{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from pathlib import Path\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import pyhf\n",
"import pyhf.readxml\n",
"from pyhf.contrib.viz import brazil\n",
"\n",
"import base64\n",
"from IPython.display import display, HTML\n",
"from ipywidgets import interact, fixed"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Binned HEP Statistical Analysis in Python\n",
"\n",
"## HistFactory\n",
"\n",
"HistFactory is a popular framework to analyze binned event data and commonly used in High Energy Physics. At its core it is a template for building a statistical model from individual binned distribution ('Histograms') and variations on them ('Systematics') that represent auxiliary measurements (for example an energy scale of the detector which affects the shape of a distribution)\n",
"\n",
"## pyhf\n",
"\n",
"`pyhf` is a work-in-progress standalone implementation of the HistFactory p.d.f. template and an implementation of the test statistics and asymptotic formulae described in the paper by Cowan, Cranmer, Gross, Vitells: *Asymptotic formulae for likelihood-based tests of new physics* [[arXiv:1007.1727](https://arxiv.org/abs/1007.1727)].\n",
"\n",
"Models can be defined using JSON specification, but existing models based on the XML + ROOT file scheme are readable as well.\n",
"\n",
"## The Demo\n",
"\n",
"The input data for the statistical analysis was built generated using the containerized workflow engine [yadage](https://github.com/yadage/yadage) (see demo from KubeCon 2018 [[youtube](https://youtu.be/2PRGUOxL36M)]). Similarly to Binder this utilizes modern container technology for reproducible science. Below you see the execution graph leading up to the model input data at the bottom."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"anim = base64.b64encode(open('workflow.gif', 'rb').read()).decode('ascii')\n",
"HTML(f'')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Read in the Model from XML and ROOT\n",
"\n",
"The ROOT files are read using scikit-hep's [uproot](https://github.com/scikit-hep/uproot) module."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"spec = pyhf.readxml.parse('meas.xml', Path.cwd())\n",
"workspace = pyhf.Workspace(spec)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the `meas.xml` spec, we construct a probability density function (p.d.f). As the model includes systematics, it will be a simultaneous joint p.d.f. of the main model (poisson) and constraint model. The latter is defined by the implied \"auxiliary measurements\"."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'name': 'meas',\n",
" 'config': {'poi': 'SigXsecOverSM',\n",
" 'parameters': [{'name': 'lumi',\n",
" 'auxdata': [1.0],\n",
" 'bounds': [[0.5, 1.5]],\n",
" 'inits': [1.0],\n",
" 'sigmas': [0.1]},\n",
" {'name': 'SigXsecOverSM',\n",
" 'bounds': [[0.0, 3.0]],\n",
" 'inits': [1.0],\n",
" 'fixed': False}]}}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pdf = workspace.model(measurement_name='meas')\n",
"data = workspace.data(pdf)\n",
"# what is the measurement?\n",
"workspace.get_measurement(measurement_name='meas')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The p.d.f is build from one data-drived \"qcd\" (or multijet) estimate and two Monte Carlo-based background samples and is parametrized by five parameters: One parameter of interest `SigXsecOverSM` and four *nuisance parameters* that affect the shape of the two Monte Carlo background estimates (both weight-only and shape systematics)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Samples:\n",
" ['mc1', 'mc2', 'qcd', 'signal']\n",
"Parameters:\n",
" ['SigXsecOverSM', 'lumi', 'mc1_shape_conv', 'mc1_weight_var1', 'mc2_shape_conv', 'mc2_weight_var1']\n"
]
}
],
"source": [
"print(f'Samples:\\n {pdf.config.samples}')\n",
"print(f'Parameters:\\n {pdf.config.parameters}')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"par_name_dict = {k: v[\"slice\"].start for k, v in pdf.config.par_map.items()}\n",
"all_par_settings = {\n",
" n[0]: tuple(m)\n",
" for n, m in zip(\n",
" sorted(reversed(list(par_name_dict.items())), key=lambda x: x[1]),\n",
" pdf.config.suggested_bounds(),\n",
" )\n",
"}\n",
"default_par_settings = {n[0]: sum(tuple(m)) / 2.0 for n, m in all_par_settings.items()}"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def get_mc_counts(pars):\n",
" deltas, factors = pdf.modifications(pars)\n",
" allsum = pyhf.tensorlib.concatenate(\n",
" deltas + [pyhf.tensorlib.astensor(pdf.nominal_rates)]\n",
" )\n",
" nom_plus_delta = pyhf.tensorlib.sum(allsum, axis=0)\n",
" nom_plus_delta = pyhf.tensorlib.reshape(\n",
" nom_plus_delta, (1,) + pyhf.tensorlib.shape(nom_plus_delta)\n",
" )\n",
" allfac = pyhf.tensorlib.concatenate(factors + [nom_plus_delta])\n",
" return pyhf.tensorlib.product(allfac, axis=0)\n",
"\n",
"\n",
"animate_plot_pieces = None\n",
"\n",
"\n",
"def init_plot(fig, ax, par_settings):\n",
" global animate_plot_pieces\n",
"\n",
" nbins = sum(list(pdf.config.channel_nbins.values()))\n",
" x = np.arange(nbins)\n",
" data = np.zeros(nbins)\n",
" items = []\n",
" for i in [3, 2, 1, 0]:\n",
" items.append(ax.bar(x, data, 1, alpha=1.0))\n",
" animate_plot_pieces = (\n",
" items,\n",
" ax.scatter(\n",
" x, workspace.data(pdf, include_auxdata=False), c=\"k\", alpha=1.0, zorder=99\n",
" ),\n",
" )\n",
"\n",
"\n",
"def animate(ax=None, fig=None, **par_settings):\n",
" global animate_plot_pieces\n",
" items, obs = animate_plot_pieces\n",
" pars = pyhf.tensorlib.astensor(pdf.config.suggested_init())\n",
" for k, v in par_settings.items():\n",
" pars[par_name_dict[k]] = v\n",
"\n",
" mc_counts = get_mc_counts(pars)\n",
" rectangle_collection = zip(*map(lambda x: x.patches, items))\n",
"\n",
" for rectangles, binvalues in zip(rectangle_collection, mc_counts[:, 0].T):\n",
" offset = 0\n",
" for sample_index in [3, 2, 1, 0]:\n",
" rect = rectangles[sample_index]\n",
" binvalue = binvalues[sample_index]\n",
" rect.set_y(offset)\n",
" rect.set_height(binvalue)\n",
" offset += rect.get_height()\n",
"\n",
" fig.canvas.draw()\n",
"\n",
"\n",
"def plot(ax=None, order=[3, 2, 1, 0], **par_settings):\n",
" pars = pyhf.tensorlib.astensor(pdf.config.suggested_init())\n",
" for k, v in par_settings.items():\n",
" pars[par_name_dict[k]] = v\n",
"\n",
" mc_counts = get_mc_counts(pars)\n",
" bottom = None\n",
" # nb: bar_data[0] because evaluating only one parset\n",
" for i, sample_index in enumerate(order):\n",
" data = mc_counts[sample_index][0]\n",
" x = np.arange(len(data))\n",
" ax.bar(x, data, 1, bottom=bottom, alpha=1.0)\n",
" bottom = data if i == 0 else bottom + data\n",
" ax.scatter(\n",
" x, workspace.data(pdf, include_auxdata=False), c=\"k\", alpha=1.0, zorder=99\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Interactive Exploration of a HistFactory Model\n",
"\n",
"One advantage of a pure-python implementation of Histfactory is the ability to explore the pdf interactively within the setting of a notebook. Try moving the sliders and oberserve the effect on the samples. For example changing the parameter of interest `SigXsecOverSM` (or µ) controls the overall normalization of the (BSM) signal sample (µ=0 for background-only and µ=1 for the nominal signal-plus-background hypothesis)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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" } else {\n",
" alert(\n",
" 'Your browser does not have WebSocket support. ' +\n",
" 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
" 'Firefox 4 and 5 are also supported but you ' +\n",
" 'have to enable WebSockets in about:config.'\n",
" );\n",
" }\n",
"};\n",
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" 'This browser does not support binary websocket messages. ' +\n",
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" }\n",
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" this.root = document.createElement('div');\n",
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"\n",
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" var titlebar = document.createElement('div');\n",
" titlebar.classList =\n",
" 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
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" this.header = titletext;\n",
"};\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
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"\n",
"mpl.figure.prototype._init_canvas = function () {\n",
" var fig = this;\n",
"\n",
" var canvas_div = (this.canvas_div = document.createElement('div'));\n",
" canvas_div.setAttribute(\n",
" 'style',\n",
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" 'outline: 0;' +\n",
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" 'resize: both;'\n",
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"\n",
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"\n",
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"\n",
" var canvas = (this.canvas = document.createElement('canvas'));\n",
" canvas.classList.add('mpl-canvas');\n",
" canvas.setAttribute('style', 'box-sizing: content-box;');\n",
"\n",
" this.context = canvas.getContext('2d');\n",
"\n",
" var backingStore =\n",
" this.context.backingStorePixelRatio ||\n",
" this.context.webkitBackingStorePixelRatio ||\n",
" this.context.mozBackingStorePixelRatio ||\n",
" this.context.msBackingStorePixelRatio ||\n",
" this.context.oBackingStorePixelRatio ||\n",
" this.context.backingStorePixelRatio ||\n",
" 1;\n",
"\n",
" this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
"\n",
" var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
" 'canvas'\n",
" ));\n",
" rubberband_canvas.setAttribute(\n",
" 'style',\n",
" 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
" );\n",
"\n",
" // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
" if (this.ResizeObserver === undefined) {\n",
" if (window.ResizeObserver !== undefined) {\n",
" this.ResizeObserver = window.ResizeObserver;\n",
" } else {\n",
" var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
" this.ResizeObserver = obs.ResizeObserver;\n",
" }\n",
" }\n",
"\n",
" this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
" var nentries = entries.length;\n",
" for (var i = 0; i < nentries; i++) {\n",
" var entry = entries[i];\n",
" var width, height;\n",
" if (entry.contentBoxSize) {\n",
" if (entry.contentBoxSize instanceof Array) {\n",
" // Chrome 84 implements new version of spec.\n",
" width = entry.contentBoxSize[0].inlineSize;\n",
" height = entry.contentBoxSize[0].blockSize;\n",
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" width = entry.contentBoxSize.inlineSize;\n",
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"\n",
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" if (entry.devicePixelContentBoxSize) {\n",
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" 'width',\n",
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" );\n",
" canvas.setAttribute(\n",
" 'height',\n",
" entry.devicePixelContentBoxSize[0].blockSize\n",
" );\n",
" } else {\n",
" canvas.setAttribute('width', width * fig.ratio);\n",
" canvas.setAttribute('height', height * fig.ratio);\n",
" }\n",
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" 'style',\n",
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" );\n",
"\n",
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"\n",
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"\n",
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" }\n",
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" buttonGroup.classList = 'mpl-button-group';\n",
" continue;\n",
" }\n",
"\n",
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" 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",
" '';\n",
" fig.close_ws(fig, msg);\n",
"};\n",
"\n",
"mpl.figure.prototype.close_ws = function (fig, msg) {\n",
" fig.send_message('closing', msg);\n",
" // fig.ws.close()\n",
"};\n",
"\n",
"mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
" // Turn the data on the canvas into data in the output cell.\n",
" var width = this.canvas.width / this.ratio;\n",
" var dataURL = this.canvas.toDataURL();\n",
" this.cell_info[1]['text/html'] =\n",
" '';\n",
"};\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function () {\n",
" // Tell IPython that the notebook contents must change.\n",
" IPython.notebook.set_dirty(true);\n",
" this.send_message('ack', {});\n",
" var fig = this;\n",
" // Wait a second, then push the new image to the DOM so\n",
" // that it is saved nicely (might be nice to debounce this).\n",
" setTimeout(function () {\n",
" fig.push_to_output();\n",
" }, 1000);\n",
"};\n",
"\n",
"mpl.figure.prototype._init_toolbar = function () {\n",
" var fig = this;\n",
"\n",
" var toolbar = document.createElement('div');\n",
" toolbar.classList = 'btn-toolbar';\n",
" this.root.appendChild(toolbar);\n",
"\n",
" function on_click_closure(name) {\n",
" return function (_event) {\n",
" return fig.toolbar_button_onclick(name);\n",
" };\n",
" }\n",
"\n",
" function on_mouseover_closure(tooltip) {\n",
" return function (event) {\n",
" if (!event.currentTarget.disabled) {\n",
" return fig.toolbar_button_onmouseover(tooltip);\n",
" }\n",
" };\n",
" }\n",
"\n",
" fig.buttons = {};\n",
" var buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" var button;\n",
" for (var toolbar_ind in mpl.toolbar_items) {\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) {\n",
" /* Instead of a spacer, we start a new button group. */\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
" buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" continue;\n",
" }\n",
"\n",
" button = fig.buttons[name] = document.createElement('button');\n",
" button.classList = 'btn btn-default';\n",
" button.href = '#';\n",
" button.title = name;\n",
" button.innerHTML = '';\n",
" button.addEventListener('click', on_click_closure(method_name));\n",
" button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
" buttonGroup.appendChild(button);\n",
" }\n",
"\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
"\n",
" // Add the status bar.\n",
" var status_bar = document.createElement('span');\n",
" status_bar.classList = 'mpl-message pull-right';\n",
" toolbar.appendChild(status_bar);\n",
" this.message = status_bar;\n",
"\n",
" // Add the close button to the window.\n",
" var buttongrp = document.createElement('div');\n",
" buttongrp.classList = 'btn-group inline pull-right';\n",
" button = document.createElement('button');\n",
" button.classList = 'btn btn-mini btn-primary';\n",
" button.href = '#';\n",
" button.title = 'Stop Interaction';\n",
" button.innerHTML = '';\n",
" button.addEventListener('click', function (_evt) {\n",
" fig.handle_close(fig, {});\n",
" });\n",
" button.addEventListener(\n",
" 'mouseover',\n",
" on_mouseover_closure('Stop Interaction')\n",
" );\n",
" buttongrp.appendChild(button);\n",
" var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
" titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
"};\n",
"\n",
"mpl.figure.prototype._remove_fig_handler = function (event) {\n",
" var fig = event.data.fig;\n",
" if (event.target !== this) {\n",
" // Ignore bubbled events from children.\n",
" return;\n",
" }\n",
" fig.close_ws(fig, {});\n",
"};\n",
"\n",
"mpl.figure.prototype._root_extra_style = function (el) {\n",
" el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
"};\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function (el) {\n",
" // this is important to make the div 'focusable\n",
" el.setAttribute('tabindex', 0);\n",
" // reach out to IPython and tell the keyboard manager to turn it's self\n",
" // off when our div gets focus\n",
"\n",
" // location in version 3\n",
" if (IPython.notebook.keyboard_manager) {\n",
" IPython.notebook.keyboard_manager.register_events(el);\n",
" } else {\n",
" // location in version 2\n",
" IPython.keyboard_manager.register_events(el);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
" var manager = IPython.notebook.keyboard_manager;\n",
" if (!manager) {\n",
" manager = IPython.keyboard_manager;\n",
" }\n",
"\n",
" // Check for shift+enter\n",
" if (event.shiftKey && event.which === 13) {\n",
" this.canvas_div.blur();\n",
" // select the cell after this one\n",
" var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
" IPython.notebook.select(index + 1);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
" fig.ondownload(fig, null);\n",
"};\n",
"\n",
"mpl.find_output_cell = function (html_output) {\n",
" // Return the cell and output element which can be found *uniquely* in the notebook.\n",
" // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
" // IPython event is triggered only after the cells have been serialised, which for\n",
" // our purposes (turning an active figure into a static one), is too late.\n",
" var cells = IPython.notebook.get_cells();\n",
" var ncells = cells.length;\n",
" for (var i = 0; i < ncells; i++) {\n",
" var cell = cells[i];\n",
" if (cell.cell_type === 'code') {\n",
" for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
" var data = cell.output_area.outputs[j];\n",
" if (data.data) {\n",
" // IPython >= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] === html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"};\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel !== null) {\n",
" IPython.notebook.kernel.comm_manager.register_target(\n",
" 'matplotlib',\n",
" mpl.mpl_figure_comm\n",
" );\n",
"}\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "52d949d1936f4f56b9147ee9039bb9e4",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(FloatSlider(value=1.0, description='lumi', max=1.5, min=0.5), FloatSlider(value=1.5, des…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib widget\n",
"fig, ax = plt.subplots(1, 1)\n",
"fig.set_size_inches(10, 5)\n",
"ax.set_ylim(0, 1.5 * np.max(workspace.data(pdf, include_auxdata=False)))\n",
"\n",
"init_plot(fig, ax, default_par_settings)\n",
"interact(animate, fig=fixed(fig), ax=fixed(ax), **all_par_settings);"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/srv/conda/envs/notebook/lib/python3.7/site-packages/pyhf/tensor/numpy_backend.py:334: RuntimeWarning: invalid value encountered in log\n",
" return n * np.log(lam) - lam - gammaln(n + 1.0)\n"
]
}
],
"source": [
"nominal = pdf.config.suggested_init()\n",
"background_only = pdf.config.suggested_init()\n",
"background_only[pdf.config.poi_index] = 0.0\n",
"best_fit = pyhf.infer.mle.fit(data, pdf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting\n",
"\n",
"We can now fit the statistical model to the observed data. The best fit of the signal strength is close to the background-only hypothesis."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"application/javascript": [
"/* Put everything inside the global mpl namespace */\n",
"/* global mpl */\n",
"window.mpl = {};\n",
"\n",
"mpl.get_websocket_type = function () {\n",
" if (typeof WebSocket !== 'undefined') {\n",
" return WebSocket;\n",
" } else if (typeof MozWebSocket !== 'undefined') {\n",
" return MozWebSocket;\n",
" } else {\n",
" alert(\n",
" 'Your browser does not have WebSocket support. ' +\n",
" 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
" 'Firefox 4 and 5 are also supported but you ' +\n",
" 'have to enable WebSockets in about:config.'\n",
" );\n",
" }\n",
"};\n",
"\n",
"mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
" this.id = figure_id;\n",
"\n",
" this.ws = websocket;\n",
"\n",
" this.supports_binary = this.ws.binaryType !== undefined;\n",
"\n",
" if (!this.supports_binary) {\n",
" var warnings = document.getElementById('mpl-warnings');\n",
" if (warnings) {\n",
" warnings.style.display = 'block';\n",
" warnings.textContent =\n",
" 'This browser does not support binary websocket messages. ' +\n",
" 'Performance may be slow.';\n",
" }\n",
" }\n",
"\n",
" this.imageObj = new Image();\n",
"\n",
" this.context = undefined;\n",
" this.message = undefined;\n",
" this.canvas = undefined;\n",
" this.rubberband_canvas = undefined;\n",
" this.rubberband_context = undefined;\n",
" this.format_dropdown = undefined;\n",
"\n",
" this.image_mode = 'full';\n",
"\n",
" this.root = document.createElement('div');\n",
" this.root.setAttribute('style', 'display: inline-block');\n",
" this._root_extra_style(this.root);\n",
"\n",
" parent_element.appendChild(this.root);\n",
"\n",
" this._init_header(this);\n",
" this._init_canvas(this);\n",
" this._init_toolbar(this);\n",
"\n",
" var fig = this;\n",
"\n",
" this.waiting = false;\n",
"\n",
" this.ws.onopen = function () {\n",
" fig.send_message('supports_binary', { value: fig.supports_binary });\n",
" fig.send_message('send_image_mode', {});\n",
" if (fig.ratio !== 1) {\n",
" fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n",
" }\n",
" fig.send_message('refresh', {});\n",
" };\n",
"\n",
" this.imageObj.onload = function () {\n",
" if (fig.image_mode === 'full') {\n",
" // Full images could contain transparency (where diff images\n",
" // almost always do), so we need to clear the canvas so that\n",
" // there is no ghosting.\n",
" fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
" }\n",
" fig.context.drawImage(fig.imageObj, 0, 0);\n",
" };\n",
"\n",
" this.imageObj.onunload = function () {\n",
" fig.ws.close();\n",
" };\n",
"\n",
" this.ws.onmessage = this._make_on_message_function(this);\n",
"\n",
" this.ondownload = ondownload;\n",
"};\n",
"\n",
"mpl.figure.prototype._init_header = function () {\n",
" var titlebar = document.createElement('div');\n",
" titlebar.classList =\n",
" 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
" var titletext = document.createElement('div');\n",
" titletext.classList = 'ui-dialog-title';\n",
" titletext.setAttribute(\n",
" 'style',\n",
" 'width: 100%; text-align: center; padding: 3px;'\n",
" );\n",
" titlebar.appendChild(titletext);\n",
" this.root.appendChild(titlebar);\n",
" this.header = titletext;\n",
"};\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
"\n",
"mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
"\n",
"mpl.figure.prototype._init_canvas = function () {\n",
" var fig = this;\n",
"\n",
" var canvas_div = (this.canvas_div = document.createElement('div'));\n",
" canvas_div.setAttribute(\n",
" 'style',\n",
" 'border: 1px solid #ddd;' +\n",
" 'box-sizing: content-box;' +\n",
" 'clear: both;' +\n",
" 'min-height: 1px;' +\n",
" 'min-width: 1px;' +\n",
" 'outline: 0;' +\n",
" 'overflow: hidden;' +\n",
" 'position: relative;' +\n",
" 'resize: both;'\n",
" );\n",
"\n",
" function on_keyboard_event_closure(name) {\n",
" return function (event) {\n",
" return fig.key_event(event, name);\n",
" };\n",
" }\n",
"\n",
" canvas_div.addEventListener(\n",
" 'keydown',\n",
" on_keyboard_event_closure('key_press')\n",
" );\n",
" canvas_div.addEventListener(\n",
" 'keyup',\n",
" on_keyboard_event_closure('key_release')\n",
" );\n",
"\n",
" this._canvas_extra_style(canvas_div);\n",
" this.root.appendChild(canvas_div);\n",
"\n",
" var canvas = (this.canvas = document.createElement('canvas'));\n",
" canvas.classList.add('mpl-canvas');\n",
" canvas.setAttribute('style', 'box-sizing: content-box;');\n",
"\n",
" this.context = canvas.getContext('2d');\n",
"\n",
" var backingStore =\n",
" this.context.backingStorePixelRatio ||\n",
" this.context.webkitBackingStorePixelRatio ||\n",
" this.context.mozBackingStorePixelRatio ||\n",
" this.context.msBackingStorePixelRatio ||\n",
" this.context.oBackingStorePixelRatio ||\n",
" this.context.backingStorePixelRatio ||\n",
" 1;\n",
"\n",
" this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
"\n",
" var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
" 'canvas'\n",
" ));\n",
" rubberband_canvas.setAttribute(\n",
" 'style',\n",
" 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
" );\n",
"\n",
" // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
" if (this.ResizeObserver === undefined) {\n",
" if (window.ResizeObserver !== undefined) {\n",
" this.ResizeObserver = window.ResizeObserver;\n",
" } else {\n",
" var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
" this.ResizeObserver = obs.ResizeObserver;\n",
" }\n",
" }\n",
"\n",
" this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
" var nentries = entries.length;\n",
" for (var i = 0; i < nentries; i++) {\n",
" var entry = entries[i];\n",
" var width, height;\n",
" if (entry.contentBoxSize) {\n",
" if (entry.contentBoxSize instanceof Array) {\n",
" // Chrome 84 implements new version of spec.\n",
" width = entry.contentBoxSize[0].inlineSize;\n",
" height = entry.contentBoxSize[0].blockSize;\n",
" } else {\n",
" // Firefox implements old version of spec.\n",
" width = entry.contentBoxSize.inlineSize;\n",
" height = entry.contentBoxSize.blockSize;\n",
" }\n",
" } else {\n",
" // Chrome <84 implements even older version of spec.\n",
" width = entry.contentRect.width;\n",
" height = entry.contentRect.height;\n",
" }\n",
"\n",
" // Keep the size of the canvas and rubber band canvas in sync with\n",
" // the canvas container.\n",
" if (entry.devicePixelContentBoxSize) {\n",
" // Chrome 84 implements new version of spec.\n",
" canvas.setAttribute(\n",
" 'width',\n",
" entry.devicePixelContentBoxSize[0].inlineSize\n",
" );\n",
" canvas.setAttribute(\n",
" 'height',\n",
" entry.devicePixelContentBoxSize[0].blockSize\n",
" );\n",
" } else {\n",
" canvas.setAttribute('width', width * fig.ratio);\n",
" canvas.setAttribute('height', height * fig.ratio);\n",
" }\n",
" canvas.setAttribute(\n",
" 'style',\n",
" 'width: ' + width + 'px; height: ' + height + 'px;'\n",
" );\n",
"\n",
" rubberband_canvas.setAttribute('width', width);\n",
" rubberband_canvas.setAttribute('height', height);\n",
"\n",
" // And update the size in Python. We ignore the initial 0/0 size\n",
" // that occurs as the element is placed into the DOM, which should\n",
" // otherwise not happen due to the minimum size styling.\n",
" if (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",
" '';\n",
" fig.close_ws(fig, msg);\n",
"};\n",
"\n",
"mpl.figure.prototype.close_ws = function (fig, msg) {\n",
" fig.send_message('closing', msg);\n",
" // fig.ws.close()\n",
"};\n",
"\n",
"mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
" // Turn the data on the canvas into data in the output cell.\n",
" var width = this.canvas.width / this.ratio;\n",
" var dataURL = this.canvas.toDataURL();\n",
" this.cell_info[1]['text/html'] =\n",
" '';\n",
"};\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function () {\n",
" // Tell IPython that the notebook contents must change.\n",
" IPython.notebook.set_dirty(true);\n",
" this.send_message('ack', {});\n",
" var fig = this;\n",
" // Wait a second, then push the new image to the DOM so\n",
" // that it is saved nicely (might be nice to debounce this).\n",
" setTimeout(function () {\n",
" fig.push_to_output();\n",
" }, 1000);\n",
"};\n",
"\n",
"mpl.figure.prototype._init_toolbar = function () {\n",
" var fig = this;\n",
"\n",
" var toolbar = document.createElement('div');\n",
" toolbar.classList = 'btn-toolbar';\n",
" this.root.appendChild(toolbar);\n",
"\n",
" function on_click_closure(name) {\n",
" return function (_event) {\n",
" return fig.toolbar_button_onclick(name);\n",
" };\n",
" }\n",
"\n",
" function on_mouseover_closure(tooltip) {\n",
" return function (event) {\n",
" if (!event.currentTarget.disabled) {\n",
" return fig.toolbar_button_onmouseover(tooltip);\n",
" }\n",
" };\n",
" }\n",
"\n",
" fig.buttons = {};\n",
" var buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" var button;\n",
" for (var toolbar_ind in mpl.toolbar_items) {\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) {\n",
" /* Instead of a spacer, we start a new button group. */\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
" buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" continue;\n",
" }\n",
"\n",
" button = fig.buttons[name] = document.createElement('button');\n",
" button.classList = 'btn btn-default';\n",
" button.href = '#';\n",
" button.title = name;\n",
" button.innerHTML = '';\n",
" button.addEventListener('click', on_click_closure(method_name));\n",
" button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
" buttonGroup.appendChild(button);\n",
" }\n",
"\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
"\n",
" // Add the status bar.\n",
" var status_bar = document.createElement('span');\n",
" status_bar.classList = 'mpl-message pull-right';\n",
" toolbar.appendChild(status_bar);\n",
" this.message = status_bar;\n",
"\n",
" // Add the close button to the window.\n",
" var buttongrp = document.createElement('div');\n",
" buttongrp.classList = 'btn-group inline pull-right';\n",
" button = document.createElement('button');\n",
" button.classList = 'btn btn-mini btn-primary';\n",
" button.href = '#';\n",
" button.title = 'Stop Interaction';\n",
" button.innerHTML = '';\n",
" button.addEventListener('click', function (_evt) {\n",
" fig.handle_close(fig, {});\n",
" });\n",
" button.addEventListener(\n",
" 'mouseover',\n",
" on_mouseover_closure('Stop Interaction')\n",
" );\n",
" buttongrp.appendChild(button);\n",
" var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
" titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
"};\n",
"\n",
"mpl.figure.prototype._remove_fig_handler = function (event) {\n",
" var fig = event.data.fig;\n",
" if (event.target !== this) {\n",
" // Ignore bubbled events from children.\n",
" return;\n",
" }\n",
" fig.close_ws(fig, {});\n",
"};\n",
"\n",
"mpl.figure.prototype._root_extra_style = function (el) {\n",
" el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
"};\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function (el) {\n",
" // this is important to make the div 'focusable\n",
" el.setAttribute('tabindex', 0);\n",
" // reach out to IPython and tell the keyboard manager to turn it's self\n",
" // off when our div gets focus\n",
"\n",
" // location in version 3\n",
" if (IPython.notebook.keyboard_manager) {\n",
" IPython.notebook.keyboard_manager.register_events(el);\n",
" } else {\n",
" // location in version 2\n",
" IPython.keyboard_manager.register_events(el);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
" var manager = IPython.notebook.keyboard_manager;\n",
" if (!manager) {\n",
" manager = IPython.keyboard_manager;\n",
" }\n",
"\n",
" // Check for shift+enter\n",
" if (event.shiftKey && event.which === 13) {\n",
" this.canvas_div.blur();\n",
" // select the cell after this one\n",
" var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
" IPython.notebook.select(index + 1);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
" fig.ondownload(fig, null);\n",
"};\n",
"\n",
"mpl.find_output_cell = function (html_output) {\n",
" // Return the cell and output element which can be found *uniquely* in the notebook.\n",
" // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
" // IPython event is triggered only after the cells have been serialised, which for\n",
" // our purposes (turning an active figure into a static one), is too late.\n",
" var cells = IPython.notebook.get_cells();\n",
" var ncells = cells.length;\n",
" for (var i = 0; i < ncells; i++) {\n",
" var cell = cells[i];\n",
" if (cell.cell_type === 'code') {\n",
" for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
" var data = cell.output_area.outputs[j];\n",
" if (data.data) {\n",
" // IPython >= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] === html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"};\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel !== null) {\n",
" IPython.notebook.kernel.comm_manager.register_target(\n",
" 'matplotlib',\n",
" mpl.mpl_figure_comm\n",
" );\n",
"}\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True, sharex=True)\n",
"fig.set_size_inches(18, 4)\n",
"ax1.set_ylim(0, 1.5 * np.max(workspace.data(pdf, include_auxdata=False)))\n",
"ax1.set_title('nominal signal + background µ = 1')\n",
"plot(ax=ax1, **{k: nominal[v] for k, v in par_name_dict.items()})\n",
"\n",
"ax2.set_title('nominal background-only µ = 0')\n",
"plot(ax=ax2, **{k: background_only[v] for k, v in par_name_dict.items()})\n",
"\n",
"ax3.set_title(f'best fit µ = {best_fit[pdf.config.poi_index]:.3g}')\n",
"plot(ax=ax3, **{k: best_fit[v] for k, v in par_name_dict.items()});"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Interval Estimation (Computing Upper Limits on µ)\n",
"\n",
"A common task in the statistical evaluation of High Energy Physics data analyses is the estimation of confidence intervals of parameters of interest. The general strategy is to perform a series of hypothesis tests and then *invert* the tests in order to obtain an interval with the correct coverage properties.\n",
"\n",
"A common figure of merit is a modified p-value, CLs. Here we compute an upper limit based on a series of CLs tests."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"mu_tests = np.linspace(0, 1, 16)\n",
"(\n",
" obs_limit,\n",
" exp_limits,\n",
" (poi_tests, tests),\n",
") = pyhf.infer.intervals.upper_limits.upper_limit(\n",
" data, pdf, mu_tests, level=0.05, return_results=True\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"application/javascript": [
"/* Put everything inside the global mpl namespace */\n",
"/* global mpl */\n",
"window.mpl = {};\n",
"\n",
"mpl.get_websocket_type = function () {\n",
" if (typeof WebSocket !== 'undefined') {\n",
" return WebSocket;\n",
" } else if (typeof MozWebSocket !== 'undefined') {\n",
" return MozWebSocket;\n",
" } else {\n",
" alert(\n",
" 'Your browser does not have WebSocket support. ' +\n",
" 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
" 'Firefox 4 and 5 are also supported but you ' +\n",
" 'have to enable WebSockets in about:config.'\n",
" );\n",
" }\n",
"};\n",
"\n",
"mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
" this.id = figure_id;\n",
"\n",
" this.ws = websocket;\n",
"\n",
" this.supports_binary = this.ws.binaryType !== undefined;\n",
"\n",
" if (!this.supports_binary) {\n",
" var warnings = document.getElementById('mpl-warnings');\n",
" if (warnings) {\n",
" warnings.style.display = 'block';\n",
" warnings.textContent =\n",
" 'This browser does not support binary websocket messages. ' +\n",
" 'Performance may be slow.';\n",
" }\n",
" }\n",
"\n",
" this.imageObj = new Image();\n",
"\n",
" this.context = undefined;\n",
" this.message = undefined;\n",
" this.canvas = undefined;\n",
" this.rubberband_canvas = undefined;\n",
" this.rubberband_context = undefined;\n",
" this.format_dropdown = undefined;\n",
"\n",
" this.image_mode = 'full';\n",
"\n",
" this.root = document.createElement('div');\n",
" this.root.setAttribute('style', 'display: inline-block');\n",
" this._root_extra_style(this.root);\n",
"\n",
" parent_element.appendChild(this.root);\n",
"\n",
" this._init_header(this);\n",
" this._init_canvas(this);\n",
" this._init_toolbar(this);\n",
"\n",
" var fig = this;\n",
"\n",
" this.waiting = false;\n",
"\n",
" this.ws.onopen = function () {\n",
" fig.send_message('supports_binary', { value: fig.supports_binary });\n",
" fig.send_message('send_image_mode', {});\n",
" if (fig.ratio !== 1) {\n",
" fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n",
" }\n",
" fig.send_message('refresh', {});\n",
" };\n",
"\n",
" this.imageObj.onload = function () {\n",
" if (fig.image_mode === 'full') {\n",
" // Full images could contain transparency (where diff images\n",
" // almost always do), so we need to clear the canvas so that\n",
" // there is no ghosting.\n",
" fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
" }\n",
" fig.context.drawImage(fig.imageObj, 0, 0);\n",
" };\n",
"\n",
" this.imageObj.onunload = function () {\n",
" fig.ws.close();\n",
" };\n",
"\n",
" this.ws.onmessage = this._make_on_message_function(this);\n",
"\n",
" this.ondownload = ondownload;\n",
"};\n",
"\n",
"mpl.figure.prototype._init_header = function () {\n",
" var titlebar = document.createElement('div');\n",
" titlebar.classList =\n",
" 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
" var titletext = document.createElement('div');\n",
" titletext.classList = 'ui-dialog-title';\n",
" titletext.setAttribute(\n",
" 'style',\n",
" 'width: 100%; text-align: center; padding: 3px;'\n",
" );\n",
" titlebar.appendChild(titletext);\n",
" this.root.appendChild(titlebar);\n",
" this.header = titletext;\n",
"};\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
"\n",
"mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
"\n",
"mpl.figure.prototype._init_canvas = function () {\n",
" var fig = this;\n",
"\n",
" var canvas_div = (this.canvas_div = document.createElement('div'));\n",
" canvas_div.setAttribute(\n",
" 'style',\n",
" 'border: 1px solid #ddd;' +\n",
" 'box-sizing: content-box;' +\n",
" 'clear: both;' +\n",
" 'min-height: 1px;' +\n",
" 'min-width: 1px;' +\n",
" 'outline: 0;' +\n",
" 'overflow: hidden;' +\n",
" 'position: relative;' +\n",
" 'resize: both;'\n",
" );\n",
"\n",
" function on_keyboard_event_closure(name) {\n",
" return function (event) {\n",
" return fig.key_event(event, name);\n",
" };\n",
" }\n",
"\n",
" canvas_div.addEventListener(\n",
" 'keydown',\n",
" on_keyboard_event_closure('key_press')\n",
" );\n",
" canvas_div.addEventListener(\n",
" 'keyup',\n",
" on_keyboard_event_closure('key_release')\n",
" );\n",
"\n",
" this._canvas_extra_style(canvas_div);\n",
" this.root.appendChild(canvas_div);\n",
"\n",
" var canvas = (this.canvas = document.createElement('canvas'));\n",
" canvas.classList.add('mpl-canvas');\n",
" canvas.setAttribute('style', 'box-sizing: content-box;');\n",
"\n",
" this.context = canvas.getContext('2d');\n",
"\n",
" var backingStore =\n",
" this.context.backingStorePixelRatio ||\n",
" this.context.webkitBackingStorePixelRatio ||\n",
" this.context.mozBackingStorePixelRatio ||\n",
" this.context.msBackingStorePixelRatio ||\n",
" this.context.oBackingStorePixelRatio ||\n",
" this.context.backingStorePixelRatio ||\n",
" 1;\n",
"\n",
" this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
"\n",
" var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
" 'canvas'\n",
" ));\n",
" rubberband_canvas.setAttribute(\n",
" 'style',\n",
" 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
" );\n",
"\n",
" // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
" if (this.ResizeObserver === undefined) {\n",
" if (window.ResizeObserver !== undefined) {\n",
" this.ResizeObserver = window.ResizeObserver;\n",
" } else {\n",
" var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
" this.ResizeObserver = obs.ResizeObserver;\n",
" }\n",
" }\n",
"\n",
" this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
" var nentries = entries.length;\n",
" for (var i = 0; i < nentries; i++) {\n",
" var entry = entries[i];\n",
" var width, height;\n",
" if (entry.contentBoxSize) {\n",
" if (entry.contentBoxSize instanceof Array) {\n",
" // Chrome 84 implements new version of spec.\n",
" width = entry.contentBoxSize[0].inlineSize;\n",
" height = entry.contentBoxSize[0].blockSize;\n",
" } else {\n",
" // Firefox implements old version of spec.\n",
" width = entry.contentBoxSize.inlineSize;\n",
" height = entry.contentBoxSize.blockSize;\n",
" }\n",
" } else {\n",
" // Chrome <84 implements even older version of spec.\n",
" width = entry.contentRect.width;\n",
" height = entry.contentRect.height;\n",
" }\n",
"\n",
" // Keep the size of the canvas and rubber band canvas in sync with\n",
" // the canvas container.\n",
" if (entry.devicePixelContentBoxSize) {\n",
" // Chrome 84 implements new version of spec.\n",
" canvas.setAttribute(\n",
" 'width',\n",
" entry.devicePixelContentBoxSize[0].inlineSize\n",
" );\n",
" canvas.setAttribute(\n",
" 'height',\n",
" entry.devicePixelContentBoxSize[0].blockSize\n",
" );\n",
" } else {\n",
" canvas.setAttribute('width', width * fig.ratio);\n",
" canvas.setAttribute('height', height * fig.ratio);\n",
" }\n",
" canvas.setAttribute(\n",
" 'style',\n",
" 'width: ' + width + 'px; height: ' + height + 'px;'\n",
" );\n",
"\n",
" rubberband_canvas.setAttribute('width', width);\n",
" rubberband_canvas.setAttribute('height', height);\n",
"\n",
" // And update the size in Python. We ignore the initial 0/0 size\n",
" // that occurs as the element is placed into the DOM, which should\n",
" // otherwise not happen due to the minimum size styling.\n",
" if (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",
" '';\n",
" fig.close_ws(fig, msg);\n",
"};\n",
"\n",
"mpl.figure.prototype.close_ws = function (fig, msg) {\n",
" fig.send_message('closing', msg);\n",
" // fig.ws.close()\n",
"};\n",
"\n",
"mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
" // Turn the data on the canvas into data in the output cell.\n",
" var width = this.canvas.width / this.ratio;\n",
" var dataURL = this.canvas.toDataURL();\n",
" this.cell_info[1]['text/html'] =\n",
" '';\n",
"};\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function () {\n",
" // Tell IPython that the notebook contents must change.\n",
" IPython.notebook.set_dirty(true);\n",
" this.send_message('ack', {});\n",
" var fig = this;\n",
" // Wait a second, then push the new image to the DOM so\n",
" // that it is saved nicely (might be nice to debounce this).\n",
" setTimeout(function () {\n",
" fig.push_to_output();\n",
" }, 1000);\n",
"};\n",
"\n",
"mpl.figure.prototype._init_toolbar = function () {\n",
" var fig = this;\n",
"\n",
" var toolbar = document.createElement('div');\n",
" toolbar.classList = 'btn-toolbar';\n",
" this.root.appendChild(toolbar);\n",
"\n",
" function on_click_closure(name) {\n",
" return function (_event) {\n",
" return fig.toolbar_button_onclick(name);\n",
" };\n",
" }\n",
"\n",
" function on_mouseover_closure(tooltip) {\n",
" return function (event) {\n",
" if (!event.currentTarget.disabled) {\n",
" return fig.toolbar_button_onmouseover(tooltip);\n",
" }\n",
" };\n",
" }\n",
"\n",
" fig.buttons = {};\n",
" var buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" var button;\n",
" for (var toolbar_ind in mpl.toolbar_items) {\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) {\n",
" /* Instead of a spacer, we start a new button group. */\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
" buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" continue;\n",
" }\n",
"\n",
" button = fig.buttons[name] = document.createElement('button');\n",
" button.classList = 'btn btn-default';\n",
" button.href = '#';\n",
" button.title = name;\n",
" button.innerHTML = '';\n",
" button.addEventListener('click', on_click_closure(method_name));\n",
" button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
" buttonGroup.appendChild(button);\n",
" }\n",
"\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
"\n",
" // Add the status bar.\n",
" var status_bar = document.createElement('span');\n",
" status_bar.classList = 'mpl-message pull-right';\n",
" toolbar.appendChild(status_bar);\n",
" this.message = status_bar;\n",
"\n",
" // Add the close button to the window.\n",
" var buttongrp = document.createElement('div');\n",
" buttongrp.classList = 'btn-group inline pull-right';\n",
" button = document.createElement('button');\n",
" button.classList = 'btn btn-mini btn-primary';\n",
" button.href = '#';\n",
" button.title = 'Stop Interaction';\n",
" button.innerHTML = '';\n",
" button.addEventListener('click', function (_evt) {\n",
" fig.handle_close(fig, {});\n",
" });\n",
" button.addEventListener(\n",
" 'mouseover',\n",
" on_mouseover_closure('Stop Interaction')\n",
" );\n",
" buttongrp.appendChild(button);\n",
" var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
" titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
"};\n",
"\n",
"mpl.figure.prototype._remove_fig_handler = function (event) {\n",
" var fig = event.data.fig;\n",
" if (event.target !== this) {\n",
" // Ignore bubbled events from children.\n",
" return;\n",
" }\n",
" fig.close_ws(fig, {});\n",
"};\n",
"\n",
"mpl.figure.prototype._root_extra_style = function (el) {\n",
" el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
"};\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function (el) {\n",
" // this is important to make the div 'focusable\n",
" el.setAttribute('tabindex', 0);\n",
" // reach out to IPython and tell the keyboard manager to turn it's self\n",
" // off when our div gets focus\n",
"\n",
" // location in version 3\n",
" if (IPython.notebook.keyboard_manager) {\n",
" IPython.notebook.keyboard_manager.register_events(el);\n",
" } else {\n",
" // location in version 2\n",
" IPython.keyboard_manager.register_events(el);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
" var manager = IPython.notebook.keyboard_manager;\n",
" if (!manager) {\n",
" manager = IPython.keyboard_manager;\n",
" }\n",
"\n",
" // Check for shift+enter\n",
" if (event.shiftKey && event.which === 13) {\n",
" this.canvas_div.blur();\n",
" // select the cell after this one\n",
" var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
" IPython.notebook.select(index + 1);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
" fig.ondownload(fig, null);\n",
"};\n",
"\n",
"mpl.find_output_cell = function (html_output) {\n",
" // Return the cell and output element which can be found *uniquely* in the notebook.\n",
" // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
" // IPython event is triggered only after the cells have been serialised, which for\n",
" // our purposes (turning an active figure into a static one), is too late.\n",
" var cells = IPython.notebook.get_cells();\n",
" var ncells = cells.length;\n",
" for (var i = 0; i < ncells; i++) {\n",
" var cell = cells[i];\n",
" if (cell.cell_type === 'code') {\n",
" for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
" var data = cell.output_area.outputs[j];\n",
" if (data.data) {\n",
" // IPython >= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] === html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"};\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel !== null) {\n",
" IPython.notebook.kernel.comm_manager.register_target(\n",
" 'matplotlib',\n",
" mpl.mpl_figure_comm\n",
" );\n",
"}\n"
],
"text/plain": [
""
]
},
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"data": {
"text/html": [
""
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"source": [
"fig, ax = plt.subplots()\n",
"fig.set_size_inches(7, 5)\n",
"\n",
"ax.set_title(\"Hypothesis Tests\")\n",
"artists = brazil.plot_results(mu_tests, tests, test_size=0.05, ax=ax)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Observed upper limit: 0.630\n",
"\n",
"Expected Limit(-2 σ): 0.297\n",
"Expected Limit(-1 σ): 0.393\n",
"Expected Limit: 0.546\n",
"Expected Limit(1 σ): 0.762\n",
"Expected Limit(2 σ): 1.000\n"
]
}
],
"source": [
"print(f\"Observed upper limit: {obs_limit:.3f}\\n\")\n",
"for i, n_sigma in enumerate(np.arange(-2, 3)):\n",
" print(\n",
" \"Expected Limit{}: {:.3f}\".format(\n",
" \"\" if n_sigma == 0 else f\"({n_sigma} σ)\", exp_limits[i]\n",
" )\n",
" )"
]
}
],
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"name": "python3"
},
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"file_extension": ".py",
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"outputs": [
{
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\n",
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