\n", "Each subplot is a **test** (with a given anatomy and side)
\n", "Each plot in the subplot is a **measurement**
\n", "
\n", "This is the way these plots are usually shown to the neurologists." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Keeping only the measurements with maximum peak-to-peak amplitude (PPA)\n", "Per test (e.g. left arm) there are multiple measurements. The general guidelines for MEP evaluation dictate that the measurement with the highest value of PPA is the most useful. The neurologists usually look at all measurements at once, however, so there may be more information from looking at them all. For our current use case, we'll keep only the maximum PPA measurements.\n", "\n", "To do so, we'll have to calculate the PPA for the time series. There are two possible approaches:\n", "* As the PPA is basically just the difference between markers 2 and 4, this value can be readily computed\n", "* Calculate the PPA from the time series directly\n", "\n", "The drawback of the first approach is missing values. To illustrate:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Missing values: 6.92%'" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "'Missing values: %.2f%%' % (ndf['marker_4_amplitude(mv)'].isnull().value_counts(normalize=True).loc[True] * 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The drawback of the second approach is the occurence of measurement artifacts.\n", "\n", "We'll use the second approach as measurement artifacts larger than the physiological peak will likely be a bad measurement anyways. For now we will not deal with such edge cases. We will, however, make sure to avoid the initial measurement artifact, present in nearly all MEP measurements. This artifact occurs due to the fact that the electrodes pick up the electrical field generated by the coil directly. This peak is uninformative, however. Since it tends to be rather large, it is important to disregard the first part of the time series when calculating the PPA.\n", "\n", "We'll define a couple of functions to do this:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "def get_maximal_peak_to_peak(df):\n", " '''Returns df containing only the repeated measurements with the maximum peak-to-peak per test\n", " \n", " df: Pandas dataframe\n", " '''\n", " _df = df.loc[[max(group.iterrows(), key=lambda k: peak_to_peak(k[1].timeseries))[0] for _, group in iterate_over(df, 'test')]]\n", " \n", " # Make sure the resulting df has one line per test, which can not be the case when the index is not unique\n", " assert iterate_over(df, 'test').ngroups == len(_df)\n", " return _df\n", "\n", "def peak_to_peak(ts, offset=100):\n", " '''Maximum peak-to-peak value for a row\n", " \n", " Parameters\n", " ts: timeseries (numpy array)\n", " offset: determines how many points to discard at the start of the measurement\n", " '''\n", " return np.max(ts[offset:]) - np.min(ts[offset:])\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "ndf = get_maximal_peak_to_peak(ndf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate the literature values\n", "The values which are usually used to describe the MEPs are:\n", "* The latency (which is directly available)\n", "* The peak-to-peak amplitude (to be calculated)\n", "* The morphological abnormality (to be calculated)\n", "\n", "We will compute these next." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Latency\n", "Not much to do here, as this is just the first marker. We just have to make sure the value is available for the timeseries we're considering" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": false }, "outputs": [], "source": [ "# We already removed measurements without a valid latency\n", "# Rename for convenience\n", "ndf['lat'] = ndf['marker_1_latency(ms)']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Peak-to-peak amplitude\n", "We already discussed how to calculate these. We'll again use the second approach, i.e., calculate the PPA directly from the timeseries. We already calculated this before, the results of which we could have cached. But for clarity, we'll calculate it here again." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Add the peak-to-peak amplitude feature, calculated directly from the timeseries\n", "ndf['ppa'] = ndf.timeseries.apply(peak_to_peak)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Morphological abnormality (ApEn)\n", "Finally, we'll calculate the morphological abnormality, which we'll quantify using the approximate entropy. For more details:
\n", "_Yperman, Jan, et al. \"Deciphering the morphology of motor evoked potentials.\" Frontiers in neuroinformatics 14 (2020): 28._" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we do this, we'll resample the timeseries that do not have 1920 samples" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "# Resample timeseries\n", "ndf.loc[ndf.timeseries.apply(len) != 1920, 'timeseries'] = ndf[ndf.timeseries.apply(len) != 1920]\\\n", " .timeseries\\\n", " .apply(\n", " lambda ts: scipy.signal.resample(ts, 1920)\n", " )" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "# https://stackoverflow.com/questions/40084931/taking-subarrays-from-numpy-array-with-given-stride-stepsize/40085052#40085052\n", "def strided_app(a, L, S ): # Window len = L, Stride len/stepsize = S\n", " nrows = ((a.size-L)//S)+1\n", " n = a.strides[0]\n", " return np.lib.stride_tricks.as_strided(a, shape=(nrows,L), strides=(S*n,n))\n", "\n", "def approximate_entropy_efficient(y, mnom, rth):\n", " '''More efficient implementation of the approximate entropy calculation\n", " using Scipy\n", " '''\n", " n = y.shape[-1] # Length of the TS\n", " r = rth * np.std(y, axis=-1, ddof=1)\n", " phi = np.zeros((2, 1))\n", "\n", " for k in range(1, 3):\n", " m = mnom + k - 1 # Pattern length\n", " x = strided_app(y, m, 1)\n", " dd = np.mean(scipy.spatial.distance.squareform(scipy.spatial.distance.pdist(x, 'chebyshev')) <= r, axis=-1)\n", " phi[k-1] = np.mean(np.log(dd))\n", "\n", " return phi[0] - phi[1]\n", "\n", "def approximate_entropy(y, mnom, rth):\n", " \"\"\"Calculate the approximate entropy of a 1D timeseries\n", " Code adapted from HCTSA package (https://github.com/benfulcher/hctsa)\n", " \"\"\"\n", " n = y.shape[-1] # Length of the TS\n", " r = rth * np.std(y, axis=-1, ddof=1)\n", " phi = np.zeros((2, 1))\n", "\n", " ds = []\n", " drs = []\n", " for k in range(1, 3):\n", " m = mnom + k - 1 # Pattern length\n", " C = np.zeros((n - m + 1, 1))\n", " x = np.zeros((n - m + 1, m))\n", "\n", " # Form vector sequences x from the time series y\n", " for i in range(n - m + 1):\n", " x[i, :] = y[i:i + m]\n", "\n", " ax = np.ones((n - m + 1, m));\n", " for i in range(n - m + 1):\n", " for j in range(m):\n", " ax[:, j] = x[i,j]; \n", " d = abs(x - ax)\n", " if m > 1:\n", " d = np.max(d, axis=-1) \n", " dr = d <= r\n", " ds.append(d)\n", " drs.append(dr)\n", " C[i] = np.sum(dr) / (n - m + 1)\n", " phi[k - 1] = np.mean(np.log(C))\n", "\n", " return phi[0] - phi[1]\n", "\n", "def normalize_apen(apen_val, nc): \n", " '''Normalize the ApEn values by the values used in the paper\n", " '''\n", " apen_norm = - (apen_val - nc['median']) / (nc['iqr'] / 1.35)\n", " apen_norm = 1. / (1 + np.exp(apen_norm))\n", " apen_norm = (apen_norm - nc['min']) / (nc['max'] - nc['min'])\n", " return apen_norm\n", "\n", "def normalized_approximate_entropy_eff(x, m=None, r=None):\n", " nc = {\n", " 'median': 0.0660287973,\n", " 'iqr': 0.0629248893,\n", " 'min': 0.230205474,\n", " 'max': 1.0,\n", " 'm': 2,\n", " 'r': 0.2,\n", " 'cutoff': 70\n", " }\n", " if len(x) != 1920:\n", " x = scipy.signal.resample(x, 1920)\n", " # ts = scipy.stats.zscore(x[nc['cutoff']:])\n", " ts = x[nc['cutoff']:]\n", " if (m is None) and (r is None):\n", " apen = approximate_entropy_efficient(ts, nc['m'], nc['r'])\n", " else:\n", " apen = approximate_entropy_efficient(ts, m, r)\n", " norm_apen = normalize_apen(apen, nc)\n", " return norm_apen\n", "\n", "def normalized_approximate_entropy(x, m=None, r=None):\n", " nc = {\n", " 'median': 0.0660287973,\n", " 'iqr': 0.0629248893,\n", " 'min': 0.230205474,\n", " 'max': 1.0,\n", " 'm': 2,\n", " 'r': 0.2,\n", " 'cutoff': 70\n", " }\n", " if len(x) != 1920:\n", " x = scipy.signal.resample(x, 1920)\n", " # ts = scipy.stats.zscore(x[nc['cutoff']:])\n", " ts = x[nc['cutoff']:]\n", " if (m is None) and (r is None):\n", " apen = approximate_entropy(ts, nc['m'], nc['r'])\n", " else:\n", " apen = approximate_entropy(ts, m, r)\n", " norm_apen = normalize_apen(apen, nc)\n", " return norm_apen" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "# As this can take some time when using a single core, use cached ApEn calculations\n", "# Alternatively, calculate from scratch.\n", "if os.path.isfile('apen_cache.p'):\n", " # Contains the ApEn for the /complete/ dataset\n", " cache = pd.read_pickle('apen_cache.p')\n", " ndf = ndf.merge(right=cache, on=['%s_uid' % s for s in ['patient', 'visit', 'test', 'measurement']], how='inner')\n", "else:\n", " # Calculate ApEn from scratch\n", " # Do this in parallel as it takes a while. This will take ~30 seconds, depending on your hardware.\n", "\n", " # In Windows the multiprocessing does not work very well, though there is a workaround:\n", " # https://medium.com/@grvsinghal/speed-up-your-python-code-using-multiprocessing-on-windows-and-jupyter-or-ipython-2714b49d6fac\n", " # For now, do not run in parallel for Windows\n", " if not os.name == 'nt':\n", " with multiprocessing.Pool() as p:\n", " results = list(tqdm.tqdm_notebook(p.imap(normalized_approximate_entropy_eff, ndf.timeseries.values, chunksize=10), total=len(ndf)))\n", " else:\n", " results = list(tqdm.tqdm_notebook(map(normalized_approximate_entropy_eff, ndf.timeseries.values), total=len(ndf)))\n", "\n", " ndf['apen'] = np.array(results).ravel()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a (admittedly small) test to see if the ApEn was correctly computed, plot a few sample time series:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "/* global mpl */\n", "window.mpl = {};\n", "\n", "mpl.get_websocket_type = function () {\n", " if (typeof WebSocket !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof MozWebSocket !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert(\n", " 'Your browser does not have WebSocket support. 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height: ' + height + 'px;'\n", " );\n", "\n", " rubberband_canvas.setAttribute('width', width);\n", " rubberband_canvas.setAttribute('height', height);\n", "\n", " // And update the size in Python. We ignore the initial 0/0 size\n", " // that occurs as the element is placed into the DOM, which should\n", " // otherwise not happen due to the minimum size styling.\n", " if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " this.resizeObserverInstance.observe(canvas_div);\n", "\n", " function on_mouse_event_closure(name) {\n", " return function (event) {\n", " return fig.mouse_event(event, name);\n", " };\n", " }\n", "\n", " rubberband_canvas.addEventListener(\n", " 'mousedown',\n", " on_mouse_event_closure('button_press')\n", " );\n", " rubberband_canvas.addEventListener(\n", " 'mouseup',\n", " on_mouse_event_closure('button_release')\n", " );\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband_canvas.addEventListener(\n", " 'mousemove',\n", " on_mouse_event_closure('motion_notify')\n", " );\n", "\n", " rubberband_canvas.addEventListener(\n", " 'mouseenter',\n", " on_mouse_event_closure('figure_enter')\n", " );\n", " rubberband_canvas.addEventListener(\n", " 'mouseleave',\n", " on_mouse_event_closure('figure_leave')\n", " );\n", "\n", " canvas_div.addEventListener('wheel', function (event) {\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " on_mouse_event_closure('scroll')(event);\n", " });\n", "\n", " canvas_div.appendChild(canvas);\n", " canvas_div.appendChild(rubberband_canvas);\n", "\n", " this.rubberband_context = rubberband_canvas.getContext('2d');\n", " this.rubberband_context.strokeStyle = '#000000';\n", "\n", " this._resize_canvas = function (width, height, forward) {\n", " if (forward) {\n", " canvas_div.style.width = width + 'px';\n", " canvas_div.style.height = height + 'px';\n", " }\n", " };\n", "\n", " // Disable right mouse context menu.\n", " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", " event.preventDefault();\n", " return false;\n", " });\n", "\n", " function set_focus() {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "};\n", "\n", "mpl.figure.prototype._init_toolbar = function () {\n", " var fig = this;\n", "\n", " var toolbar = document.createElement('div');\n", " toolbar.classList = 'mpl-toolbar';\n", " this.root.appendChild(toolbar);\n", "\n", " function on_click_closure(name) {\n", " return function (_event) {\n", " return fig.toolbar_button_onclick(name);\n", " };\n", " }\n", "\n", " function on_mouseover_closure(tooltip) {\n", " return function (event) {\n", " if (!event.currentTarget.disabled) {\n", " return fig.toolbar_button_onmouseover(tooltip);\n", " }\n", " };\n", " }\n", "\n", " fig.buttons = {};\n", " var buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'mpl-button-group';\n", " for (var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " /* Instead of a spacer, we start a new button group. */\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", " buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'mpl-button-group';\n", " continue;\n", " }\n", "\n", " var button = (fig.buttons[name] = document.createElement('button'));\n", " button.classList = 'mpl-widget';\n", " button.setAttribute('role', 'button');\n", " button.setAttribute('aria-disabled', 'false');\n", " button.addEventListener('click', on_click_closure(method_name));\n", " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", "\n", " var icon_img = document.createElement('img');\n", " icon_img.src = '_images/' + image + '.png';\n", " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", " icon_img.alt = tooltip;\n", " button.appendChild(icon_img);\n", "\n", " buttonGroup.appendChild(button);\n", " }\n", "\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", "\n", " var fmt_picker = document.createElement('select');\n", " fmt_picker.classList = 'mpl-widget';\n", " toolbar.appendChild(fmt_picker);\n", " this.format_dropdown = fmt_picker;\n", "\n", " for (var ind in mpl.extensions) {\n", " var fmt = mpl.extensions[ind];\n", " var option = document.createElement('option');\n", " option.selected = fmt === mpl.default_extension;\n", " option.innerHTML = fmt;\n", " fmt_picker.appendChild(option);\n", " }\n", "\n", " var status_bar = document.createElement('span');\n", " status_bar.classList = 'mpl-message';\n", " toolbar.appendChild(status_bar);\n", " this.message = status_bar;\n", "};\n", "\n", "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", " // which will in turn request a refresh of the image.\n", " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", "};\n", "\n", "mpl.figure.prototype.send_message = function (type, properties) {\n", " properties['type'] = type;\n", " properties['figure_id'] = this.id;\n", " this.ws.send(JSON.stringify(properties));\n", "};\n", "\n", "mpl.figure.prototype.send_draw_message = function () {\n", " if (!this.waiting) {\n", " this.waiting = true;\n", " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " var format_dropdown = fig.format_dropdown;\n", " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", " fig.ondownload(fig, format);\n", "};\n", "\n", "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", " var size = msg['size'];\n", " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", " fig._resize_canvas(size[0], size[1], msg['forward']);\n", " fig.send_message('refresh', {});\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", " var x0 = msg['x0'] / fig.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", " var x1 = msg['x1'] / fig.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / fig.ratio,\n", " fig.canvas.height / fig.ratio\n", " );\n", "\n", " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", "};\n", "\n", "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", " // Updates the figure title.\n", " fig.header.textContent = msg['label'];\n", "};\n", "\n", "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", " var cursor = msg['cursor'];\n", " switch (cursor) {\n", " case 0:\n", " cursor = 'pointer';\n", " break;\n", " case 1:\n", " cursor = 'default';\n", " break;\n", " case 2:\n", " cursor = 'crosshair';\n", " break;\n", " case 3:\n", " cursor = 'move';\n", " break;\n", " }\n", " fig.rubberband_canvas.style.cursor = cursor;\n", "};\n", "\n", "mpl.figure.prototype.handle_message = function (fig, msg) {\n", " fig.message.textContent = msg['message'];\n", "};\n", "\n", "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", " // Request the server to send over a new figure.\n", " fig.send_draw_message();\n", "};\n", "\n", "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", " fig.image_mode = msg['mode'];\n", "};\n", "\n", "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", " for (var key in msg) {\n", " if (!(key in fig.buttons)) {\n", " continue;\n", " }\n", " fig.buttons[key].disabled = !msg[key];\n", " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", " if (msg['mode'] === 'PAN') {\n", " fig.buttons['Pan'].classList.add('active');\n", " fig.buttons['Zoom'].classList.remove('active');\n", " } else if (msg['mode'] === 'ZOOM') {\n", " fig.buttons['Pan'].classList.remove('active');\n", " fig.buttons['Zoom'].classList.add('active');\n", " } else {\n", " fig.buttons['Pan'].classList.remove('active');\n", " fig.buttons['Zoom'].classList.remove('active');\n", " }\n", "};\n", "\n", "mpl.figure.prototype.updated_canvas_event = function () {\n", " // Called whenever the canvas gets updated.\n", " this.send_message('ack', {});\n", "};\n", "\n", "// A function to construct a web socket function for onmessage handling.\n", "// Called in the figure constructor.\n", "mpl.figure.prototype._make_on_message_function = function (fig) {\n", " return function socket_on_message(evt) {\n", " if (evt.data instanceof Blob) {\n", " /* FIXME: We get \"Resource interpreted as Image but\n", " * transferred with MIME type text/plain:\" errors on\n", " * Chrome. But how to set the MIME type? It doesn't seem\n", " * to be part of the websocket stream */\n", " evt.data.type = 'image/png';\n", "\n", " /* Free the memory for the previous frames */\n", " if (fig.imageObj.src) {\n", " (window.URL || window.webkitURL).revokeObjectURL(\n", " fig.imageObj.src\n", " );\n", " }\n", "\n", " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", " evt.data\n", " );\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " } else if (\n", " typeof evt.data === 'string' &&\n", " evt.data.slice(0, 21) === 'data:image/png;base64'\n", " ) {\n", " fig.imageObj.src = evt.data;\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", "\n", " var msg = JSON.parse(evt.data);\n", " var msg_type = msg['type'];\n", "\n", " // Call the \"handle_{type}\" callback, which takes\n", " // the figure and JSON message as its only arguments.\n", " try {\n", " var callback = fig['handle_' + msg_type];\n", " } catch (e) {\n", " console.log(\n", " \"No handler for the '\" + msg_type + \"' message type: \",\n", " msg\n", " );\n", " return;\n", " }\n", "\n", " if (callback) {\n", " try {\n", " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", " callback(fig, msg);\n", " } catch (e) {\n", " console.log(\n", " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", " e,\n", " e.stack,\n", " msg\n", " );\n", " }\n", " }\n", " };\n", "};\n", "\n", "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", "mpl.findpos = function (e) {\n", " //this section is from http://www.quirksmode.org/js/events_properties.html\n", " var targ;\n", " if (!e) {\n", " e = window.event;\n", " }\n", " if (e.target) {\n", " targ = e.target;\n", " } else if (e.srcElement) {\n", " targ = e.srcElement;\n", " }\n", " if (targ.nodeType === 3) {\n", " // defeat Safari bug\n", " targ = targ.parentNode;\n", " }\n", "\n", " // pageX,Y are the mouse positions relative to the document\n", " var boundingRect = targ.getBoundingClientRect();\n", " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", "\n", " return { x: x, y: y };\n", "};\n", "\n", "/*\n", " * return a copy of an object with only non-object keys\n", " * we need this to avoid circular references\n", " * http://stackoverflow.com/a/24161582/3208463\n", " */\n", "function simpleKeys(original) {\n", " return Object.keys(original).reduce(function (obj, key) {\n", " if (typeof original[key] !== 'object') {\n", " obj[key] = original[key];\n", " }\n", " return obj;\n", " }, {});\n", "}\n", "\n", "mpl.figure.prototype.mouse_event = function (event, name) {\n", " var canvas_pos = mpl.findpos(event);\n", "\n", " if (name === 'button_press') {\n", " this.canvas.focus();\n", " this.canvas_div.focus();\n", " }\n", "\n", " var x = canvas_pos.x * this.ratio;\n", " var y = canvas_pos.y * this.ratio;\n", "\n", " this.send_message(name, {\n", " x: x,\n", " y: y,\n", " button: event.button,\n", " step: event.step,\n", " guiEvent: simpleKeys(event),\n", " });\n", "\n", " /* This prevents the web browser from automatically changing to\n", " * the text insertion cursor when the button is pressed. We want\n", " * to control all of the cursor setting manually through the\n", " * 'cursor' event from matplotlib */\n", " event.preventDefault();\n", " return false;\n", "};\n", "\n", "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", " // Handle any extra behaviour associated with a key event\n", "};\n", "\n", "mpl.figure.prototype.key_event = function (event, name) {\n", " // Prevent repeat events\n", " if (name === 'key_press') {\n", " if (event.which === this._key) {\n", " return;\n", " } else {\n", " this._key = event.which;\n", " }\n", " }\n", " if (name === 'key_release') {\n", " this._key = null;\n", " }\n", "\n", " var value = '';\n", " if (event.ctrlKey && event.which !== 17) {\n", " value += 'ctrl+';\n", " }\n", " if (event.altKey && event.which !== 18) {\n", " value += 'alt+';\n", " }\n", " if (event.shiftKey && event.which !== 16) {\n", " value += 'shift+';\n", " }\n", "\n", " value += 'k';\n", " value += event.which.toString();\n", "\n", " this._key_event_extra(event, name);\n", "\n", " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", " return false;\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", " if (name === 'download') {\n", " this.handle_save(this, null);\n", " } else {\n", " this.send_message('toolbar_button', { name: name });\n", " }\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", " this.message.textContent = tooltip;\n", "};\n", "\n", "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", "// prettier-ignore\n", "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", "\n", "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", "\n", "mpl.default_extension = \"png\";/* global mpl */\n", "\n", "var comm_websocket_adapter = function (comm) {\n", " // Create a \"websocket\"-like object which calls the given IPython comm\n", " // object with the appropriate methods. Currently this is a non binary\n", " // socket, so there is still some room for performance tuning.\n", " var ws = {};\n", "\n", " ws.close = function () {\n", " comm.close();\n", " };\n", " ws.send = function (m) {\n", " //console.log('sending', m);\n", " comm.send(m);\n", " };\n", " // Register the callback with on_msg.\n", " comm.on_msg(function (msg) {\n", " //console.log('receiving', msg['content']['data'], msg);\n", " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", " ws.onmessage(msg['content']['data']);\n", " });\n", " return ws;\n", "};\n", "\n", "mpl.mpl_figure_comm = function (comm, msg) {\n", " // This is the function which gets called when the mpl process\n", " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", "\n", " var id = msg.content.data.id;\n", " // Get hold of the div created by the display call when the Comm\n", " // socket was opened in Python.\n", " var element = document.getElementById(id);\n", " var ws_proxy = comm_websocket_adapter(comm);\n", "\n", " function ondownload(figure, _format) {\n", " window.open(figure.canvas.toDataURL());\n", " }\n", "\n", " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", "\n", " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", " // web socket which is closed, not our websocket->open comm proxy.\n", " ws_proxy.onopen();\n", "\n", " fig.parent_element = element;\n", " fig.cell_info = mpl.find_output_cell(\"\");\n", " if (!fig.cell_info) {\n", " console.error('Failed to find cell for figure', id, fig);\n", " return;\n", " }\n", " fig.cell_info[0].output_area.element.on(\n", " 'cleared',\n", " { fig: fig },\n", " fig._remove_fig_handler\n", " );\n", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / fig.ratio;\n", " fig.cell_info[0].output_area.element.off(\n", " 'cleared',\n", " fig._remove_fig_handler\n", " );\n", " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", "\n", " // Update the output cell to use the data from the current canvas.\n", " fig.push_to_output();\n", " var dataURL = fig.canvas.toDataURL();\n", " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", " // the notebook keyboard shortcuts fail.\n", " IPython.keyboard_manager.enable();\n", " fig.parent_element.innerHTML =\n", " '