
      "initial Cl positions:\n",
      " [[0.2 0.  0. ]\n",
      " [0.  0.2 0. ]]\n",
      "initial positions flattened shape:\n",
      " [0.  0.  0.  0.2 0.2 0.  0.2 0.  0.  0.  0.2 0. ]\n",
      "initial V  : -10.008974314537344\n"
     ]
    }
   ],
   "source": [
    "a = 0.2\n",
    "\n",
    "r_na = np.array( [ [ 0, 0, 0 ], [ a, a, 0 ] ] )\n",
    "r_cl = np.array( [ [ a, 0, 0 ], [ 0, a, 0 ] ] )\n",
    "\n",
    "cluster = Cluster(r_na, r_cl)\n",
    "vals_init = cluster.get_vals()\n",
    "print('initial Na positions:\\n', r_na)\n",
    "print('initial Cl positions:\\n', r_cl)\n",
    "print('initial positions flattened shape:\\n', vals_init )\n",
    "print('initial V  :', cluster.V() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the optimization\n",
    "\n",
    "Here, the optimizer will create a vector out of all of the molecular positions.\n",
    "These can then be sent to our `Cluster` class via the `set_vals` method and interpreted correctly. \n",
    "At each iteration, the `Cluster` object will recalculate the potential.\n",
    "The `minimize` function will adjust the values of the cluster positions\n",
    "until the potential is minimized. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final optimized cluster positions\n",
      "[[-0.02354035 -0.02413403 -0.00071742]\n",
      " [ 0.22348817  0.22408303  0.00070939]\n",
      " [ 0.22394609 -0.0234489   0.00753758]\n",
      " [-0.02399878  0.22339753 -0.00754628]]\n",
      "Final potential: -13.069100259631682\n"
     ]
    }
   ],
   "source": [
    "res = scipy.optimize.minimize( fun=cluster, x0=vals_init, tol=1e-3, method=\"BFGS\")\n",
    "cluster.set_vals(res.x)  # For some reason, \"minimize\" is not updating the class at the last iteration\n",
    "print (\"Final optimized cluster positions\")\n",
    "print(cluster.positions)\n",
    "print(\"Final potential:\", res.fun)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make an interactive plot of the results\n",
    "\n",
    "The blue dots are Cl, the red dots are Na. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
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       "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": [
    "%matplotlib notebook\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "charges = cluster.charges\n",
    "x,y,z = cluster.positions[:, 0], cluster.positions[:, 1], cluster.positions[:, 2]\n",
    "ax.scatter( x,y,z, c=charges, cmap='coolwarm' )\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('z')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
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