{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "One of the simplest models that can predict the fundamental free motion of a bicycle or motorcycle takes the following form:\n", "\n", "$$\n", "\\mathbf{M\\ddot{q}}\n", "+v\\mathbf{C}_1\\mathbf{\\dot{q}}\n", "+\\left[g\\mathbf{K}_0\n", "+v^2\\mathbf{K}_2\\right]\\mathbf{q}\n", "=0\n", "$$\n", "\n", "where\n", "\n", "$$\n", "\\mathbf{q} =\n", "[\\phi \\quad \\delta]^T\n", "$$\n", "\n", "$\\delta$, the steer angle, is a generalized coordinate that tracks the angle between the front frame (handlebar/fork) and the rear frame (frame, seat, etc) and $\\phi$, the roll angle, is a generalized coordinate that tracks the roll angle of the rear frame relative to the ground. If each of these are zero the bicycle is standing upright and the steering is pointed straight ahead. Positive steer angle is to the right and negative steer angle is to the left. Positive roll is to the right and negative to the left." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The system has a mass matrix, $\\mathbf{M}$, and effective damping and stiffness matrices, $\\mathbf{C}=v\\mathbf{C}_1$ and $\\mathbf{K}=g\\mathbf{K}_0 + v^2\\mathbf{K}_2$, that are parameterized by the speed of the bicycle $v$ and the acceleration due to gravity $g$. These matrices are a function of the vehicle's geometry and mass distribution. Typical values for the four matrices in SI units are:\n", "\n", "$$\n", "\\mathbf{M} =\n", "\\begin{bmatrix}\n", "80.81722 & 2.31941332208709 \\\\\n", "2.31941332208709 & 0.29784188199686\n", "\\end{bmatrix}\n", "$$\n", "\n", "$$\n", "\\mathbf{K}_0 =\n", "\\begin{bmatrix}\n", "-80.95 & -2.599516 852 498 72 \\\\\n", "-2.599516 852 498 72 & -0.803 294 884 586 18\n", "\\end{bmatrix}\n", "$$\n", "\n", "$$\n", "\\mathbf{K}_2 =\n", "\\begin{bmatrix}\n", "0 & 76.597 345 895 732 22 \\\\\n", "0 & 2.654 315 237 946 04\n", "\\end{bmatrix}\n", "$$\n", "\n", "$$\n", "\\mathbf{C}_1 =\n", "\\begin{bmatrix}\n", "0 & 33.866 414 914 924 94 \\\\\n", "-0.850 356 414 569 78 & 1.685 403 973 975 60\n", "\\end{bmatrix}\n", "$$\n", "\n", "The speed $v$ is in meters per second and $g$ is in meters per second squared." ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "np.set_printoptions(precision=4, linewidth=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Eigenvalues and Eigenvectors\n", "\n", "In the previous class we learned that the free response of the system can be formulated by solving an eigenvalue problem. This applies to systems with or without damping. All scientific computing software provides efficient numerical routines to compute the eigenvalues and eigenvectors of a square matrix. In Python you can use `numpy.linalg.eig`. For systems that have a general damping matric, this computation requires that the system be in state space form:\n", "\n", "$$\\dot{\\mathbf{x}} = \\mathbf{A} \\mathbf{x}$$\n", "\n", "where $\\mathbf{x}$ is the state vector.\n", "\n", "# Exercise\n", "\n", "Write a function that takes the matrices $\\mathbf{M,K_0, K_2, C_1}$, the speed, and gravity as an input and returns the A matrix." ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def compute_state_matrix(v, g, M, C1, K0, K2):\n", " \"\"\"Returns the state matrix.\n", " \n", " Parameters\n", " ----------\n", " v : float\n", " Bicycle speed in meters per second.\n", " g : float\n", " Acceleration due to gravity in meters per second squared.\n", " M : array_like, shape(2,2)\n", " The mass matrix.\n", " C1 : array_like, shape(2,2)\n", " The speed proportional damping matrix.\n", " K0 : array_like, shape(2,2)\n", " The gravity proportional stiffness matrix.\n", " K2 : array_like, shape(2,2)\n", " The speed squared proportional stiffness matrix.\n", " \n", " Returns\n", " -------\n", "\n", " As : ndarray, shape(n,4,4)\n", " The state matrices evaluated at each speed in `speeds`.\n", "\n", " Notes\n", " -----\n", " The second order equations of motion take this form:\n", " \n", " M * q'' + v * C1 * q' + [g * K0 + v**2 * K2] * q = 0\n", " \n", " where q = [roll angle,\n", " steer angle]\n", " \n", " The first order equations of motion take this form:\n", " \n", " x' = A * x + B * u\n", " \n", " where x = [roll angle,\n", " steer angle,\n", " roll rate,\n", " steer rate]\n", "\n", " \"\"\"\n", " \n", " # write your code here\n", " \n", " invM = np.linalg.inv(M)\n", " \n", " # sub-matrices\n", " a11 = np.zeros((2, 2))\n", " a12 = np.eye(2)\n", " a21 = -invM @ (g * K0 + v**2 * K2)\n", " a22 = -invM @ (v * C1)\n", "\n", " # note that np.bmat returns a matrix but we don't want that! so make it an array\n", " A = np.array(np.bmat([[a11, a12], [a21, a22]]))\n", "\n", " return A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now use the function to create a state matrix, $\\mathbf{A}$, for $v=5.4 \\textrm{m/s}$ and $g=9.81$. This speed is normal \"around town\" riding speed (12 mph)." ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0. , 1. , 0. ],\n", " [ 0. , 0. , 0. , 1. ],\n", " [ 9.4898, -26.5588, -0.5698, -1.7848],\n", " [ 11.7195, -26.5865, 19.8547, -16.6583]])" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = np.array([[ 80.81722 , 2.31941332],\n", " [ 2.31941332, 0.29784188]])\n", "C1 = np.array([[ 0. , 33.86641391],\n", " [ -0.85035641, 1.68540397]])\n", "K0 = np.array([[-80.95 , -2.59951685],\n", " [ -2.59951685, -0.80329488]])\n", "K2 = np.array([[ 0. , 76.5973459 ],\n", " [ 0. , 2.65431524]])\n", "\n", "v = 5.4\n", "g = 9.81\n", "\n", "A = compute_state_matrix(v, g, M, C1, K0, K2)\n", "A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now compute the eigenvalues and eigenvectors of the the system using `numpy.linalg.eig`, see https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html." ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": true }, "outputs": [], "source": [ "eigenvalues, eigenvectors = np.linalg.eig(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The eigenvalues are, in general, complex numbers. The complex eigenvalues come in complex conjugate pairs. Each pair corresponds to one osciallatory mode of motion. The real eigenvalues each correspond to one non-osciallatory mode of motion." ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ -0.1487+0.j , -1.1037+5.0438j, -1.1037-5.0438j, -14.8720+0.j ])" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eigenvalues" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 9.2967e-01+0.j , -1.1363e-02-0.1127j, -1.1363e-02+0.1127j, 5.1082e-06+0.j ],\n", " [ 3.3775e-01+0.j , -3.2652e-02-0.1492j, -3.2652e-02+0.1492j, -6.7089e-02+0.j ],\n", " [ -1.3825e-01+0.j , 5.8083e-01+0.067j , 5.8083e-01-0.067j , -7.5969e-05+0.j ],\n", " [ -5.0226e-02+0.j , 7.8866e-01+0.j , 7.8866e-01-0.j , 9.9775e-01+0.j ]])" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eigenvectors" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Plot eigenvectors on polar plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One way to visualize the modes of motion is by plotting phasor plots of each of the eigenvector components. Eigenvectors are made up of $n$ components, each which may be real or imaginary, that correspond to the states variables. In our case each each component is tied to the roll angle, steer angle, roll angular rate, and steer angular rate. It is also important to note that the phasor plot for osciallation (underdamped) of the derivative of one of the variables simply increases the magnitue by a factor $\\omega_i$ and phase shifts the variable by $90^\\circ$, i.e.:\n", "\n", "$$\n", "r_i(t) = A_i e^{-\\zeta_i \\omega_i t} \\sin(\\omega_{di} t + \\phi_i) \\\\\n", "\\dot{r}_i(t) = \\omega_{di} A_i e^{-\\zeta_i \\omega_i t} \\cos(\\omega_{di} t + \\phi_i)\n", "$$\n", "\n", "This means that we only need to look at the components associated with the angles to see how the vehicle is moving.\n", "\n", "A nice way to plot phasors that are using a polar plot. For example if I have an eigenvalue of $-1.2 + 6j$ that has an associated eigenvector of $[-0.011-0.123j, -0.032-0.149j, 0.581+ 0.067j, 0.789]$ then we can select the first two components and plot a line that is equivlanent to the magnitude of the component and at an angle based on the tangent of the imaginary over the real part." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib notebook" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\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('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
');\n", " this._root_extra_style(this.root)\n", " this.root.attr('style', 'display: inline-block');\n", "\n", " $(parent_element).append(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", " fig.send_message(\"send_image_mode\", {});\n", " 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", " this.ws.close();\n", " }\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "}\n", "\n", "mpl.figure.prototype._init_header = function() {\n", " var titlebar = $(\n", " '');\n", " var titletext = $(\n", " '');\n", " titlebar.append(titletext)\n", " this.root.append(titlebar);\n", " this.header = titletext[0];\n", "}\n", "\n", "\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "\n", "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "mpl.figure.prototype._init_canvas = function() {\n", " var fig = this;\n", "\n", " var canvas_div = $('');\n", "\n", " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", "\n", " function canvas_keyboard_event(event) {\n", " return fig.key_event(event, event['data']);\n", " }\n", "\n", " canvas_div.keydown('key_press', canvas_keyboard_event);\n", " canvas_div.keyup('key_release', canvas_keyboard_event);\n", " this.canvas_div = canvas_div\n", " this._canvas_extra_style(canvas_div)\n", " this.root.append(canvas_div);\n", "\n", " var canvas = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width);\n", " canvas.attr('height', height);\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('')\n", " nav_element.attr('style', 'width: 100%');\n", " this.root.append(nav_element);\n", "\n", " // Define a callback function for later on.\n", " function toolbar_event(event) {\n", " return fig.toolbar_button_onclick(event['data']);\n", " }\n", " function toolbar_mouse_event(event) {\n", " return fig.toolbar_button_onmouseover(event['data']);\n", " }\n", "\n", " for(var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " // put a spacer in here.\n", " continue;\n", " }\n", " var button = $('');\n", " button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n", " 'ui-button-icon-only');\n", " button.attr('role', 'button');\n", " button.attr('aria-disabled', 'false');\n", " button.click(method_name, toolbar_event);\n", " button.mouseover(tooltip, toolbar_mouse_event);\n", "\n", " var icon_img = $('');\n", " icon_img.addClass('ui-button-icon-primary ui-icon');\n", " icon_img.addClass(image);\n", " icon_img.addClass('ui-corner-all');\n", "\n", " var tooltip_span = $('');\n", " tooltip_span.addClass('ui-button-text');\n", " tooltip_span.html(tooltip);\n", "\n", " button.append(icon_img);\n", " button.append(tooltip_span);\n", "\n", " nav_element.append(button);\n", " }\n", "\n", " var fmt_picker_span = $('');\n", "\n", " var fmt_picker = $('');\n", " fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n", " fmt_picker_span.append(fmt_picker);\n", " nav_element.append(fmt_picker_span);\n", " this.format_dropdown = fmt_picker[0];\n", "\n", " for (var ind in mpl.extensions) {\n", " var fmt = mpl.extensions[ind];\n", " var option = $(\n", " '', {selected: fmt === mpl.default_extension}).html(fmt);\n", " fmt_picker.append(option)\n", " }\n", "\n", " // Add hover states to the ui-buttons\n", " $( \".ui-button\" ).hover(\n", " function() { $(this).addClass(\"ui-state-hover\");},\n", " function() { $(this).removeClass(\"ui-state-hover\");}\n", " );\n", "\n", " var status_bar = $('');\n", " nav_element.append(status_bar);\n", " this.message = status_bar[0];\n", "}\n", "\n", "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n", " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", " // which will in turn request a refresh of the image.\n", " this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n", "}\n", "\n", "mpl.figure.prototype.send_message = function(type, properties) {\n", " properties['type'] = type;\n", " properties['figure_id'] = this.id;\n", " this.ws.send(JSON.stringify(properties));\n", "}\n", "\n", "mpl.figure.prototype.send_draw_message = function() {\n", " if (!this.waiting) {\n", " this.waiting = true;\n", " this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n", " }\n", "}\n", "\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " var format_dropdown = fig.format_dropdown;\n", " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", " fig.ondownload(fig, format);\n", "}\n", "\n", "\n", "mpl.figure.prototype.handle_resize = function(fig, msg) {\n", " var size = msg['size'];\n", " if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n", " fig._resize_canvas(size[0], size[1]);\n", " fig.send_message(\"refresh\", {});\n", " };\n", "}\n", "\n", "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n", " var x0 = msg['x0'];\n", " var y0 = fig.canvas.height - msg['y0'];\n", " var x1 = msg['x1'];\n", " var y1 = fig.canvas.height - msg['y1'];\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0, 0, fig.canvas.width, fig.canvas.height);\n", "\n", " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", "}\n", "\n", "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n", " // Updates the figure title.\n", " fig.header.textContent = msg['label'];\n", "}\n", "\n", "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n", " var cursor = msg['cursor'];\n", " switch(cursor)\n", " {\n", " case 0:\n", " cursor = 'pointer';\n", " break;\n", " case 1:\n", " cursor = 'default';\n", " break;\n", " case 2:\n", " cursor = 'crosshair';\n", " break;\n", " case 3:\n", " cursor = 'move';\n", " break;\n", " }\n", " fig.rubberband_canvas.style.cursor = cursor;\n", "}\n", "\n", "mpl.figure.prototype.handle_message = function(fig, msg) {\n", " fig.message.textContent = msg['message'];\n", "}\n", "\n", "mpl.figure.prototype.handle_draw = function(fig, msg) {\n", " // Request the server to send over a new figure.\n", " fig.send_draw_message();\n", "}\n", "\n", "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n", " fig.image_mode = msg['mode'];\n", "}\n", "\n", "mpl.figure.prototype.updated_canvas_event = function() {\n", " // Called whenever the canvas gets updated.\n", " this.send_message(\"ack\", {});\n", "}\n", "\n", "// A function to construct a web socket function for onmessage handling.\n", "// Called in the figure constructor.\n", "mpl.figure.prototype._make_on_message_function = function(fig) {\n", " return function socket_on_message(evt) {\n", " if (evt.data instanceof Blob) {\n", " /* FIXME: We get \"Resource interpreted as Image but\n", " * transferred with MIME type text/plain:\" errors on\n", " * Chrome. But how to set the MIME type? It doesn't seem\n", " * to be part of the websocket stream */\n", " evt.data.type = \"image/png\";\n", "\n", " /* Free the memory for the previous frames */\n", " if (fig.imageObj.src) {\n", " (window.URL || window.webkitURL).revokeObjectURL(\n", " fig.imageObj.src);\n", " }\n", "\n", " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", " evt.data);\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", " else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n", " fig.imageObj.src = evt.data;\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", "\n", " var msg = JSON.parse(evt.data);\n", " var msg_type = msg['type'];\n", "\n", " // Call the \"handle_{type}\" callback, which takes\n", " // the figure and JSON message as its only arguments.\n", " try {\n", " var callback = fig[\"handle_\" + msg_type];\n", " } catch (e) {\n", " console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n", " return;\n", " }\n", "\n", " if (callback) {\n", " try {\n", " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", " callback(fig, msg);\n", " } catch (e) {\n", " console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n", " }\n", " }\n", " };\n", "}\n", "\n", "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", "mpl.findpos = function(e) {\n", " //this section is from http://www.quirksmode.org/js/events_properties.html\n", " var targ;\n", " if (!e)\n", " e = window.event;\n", " if (e.target)\n", " targ = e.target;\n", " else if (e.srcElement)\n", " targ = e.srcElement;\n", " if (targ.nodeType == 3) // defeat Safari bug\n", " targ = targ.parentNode;\n", "\n", " // jQuery normalizes the pageX and pageY\n", " // pageX,Y are the mouse positions relative to the document\n", " // offset() returns the position of the element relative to the document\n", " var x = e.pageX - $(targ).offset().left;\n", " var y = e.pageY - $(targ).offset().top;\n", "\n", " return {\"x\": x, \"y\": y};\n", "};\n", "\n", "/*\n", " * return a copy of an object with only non-object keys\n", " * we need this to avoid circular references\n", " * http://stackoverflow.com/a/24161582/3208463\n", " */\n", "function simpleKeys (original) {\n", " return Object.keys(original).reduce(function (obj, key) {\n", " if (typeof original[key] !== 'object')\n", " obj[key] = original[key]\n", " return obj;\n", " }, {});\n", "}\n", "\n", "mpl.figure.prototype.mouse_event = function(event, name) {\n", " var canvas_pos = mpl.findpos(event)\n", "\n", " if (name === 'button_press')\n", " {\n", " this.canvas.focus();\n", " this.canvas_div.focus();\n", " }\n", "\n", " var x = canvas_pos.x;\n", " var y = canvas_pos.y;\n", "\n", " this.send_message(name, {x: x, y: y, button: event.button,\n", " step: event.step,\n", " guiEvent: simpleKeys(event)});\n", "\n", " /* This prevents the web browser from automatically changing to\n", " * the text insertion cursor when the button is pressed. We want\n", " * to control all of the cursor setting manually through the\n", " * 'cursor' event from matplotlib */\n", " event.preventDefault();\n", " return false;\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " // Handle any extra behaviour associated with a key event\n", "}\n", "\n", "mpl.figure.prototype.key_event = function(event, name) {\n", "\n", " // Prevent repeat events\n", " if (name == 'key_press')\n", " {\n", " if (event.which === this._key)\n", " return;\n", " else\n", " this._key = event.which;\n", " }\n", " if (name == 'key_release')\n", " this._key = null;\n", "\n", " var value = '';\n", " if (event.ctrlKey && event.which != 17)\n", " value += \"ctrl+\";\n", " if (event.altKey && event.which != 18)\n", " value += \"alt+\";\n", " if (event.shiftKey && event.which != 16)\n", " value += \"shift+\";\n", "\n", " value += 'k';\n", " value += event.which.toString();\n", "\n", " this._key_event_extra(event, name);\n", "\n", " this.send_message(name, {key: value,\n", " guiEvent: simpleKeys(event)});\n", " return false;\n", "}\n", "\n", "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n", " if (name == 'download') {\n", " this.handle_save(this, null);\n", " } else {\n", " this.send_message(\"toolbar_button\", {name: name});\n", " }\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n", " this.message.textContent = tooltip;\n", "};\n", "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", "\n", "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", "\n", "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n", " // Create a \"websocket\"-like object which calls the given IPython comm\n", " // object with the appropriate methods. Currently this is a non binary\n", " // socket, so there is still some room for performance tuning.\n", " var ws = {};\n", "\n", " ws.close = function() {\n", " comm.close()\n", " };\n", " ws.send = function(m) {\n", " //console.log('sending', m);\n", " comm.send(m);\n", " };\n", " // Register the callback with on_msg.\n", " comm.on_msg(function(msg) {\n", " //console.log('receiving', msg['content']['data'], msg);\n", " // Pass the mpl event to the overriden (by mpl) onmessage function.\n", " ws.onmessage(msg['content']['data'])\n", " });\n", " return ws;\n", "}\n", "\n", "mpl.mpl_figure_comm = function(comm, msg) {\n", " // This is the function which gets called when the mpl process\n", " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", "\n", " var id = msg.content.data.id;\n", " // Get hold of the div created by the display call when the Comm\n", " // socket was opened in Python.\n", " var element = $(\"#\" + id);\n", " var ws_proxy = comm_websocket_adapter(comm)\n", "\n", " function ondownload(figure, format) {\n", " window.open(figure.imageObj.src);\n", " }\n", "\n", " var fig = new mpl.figure(id, ws_proxy,\n", " ondownload,\n", " element.get(0));\n", "\n", " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", " // web socket which is closed, not our websocket->open comm proxy.\n", " ws_proxy.onopen();\n", "\n", " fig.parent_element = element.get(0);\n", " fig.cell_info = mpl.find_output_cell(\"\");\n", " if (!fig.cell_info) {\n", " console.error(\"Failed to find cell for figure\", id, fig);\n", " return;\n", " }\n", "\n", " var output_index = fig.cell_info[2]\n", " var cell = fig.cell_info[0];\n", "\n", "};\n", "\n", "mpl.figure.prototype.handle_close = function(fig, msg) {\n", " fig.root.unbind('remove')\n", "\n", " // Update the output cell to use the data from the current canvas.\n", " fig.push_to_output();\n", " var dataURL = fig.canvas.toDataURL();\n", " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", " // the notebook keyboard shortcuts fail.\n", " IPython.keyboard_manager.enable()\n", " $(fig.parent_element).html('');\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 dataURL = this.canvas.toDataURL();\n", " this.cell_info[1]['text/html'] = '';\n", "}\n", "\n", "mpl.figure.prototype.updated_canvas_event = function() {\n", " // Tell IPython that the notebook contents must change.\n", " IPython.notebook.set_dirty(true);\n", " this.send_message(\"ack\", {});\n", " var fig = this;\n", " // Wait a second, then push the new image to the DOM so\n", " // that it is saved nicely (might be nice to debounce this).\n", " setTimeout(function () { fig.push_to_output() }, 1000);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('')\n", " nav_element.attr('style', 'width: 100%');\n", " this.root.append(nav_element);\n", "\n", " // Define a callback function for later on.\n", " function toolbar_event(event) {\n", " return fig.toolbar_button_onclick(event['data']);\n", " }\n", " function toolbar_mouse_event(event) {\n", " return fig.toolbar_button_onmouseover(event['data']);\n", " }\n", "\n", " for(var toolbar_ind in mpl.toolbar_items){\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) { continue; };\n", "\n", " var button = $('');\n", " button.click(method_name, toolbar_event);\n", " button.mouseover(tooltip, toolbar_mouse_event);\n", " nav_element.append(button);\n", " }\n", "\n", " // Add the status bar.\n", " var status_bar = $('');\n", " nav_element.append(status_bar);\n", " this.message = status_bar[0];\n", "\n", " // Add the close button to the window.\n", " var buttongrp = $('');\n", " var button = $('');\n", " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", " buttongrp.append(button);\n", " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", " titlebar.prepend(buttongrp);\n", "}\n", "\n", "mpl.figure.prototype._root_extra_style = function(el){\n", " var fig = this\n", " el.on(\"remove\", function(){\n", "\tfig.close_ws(fig, {});\n", " });\n", "}\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(el){\n", " // this is important to make the div 'focusable\n", " el.attr('tabindex', 0)\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " }\n", " else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager)\n", " manager = IPython.keyboard_manager;\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which == 13) {\n", " this.canvas_div.blur();\n", " // select the cell after this one\n", " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", " IPython.notebook.select(index + 1);\n", " }\n", "}\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " fig.ondownload(fig, null);\n", "}\n", "\n", "\n", "mpl.find_output_cell = function(html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i=0; i