{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Curve fitting and the $\\chi^2$ error surface\n", "#### Material to accompany Hughes and Hase Section 6.5, this time with a nonlinear fit (Gaussian)\n", "\n", "Tom Solomon, March 2021; based on curve_fit_w_contour (Marty Ligare, August 2020) that does a linear fit." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy import optimize\n", "from scipy import stats\n", "\n", "import urllib # for importing from a URL\n", "\n", "import matplotlib as mpl\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "from matplotlib.ticker import LinearLocator, FormatStrFormatter" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Following is an Ipython magic command that puts figures in notebook.\n", "%matplotlib notebook\n", "\n", "# M.L. modification of matplotlib defaults\n", "# Changes can also be put in matplotlibrc file, \n", "# or effected using mpl.rcParams[]\n", "mpl.style.use('classic') \n", "plt.rc('figure', figsize = (6, 4.5)) # Reduces overall size of figures\n", "plt.rc('axes', labelsize=16, titlesize=14)\n", "plt.rc('figure', autolayout = True) # Adjusts supblot params for new size" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Define functions" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def f(x,A,x0,b,c):\n", " '''Simple Gaussian function with amplitude A, center x0, width b and offset c'''\n", " return A*np.exp(-1.0*(x-x0)**2/b) + c\n", "\n", "def chi2(x, y, u, A, x0, b, c):\n", " '''Chisquare as a function of data (x, y, and yerr=u), and model \n", " parameters Amplitude A, center x0, width b and offset c'''\n", " return np.sum((y - f(x, A, x0, b, c))**2/u**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear fit to data for $A$, $x_0$, $b$ and $c$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Data to be fit:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "g = urllib.request.urlopen('https://www.eg.bucknell.edu/~phys310/skills/data_analysis/GaussianData.dat')\n", "data = np.loadtxt(g)\n", "# data = np.loadtxt(\"GaussianData.dat\") \n", "# Format: [[x1,y1,u1], [x2,y2,u2], ... ] where u1 is uncertainty in y1\n", "# data = np.array([[1, 2.947032612427293, 0.5],\n", "# [2, 6.168779380682309, 0.5],\n", "# [3, 7.1618838821688, 0.5],\n", "# [4, 9.590549514954866, 0.5],\n", "# [5, 11.20657, 0.5]])\n", "\n", "x, y, u = data.T" ] }, { "cell_type": "code", "execution_count": 5, "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 (mpl.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: mpl.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = 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", " mpl.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", " var resizeObserver = new 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 * mpl.ratio);\n", " canvas.setAttribute('height', height * mpl.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 (width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " resizeObserver.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'] / mpl.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n", " var x1 = msg['x1'] / mpl.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / mpl.ratio,\n", " fig.canvas.height / mpl.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 * mpl.ratio;\n", " var y = canvas_pos.y * mpl.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", "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", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / mpl.ratio;\n", " fig.root.removeEventListener('remove', this._remove_fig_handler);\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 / mpl.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 () {\n", " this.close_ws(this, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", " el.addEventListener('remove', this._remove_fig_handler);\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": [ "xc = np.linspace(0,4,201) # quasi-continuous set of x's for function plot\n", "plt.figure()\n", "plt.title(\"data\",fontsize=14)\n", "plt.xlabel('$x$')\n", "plt.ylabel('$y$')\n", "plt.axhline(0,color='magenta')\n", "plt.xlim(0,4) \n", "plt.errorbar(x,y,yerr=u,fmt='o');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Initial estimates for parameters" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# I am purposefully picking some so-so values because as long as we are\n", "# close, the fitting should be able to make it work.\n", "A = 2.0\n", "x0 = 1.5\n", "b = 0.5\n", "c= 0.5\n", "p0 = A, x0, b, c" ] }, { "cell_type": "code", "execution_count": 7, "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 (mpl.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: mpl.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = 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", " mpl.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", " var resizeObserver = new 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 * mpl.ratio);\n", " canvas.setAttribute('height', height * mpl.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 (width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " resizeObserver.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'] / mpl.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n", " var x1 = msg['x1'] / mpl.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / mpl.ratio,\n", " fig.canvas.height / mpl.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 * mpl.ratio;\n", " var y = canvas_pos.y * mpl.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", "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", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / mpl.ratio;\n", " fig.root.removeEventListener('remove', this._remove_fig_handler);\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 / mpl.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 () {\n", " this.close_ws(this, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", " el.addEventListener('remove', this._remove_fig_handler);\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": [ "plt.figure()\n", "xc = np.linspace(0,4,201)\n", "yc = f(xc, *p0)\n", "plt.plot(xc, yc)\n", "plt.errorbar(x,y,u,fmt='o')\n", "plt.xlabel('$x$')\n", "plt.ylabel('$y$')\n", "plt.title(\"Preliminary graph with estimated parameters\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Perform fit" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A = 2.4275159277659473 +/- 0.0981189904595323 \n", "\n", "x0 = 1.757434802419164 +/- 0.01689107154392164 \n", "\n", "b = 0.2889595362371085 +/- 0.02938444989729009 \n", "\n", "c = 0.6993908206018963 +/- 0.04241556039848094 \n", "\n", "covariance matrix = \n", " [[ 9.62733629e-03 1.19406380e-09 -9.56886229e-04 -1.27216656e-03]\n", " [ 1.19406380e-09 2.85308298e-04 5.25913391e-10 -1.60653539e-09]\n", " [-9.56886229e-04 5.25913391e-10 8.63445896e-04 -6.05692897e-04]\n", " [-1.27216656e-03 -1.60653539e-09 -6.05692897e-04 1.79907976e-03]] \n", "\n", "chi2 = 20.368136771219355\n" ] } ], "source": [ "popt, pcov = optimize.curve_fit(f, x, y, p0, sigma=u, absolute_sigma=True)\n", "A = popt[0]\n", "x0 = popt[1]\n", "b = popt[2]\n", "c = popt[3]\n", "\n", "αA = np.sqrt(pcov[0,0])\n", "αx0 = np.sqrt(pcov[1,1])\n", "αb = np.sqrt(pcov[2,2])\n", "αc = np.sqrt(pcov[3,3])\n", "\n", "print(\"A =\", A,\"+/-\", αA,\"\\n\")\n", "print(\"x0 =\", x0,\"+/-\", αx0,\"\\n\")\n", "print(\"b =\", b,\"+/-\", αb,\"\\n\")\n", "print(\"c =\", c,\"+/-\", αc,\"\\n\")\n", "\n", "print(\"covariance matrix =\",\"\\n\",pcov,\"\\n\")\n", "pcov_data = pcov\n", "\n", "print(\"chi2 =\", chi2(x, y, u,*popt))\n", "# print(\"reduced chi2 = chi2/(len(x)-len(popt)) =\", chi2(x, y, u, *popt)/(len(x)-len(popt)))\n", "\n", "a = chi2(x,y,u,*popt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Written in standard notation\n", "\n", "### A = 2.43 $\\pm$ 0.10\n", "\n", "### $x_0$ = 1.757 $\\pm$ 0.017\n", "\n", "### b = 0.29 $\\pm$ 0.03\n", "\n", "### c = 0.70 $\\pm$ 0.04\n", "\n", "(Note: I generated this data with A = 2.50, $x_0$ = 1.75, b = 0.27 and c = 0.65, with some additive noise with standard deviation of 0.14, so the fit came up with the \"true\" parameters within two uncertainties.)" ] }, { "cell_type": "code", "execution_count": 9, "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 (mpl.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: mpl.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = 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", " mpl.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", " var resizeObserver = new 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 * mpl.ratio);\n", " canvas.setAttribute('height', height * mpl.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 (width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " resizeObserver.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'] / mpl.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n", " var x1 = msg['x1'] / mpl.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / mpl.ratio,\n", " fig.canvas.height / mpl.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 * mpl.ratio;\n", " var y = canvas_pos.y * mpl.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", "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", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / mpl.ratio;\n", " fig.root.removeEventListener('remove', this._remove_fig_handler);\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 / mpl.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 () {\n", " this.close_ws(this, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", " el.addEventListener('remove', this._remove_fig_handler);\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": [ "xc = np.linspace(0,4,201) # quasi-continuous set of x's function plot\n", "plt.figure()\n", "plt.title(\"data with best fit line\",fontsize=14)\n", "plt.xlabel('$x$')\n", "plt.ylabel('$y$')\n", "plt.axhline(0, color='magenta')\n", "plt.xlim(0,4) # Pad x-range on plot\n", "plt.errorbar(x, y, yerr=u, fmt='o');\n", "plt.plot(xc ,f(xc, A, x0, b, c));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Residuals:" ] }, { "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 (mpl.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: mpl.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = 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", " mpl.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", " var resizeObserver = new 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 * mpl.ratio);\n", " canvas.setAttribute('height', height * mpl.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 (width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " resizeObserver.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'] / mpl.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n", " var x1 = msg['x1'] / mpl.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / mpl.ratio,\n", " fig.canvas.height / mpl.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 * mpl.ratio;\n", " var y = canvas_pos.y * mpl.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", "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", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / mpl.ratio;\n", " fig.root.removeEventListener('remove', this._remove_fig_handler);\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 / mpl.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 () {\n", " this.close_ws(this, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", " el.addEventListener('remove', this._remove_fig_handler);\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": [ "plt.figure()\n", "plt.axhline(0,color='magenta')\n", "plt.title('normalized residuals')\n", "plt.xlabel('$x$')\n", "plt.ylabel('normalized residuals')\n", "plt.grid(True)\n", "plt.errorbar(x,(f(x,A, x0, b, c)-y)/u,1,fmt='o')\n", "plt.xlim(-0.5,4.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The normalized residuals look fine. First, most but not all are between -1 and +1. Second, there are no patterns in the residuals; rather, they are randomly fluctuating between negative and positive." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Make \"data\" for contour plot\n", "\n", "We have four parameters, so we should plot two at a time. Let's pair up A with c and x0 with b. Start with A and c\n", "\n", "+ Choose ranges of $A$ and $c$ for contour plot. The ranges should range from below to above the best fit values for each. If the range ends up crappy, you can always change the range and re-do the calculations, or you can zoom in and out of the contour plot.\n", "+ Calculate values of $\\chi^2$ at grid points" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "AA = np.linspace(2, 3.0, 201)\n", "cc = np.linspace(0, 1, 201)\n", "\n", "Z = np.zeros((len(AA),len(cc)))\n", "\n", "for i in range(len(AA)):\n", " for j in range(len(cc)):\n", " Z[j,i] = chi2(x, y, u, AA[i], x0, b, cc[j]) - chi2(x, y, u, *popt)" ] }, { "cell_type": "code", "execution_count": 14, "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 (mpl.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: mpl.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = 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", " mpl.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", " var resizeObserver = new 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 * mpl.ratio);\n", " canvas.setAttribute('height', height * mpl.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 (width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " resizeObserver.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'] / mpl.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n", " var x1 = msg['x1'] / mpl.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / mpl.ratio,\n", " fig.canvas.height / mpl.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 * mpl.ratio;\n", " var y = canvas_pos.y * mpl.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", "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", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / mpl.ratio;\n", " fig.root.removeEventListener('remove', this._remove_fig_handler);\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 / mpl.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 () {\n", " this.close_ws(this, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", " el.addEventListener('remove', this._remove_fig_handler);\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": [ "plt.figure()\n", "AA, cc = np.meshgrid(AA, cc)\n", "CS = plt.contour(AA, cc, Z, levels=[1,2,5,10,20,50])\n", "plt.xlabel('$A$')\n", "plt.ylabel('$c$')\n", "plt.grid()\n", "plt.axhline(c)\n", "plt.axvline(A)\n", "plt.clabel(CS, inline=1, fontsize=10);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Let's focus on the $\\chi^2_{reduced} - \\chi^2_{best} = 1$ contour. That's where we can determine uncertainties for A and c" ] }, { "cell_type": "code", "execution_count": 15, "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 (mpl.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: mpl.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = 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", " mpl.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", " var resizeObserver = new 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 * mpl.ratio);\n", " canvas.setAttribute('height', height * mpl.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 (width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " resizeObserver.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'] / mpl.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n", " var x1 = msg['x1'] / mpl.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / mpl.ratio,\n", " fig.canvas.height / mpl.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 * mpl.ratio;\n", " var y = canvas_pos.y * mpl.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", "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", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / mpl.ratio;\n", " fig.root.removeEventListener('remove', this._remove_fig_handler);\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 / mpl.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 () {\n", " this.close_ws(this, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", " el.addEventListener('remove', this._remove_fig_handler);\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": [ "AA = np.linspace(2.2, 2.6, 201)\n", "cc = np.linspace(0.6, 0.8, 201)\n", "\n", "Z = np.zeros((len(AA),len(cc)))\n", "\n", "for i in range(len(AA)):\n", " for j in range(len(cc)):\n", " Z[j,i] = chi2(x, y, u, AA[i], x0, b, cc[j]) - chi2(x, y, u, *popt)\n", "\n", "plt.figure()\n", "AA, cc = np.meshgrid(AA, cc)\n", "CS = plt.contour(AA, cc, Z, levels=[1])\n", "plt.xlabel('$A$')\n", "plt.ylabel('$c$')\n", "plt.grid()\n", "plt.axhline(c)\n", "plt.axvline(A)\n", "plt.clabel(CS, inline=1, fontsize=10);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Okay, so the contour $\\chi^2_{reduced} - \\chi^2_{best} = 1$ curve goes from a minimum in A from around 2.33 to a maximum of around 2.52, so if we take half of that range, that would get us $\\alpha_A \\approx 0.10$, which is consistent with what the curve fitting routine returned for the uncertainty. And the same contour curve goes from a minimum in c of around 0.67 to a maximum of around 0.73, so half of that range would get us $\\alpha_c \\approx 0.03$, which isn't exactly what the curve fitting returned, but frankly an uncertainty of 0.03 vs 0.04 isn't worth losing sleep over.\n", "\n", "#### Now let's look at the other two parameters $x_0$ and $b$. Generate an array with $x_0$ going from below to above the best fit value of 1.79 and $b$ going from below to above the best fit value of 0.29" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "x0b = np.linspace(1.5, 2.0, 201)\n", "bb = np.linspace(0.1, 0.5, 201)\n", "\n", "Z = np.zeros((len(x0b),len(bb)))\n", "\n", "for i in range(len(x0b)):\n", " for j in range(len(bb)):\n", " Z[j,i] = chi2(x, y, u, A, x0b[i], bb[j], c) - chi2(x, y, u, *popt)" ] }, { "cell_type": "code", "execution_count": 17, "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 (mpl.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: mpl.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = 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", " mpl.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", " var resizeObserver = new 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 * mpl.ratio);\n", " canvas.setAttribute('height', height * mpl.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 (width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " resizeObserver.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'] / mpl.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n", " var x1 = msg['x1'] / mpl.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / mpl.ratio,\n", " fig.canvas.height / mpl.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 * mpl.ratio;\n", " var y = canvas_pos.y * mpl.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", "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", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / mpl.ratio;\n", " fig.root.removeEventListener('remove', this._remove_fig_handler);\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 / mpl.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 () {\n", " this.close_ws(this, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", " el.addEventListener('remove', this._remove_fig_handler);\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": [ "plt.figure()\n", "x0b, bb = np.meshgrid(x0b, bb)\n", "CS = plt.contour(x0b, bb, Z, levels=[1,2,5,10,20,50])\n", "plt.xlabel('$x0$')\n", "plt.ylabel('$b$')\n", "plt.grid()\n", "plt.axhline(b)\n", "plt.axvline(x0)\n", "plt.clabel(CS, inline=1, fontsize=10);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Okay, now zoom in on the $\\chi^2_{reduced} - \\chi^2_{best} = 1$ contour. That's where we can determine uncertainties for x0 and b" ] }, { "cell_type": "code", "execution_count": 18, "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 (mpl.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: mpl.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = 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", " mpl.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", " var resizeObserver = new 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 * mpl.ratio);\n", " canvas.setAttribute('height', height * mpl.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 (width != 0 && height != 0) {\n", " fig.request_resize(width, height);\n", " }\n", " }\n", " });\n", " resizeObserver.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'] / mpl.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n", " var x1 = msg['x1'] / mpl.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / mpl.ratio,\n", " fig.canvas.height / mpl.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 * mpl.ratio;\n", " var y = canvas_pos.y * mpl.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", "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", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / mpl.ratio;\n", " fig.root.removeEventListener('remove', this._remove_fig_handler);\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 / mpl.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 () {\n", " this.close_ws(this, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", " el.addEventListener('remove', this._remove_fig_handler);\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": [ "x0b = np.linspace(1.7, 1.8, 201)\n", "bb = np.linspace(0.25, 0.35, 201)\n", "\n", "Z = np.zeros((len(x0b),len(bb)))\n", "\n", "for i in range(len(x0b)):\n", " for j in range(len(bb)):\n", " Z[j,i] = chi2(x, y, u, A, x0b[i], bb[j], c) - chi2(x, y, u, *popt)\n", " \n", "plt.figure()\n", "x0b, bb = np.meshgrid(x0b, bb)\n", "CS = plt.contour(x0b, bb, Z, levels=[1])\n", "plt.xlabel('$x0$')\n", "plt.ylabel('$b$')\n", "plt.grid()\n", "plt.axhline(b)\n", "plt.axvline(x0)\n", "plt.clabel(CS, inline=1, fontsize=10);\n", "\n", "# I then used the zoom feature, i.e., hold \"cntl\" key, and right-click and drag to zoom in. \n", "# You could also simply narrow the range to zoom in.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Okay, so the contour $\\chi^2_{reduced} - \\chi^2_{best} = 1$ curve goes from a minimum in $x_0$ from around 0.04 to a maximum of around 0.074, so if we take half of that range, that would get us $\\alpha_x0 \\approx 0.017$, which is consistent with what the curve fitting routine returned for the uncertainty. And the same contour curve goes from a minimum in b of around 0.27 to a maximum of around 0.31, so half of that range would get us $\\alpha_b \\approx 0.02$, which isn't exactly what the curve fitting returned, but frankly an uncertainty of 0.02 vs 0.03 isn't worth losing sleep over.\n", "\n", "#### So, yeah. That's basically where the uncertainties in the curve-fitting come from." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.8" } }, "nbformat": 4, "nbformat_minor": 1 }