Unfolding.ipynb

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      "text/plain": [
       "_ColormakerRegistry()"
      ]
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    }
   ],
   "source": [
    "import pytraj as pt\n",
    "import nglview as nv\n",
    "import numpy as np\n",
    "from scipy.spatial.transform import Rotation\n",
    "\n",
    "%matplotlib notebook\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import copy"
   ]
  },
  {
   "cell_type": "code",
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       "NGLWidget(max_frame=9)"
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   "source": [
    "# load the PDB file\n",
    "prot = pt.load('../proteins/6ct4.pdb')\n",
    "\n",
    "# display the protein\n",
    "view = nv.show_pytraj(prot)\n",
    "#view.add_representation('licorice')\n",
    "view"
   ]
  },
  {
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   "source": [
    "view.close()"
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   "execution_count": 3,
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   "source": [
    "n_atoms = 0\n",
    "residues = {}\n",
    "for atom in prot.top.atoms:\n",
    "    if atom.resid not in residues:\n",
    "        # new residue\n",
    "        residues[atom.resid] = {}\n",
    "        atom_index = 0\n",
    "        \n",
    "    # add current atom to the residue dict\n",
    "    residues[atom.resid][atom.name] = [prot.xyz[0][atom.index], atom.resname, atom.resid,\n",
    "                                       atom.mass, n_atoms, atom_index]\n",
    "    atom_index += 1\n",
    "    n_atoms += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
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   "source": [
    "def angle(v1, v2):\n",
    "    '''Returns the angle between v1 and v2 in radians'''\n",
    "    return np.arccos(np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2)))\n",
    "\n",
    "def project_angle(v, p1, p2):\n",
    "    '''Projects v onto the plane established by p1 and p2 and then returns the angle between v and the projection'''\n",
    "    normal = np.cross(p1, p2)\n",
    "    scalar_projection = np.linalg.norm(v) * (np.dot(v, normal) / (np.linalg.norm(v) * np.linalg.norm(normal)))\n",
    "    vector_projection = scalar_projection * (normal / np.linalg.norm(normal))\n",
    "    plane_projection = v - vector_projection\n",
    "    return angle(plane_projection, p1)\n",
    "\n",
    "def plot(residues, positions=None):\n",
    "    fig = plt.figure(figsize=(9, 6))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "    for i, res in residues.items():\n",
    "        if positions is None:\n",
    "            #bb = np.stack([res['N'][0], res['CA'][0], res['C'][0]])\n",
    "            bb = np.stack([res['N'][0], res['C'][0]])\n",
    "        else:\n",
    "            #bb = positions[[res['N'][-2], res['CA'][-2], res['C'][-2]]]\n",
    "            bb = positions[[res['N'][-2], res['C'][-2]]]\n",
    "        ax.plot(bb[:,0], bb[:,1], bb[:,2],\n",
    "                linewidth=4,\n",
    "                c=plt.get_cmap('jet')(i / len(residues)))\n",
    "\n",
    "    ax.axis('off')\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "source": [
    "distance = []\n",
    "pitch = []\n",
    "yaw = []\n",
    "roll = []\n",
    "folded = np.array([a[0] for res in residues.values() for a in res.values()])\n",
    "for i in range(1, len(residues)):\n",
    "    # -------- get external bond distance --------\n",
    "    res0, res1 = residues[i-1], residues[i]\n",
    "    distance.append(np.linalg.norm(folded[res0['C'][-2]] - folded[res1['N'][-2]]))\n",
    "    \n",
    "    # -------- get residue orientation --------\n",
    "    res0_bb_vec = folded[res0['C'][-2]] - folded[res0['N'][-2]]\n",
    "    res1_bb_vec = folded[res1['C'][-2]] - folded[res1['N'][-2]]\n",
    "    \n",
    "    res0_side_vec = folded[res0['CB'][-2]] - folded[res0['CA'][-2]]\n",
    "    res1_side_vec = folded[res1['CB'][-2]] - folded[res1['CA'][-2]]\n",
    "    \n",
    "    res0_normal_vec = np.cross(res0_bb_vec, res0_side_vec)\n",
    "    res1_normal_vec = np.cross(res1_bb_vec, res1_side_vec)\n",
    "    \n",
    "    # -------- get relative pitch and yaw angles --------\n",
    "    pitch.append(project_angle(res1_bb_vec, res0_bb_vec, res0_side_vec))\n",
    "    yaw.append(project_angle(res1_bb_vec, res0_bb_vec, res0_normal_vec))\n",
    "    \n",
    "    # -------- remove backbone pitch and yaw --------\n",
    "    pitch_axis = res0_normal_vec / np.linalg.norm(res0_normal_vec)\n",
    "    yaw_axis = res0_side_vec / np.linalg.norm(res0_side_vec)\n",
    "\n",
    "    rot = Rotation.from_rotvec(pitch_axis * pitch[-1]) * Rotation.from_rotvec(yaw_axis * yaw[-1])\n",
    "    rot_center = folded[res0['C'][-2]]\n",
    "    ca_rot = rot.apply(folded[res1['CA'][-2]] - rot_center) + rot_center\n",
    "    cb_rot = rot.apply(folded[res1['CB'][-2]] - rot_center) + rot_center\n",
    "\n",
    "    # -------- get dihedral torsion angle (roll) --------\n",
    "    roll.append(angle(res0_side_vec, cb_rot - ca_rot))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"900\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(residues, folded)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "unfolded = np.array([a[0] for res in residues.values() for a in res.values()])\n",
    "for i, res0 in residues.items():\n",
    "    if i == len(residues) - 1:\n",
    "        break\n",
    "    res1 = residues[i+1]\n",
    "    \n",
    "    roll_axis = unfolded[res0['C'][-2]] - unfolded[res0['N'][-2]]\n",
    "    yaw_axis = unfolded[res0['CB'][-2]] - unfolded[res0['CA'][-2]]\n",
    "    pitch_axis = np.cross(roll_axis, yaw_axis)\n",
    "    \n",
    "    last_atom_idx = max(res[-2] for res in res0.values())\n",
    "    \n",
    "    # distance\n",
    "    vec = unfolded[res1['N'][-2]] - unfolded[res0['C'][-2]]\n",
    "    unfolded[last_atom_idx+1:] -= distance[i] * (vec / np.linalg.norm(vec))\n",
    "    \n",
    "    # pitch\n",
    "    rot = Rotation.from_rotvec(pitch_axis / np.linalg.norm(pitch_axis) * pitch[i])\n",
    "    rot_center = unfolded[res0['C'][-2]]\n",
    "    unfolded[last_atom_idx+1:] = rot.apply(unfolded[last_atom_idx+1:] - rot_center) + rot_center\n",
    "    \n",
    "    # yaw\n",
    "    rot = Rotation.from_rotvec(yaw_axis / np.linalg.norm(yaw_axis) * yaw[i])\n",
    "    rot_center = unfolded[res0['C'][-2]]\n",
    "    unfolded[last_atom_idx+1:] = rot.apply(unfolded[last_atom_idx+1:] - rot_center) + rot_center\n",
    "\n",
    "    # roll\n",
    "    rot = Rotation.from_rotvec(roll_axis / np.linalg.norm(roll_axis) * roll[i])\n",
    "    rot_center = unfolded[res0['C'][-2]]\n",
    "    unfolded[last_atom_idx+1:] = rot.apply(unfolded[last_atom_idx+1:] - rot_center) + rot_center"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dist\t -1.3096064294283212\n",
      "pitch\t 0.22738919285305131\n",
      "yaw\t -0.32956028252401937\n",
      "roll\t -1.152896282880793\n",
      "\n",
      "dist\t -1.2992343899389371\n",
      "pitch\t 0.008258620201736955\n",
      "yaw\t 0.1292256338125814\n",
      "roll\t -2.2682061247917567\n",
      "\n",
      "dist\t -1.3194881583401952\n",
      "pitch\t 0.5368845430174052\n",
      "yaw\t 0.8456431668753562\n",
      "roll\t -2.5600294901284197\n",
      "\n",
      "dist\t -1.3260369527279372\n",
      "pitch\t 2.0237612187112894\n",
      "yaw\t 2.7014542597665994\n",
      "roll\t -1.2963696912414637\n",
      "\n",
      "dist\t -1.3223335433996968\n",
      "pitch\t 1.943241726329009\n",
      "yaw\t 2.514120516510566\n",
      "roll\t -1.155696753694557\n",
      "\n",
      "dist\t -1.329765016835678\n",
      "pitch\t 2.0543183725255294\n",
      "yaw\t 2.6062097555183725\n",
      "roll\t -1.2165344812304433\n",
      "\n",
      "dist\t -1.3303033488644591\n",
      "pitch\t 1.7995164086625879\n",
      "yaw\t 2.282810938395145\n",
      "roll\t -1.0273868911917958\n",
      "\n",
      "dist\t -1.3215059591239058\n",
      "pitch\t 1.8228672762378144\n",
      "yaw\t 2.363434357526404\n",
      "roll\t -1.0703604275636067\n",
      "\n",
      "dist\t -1.3171290749201447\n",
      "pitch\t 1.5454409104896223\n",
      "yaw\t 2.182286889332985\n",
      "roll\t -0.960569685110316\n",
      "\n",
      "dist\t -1.313249785836642\n",
      "pitch\t 2.0512434922585703\n",
      "yaw\t 2.8542723434895074\n",
      "roll\t -1.4478247494362562\n",
      "\n",
      "dist\t -1.3330588884216625\n",
      "pitch\t 1.770993156367848\n",
      "yaw\t 2.2955666764122102\n",
      "roll\t -1.0096396630996285\n",
      "\n",
      "dist\t -1.3182909390570707\n",
      "pitch\t 1.899169361685487\n",
      "yaw\t 2.7380425485988646\n",
      "roll\t -1.6931530257243392\n",
      "\n",
      "dist\t -1.3277206031390714\n",
      "pitch\t 0.8593194799567041\n",
      "yaw\t 1.2108819875094174\n",
      "roll\t -0.34051954634770343\n",
      "\n",
      "dist\t -1.3010384314077728\n",
      "pitch\t 0.3812399600723708\n",
      "yaw\t 0.5451149024444296\n",
      "roll\t 0.19142433583404372\n",
      "\n",
      "dist\t -1.3027636009652634\n",
      "pitch\t -0.08840521198769763\n",
      "yaw\t -0.08749832968673653\n",
      "roll\t -2.971498378902347\n",
      "\n",
      "dist\t -1.3465129037628965\n",
      "pitch\t 0.11456949350019696\n",
      "yaw\t 0.18850859869379255\n",
      "roll\t -1.7071303470029835\n",
      "\n",
      "dist\t -1.2947621403176544\n",
      "pitch\t 0.2685133803876195\n",
      "yaw\t 0.327755963840659\n",
      "roll\t -2.842660610261584\n",
      "\n",
      "dist\t -1.3141879622032764\n",
      "pitch\t 0.0110730453749609\n",
      "yaw\t -0.6224735267660201\n",
      "roll\t -0.8697951643519801\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i, res0 in residues.items():\n",
    "    if i == len(residues) - 1:\n",
    "        break\n",
    "    res1 = residues[i+1]\n",
    "    \n",
    "    external_distance = np.linalg.norm(unfolded[res0['C'][-2]] - unfolded[res1['N'][-2]])\n",
    "    \n",
    "    res0_roll_axis = unfolded[res0['C'][-2]] - unfolded[res0['N'][-2]]\n",
    "    res0_yaw_axis = unfolded[res0['CB'][-2]] - unfolded[res0['CA'][-2]]\n",
    "    res0_pitch_axis = np.cross(res0_roll_axis, res0_yaw_axis)\n",
    "    \n",
    "    res1_roll_axis = unfolded[res1['C'][-2]] - unfolded[res1['N'][-2]]\n",
    "    res1_yaw_axis = unfolded[res1['CB'][-2]] - unfolded[res1['CA'][-2]]\n",
    "    res1_pitch_axis = np.cross(res1_roll_axis, res1_yaw_axis)\n",
    "    \n",
    "    print('dist\\t', external_distance - distance[i])\n",
    "    print('pitch\\t', angle(res0_pitch_axis, res1_pitch_axis) - pitch[i])\n",
    "    print('yaw\\t', angle(res0_yaw_axis, res1_yaw_axis) - yaw[i])\n",
    "    print('roll\\t', angle(res0_roll_axis, res1_roll_axis) - roll[i])\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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IQBExBE3V79pdN6q1MsAoHkEIQBExM+nVQfhHY+nXgYAzSMIASAifvdgdRD+6eHUywCgeQQhAETE1HnVQThueuplANA8ghAAIuLRFdVBeNSU1MsAoHkEIQBERE9/dRB+a2LqZQDQPIIQAFbb+pRyEH7qytSrAKB5BCEArPb348pB+K4LU68CgOYRhACw2rsvKgfh349LvQoAmkcQAsBq/35lOQi3PiX1KgBoHkEIAKvtP7H6xTI9/amXAUBzCEIAWO2oKdVB+Mjy1MsAoDkEIQCs9qvp1UE4ZW7qZQDQHIIQAFa76q/VQfi7B1MvA4DmEIQAsNqdC6qD8Ky7Ui8DgOYQhACw2vxV1UH4o5tTLwOA5hCEALBavRGx4fHlIPzK1amXAUBzCEIAWMM2p5eDcI8rUq8CgOYQhACwhp3OKQfh2y5IvQoAmkMQAsAa3n9JOQhf+YvUqwCgOQQhAKxhnz+Vg3Dzk1KvAoDmEIQAsIYDr61+0+jK3tTLAGD0CUIAWMPxt64RgidG1MZF1M6JeHBp6mUAMPoEIQCs4QfTImoXRtT+FFG7dvV1dcR1s1MvA4DRJwgBYA173L5GCK5xHTM99TIAGH2CEADWcOpfq4Pww5NTLwOA0ScIAWANs1ZG1CaWg3CHa1MvA4DRJwgBYA1FEbHBleUg3GhSRFc99ToAGF2CEACe5nV/rn5s9C9LUi8DgNElCAHgaW5eXh2EBz6UehkAjC5BCABP019EbHVDOQj/8bbUywBgdAlCAKjw0enVdwkX9KZeBgCjRxACQIXTHqsOwgseT70MAEaPIASACg90VQfh5+5NvQwARo8gBIAKRRHx8snlIHzJ5IF/BgCdQBACwCD2va/6LuG9T6ReBgCjQxACwCAuXFAdhCfPSb0MAEaHIASAQSzqi9igIgg/ND31MgAYHYIQAJ7Bm24rB+Fzbojoa6ReBgDrTxACwDM4+OHqx0ZvWJZ6GQCsP0EIAM/gmiXVQfiDWamXAcD6E4QA8Ax6GhGbXV8OwrfdkXoZAKw/QQgA6/D+aeUg3OjaiOX9qZcBwPoRhACwDj+dXf3Y6BWLUi8DgPUjCAFgHe5aWR2EX3sg9TIAWD+CEADWoSgitrmpHIR/NzX1MgBYP4IQAIZg75nVdwkf7U69DABGThACwBCMm1cdhL+cl3oZAIycIASAIZjTUx2En7on9TIAGDlBCABD9Pe3lIPwBTdFNIrUywBgZAQhAAzRNx6ovkt4x8rUywBgZAQhAAzR7xdVB+Exj6ZeBgAjIwgBYIhW9EdsfF05CN97V+plADAyghAAhuEdd0TUrm/EhlP6Y6M7euJZ07ti8wdWxaR6b+ppADBsghAAhuGQRxqxVe+80vW5lStSTwOAYROEADAMNy0vYsvuchC+Zcmy1NMAYNgEIQAMQ38RsdXyBaUg3HbR4tTTAGDYBCEADNNLly0qBeEWSxfGAscIAWgzghAAhuntK5aWgvD5XfPjga7UywBgeAQhAAzTl7qXV75YprsoUk8DgGERhAAwTCfWV1UG4V+L/tTTAGBYBCEADNNF9a7KILyp4RAhAO1FEALAMF3X6KkMwkvrDhEC0F4EIQAM0wNFf2UQnlpflXoaAAyLIASAYVpRNCqD8Hv9K1JPA4BhEYQAMAIv7p1fCsIv9C9NPQsAhkUQAsAIvLl3QSkI/61vcepZADAsghAARmD3vsWlIHxT74LUswBgWAQhAIzAF/qXloJw+975qWcBwLAIQgAYgcP7V1S+WGZF0Ug9DQCGTBACwAicXl9VGYT3Ff2ppwHAkAlCABiByxvdlUE4qdGTehoADJkgBIARmNzorQzC39S7Uk8DgCEThAAwArOK/sogPKG+MvU0ABgyQQgAI9BTFJVBeFD/8tTTAGDIBCEAjNAreueXgnCfviWpZwHAkAlCABiht/YtLAXh+/oWpZ4FAEMmCAFghD7Wt7gUhDv2Lkg9CwCGTBACwAh9tX9ZKQhf2DsviqJIPQ0AhkQQAsAIHdG/ovLFMouKRuppADAkghAARuiX9Scqg/DuRl/qaQAwJIIQAEboD43uyiAc3+hJPQ0AhkQQAsAI3d7oqwzCc+pPpJ4GAEMiCAFghOYW9dURODde0PtIvKT/vvh/9Tvj0PrjqacBwJAIQgAYodnFE/GGxuR4SzEpdokJT12fqt+fehoADIkgBIARWhX9sXMxYa0Y3CUmxK6NO1JPA4AhEYQAsB7eWtxYCsK3FjemngUAQyIIAWA9/EvjjlIQ7lxMiK6op54GAOskCAFgPXyqfl8pCHeJCXF7sTT1NABYJ0EIAOvhlMb8yiC8sHg09TQAWCdBCADrYVX0VwbhEXFP6mkAsE6CEADW0yfj5lIQ7h1TUs8CgHUShACwng6P6aUgfFtMiG4vlgGgxQlCAFhP58UjlY+NTotlqacBwDMShACwnm6LJZVBeEnMTj0NAJ6RIASA9bRykBfL/NiLZQBocYIQAEbBJypeLPMZL5YBoMUJQgAYBd+reLHM22Ni9HixDAAtTBACwCgY7MUy071YBoAWJggBYBTcOuiLZeakngYAgxKEADAKBnuxzJExM/U0ABiUIASAUbJnxYtl9ompqWcBwKAEIQCMksO8WAaANiMIAWCU/HqQF8vMiOWppwFAJUEIAKPklkFeLPNbL5YBoEUJQgAYJSuirzIIf+LFMgC0KEEIAKPo414sA0AbEYQAMIq8WAaAdiIIAWAUnRuzvFgGgLYhCAFgFN0SiyuD8FIvlgGgBQlCABhFy71YBoA2IggBYJR9LG4qBeF/eLEMAC1IEALAKDs07i4F4TtiYvRGI/U0AFiLIASAUXbOIC+WuceLZQBoMYIQAEbZ1EFeLHOZF8sA0GIEIQCMsrVfLHNNvCv+GB+I38ahMSH1NABYiyAEgCb4dFwSe8dZ8fk4KfaLE2K/OCH2jZ+nngUAaxGEANAEX4vznwrBJ68vxImxKvpSTwOApwhCAGiCI+MvpSDcL06ISfFw6mkA8BRBCABN8Nu4uzIIT4rrU08DgKcIQgBogsdieWUQHhSXpp4GAE8RhADQJF+I00tB+JO4IPUsAHiKIASAJjktfl8Kwq/EyVGPeuppABARghAAmubKmFL52OjsWJB6GgBEhCAEgKaZFg9XBuGNMSP1NACICEEIAE2zPFZVBuH5MTH1NACICEEIAE11YPy8FIRHx4WpZwFARAhCAGiqk+OKUhB+LU6JRjRSTwMAQQgAzfS7uLnysdHHYlHqaQAgCAGgme6MhyqD8OaYmXoaAAhCAGimJbGyMggvjEmppwGAIASAZiqiiAPizFIQHhsXp54GAIIQAJrtxLisFITfiNOiEUXqaQBkThACQJNdFjdWPjY6P5akngZA5gQhADTZbfFAZRBOjXtTTwMgc4IQAJpsUSyvDMJL4vrU0wDInCAEgCYrooj944xSEB4Xl6SeBkDmBCEAjIGfxW9LQfitOD0KL5YBICFBCABj4LdxfeVjowtjWeppAGRMEALAGLgl7qsMwlvj/tTTAMiYIASAMfB4LK0MwkvjhtTTAMiYIASAMVBEEd+M00pBeEJclnoaABkThAAwRn4al5SC8L/iTC+WASAZQQgAY+TiuK7ysdHFsSL1NAAyJQgBYIxMiZmlGPxiHB9T4+7U0wDIlCAEgDEyNxbGAfGj+G4cGj+KA+Lo+Fr8LPaLcXFi6mkAZEoQAsAYqUcjjosvVzw0+t3U0wDIlCAEgDF0fBxUCsLj4qupZwGQKUEIAGPorDiu4g7hfjE/5qeeBkCGBCEAjKEr4qLKIJwUE1JPAyBDghAAxtC0uKMyCG+IK1NPAyBDghAAxlB3dMcJ8cVSEP4lfpV6GgAZEoQAMMZ+Fd8rBeH58ePUswDIkCAEgDF2ZZxRCsKT46vRiEbqaQBkRhACwBibHL+vPEe4JOalngZAZgQhAIyxBwd5scz9cWvqaQBkRhACwBhbFgsqg/CmuDz1NAAyIwgBYIwV0YhT4+ulIPxdnJp6GgCZEYQAkMCFcVQpCM+OQ1LPAiAzghAAErg6zq18bLQnulJPAyAjghAAErgzJlQG4WPxYOppAGREEAJAAnPi/sogvCsmpZ4GQEYEIQAk0BNPVAbhNXFe6mkAZEQQAkAiv4yDS0F4YRydehYAGRGEAJDI5XFyKQhPi29EEUXqaQBkQhACQCI3xKWVj40uj0WppwGQCUEIAIncG1Mrg/ChuDP1NAAyIQgBIJFF8VhlEE6JP6SeBkAmBCEAJFKPepwcXykF4R/jrNTTAMiEIASAhM6LI0pBeE58P/UsADIhCAEgoT/H2aUgPDG+GP3Rl3oaABkQhACQ0G3xl8pzhI/HI6mnAZABQQgACc2KGZVBOCNuTD0NgAwIQgBIaFUsqwzCa+Oi1NMAyIAgBICEiijizDigFIS/jZ+lngZABgQhACT22zj+qRA8OT4Xv4o944LYO/UsADIgCAEgsUlxSpwfH44r4z1xTewSE2KX+HO8I1bG0tTTAOhwghAAErs5/ismrA7BNa/74o+ppwHQ4QQhACT2QFxaGYQ3xqGppwHQ4QQhACTWE8vi6nhrKQivjo+kngZAhxOEANAC/hC7lYLwmtglep0jBKCJBCEAtIDxcUDlY6Pz4qrU0wDoYIIQAFrAEzG7MghnxPdTTwOggwlCAGgRN8cnSkF4Xbw/iqinngZAhxKEANAi7o+fVd4lXBbTUk8DoEMJQgBoEYtjcmUQPhRnpp4GQIcShADQIurRE5Pi3aUgnBqfTT0NgA4lCAGghdwV36m8S9gTC1NPA6ADCUIAaCFz4tLKIJwbv089DYAOJAgBoIV0x9zKILw7vpt6GgAdSBACQIuZEnuVgvDa2DUa0Z96GgAdRhACQIt5IE6pvEu4JG5PPQ2ADiMIAaDFLInbK4PwwTgl9TQAOowgBIAW04j+uDZ2LQXhlNg79TQAOowgBIAWdHd8t/IuYXfMSz0NgA4iCAGgBc2N31cG4Zy4LPU0ADqIIASAFtQTCyuDcFp8J/U0ADqIIASAFjU1PlsKwknx7mhEb+ppAHQIQQgALeqhOLPyLuHimJJ6GgAdQhACQItaFtMqg/D+OCH1NAA6hCAEgBZVRD2ui/eXgvDm+GTqaQB0CEEIAC1sRny/8i7hEzE79TQAOoAgBIAWNi+uqgzC2XFR6mkAdABBCAAtrDeWxoR4a0yIXWJi/P+YEjvG9NghHoo3p54GQAcQhADQ4qbHB+KB2D4ei+fGvNgq5sVWMTeeG/2xMPU0ANqcIASAFvdo7PVUCK55PR7HpZ4GQJsThADQ4pbGFZVBOCvek3oaAG1OEAJAi2tEf8yOF5SC8NHYNoooUs8DoI0JQgBoA7Nil8q7hL0xI/U0ANqYIASANjA/vl8ZhKvirNTTAGhjghAA2kAjFsa8Nd4y+uS1JD6ZehoAbUwQAkCbWBjvKgXh/NguiuhNPQ2ANiUIAaBNrIgjKh8b7YlrU08DoE0JQgBoE71xU2UQrojDU08DoE0JQgBoE0X0x/x4SSkIF8bbUk8DoE0JQgBoI0vi05V3CesxL/U0ANqQIASANvJEjKsMwq44L/U0ANqQIASANlKPRyqDcGl8LvU0ANqQIASANrMg3lzx+Ykdooh66mkAtBlBCABtZnkcXHmXsDduTT0NgDYjCAGgzfTE+MogXBlHp54GQJsRhADQZoroinmxTSkIF8X7Uk8DoM0IQgBoQ4vjoxV3CbeORixNPQ2ANiIIAaANrYpTKh8b7Y7LU08DoI0IQgBoQ/0xszIIl8XXU08DoI0IQgBoQ0UU8Xi8rhSEj8dro4gi9TwA2oQgBIA2tSy+XnmXsD9mpp4GQJsQhADQprrj8sogXBUnp54GQJsQhADQphqxNObF80pBuDg+mnoaAG1CEAJAG1sU76u4S7hNFNGVehoAbUAQAkAbWxlHrxWDC7u2iPn1LaMnxqeeBkAbEIQA0MZ649anYnDp0s2imF6L7lkbx/LioNTTAGgDghAA2lgR9ZhfvEoWYxwAAAizSURBVDxWzd0k4u7aU9eq+X+behoAbUAQAkA7618cfQ9vt1YMPnnVl52eeh0ALU4QAkA765sdxcytKoOwmLFpRPe01AsBaGGCEADaXH3VFVFMLwdh3F2LuPcVEf2LU08EoEUJQgDoACsWv6I6CO+uRTy8a0TRn3oiAC1IEAJAB1gVp0TvYzsNHoVzD0g9EYAWJAgBoFM0eiMeevvgUbj016kXAtBiBCEAdJL++REzX1wdhNP/JqLr1tQLAWghghAAOk3XLQPxVxWFM188EI0AEIIQADrTknMGf3T0obcPPF4KQPYEIQB0qrn7Dx6Fj3059ToAWoAgBIBOVfQPfHJisChcfFbqhQAkJggBoJP1L4q4d4dBXjLzrIgnbky9EICEBCEAdLruuyKmP3uQl8xsG9E3J/VCABIRhACQg2UXD/7o6INvjmh0p14IQAKCEAByMf/QwaNw9n9EFEXqhQCMMUEIALkoGhGzdhs8ChedmHohAGNMEAJATurLIu77u0GicKOIldekXgjAGBKEAJCbnnsjZmxZHYX3PD+i9+HUCwEYI4IQAHK04sqIuzeojsIHdoporEq9EIAxIAgBIFeP//j/IvCuWsQttYiptYjJtYi73hXx6O8iuhemXglAEwlCAMhVUUQ88vGBILyhFnFuxTV3fOqVADSRIASAnNVXRty/Y8RNgwTh/YenXghAEwlCAMhd70MRU7esDsLrN4vouS/1QgCaRBACABFzzqgOwptfE9HvHCFApxKEAEDE8vurg3Cmj9UDdDJBCABEPDGnOghnHDvq/6ui0YiiKEb97wIwfIIQAIjoWVwdhHf9cFT/N11//Wvc+u53x7zzzx/VvwvAyAhCACCi3l0dhLcfNCp/viiKmH3mmTFhiy1ifK0WE7feOnrmzh2Vvw3AyAlCAGDgm4TnblAOwqnfWO8/3T17dtz+/vfH+FptreuO3Xbz6ChAYoIQABhw/rMr3jK674j/XFEU8di4cTFxq61KMfjk9di4caO3H4BhE4QAwICLXlDxHcK9RvSneubOjTt2333QEHzyuvkNb4ii0RjlHwLAUAlCAGDApS8tB+GkjwzrTzSWL4/HfvSDmPS8560zBmfsu2/0L1/epB8DwFAIQgBgwAU7RJxRizi1FnFyLeLEWsQF/zTk/7z7tlvj9q23XGcIXrfddrHwj39s4g8BYKgEIQAw4LDNIr5ZW/v64VZD+k/n/eTImLThBuuMwen77BN9S5Y0+YcAMFSCEAAY8P3nlIPwe89e5382Y9f3rDMEr91mm3j88svH4EcAMByCEAAYcMTzykH43U0G/deLej36DjswZm3yzDE47ZOfjN6FC8fwhwAwVIIQABjw39uWg/CgjSv/1WLFiujZc/fo2rwWTzy7FrdtVA7BiRtvFPNOO3WMfwQAwyEIAYABP31pOQi/vUHpX2vM+mt0v2XH6Nq89tS17Nm1mLhGDN6+/bbR/eCDCX4EAMMhCAGAAWf/WzkIv7P2GcL6TTdE18teuFYMPnk9umktJtRqMfvDu0Wjvz/RjwBgOAQhADDgkq+Xg/BbG0YURcTShdH/6XdF19abVMZg1+a1gX92pkdEAdqJIAQABvzuoHIQfrMWxYol0bfzSwYPwc1r0fWyF0b95htT/wIAhkkQAgAD/vTDcgx+qRY9//DiZ4zB7rfsGI1HZqVeD8AICEIAYMA1x64dg1+pRfffPsNdwc1r0fOJD0WxYkXq5QCMkCAEAAZcf9radwg/V4u+Vwweg33f/loU9Xrq1QCsB0EIAAyY8qv/i8Ev1SLeU4vinbXo2e5pMbhFLfqPPyL1WgBGgSAEAAbccdFADH61FvG+WsQ/D1zF22vR/fzVMbhVLepn/CT1UgBGiSAEAAZMvzLiG7WI3f4vBp+8GjvXomfbWjSOPyD1SgBGkSAEAAbcPyHi4+UYfOr64acGvkkIQMcQhADAgP85dPAY3O+fInq6Ui8EYJQJQgAgYuFjEbtuUh2Du20VsWBO6oUANIEgBAAG/OH0iHc/LQbfVYs4z7lBgE4lCAGAAcvnRexXi9h1jSD8z2dFTDoh9TIAmkQQAgADGvWIxbMi5twT8dW3Rpx1SOpFADSZIAQAyvp6IxqN1CsAaDJBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkClBCAAAkKn/BbaQ2yjjMa6xAAAAAElFTkSuQmCC\" width=\"900\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(residues, unfolded)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}