{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this blog post, we will look at the vibrating string equation and solve it using two different mathematical methods.\n", "First, we will use a time-domain finite difference method. In a second step, we will use a frequency domain approach (i.e. a Fourier method) to solve the same problem. \n", "\n", "I wrote this post while going through the excellent MOOC Fundamentals of Waves and Vibrations. Feel free to check out what I wrote about the experience [here](http://flothesof.github.io/anki-MOOC-fundamentals-waves-vibrations.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The vibrating string equation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start by introducing the [vibrating string](https://en.wikipedia.org/wiki/String_vibration) equation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equation of the transverse displacement of a vibrating string $y(x,t)$ is, $\\forall x \\in [0, L]$, $\\forall t \\geq 0$:\n", "\n", "$$\n", "m \\dfrac{\\partial^2 y}{\\partial t^2} - T \\dfrac{\\partial^2 y}{\\partial x^2} = 0\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will solve this with so-called Dirichlet boundary conditions, meaning that the string has a zero displacement at its ends, i.e. $\\forall t \\geq 0 \\; y(0, t) = y(L, t) = 0$. Initial conditions will be as follows:\n", "\n", "- $\\forall x \\in [0, L], \\quad y(x, 0) = y_0(x)$\n", "- $\\forall x \\in [0, L], \\quad \\dot{y}(x, 0) = 0$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Time-domain solution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's implement a time-domain solution known as finite differences. The partial differential equation above, once discretized on a 1D grid, becomes:\n", "\n", "$$\n", "m \\dfrac{y_i^{n+1} - 2 y_i^{n} + y_i^{n-1}}{\\Delta t^2} - T \\dfrac{y_{i+1}^{n} - 2 y_{i}^{n} + y_{i-1}^{n}}{\\Delta x^2} = 0\n", "$$\n", "\n", "After reordering the terms, we obtain the following *propagation step*:\n", "\n", "$$\n", "\\forall i \\in [1, N-1] \\quad y_i^{n+1} = 2 y_i^{n} - y_i^{n-1} + \\dfrac{T}{m} \\dfrac{\\Delta t^2}{\\Delta x^2} \\left ( y_{i+1}^{n} - 2 y_{i}^{n} + y_{i-1}^{n}\\right )\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can setup a simple implementation of the solution as follows:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "class TimeDomainSolver:\n", " \n", " def __init__(self, L, nx, T, m, y0):\n", " \"\"\"Setup of the time domain solver.\"\"\"\n", " self.x = np.linspace(0, L, num=nx)\n", " self.dx = self.x[1] - self.x[0]\n", " c = np.sqrt(T/m)\n", " self.dt = self.dx / c\n", " self.uprev = y0(self.x)\n", " self.ucurr = y0(self.x)\n", " self.alpha = T / m * self.dt ** 2 / self.dx **2\n", " \n", " \n", " def step(self):\n", " \"\"\"Steps the system forward in time.\"\"\"\n", " unext = np.zeros_like(self.ucurr)\n", " unext[1: -1] = 2 * self.ucurr[1:-1] - self.uprev[1:-1] + \\\n", " self.alpha * (self.ucurr[2:] - 2 * self.ucurr[1:-1] + self.ucurr[:-2])\n", " self.ucurr, self.uprev = unext, self.ucurr\n", " \n", " def steps(self, n):\n", " for _ in range(n):\n", " self.step()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To test our implementation, we will consider a triangular initial string with the properties of a low E string of a guitar (such as those that you can find on the back of electric guitar strings, as [here](http://www.daddario.com/DAstringtensionguide.Page?sid=91901025-4136-404a-8c26-e020667e8b5e))." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "L = 0.6477 # m\n", "T = 7.93 * 9.81 # kg * m.s^-2\n", "f0 = 82.4 # Hz\n", "c = 2 * L * f0\n", "m = T / c**2\n", "\n", "triangle = lambda x: (x * 2 / L) * (x < L/2) + (-x * 2 / L + 2) * (x >= L/2) \n", "\n", "td_solver = TimeDomainSolver(L, 200, T, m, triangle)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize the initial position of the string:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "\n", "(function(root) {\n", " function now() {\n", " return new Date();\n", " }\n", "\n", " var force = true;\n", "\n", " if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n", " root._bokeh_onload_callbacks = [];\n", " root._bokeh_is_loading = undefined;\n", " }\n", "\n", " var JS_MIME_TYPE = 'application/javascript';\n", " var HTML_MIME_TYPE = 'text/html';\n", " var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n", " var CLASS_NAME = 'output_bokeh rendered_html';\n", "\n", " /**\n", " * Render data to the DOM node\n", " */\n", " function render(props, node) {\n", " var script = document.createElement(\"script\");\n", " node.appendChild(script);\n", " }\n", "\n", " /**\n", " * Handle when an output is cleared or removed\n", " */\n", " function handleClearOutput(event, handle) {\n", " var cell = handle.cell;\n", "\n", " var id = cell.output_area._bokeh_element_id;\n", " var server_id = cell.output_area._bokeh_server_id;\n", " // Clean up Bokeh references\n", " if (id != null && id in Bokeh.index) {\n", " Bokeh.index[id].model.document.clear();\n", " delete Bokeh.index[id];\n", " }\n", "\n", " if (server_id !== undefined) {\n", " // Clean up Bokeh references\n", " var cmd = \"from bokeh.io.state import curstate; 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h=l[0],u=l[1],c=l[2],_=l[3];h+c==this.canvas._width.value&&(c-=1),u+_==this.canvas._height.value&&(_-=1),s.strokeRect(h,u,c,_)}s.restore(),this._paint_levels(s,[\"image\",\"underlay\",\"glyph\"],l,!0),this.blit_webgl(a),this._paint_levels(s,[\"annotation\"],l,!0),this._paint_levels(s,[\"overlay\"],l,!1),null==this._initial_state_info.range&&this.set_initial_range(),s.restore(),this._has_finished||(this._has_finished=!0,this.notify_finished())}},t.prototype._paint_levels=function(t,e,i,n){t.save(),n&&(t.beginPath(),t.rect.apply(t,i),t.clip());for(var r={},o=0;oc&&(\"start\"==this.follow?r=n+u*c:\"end\"==this.follow&&(n=r-u*c)),[n,r]},t.prototype.update=function(t,e,i,n){if(!this.have_updated_interactively){var r=this.computed_renderers(),o=this._compute_plot_bounds(r,t);null!=n&&(o=this.adjust_bounds_for_aspect(o,n)),this._plot_bounds[i]=o;var s=this._compute_min_max(this._plot_bounds,e),a=s[0],l=s[1],h=this._compute_range(a,l),u=h[0],c=h[1];null!=this._initial_start&&(\"log\"==this.scale_hint?0this.end},enumerable:!0,configurable:!0}),t}(r.Model);(i.Range=a).initClass()},function(t,e,i){var n=t(391),r=t(183),o=t(15),s=function(e){function t(t){return e.call(this,t)||this}return n.__extends(t,e),t.initClass=function(){this.prototype.type=\"Range1d\",this.define({start:[o.Number,0],end:[o.Number,1],reset_start:[o.Number],reset_end:[o.Number]})},t.prototype._set_auto_bounds=function(){if(\"auto\"==this.bounds){var t=Math.min(this.reset_start,this.reset_end),e=Math.max(this.reset_start,this.reset_end);this.setv({bounds:[t,e]},{silent:!0})}},t.prototype.initialize=function(){e.prototype.initialize.call(this),null==this.reset_start&&(this.reset_start=this.start),null==this.reset_end&&(this.reset_end=this.end),this._set_auto_bounds()},Object.defineProperty(t.prototype,\"min\",{get:function(){return 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n&&_.extend(e,t.fill),r&&_.extend(e,t.line),new i.constructor(e)}delete o.id,this.glyph=this.build_glyph_view(i);var s=this.model.selection_glyph;null==s?s=e({fill:{},line:{}}):\"auto\"===s&&(s=e(p)),this.selection_glyph=this.build_glyph_view(s);var a=this.model.nonselection_glyph;null==a?a=e({fill:{},line:{}}):\"auto\"===a&&(a=e(f)),this.nonselection_glyph=this.build_glyph_view(a);var l=this.model.hover_glyph;null!=l&&(this.hover_glyph=this.build_glyph_view(l));var h=this.model.muted_glyph;null!=h&&(this.muted_glyph=this.build_glyph_view(h));var u=e(d);this.decimated_glyph=this.build_glyph_view(u),this.xscale=this.plot_view.frame.xscales[this.model.x_range_name],this.yscale=this.plot_view.frame.yscales[this.model.y_range_name],this.set_data(!1)},t.prototype.build_glyph_view=function(t){return new t.default_view({model:t,renderer:this,plot_view:this.plot_view,parent:this})},t.prototype.connect_signals=function(){var e=this;c.prototype.connect_signals.call(this),this.connect(this.model.change,function(){return e.request_render()}),this.connect(this.model.glyph.change,function(){return e.set_data()}),this.connect(this.model.data_source.change,function(){return e.set_data()}),this.connect(this.model.data_source.streaming,function(){return e.set_data()}),this.connect(this.model.data_source.patching,function(t){return e.set_data(!0,t)}),this.connect(this.model.data_source.selected.change,function(){return e.request_render()}),this.connect(this.model.data_source._select,function(){return e.request_render()}),null!=this.hover_glyph&&this.connect(this.model.data_source.inspect,function(){return e.request_render()}),this.connect(this.model.properties.view.change,function(){return e.set_data()}),this.connect(this.model.view.change,function(){return e.set_data()});var t=this.plot_model.frame,i=t.x_ranges,n=t.y_ranges;for(var r in i){var o=i[r];o instanceof l.FactorRange&&this.connect(o.change,function(){return e.set_data()})}for(var s in n){var o=n[s];o instanceof l.FactorRange&&this.connect(o.change,function(){return e.set_data()})}this.connect(this.model.glyph.transformchange,function(){return e.set_data()})},t.prototype.have_selection_glyphs=function(){return null!=this.selection_glyph&&null!=this.nonselection_glyph},t.prototype.set_data=function(t,e){void 0===t&&(t=!0),void 0===e&&(e=null);var i=Date.now(),n=this.model.data_source;this.all_indices=this.model.view.indices,this.glyph.model.setv({x_range_name:this.model.x_range_name,y_range_name:this.model.y_range_name},{silent:!0}),this.glyph.set_data(n,this.all_indices,e),this.glyph.set_visuals(n),this.decimated_glyph.set_visuals(n),this.have_selection_glyphs()&&(this.selection_glyph.set_visuals(n),this.nonselection_glyph.set_visuals(n)),null!=this.hover_glyph&&this.hover_glyph.set_visuals(n),null!=this.muted_glyph&&this.muted_glyph.set_visuals(n);var r=this.plot_model.plot.lod_factor;this.decimated=[];for(var o=0,s=Math.floor(this.all_indices.length/r);ov?(o=this.decimated,_=this.decimated_glyph,p=this.decimated_glyph):(_=this.model.muted&&null!=this.muted_glyph?this.muted_glyph:this.glyph,p=this.nonselection_glyph),d=this.selection_glyph,null!=this.hover_glyph&&f.length&&(o=N.difference(o,f));var m,g=null;if(l.length&&this.have_selection_glyphs()){for(var y=Date.now(),b={},x=0,w=l;xi?n.slice(-i):n}if(S.isTypedArray(t)){var r=t.length+e.length;if(null!=i&&i=Math.pow(2,i))||e<0||e>=Math.pow(2,i))},t.prototype.parent_by_tile_xyz=function(t,e,i){var n=this.tile_xyz_to_quadkey(t,e,i),r=n.substring(0,n.length-1);return this.quadkey_to_tile_xyz(r)},t.prototype.get_resolution=function(t){return this._computed_initial_resolution()/Math.pow(2,t)},t.prototype.get_resolution_by_extent=function(t,e,i){var n=(t[2]-t[0])/i,r=(t[3]-t[1])/e;return[n,r]},t.prototype.get_level_by_extent=function(t,e,i){for(var n=(t[2]-t[0])/i,r=(t[3]-t[1])/e,o=Math.max(n,r),s=0,a=0,l=this._resolutions;ar.end)&&(this.v_axis_only=!0),(io.end)&&(this.h_axis_only=!0)}null!=this.model.document&&this.model.document.interactive_start(this.plot_model.plot)},e.prototype._pan=function(t){this._update(t.deltaX,t.deltaY),null!=this.model.document&&this.model.document.interactive_start(this.plot_model.plot)},e.prototype._pan_end=function(t){this.h_axis_only=!1,this.v_axis_only=!1,null!=this.pan_info&&this.plot_view.push_state(\"pan\",{range:this.pan_info})},e.prototype._update=function(t,e){var i,n,r,o,s,a,l=this.plot_model.frame,h=t-this.last_dx,u=e-this.last_dy,c=l.bbox.h_range,_=c.start-h,p=c.end-h,d=l.bbox.v_range,f=d.start-u,v=d.end-u,m=this.model.dimensions;\"width\"!=m&&\"both\"!=m||this.v_axis_only?(i=c.start,n=c.end,r=0):(i=_,n=p,r=-h),\"height\"!=m&&\"both\"!=m||this.h_axis_only?(o=d.start,s=d.end,a=0):(o=f,s=v,a=-u),this.last_dx=t,this.last_dy=e;var g=l.xscales,y=l.yscales,b={};for(var x in g){var w=g[x],k=w.r_invert(i,n),S=k[0],C=k[1];b[x]={start:S,end:C}}var T={};for(var A in y){var w=y[A],E=w.r_invert(o,s),S=E[0],C=E[1];T[A]={start:S,end:C}}this.pan_info={xrs:b,yrs:T,sdx:r,sdy:a},this.plot_view.update_range(this.pan_info,!0)},e}(r.GestureToolView);i.PanToolView=s;var a=function(i){function t(t){var e=i.call(this,t)||this;return e.tool_name=\"Pan\",e.event_type=\"pan\",e.default_order=10,e}return n.__extends(t,i),t.initClass=function(){this.prototype.type=\"PanTool\",this.prototype.default_view=s,this.define({dimensions:[o.Dimensions,\"both\"]})},Object.defineProperty(t.prototype,\"tooltip\",{get:function(){return this._get_dim_tooltip(\"Pan\",this.dimensions)},enumerable:!0,configurable:!0}),Object.defineProperty(t.prototype,\"icon\",{get:function(){switch(this.dimensions){case\"both\":return\"bk-tool-icon-pan\";case\"width\":return\"bk-tool-icon-xpan\";case\"height\":return\"bk-tool-icon-ypan\"}},enumerable:!0,configurable:!0}),t}(r.GestureTool);(i.PanTool=a).initClass()},function(t,e,i){var l=t(391),n=t(256),r=t(71),o=t(5),s=t(15),a=t(21),h=function(e){function t(){return null!==e&&e.apply(this,arguments)||this}return l.__extends(t,e),t.prototype.initialize=function(t){e.prototype.initialize.call(this,t),this.data={sx:[],sy:[]}},t.prototype.connect_signals=function(){var t=this;e.prototype.connect_signals.call(this),this.connect(this.model.properties.active.change,function(){return t._active_change()})},t.prototype._active_change=function(){this.model.active||this._clear_data()},t.prototype._keyup=function(t){t.keyCode==o.Keys.Enter&&this._clear_data()},t.prototype._doubletap=function(t){var e=t.shiftKey;this._do_select(this.data.sx,this.data.sy,!0,e),this.plot_view.push_state(\"poly_select\",{selection:this.plot_view.get_selection()}),this._clear_data()},t.prototype._clear_data=function(){this.data={sx:[],sy:[]},this.model.overlay.update({xs:[],ys:[]})},t.prototype._tap=function(t){var e=t.sx,i=t.sy,n=this.plot_model.frame;n.bbox.contains(e,i)&&(this.data.sx.push(e),this.data.sy.push(i),this.model.overlay.update({xs:a.copy(this.data.sx),ys:a.copy(this.data.sy)}))},t.prototype._do_select=function(t,e,i,n){var r={type:\"poly\",sx:t,sy:e};this._select(r,i,n)},t.prototype._emit_callback=function(t){var e=this.computed_renderers[0],i=this.plot_model.frame,n=i.xscales[e.x_range_name],r=i.yscales[e.y_range_name],o=n.v_invert(t.sx),s=r.v_invert(t.sy),a=l.__assign({x:o,y:s},t);this.model.callback.execute(this.model,{geometry:a})},t}(n.SelectToolView);i.PolySelectToolView=h;var u=function(){return new r.PolyAnnotation({level:\"overlay\",xs_units:\"screen\",ys_units:\"screen\",fill_color:{value:\"lightgrey\"},fill_alpha:{value:.5},line_color:{value:\"black\"},line_alpha:{value:1},line_width:{value:2},line_dash:{value:[4,4]}})},c=function(i){function t(t){var e=i.call(this,t)||this;return e.tool_name=\"Poly Select\",e.icon=\"bk-tool-icon-polygon-select\",e.event_type=\"tap\",e.default_order=11,e}return l.__extends(t,i),t.initClass=function(){this.prototype.type=\"PolySelectTool\",this.prototype.default_view=h,this.define({callback:[s.Instance],overlay:[s.Instance,u]})},t}(n.SelectTool);(i.PolySelectTool=c).initClass()},function(t,e,i){var n=t(391),_=t(64),r=t(14),o=t(15),s=t(251);function p(t,e,i,n){if(null==e)return!1;var r=i.compute(e);return Math.abs(t-r)r.right)&&(o=!1)}if(null!=r.bottom&&null!=r.top){var a=n.invert(e);(ar.top)&&(o=!1)}return o}function l(t,e,i,n){var r=e.compute(t),o=e.invert(r+i);return o>=n.start&&o<=n.end?o:t}function h(t,e,i,n){var r=e.r_compute(t.start,t.end),o=r[0],s=r[1],a=e.r_invert(o+i,s+i),l=a[0],h=a[1];l>=n.start&&l<=n.end&&h>=n.start&&h<=n.end&&(t.start=l,t.end=h)}i.is_near=p,i.is_inside=d,i.compute_value=l,i.update_range=h;var a=function(e){function t(){return null!==e&&e.apply(this,arguments)||this}return n.__extends(t,e),t.prototype.initialize=function(t){e.prototype.initialize.call(this,t),this.side=0,this.model.update_overlay_from_ranges()},t.prototype.connect_signals=function(){var t=this;e.prototype.connect_signals.call(this),null!=this.model.x_range&&this.connect(this.model.x_range.change,function(){return t.model.update_overlay_from_ranges()}),null!=this.model.y_range&&this.connect(this.model.y_range.change,function(){return t.model.update_overlay_from_ranges()})},t.prototype._pan_start=function(t){this.last_dx=0,this.last_dy=0;var e=this.model.x_range,i=this.model.y_range,n=this.plot_model.frame,r=n.xscales.default,o=n.yscales.default,s=this.model.overlay,a=s.left,l=s.right,h=s.top,u=s.bottom,c=this.model.overlay.properties.line_width.value()+_.EDGE_TOLERANCE;null!=e&&this.model.x_interaction&&(p(t.sx,a,r,c)?this.side=1:p(t.sx,l,r,c)?this.side=2:d(t.sx,t.sy,r,o,s)&&(this.side=3)),null!=i&&this.model.y_interaction&&(0==this.side&&p(t.sy,u,o,c)&&(this.side=4),0==this.side&&p(t.sy,h,o,c)?this.side=5:d(t.sx,t.sy,r,o,this.model.overlay)&&(3==this.side?this.side=7:this.side=6))},t.prototype._pan=function(t){var e=this.plot_model.frame,i=t.deltaX-this.last_dx,n=t.deltaY-this.last_dy,r=this.model.x_range,o=this.model.y_range,s=e.xscales.default,a=e.yscales.default;null!=r&&(3==this.side||7==this.side?h(r,s,i,e.x_range):1==this.side?r.start=l(r.start,s,i,e.x_range):2==this.side&&(r.end=l(r.end,s,i,e.x_range))),null!=o&&(6==this.side||7==this.side?h(o,a,n,e.y_range):4==this.side?o.start=l(o.start,a,n,e.y_range):5==this.side&&(o.end=l(o.end,a,n,e.y_range))),this.last_dx=t.deltaX,this.last_dy=t.deltaY},t.prototype._pan_end=function(t){this.side=0},t}(s.GestureToolView);i.RangeToolView=a;var u=function(){return new _.BoxAnnotation({level:\"overlay\",render_mode:\"css\",fill_color:\"lightgrey\",fill_alpha:{value:.5},line_color:{value:\"black\"},line_alpha:{value:1},line_width:{value:.5},line_dash:[2,2]})},c=function(i){function t(t){var e=i.call(this,t)||this;return e.tool_name=\"Range Tool\",e.icon=\"bk-tool-icon-range\",e.event_type=\"pan\",e.default_order=1,e}return n.__extends(t,i),t.initClass=function(){this.prototype.type=\"RangeTool\",this.prototype.default_view=a,this.define({x_range:[o.Instance,null],x_interaction:[o.Bool,!0],y_range:[o.Instance,null],y_interaction:[o.Bool,!0],overlay:[o.Instance,u]})},t.prototype.initialize=function(){i.prototype.initialize.call(this),this.overlay.in_cursor=\"grab\",this.overlay.ew_cursor=null!=this.x_range&&this.x_interaction?\"ew-resize\":null,this.overlay.ns_cursor=null!=this.y_range&&this.y_interaction?\"ns-resize\":null},t.prototype.update_overlay_from_ranges=function(){null==this.x_range&&null==this.y_range&&(this.overlay.left=null,this.overlay.right=null,this.overlay.bottom=null,this.overlay.top=null,r.logger.warn(\"RangeTool not configured with any Ranges.\")),null==this.x_range?(this.overlay.left=null,this.overlay.right=null):(this.overlay.left=this.x_range.start,this.overlay.right=this.x_range.end),null==this.y_range?(this.overlay.bottom=null,this.overlay.top=null):(this.overlay.bottom=this.y_range.start,this.overlay.top=this.y_range.end)},t}(s.GestureTool);(i.RangeTool=c).initClass()},function(t,e,i){var y=t(391),n=t(251),o=t(186),r=t(271),s=t(15),a=t(5),b=t(3),l=function(t){function e(){return null!==t&&t.apply(this,arguments)||this}return y.__extends(e,t),Object.defineProperty(e.prototype,\"computed_renderers\",{get:function(){var t=this.model.renderers,e=this.plot_model.plot.renderers,i=this.model.names;return r.compute_renderers(t,e,i)},enumerable:!0,configurable:!0}),e.prototype._computed_renderers_by_data_source=function(){for(var t={},e=0,i=this.computed_renderers;ee.x?-1:t.x==e.x?0:1}):r.sort(function(t,e){return t.xthis._x_sorted[this._x_sorted.length-1])return 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notice,\n", " * this list of conditions and the following disclaimer.\n", " * \n", " * Redistributions in binary form must reproduce the above copyright notice,\n", " * this list of conditions and the following disclaimer in the documentation\n", " * and/or other materials provided with the distribution.\n", " * \n", " * Neither the name of Anaconda nor the names of any contributors\n", " * may be used to endorse or promote products derived from this software\n", " * without specific prior written permission.\n", " * \n", " * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\n", " * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\n", " * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE\n", " * ARE DISCLAIMED. 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\").css(\"width\",getCanvasWidth()+scrollbarDimensions.width+\"px\").appendTo($footerRowScroller),options.showFooterRow||$footerRowScroller.hide()),options.numberedMultiColumnSort&&(sortIndicatorCssClass=\"slick-sort-indicator-numbered\"),$focusSink2=$focusSink.clone().appendTo($container),options.explicitInitialization||finishInitialization()}function finishInitialization(){initialized||(initialized=!0,viewportW=parseFloat($.css($container[0],\"width\",!0)),measureCellPaddingAndBorder(),disableSelection($headers),options.enableTextSelectionOnCells||$viewport.on(\"selectstart.ui\",function(e){return $(e.target).is(\"input,textarea\")}),updateColumnCaches(),createColumnHeaders(),setupColumnSort(),createCssRules(),resizeCanvas(),bindAncestorScrollEvents(),$container.on(\"resize.slickgrid\",resizeCanvas),$viewport.on(\"scroll\",handleScroll),$headerScroller.on(\"contextmenu\",handleHeaderContextMenu).on(\"click\",handleHeaderClick).on(\"mouseenter\",\".slick-header-column\",handleHeaderMouseEnter).on(\"mouseleave\",\".slick-header-column\",handleHeaderMouseLeave),$headerRowScroller.on(\"scroll\",handleHeaderRowScroll),options.createFooterRow&&$footerRowScroller.on(\"scroll\",handleFooterRowScroll),options.createPreHeaderPanel&&$preHeaderPanelScroller.on(\"scroll\",handlePreHeaderPanelScroll),$focusSink.add($focusSink2).on(\"keydown\",handleKeyDown),$canvas.on(\"keydown\",handleKeyDown).on(\"click\",handleClick).on(\"dblclick\",handleDblClick).on(\"contextmenu\",handleContextMenu).on(\"draginit\",handleDragInit).on(\"dragstart\",{distance:3},handleDragStart).on(\"drag\",handleDrag).on(\"dragend\",handleDragEnd).on(\"mouseenter\",\".slick-cell\",handleMouseEnter).on(\"mouseleave\",\".slick-cell\",handleMouseLeave),navigator.userAgent.toLowerCase().match(/webkit/)&&navigator.userAgent.toLowerCase().match(/macintosh/)&&$canvas.on(\"mousewheel\",handleMouseWheel),restoreCssFromHiddenInit())}function cacheCssForHiddenInit(){($hiddenParents=$container.parents().addBack().not(\":visible\")).each(function(){var e={};for(var t in cssShow)e[t]=this.style[t],this.style[t]=cssShow[t];oldProps.push(e)})}function restoreCssFromHiddenInit(){$hiddenParents.each(function(e){var t=oldProps[e];for(var n in cssShow)this.style[n]=t[n]})}function registerPlugin(e){plugins.unshift(e),e.init(self)}function unregisterPlugin(e){for(var t=plugins.length;0<=t;t--)if(plugins[t]===e){plugins[t].destroy&&plugins[t].destroy(),plugins.splice(t,1);break}}function setSelectionModel(e){selectionModel&&(selectionModel.onSelectedRangesChanged.unsubscribe(handleSelectedRangesChanged),selectionModel.destroy&&selectionModel.destroy()),(selectionModel=e)&&(selectionModel.init(self),selectionModel.onSelectedRangesChanged.subscribe(handleSelectedRangesChanged))}function getSelectionModel(){return selectionModel}function getCanvasNode(){return $canvas[0]}function measureScrollbar(){var e=$(\"
\").appendTo(\"body\"),t={width:e.width()-e[0].clientWidth,height:e.height()-e[0].clientHeight};return e.remove(),t}function getColumnTotalWidth(e){for(var t=0,n=0,o=columns.length;nviewportW-scrollbarDimensions.width);var n=canvasWidth+(viewportHasVScroll?scrollbarDimensions.width:0);$headerRowSpacer.width(n),options.createFooterRow&&$footerRowSpacer.width(n),options.createPreHeaderPanel&&$preHeaderPanelSpacer.width(n),(canvasWidth!=t||e)&&applyColumnWidths()}function disableSelection(e){e&&e.jquery&&e.attr(\"unselectable\",\"on\").css(\"MozUserSelect\",\"none\").on(\"selectstart.ui\",function(){return!1})}function getMaxSupportedCssHeight(){for(var e=1e6,t=navigator.userAgent.toLowerCase().match(/firefox/)?6e6:1e9,n=$(\"
\").appendTo(document.body);;){var o=2*e;if(n.css(\"height\",o),t\").html(\"\"+o.name+\"\").width(o.width-headerColumnWidthDiff).attr(\"id\",\"\"+uid+o.id).attr(\"title\",o.toolTip||\"\").data(\"column\",o).addClass(o.headerCssClass||\"\").appendTo($headers);if((options.enableColumnReorder||o.sortable)&&r.on(\"mouseenter\",e).on(\"mouseleave\",t),o.sortable&&(r.addClass(\"slick-header-sortable\"),r.append(\"\")),trigger(self.onHeaderCellRendered,{node:r[0],column:o,grid:self}),options.showHeaderRow){var i=$(\"
\").data(\"column\",o).appendTo($headerRow);trigger(self.onHeaderRowCellRendered,{node:i[0],column:o,grid:self})}if(options.createFooterRow&&options.showFooterRow){var l=$(\"
\").data(\"column\",o).appendTo($footerRow);trigger(self.onFooterRowCellRendered,{node:l[0],column:o})}}setSortColumns(sortColumns),setupColumnResize(),options.enableColumnReorder&&(\"function\"==typeof options.enableColumnReorder?options.enableColumnReorder(self,$headers,headerColumnWidthDiff,setColumns,setupColumnResize,columns,getColumnIndex,uid,trigger):setupColumnReorder())}function setupColumnSort(){$headers.click(function(e){if(e.metaKey=e.metaKey||e.ctrlKey,!$(e.target).hasClass(\"slick-resizable-handle\")){var t=$(e.target).closest(\".slick-header-column\");if(t.length){var n=t.data(\"column\");if(n.sortable){if(!getEditorLock().commitCurrentEdit())return;for(var o=null,r=0;r=columns.length||columns[e].resizable&&(void 0===n&&(n=e),o=e)}),void 0!==n&&u.each(function(l,e){l>=columns.length||l\").appendTo(e).on(\"dragstart\",function(e,t){if(!getEditorLock().commitCurrentEdit())return!1;c=e.pageX,$(this).parent().addClass(\"slick-header-column-active\");var n=null,o=null;if(u.each(function(e,t){e>=columns.length||(columns[e].previousWidth=$(t).outerWidth())}),options.forceFitColumns)for(o=n=0,s=l+1;s
\").appendTo($headers),headerColumnWidthDiff=headerColumnHeightDiff=0,\"border-box\"!=n.css(\"box-sizing\")&&\"border-box\"!=n.css(\"-moz-box-sizing\")&&\"border-box\"!=n.css(\"-webkit-box-sizing\")&&($.each(e,function(e,t){headerColumnWidthDiff+=parseFloat(n.css(t))||0}),$.each(t,function(e,t){headerColumnHeightDiff+=parseFloat(n.css(t))||0})),n.remove();var r=$(\"
\").appendTo($canvas);n=$(\"\").appendTo(r),cellWidthDiff=cellHeightDiff=0,\"border-box\"!=n.css(\"box-sizing\")&&\"border-box\"!=n.css(\"-moz-box-sizing\")&&\"border-box\"!=n.css(\"-webkit-box-sizing\")&&($.each(e,function(e,t){cellWidthDiff+=parseFloat(n.css(t))||0}),$.each(t,function(e,t){cellHeightDiff+=parseFloat(n.css(t))||0})),r.remove(),absoluteColumnMinWidth=Math.max(headerColumnWidthDiff,cellWidthDiff)}function createCssRules(){$style=$(\"\n", "\n", "\n", "
\n", "\n", "\n", "\n", " \n", " \n", "\n", "\n", "\n", "\n", "
\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "function HoloViewsWidget() {\n", "}\n", "\n", "HoloViewsWidget.prototype.init_slider = function(init_val){\n", " if(this.load_json) {\n", " this.from_json()\n", " } else {\n", " this.update_cache();\n", " }\n", "}\n", "\n", "HoloViewsWidget.prototype.populate_cache = function(idx){\n", " this.cache[idx].innerHTML = this.frames[idx];\n", " if (this.embed) {\n", " delete this.frames[idx];\n", " }\n", "}\n", "\n", "HoloViewsWidget.prototype.process_error = function(msg){\n", "}\n", "\n", "HoloViewsWidget.prototype.from_json = function() {\n", " var data_url = this.json_path + this.id + '.json';\n", " $.getJSON(data_url, $.proxy(function(json_data) {\n", " this.frames = json_data;\n", " this.update_cache();\n", " this.update(0);\n", " }, this));\n", "}\n", "\n", "HoloViewsWidget.prototype.dynamic_update = function(current){\n", " if (current === undefined) {\n", " return\n", " }\n", " this.current = current;\n", " if (this.comm) {\n", " var msg = {comm_id: this.id+'_client', content: current}\n", " this.comm.send(msg);\n", " }\n", "}\n", "\n", "HoloViewsWidget.prototype.update_cache = function(force){\n", " var frame_len = Object.keys(this.frames).length;\n", " for (var i=0; i 0) {\n", " that.time = Date.now();\n", " that.dynamic_update(that.queue[that.queue.length-1]);\n", " that.queue = [];\n", " } else {\n", " that.wait = false;\n", " }\n", " if ((msg.msg_type == \"Ready\") && msg.content) {\n", " console.log(\"Python callback returned following output:\", msg.content);\n", " } else if (msg.msg_type == \"Error\") {\n", " console.log(\"Python failed with the following traceback:\", msg.traceback)\n", " }\n", " }\n", " var comm = HoloViews.comm_manager.get_client_comm(this.plot_id, this.id+'_client', ack_callback);\n", " return comm\n", " }\n", "}\n", "\n", "HoloViewsWidget.prototype.msg_handler = function(msg) {\n", " var metadata = msg.metadata;\n", " if ((metadata.msg_type == \"Ready\")) {\n", " if (metadata.content) {\n", " console.log(\"Python callback returned following output:\", metadata.content);\n", " }\n", "\treturn;\n", " } else if (metadata.msg_type == \"Error\") {\n", " console.log(\"Python failed with the following traceback:\", metadata.traceback)\n", " return\n", " }\n", " this.process_msg(msg)\n", "}\n", "\n", "HoloViewsWidget.prototype.process_msg = function(msg) {\n", "}\n", "\n", "function SelectionWidget(frames, id, slider_ids, keyMap, dim_vals, notFound, load_json, mode, cached, json_path, dynamic, plot_id){\n", " this.frames = frames;\n", " this.id = id;\n", " this.plot_id = plot_id;\n", " this.slider_ids = slider_ids;\n", " this.keyMap = keyMap\n", " this.current_frame = 0;\n", " this.current_vals = dim_vals;\n", " this.load_json = load_json;\n", " this.mode = mode;\n", " this.notFound = notFound;\n", " this.cached = cached;\n", " this.dynamic = dynamic;\n", " this.cache = {};\n", " this.json_path = json_path;\n", " this.init_slider(this.current_vals[0]);\n", " this.queue = [];\n", " this.wait = false;\n", " if (!this.cached || this.dynamic) {\n", " this.comm = this.init_comms();\n", " }\n", "}\n", "\n", "SelectionWidget.prototype = new HoloViewsWidget;\n", "\n", "\n", "SelectionWidget.prototype.get_key = function(current_vals) {\n", " var key = \"(\";\n", " for (var i=0; i Date.now()))) {\n", " this.queue.push(key);\n", " return\n", " }\n", " this.queue = [];\n", " this.time = Date.now();\n", " this.current_frame = key;\n", " this.wait = true;\n", " this.dynamic_update(key)\n", " } else if (key !== undefined) {\n", " this.update(key)\n", " }\n", "}\n", "\n", "\n", "/* Define the ScrubberWidget class */\n", "function ScrubberWidget(frames, num_frames, id, interval, load_json, mode, cached, json_path, dynamic, plot_id){\n", " this.slider_id = \"_anim_slider\" + id;\n", " this.loop_select_id = \"_anim_loop_select\" + id;\n", " this.id = id;\n", " this.plot_id = plot_id;\n", " this.interval = interval;\n", " this.current_frame = 0;\n", " this.direction = 0;\n", " this.dynamic = dynamic;\n", " this.timer = null;\n", " this.load_json = load_json;\n", " this.mode = mode;\n", " this.cached = cached;\n", " this.frames = frames;\n", " this.cache = {};\n", " this.length = num_frames;\n", " this.json_path = json_path;\n", " document.getElementById(this.slider_id).max = this.length - 1;\n", " this.init_slider(0);\n", " this.wait = false;\n", " this.queue = [];\n", " if (!this.cached || this.dynamic) {\n", " this.comm = this.init_comms()\n", " }\n", "}\n", "\n", "ScrubberWidget.prototype = new HoloViewsWidget;\n", "\n", "ScrubberWidget.prototype.set_frame = function(frame){\n", " this.current_frame = frame;\n", " var widget = document.getElementById(this.slider_id);\n", " if (widget === null) {\n", " this.pause_animation();\n", " return\n", " }\n", " widget.value = this.current_frame;\n", " if (this.dynamic || !this.cached) {\n", " if ((this.time !== undefined) && ((this.wait) && ((this.time + 10000) > Date.now()))) {\n", " this.queue.push(frame);\n", " return\n", " }\n", " this.queue = [];\n", " this.time = Date.now();\n", " this.wait = true;\n", " this.dynamic_update(frame)\n", " } else {\n", " this.update(frame)\n", " }\n", "}\n", "\n", "ScrubberWidget.prototype.get_loop_state = function(){\n", " var button_group = document[this.loop_select_id].state;\n", " for (var i = 0; i < button_group.length; i++) {\n", " var button = button_group[i];\n", " if (button.checked) {\n", " return button.value;\n", " }\n", " }\n", " return undefined;\n", "}\n", "\n", "\n", "ScrubberWidget.prototype.next_frame = function() {\n", " this.set_frame(Math.min(this.length - 1, this.current_frame + 1));\n", "}\n", "\n", "ScrubberWidget.prototype.previous_frame = function() {\n", " this.set_frame(Math.max(0, this.current_frame - 1));\n", "}\n", "\n", "ScrubberWidget.prototype.first_frame = function() {\n", " this.set_frame(0);\n", "}\n", "\n", "ScrubberWidget.prototype.last_frame = function() {\n", " this.set_frame(this.length - 1);\n", "}\n", "\n", "ScrubberWidget.prototype.slower = function() {\n", " this.interval /= 0.7;\n", " if(this.direction > 0){this.play_animation();}\n", " else if(this.direction < 0){this.reverse_animation();}\n", "}\n", "\n", "ScrubberWidget.prototype.faster = function() {\n", " this.interval *= 0.7;\n", " if(this.direction > 0){this.play_animation();}\n", " else if(this.direction < 0){this.reverse_animation();}\n", "}\n", "\n", "ScrubberWidget.prototype.anim_step_forward = function() {\n", " if(this.current_frame < this.length - 1){\n", " this.next_frame();\n", " }else{\n", " var loop_state = this.get_loop_state();\n", " if(loop_state == \"loop\"){\n", " this.first_frame();\n", " }else if(loop_state == \"reflect\"){\n", " this.last_frame();\n", " this.reverse_animation();\n", " }else{\n", " this.pause_animation();\n", " this.last_frame();\n", " }\n", " }\n", "}\n", "\n", "ScrubberWidget.prototype.anim_step_reverse = function() {\n", " if(this.current_frame > 0){\n", " this.previous_frame();\n", " } else {\n", " var loop_state = this.get_loop_state();\n", " if(loop_state == \"loop\"){\n", " this.last_frame();\n", " }else if(loop_state == \"reflect\"){\n", " this.first_frame();\n", " this.play_animation();\n", " }else{\n", " this.pause_animation();\n", " this.first_frame();\n", " }\n", " }\n", "}\n", "\n", "ScrubberWidget.prototype.pause_animation = function() {\n", " this.direction = 0;\n", " if (this.timer){\n", " clearInterval(this.timer);\n", " this.timer = null;\n", " }\n", "}\n", "\n", "ScrubberWidget.prototype.play_animation = function() {\n", " this.pause_animation();\n", " this.direction = 1;\n", " var t = this;\n", " if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n", "}\n", "\n", "ScrubberWidget.prototype.reverse_animation = function() {\n", " this.pause_animation();\n", " this.direction = -1;\n", " var t = this;\n", " if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n", "}\n", "\n", "function extend(destination, source) {\n", " for (var k in source) {\n", " if (source.hasOwnProperty(k)) {\n", " destination[k] = source[k];\n", " }\n", " }\n", " return destination;\n", "}\n", "\n", "function update_widget(widget, values) {\n", " if (widget.hasClass(\"ui-slider\")) {\n", " widget.slider('option', {\n", " min: 0,\n", " max: values.length-1,\n", " dim_vals: values,\n", " value: 0,\n", " dim_labels: values\n", " })\n", " widget.slider('option', 'slide').call(widget, event, {value: 0})\n", " } else {\n", " widget.empty();\n", " for (var i=0; i\", {\n", " value: i,\n", " text: values[i]\n", " }))\n", " };\n", " widget.data('values', values);\n", " widget.data('value', 0);\n", " widget.trigger(\"change\");\n", " };\n", "}\n", "\n", "function init_slider(id, plot_id, dim, values, next_vals, labels, dynamic, step, value, next_dim,\n", " dim_idx, delay, jQueryUI_CDN, UNDERSCORE_CDN) {\n", " // Slider JS Block START\n", " function loadcssfile(filename){\n", " var fileref=document.createElement(\"link\")\n", " fileref.setAttribute(\"rel\", \"stylesheet\")\n", " fileref.setAttribute(\"type\", \"text/css\")\n", " fileref.setAttribute(\"href\", filename)\n", " document.getElementsByTagName(\"head\")[0].appendChild(fileref)\n", " }\n", " loadcssfile(\"https://code.jquery.com/ui/1.10.4/themes/smoothness/jquery-ui.css\");\n", " /* Check if jQuery and jQueryUI have been loaded\n", " otherwise load with require.js */\n", " var jQuery = window.jQuery,\n", " // check for old versions of jQuery\n", " oldjQuery = jQuery && !!jQuery.fn.jquery.match(/^1\\.[0-4](\\.|$)/),\n", " jquery_path = '',\n", " paths = {},\n", " noConflict;\n", " var jQueryUI = jQuery.ui;\n", " // check for jQuery\n", " if (!jQuery || oldjQuery) {\n", " // load if it's not available or doesn't meet min standards\n", " paths.jQuery = jQuery;\n", " noConflict = !!oldjQuery;\n", " } else {\n", " // register the current jQuery\n", " define('jquery', [], function() { return jQuery; });\n", " }\n", " if (!jQueryUI) {\n", " paths.jQueryUI = jQueryUI_CDN.slice(null, -3);\n", " } else {\n", " define('jQueryUI', [], function() { return jQuery.ui; });\n", " }\n", " paths.underscore = UNDERSCORE_CDN.slice(null, -3);\n", " var jquery_require = {\n", " paths: paths,\n", " shim: {\n", " \"jQueryUI\": {\n", " exports:\"$\",\n", " deps: ['jquery']\n", " },\n", " \"underscore\": {\n", " exports: '_'\n", " }\n", " }\n", " }\n", " require.config(jquery_require);\n", " require([\"jQueryUI\", \"underscore\"], function(jUI, _){\n", " if (noConflict) $.noConflict(true);\n", " var vals = values;\n", " if (dynamic && vals.constructor === Array) {\n", " var default_value = parseFloat(value);\n", " var min = parseFloat(vals[0]);\n", " var max = parseFloat(vals[vals.length-1]);\n", " var wstep = step;\n", " var wlabels = [default_value];\n", " var init_label = default_value;\n", " } else {\n", " var min = 0;\n", " if (dynamic) {\n", " var max = Object.keys(vals).length - 1;\n", " var init_label = labels[value];\n", " var default_value = values[value];\n", " } else {\n", " var max = vals.length - 1;\n", " var init_label = labels[value];\n", " var default_value = value;\n", " }\n", " var wstep = 1;\n", " var wlabels = labels;\n", " }\n", " function adjustFontSize(text) {\n", " var width_ratio = (text.parent().width()/8)/text.val().length;\n", " var size = Math.min(0.9, Math.max(0.6, width_ratio))+'em';\n", " text.css('font-size', size);\n", " }\n", " var slider = $('#_anim_widget'+id+'_'+dim);\n", " slider.slider({\n", " animate: \"fast\",\n", " min: min,\n", " max: max,\n", " step: wstep,\n", " value: default_value,\n", " dim_vals: vals,\n", " dim_labels: wlabels,\n", " next_vals: next_vals,\n", " slide: function(event, ui) {\n", " var vals = slider.slider(\"option\", \"dim_vals\");\n", " var next_vals = slider.slider(\"option\", \"next_vals\");\n", " var dlabels = slider.slider(\"option\", \"dim_labels\");\n", " if (dynamic) {\n", " var dim_val = ui.value;\n", " if (vals.constructor === Array) {\n", " var label = ui.value;\n", " } else {\n", " var label = dlabels[ui.value];\n", " }\n", " } else {\n", " var dim_val = vals[ui.value];\n", " var label = dlabels[ui.value];\n", " }\n", " var text = $('#textInput'+id+'_'+dim);\n", " text.val(label);\n", " adjustFontSize(text);\n", " HoloViews.index[plot_id].set_frame(dim_val, dim_idx);\n", " if (Object.keys(next_vals).length > 0) {\n", " var new_vals = next_vals[dim_val];\n", " var next_widget = $('#_anim_widget'+id+'_'+next_dim);\n", " update_widget(next_widget, new_vals);\n", " }\n", " }\n", " });\n", " slider.keypress(function(event) {\n", " if (event.which == 80 || event.which == 112) {\n", " var start = slider.slider(\"option\", \"value\");\n", " var stop = slider.slider(\"option\", \"max\");\n", " for (var i=start; i<=stop; i++) {\n", " var delay = i*delay;\n", " $.proxy(function doSetTimeout(i) { setTimeout($.proxy(function() {\n", " var val = {value:i};\n", " slider.slider('value',i);\n", " slider.slider(\"option\", \"slide\")(null, val);\n", " }, slider), delay);}, slider)(i);\n", " }\n", " }\n", " if (event.which == 82 || event.which == 114) {\n", " var start = slider.slider(\"option\", \"value\");\n", " var stop = slider.slider(\"option\", \"min\");\n", " var count = 0;\n", " for (var i=start; i>=stop; i--) {\n", " var delay = count*delay;\n", " count = count + 1;\n", " $.proxy(function doSetTimeout(i) { setTimeout($.proxy(function() {\n", " var val = {value:i};\n", " slider.slider('value',i);\n", " slider.slider(\"option\", \"slide\")(null, val);\n", " }, slider), delay);}, slider)(i);\n", " }\n", " }\n", " });\n", " var textInput = $('#textInput'+id+'_'+dim)\n", " textInput.val(init_label);\n", " adjustFontSize(textInput);\n", " });\n", "}\n", "\n", "function init_dropdown(id, plot_id, dim, vals, value, next_vals, labels, next_dim, dim_idx, dynamic) {\n", " var widget = $(\"#_anim_widget\"+id+'_'+dim);\n", " widget.data('values', vals)\n", " for (var i=0; i\", {\n", " value: val,\n", " text: labels[i]\n", " }));\n", " };\n", " widget.data(\"next_vals\", next_vals);\n", " widget.val(value);\n", " widget.on('change', function(event, ui) {\n", " if (dynamic) {\n", " var dim_val = parseInt(this.value);\n", " } else {\n", " var dim_val = $.data(this, 'values')[this.value];\n", " }\n", " var next_vals = $.data(this, \"next_vals\");\n", " if (Object.keys(next_vals).length > 0) {\n", " var new_vals = next_vals[dim_val];\n", " var next_widget = $('#_anim_widget'+id+'_'+next_dim);\n", " update_widget(next_widget, new_vals);\n", " }\n", " var widgets = HoloViews.index[plot_id]\n", " if (widgets) {\n", " widgets.set_frame(dim_val, dim_idx);\n", " }\n", " });\n", "}\n", "\n", "\n", "if (window.HoloViews === undefined) {\n", " window.HoloViews = {}\n", " window.PyViz = window.HoloViews\n", "} else if (window.PyViz === undefined) {\n", " window.PyViz = window.HoloViews\n", "}\n", "\n", "\n", "var _namespace = {\n", " init_slider: init_slider,\n", " init_dropdown: init_dropdown,\n", " comms: {},\n", " comm_status: {},\n", " index: {},\n", " plot_index: {},\n", " kernels: {},\n", " receivers: {}\n", "}\n", "\n", "for (var k in _namespace) {\n", " if (!(k in window.HoloViews)) {\n", " window.HoloViews[k] = _namespace[k];\n", " }\n", "}\n", "\n", "// Define Bokeh specific subclasses\n", "function BokehSelectionWidget() {\n", " SelectionWidget.apply(this, arguments);\n", "}\n", "\n", "function BokehScrubberWidget() {\n", " ScrubberWidget.apply(this, arguments);\n", "}\n", "\n", "// Let them inherit from the baseclasses\n", "BokehSelectionWidget.prototype = Object.create(SelectionWidget.prototype);\n", "BokehScrubberWidget.prototype = Object.create(ScrubberWidget.prototype);\n", "\n", "// Define methods to override on widgets\n", "var BokehMethods = {\n", " update_cache : function(){\n", " for (var index in this.frames) {\n", " this.frames[index] = JSON.parse(this.frames[index]);\n", " }\n", " },\n", " update : function(current){\n", " if (current === undefined) {\n", " return;\n", " }\n", " var data = this.frames[current];\n", " if (data !== undefined) {\n", " if (data.root in HoloViews.plot_index) {\n", " var doc = HoloViews.plot_index[data.root].model.document;\n", " } else {\n", " var doc = Bokeh.index[data.root].model.document;\n", " }\n", " doc.apply_json_patch(data.content);\n", " }\n", " },\n", " init_comms: function() {\n", " if (Bokeh.protocol !== undefined) {\n", " this.receiver = new Bokeh.protocol.Receiver()\n", " } else {\n", " this.receiver = null;\n", " }\n", " return HoloViewsWidget.prototype.init_comms.call(this);\n", " },\n", " process_msg : function(msg) {\n", " if (this.plot_id in HoloViews.plot_index) {\n", " var doc = HoloViews.plot_index[this.plot_id].model.document;\n", " } else {\n", " var doc = Bokeh.index[this.plot_id].model.document;\n", " }\n", " if (this.receiver === null) { return }\n", " var receiver = this.receiver;\n", " if (msg.buffers.length > 0) {\n", " receiver.consume(msg.buffers[0].buffer)\n", " } else {\n", " receiver.consume(msg.content.data)\n", " }\n", " const comm_msg = receiver.message;\n", " if ((comm_msg != null) && (doc != null)) {\n", " doc.apply_json_patch(comm_msg.content, comm_msg.buffers)\n", " }\n", " }\n", "}\n", "\n", "// Extend Bokeh widgets with backend specific methods\n", "extend(BokehSelectionWidget.prototype, BokehMethods);\n", "extend(BokehScrubberWidget.prototype, BokehMethods);\n", "\n", "window.HoloViews.BokehSelectionWidget = BokehSelectionWidget\n", "window.HoloViews.BokehScrubberWidget = BokehScrubberWidget\n", "\n", " function JupyterCommManager() {\n", " }\n", "\n", " JupyterCommManager.prototype.register_target = function(plot_id, comm_id, msg_handler) {\n", " if (window.comm_manager || ((window.Jupyter !== undefined) && (Jupyter.notebook.kernel != null))) {\n", " var comm_manager = window.comm_manager || Jupyter.notebook.kernel.comm_manager;\n", " comm_manager.register_target(comm_id, function(comm) {\n", " comm.on_msg(msg_handler);\n", " });\n", " } else if ((plot_id in window.PyViz.kernels) && (window.PyViz.kernels[plot_id])) {\n", " window.PyViz.kernels[plot_id].registerCommTarget(comm_id, function(comm) {\n", " comm.onMsg = msg_handler;\n", " });\n", " }\n", " }\n", "\n", " JupyterCommManager.prototype.get_client_comm = function(plot_id, comm_id, msg_handler) {\n", " if (comm_id in window.PyViz.comms) {\n", " return window.PyViz.comms[comm_id];\n", " } else if (window.comm_manager || ((window.Jupyter !== undefined) && (Jupyter.notebook.kernel != null))) {\n", " var comm_manager = window.comm_manager || Jupyter.notebook.kernel.comm_manager;\n", " var comm = comm_manager.new_comm(comm_id, {}, {}, {}, comm_id);\n", " if (msg_handler) {\n", " comm.on_msg(msg_handler);\n", " }\n", " } else if ((plot_id in window.PyViz.kernels) && (window.PyViz.kernels[plot_id])) {\n", " var comm = window.PyViz.kernels[plot_id].connectToComm(comm_id);\n", " comm.open();\n", " if (msg_handler) {\n", " comm.onMsg = msg_handler;\n", " }\n", " }\n", "\n", " window.PyViz.comms[comm_id] = comm;\n", " return comm;\n", " }\n", "\n", " window.PyViz.comm_manager = new JupyterCommManager();\n", " \n", "\n", "var JS_MIME_TYPE = 'application/javascript';\n", "var HTML_MIME_TYPE = 'text/html';\n", "var EXEC_MIME_TYPE = 'application/vnd.holoviews_exec.v0+json';\n", "var CLASS_NAME = 'output';\n", "\n", "/**\n", " * Render data to the DOM node\n", " */\n", "function render(props, node) {\n", " var div = document.createElement(\"div\");\n", " var script = document.createElement(\"script\");\n", " node.appendChild(div);\n", " node.appendChild(script);\n", "}\n", "\n", "/**\n", " * Handle when a new output is added\n", " */\n", "function handle_add_output(event, handle) {\n", " var output_area = handle.output_area;\n", " var output = handle.output;\n", " if ((output.data == undefined) || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n", " return\n", " }\n", " var id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n", " var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n", " if (id !== undefined) {\n", " var nchildren = toinsert.length;\n", " toinsert[nchildren-1].children[0].innerHTML = output.data[HTML_MIME_TYPE];\n", " toinsert[nchildren-1].children[1].textContent = output.data[JS_MIME_TYPE];\n", " output_area._hv_plot_id = id;\n", " if ((window.Bokeh !== undefined) && (id in Bokeh.index)) {\n", " window.PyViz.plot_index[id] = Bokeh.index[id];\n", " } else {\n", " window.PyViz.plot_index[id] = null;\n", " }\n", " }\n", "}\n", "\n", "/**\n", " * Handle when an output is cleared or removed\n", " */\n", "function handle_clear_output(event, handle) {\n", " var id = handle.cell.output_area._hv_plot_id;\n", " if ((id === undefined) || !(id in PyViz.plot_index)) { return; }\n", " var comm = window.PyViz.comm_manager.get_client_comm(\"hv-extension-comm\", \"hv-extension-comm\", function () {});\n", " if (comm !== null) {\n", " comm.send({event_type: 'delete', 'id': id});\n", " }\n", " delete PyViz.plot_index[id];\n", " if ((window.Bokeh !== undefined) & (id in window.Bokeh.index)) {\n", " var doc = window.Bokeh.index[id].model.document\n", " doc.clear();\n", " const i = window.Bokeh.documents.indexOf(doc);\n", " if (i > -1) {\n", " window.Bokeh.documents.splice(i, 1);\n", " }\n", " }\n", "}\n", "\n", "/**\n", " * Handle kernel restart event\n", " */\n", "function handle_kernel_cleanup(event, handle) {\n", " delete PyViz.comms[\"hv-extension-comm\"];\n", " window.PyViz.plot_index = {}\n", "}\n", "\n", "/**\n", " * Handle update_display_data messages\n", " */\n", "function handle_update_output(event, handle) {\n", " handle_clear_output(event, {cell: {output_area: handle.output_area}})\n", " handle_add_output(event, handle)\n", "}\n", "\n", "function register_renderer(events, OutputArea) {\n", " function append_mime(data, metadata, element) {\n", " // create a DOM node to render to\n", " var toinsert = this.create_output_subarea(\n", " metadata,\n", " CLASS_NAME,\n", " EXEC_MIME_TYPE\n", " );\n", " this.keyboard_manager.register_events(toinsert);\n", " // Render to node\n", " var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n", " render(props, toinsert[0]);\n", " element.append(toinsert);\n", " return toinsert\n", " }\n", "\n", " events.on('output_added.OutputArea', handle_add_output);\n", " events.on('output_updated.OutputArea', handle_update_output);\n", " events.on('clear_output.CodeCell', handle_clear_output);\n", " events.on('delete.Cell', handle_clear_output);\n", " events.on('kernel_ready.Kernel', handle_kernel_cleanup);\n", "\n", " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n", " safe: true,\n", " index: 0\n", " });\n", "}\n", "\n", "if (window.Jupyter !== undefined) {\n", " try {\n", " var events = require('base/js/events');\n", " var OutputArea = require('notebook/js/outputarea').OutputArea;\n", " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n", " register_renderer(events, OutputArea);\n", " }\n", " } catch(err) {\n", " }\n", "}\n" ], "application/vnd.holoviews_load.v0+json": "function HoloViewsWidget() {\n}\n\nHoloViewsWidget.prototype.init_slider = function(init_val){\n if(this.load_json) {\n this.from_json()\n } else {\n this.update_cache();\n }\n}\n\nHoloViewsWidget.prototype.populate_cache = function(idx){\n this.cache[idx].innerHTML = this.frames[idx];\n if (this.embed) {\n delete this.frames[idx];\n }\n}\n\nHoloViewsWidget.prototype.process_error = function(msg){\n}\n\nHoloViewsWidget.prototype.from_json = function() {\n var data_url = this.json_path + this.id + '.json';\n $.getJSON(data_url, $.proxy(function(json_data) {\n this.frames = json_data;\n this.update_cache();\n this.update(0);\n }, this));\n}\n\nHoloViewsWidget.prototype.dynamic_update = function(current){\n if (current === undefined) {\n return\n }\n this.current = current;\n if (this.comm) {\n var msg = {comm_id: this.id+'_client', content: current}\n this.comm.send(msg);\n }\n}\n\nHoloViewsWidget.prototype.update_cache = function(force){\n var frame_len = Object.keys(this.frames).length;\n for (var i=0; i 0) {\n that.time = Date.now();\n that.dynamic_update(that.queue[that.queue.length-1]);\n that.queue = [];\n } else {\n that.wait = false;\n }\n if ((msg.msg_type == \"Ready\") && msg.content) {\n console.log(\"Python callback returned following output:\", msg.content);\n } else if (msg.msg_type == \"Error\") {\n console.log(\"Python failed with the following traceback:\", msg.traceback)\n }\n }\n var comm = HoloViews.comm_manager.get_client_comm(this.plot_id, this.id+'_client', ack_callback);\n return comm\n }\n}\n\nHoloViewsWidget.prototype.msg_handler = function(msg) {\n var metadata = msg.metadata;\n if ((metadata.msg_type == \"Ready\")) {\n if (metadata.content) {\n console.log(\"Python callback returned following output:\", metadata.content);\n }\n\treturn;\n } else if (metadata.msg_type == \"Error\") {\n console.log(\"Python failed with the following traceback:\", metadata.traceback)\n return\n }\n this.process_msg(msg)\n}\n\nHoloViewsWidget.prototype.process_msg = function(msg) {\n}\n\nfunction SelectionWidget(frames, id, slider_ids, keyMap, dim_vals, notFound, load_json, mode, cached, json_path, dynamic, plot_id){\n this.frames = frames;\n this.id = id;\n this.plot_id = plot_id;\n this.slider_ids = slider_ids;\n this.keyMap = keyMap\n this.current_frame = 0;\n this.current_vals = dim_vals;\n this.load_json = load_json;\n this.mode = mode;\n this.notFound = notFound;\n this.cached = cached;\n this.dynamic = dynamic;\n this.cache = {};\n this.json_path = json_path;\n this.init_slider(this.current_vals[0]);\n this.queue = [];\n this.wait = false;\n if (!this.cached || this.dynamic) {\n this.comm = this.init_comms();\n }\n}\n\nSelectionWidget.prototype = new HoloViewsWidget;\n\n\nSelectionWidget.prototype.get_key = function(current_vals) {\n var key = \"(\";\n for (var i=0; i Date.now()))) {\n this.queue.push(key);\n return\n }\n this.queue = [];\n this.time = Date.now();\n this.current_frame = key;\n this.wait = true;\n this.dynamic_update(key)\n } else if (key !== undefined) {\n this.update(key)\n }\n}\n\n\n/* Define the ScrubberWidget class */\nfunction ScrubberWidget(frames, num_frames, id, interval, load_json, mode, cached, json_path, dynamic, plot_id){\n this.slider_id = \"_anim_slider\" + id;\n this.loop_select_id = \"_anim_loop_select\" + id;\n this.id = id;\n this.plot_id = plot_id;\n this.interval = interval;\n this.current_frame = 0;\n this.direction = 0;\n this.dynamic = dynamic;\n this.timer = null;\n this.load_json = load_json;\n this.mode = mode;\n this.cached = cached;\n this.frames = frames;\n this.cache = {};\n this.length = num_frames;\n this.json_path = json_path;\n document.getElementById(this.slider_id).max = this.length - 1;\n this.init_slider(0);\n this.wait = false;\n this.queue = [];\n if (!this.cached || this.dynamic) {\n this.comm = this.init_comms()\n }\n}\n\nScrubberWidget.prototype = new HoloViewsWidget;\n\nScrubberWidget.prototype.set_frame = function(frame){\n this.current_frame = frame;\n var widget = document.getElementById(this.slider_id);\n if (widget === null) {\n this.pause_animation();\n return\n }\n widget.value = this.current_frame;\n if (this.dynamic || !this.cached) {\n if ((this.time !== undefined) && ((this.wait) && ((this.time + 10000) > Date.now()))) {\n this.queue.push(frame);\n return\n }\n this.queue = [];\n this.time = Date.now();\n this.wait = true;\n this.dynamic_update(frame)\n } else {\n this.update(frame)\n }\n}\n\nScrubberWidget.prototype.get_loop_state = function(){\n var button_group = document[this.loop_select_id].state;\n for (var i = 0; i < button_group.length; i++) {\n var button = button_group[i];\n if (button.checked) {\n return button.value;\n }\n }\n return undefined;\n}\n\n\nScrubberWidget.prototype.next_frame = function() {\n this.set_frame(Math.min(this.length - 1, this.current_frame + 1));\n}\n\nScrubberWidget.prototype.previous_frame = function() {\n this.set_frame(Math.max(0, this.current_frame - 1));\n}\n\nScrubberWidget.prototype.first_frame = function() {\n this.set_frame(0);\n}\n\nScrubberWidget.prototype.last_frame = function() {\n this.set_frame(this.length - 1);\n}\n\nScrubberWidget.prototype.slower = function() {\n this.interval /= 0.7;\n if(this.direction > 0){this.play_animation();}\n else if(this.direction < 0){this.reverse_animation();}\n}\n\nScrubberWidget.prototype.faster = function() {\n this.interval *= 0.7;\n if(this.direction > 0){this.play_animation();}\n else if(this.direction < 0){this.reverse_animation();}\n}\n\nScrubberWidget.prototype.anim_step_forward = function() {\n if(this.current_frame < this.length - 1){\n this.next_frame();\n }else{\n var loop_state = this.get_loop_state();\n if(loop_state == \"loop\"){\n this.first_frame();\n }else if(loop_state == \"reflect\"){\n this.last_frame();\n this.reverse_animation();\n }else{\n this.pause_animation();\n this.last_frame();\n }\n }\n}\n\nScrubberWidget.prototype.anim_step_reverse = function() {\n if(this.current_frame > 0){\n this.previous_frame();\n } else {\n var loop_state = this.get_loop_state();\n if(loop_state == \"loop\"){\n this.last_frame();\n }else if(loop_state == \"reflect\"){\n this.first_frame();\n this.play_animation();\n }else{\n this.pause_animation();\n this.first_frame();\n }\n }\n}\n\nScrubberWidget.prototype.pause_animation = function() {\n this.direction = 0;\n if (this.timer){\n clearInterval(this.timer);\n this.timer = null;\n }\n}\n\nScrubberWidget.prototype.play_animation = function() {\n this.pause_animation();\n this.direction = 1;\n var t = this;\n if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n}\n\nScrubberWidget.prototype.reverse_animation = function() {\n this.pause_animation();\n this.direction = -1;\n var t = this;\n if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n}\n\nfunction extend(destination, source) {\n for (var k in source) {\n if (source.hasOwnProperty(k)) {\n destination[k] = source[k];\n }\n }\n return destination;\n}\n\nfunction update_widget(widget, values) {\n if (widget.hasClass(\"ui-slider\")) {\n widget.slider('option', {\n min: 0,\n max: values.length-1,\n dim_vals: values,\n value: 0,\n dim_labels: values\n })\n widget.slider('option', 'slide').call(widget, event, {value: 0})\n } else {\n widget.empty();\n for (var i=0; i\", {\n value: i,\n text: values[i]\n }))\n };\n widget.data('values', values);\n widget.data('value', 0);\n widget.trigger(\"change\");\n };\n}\n\nfunction init_slider(id, plot_id, dim, values, next_vals, labels, dynamic, step, value, next_dim,\n dim_idx, delay, jQueryUI_CDN, UNDERSCORE_CDN) {\n // Slider JS Block START\n function loadcssfile(filename){\n var fileref=document.createElement(\"link\")\n fileref.setAttribute(\"rel\", \"stylesheet\")\n fileref.setAttribute(\"type\", \"text/css\")\n fileref.setAttribute(\"href\", filename)\n document.getElementsByTagName(\"head\")[0].appendChild(fileref)\n }\n loadcssfile(\"https://code.jquery.com/ui/1.10.4/themes/smoothness/jquery-ui.css\");\n /* Check if jQuery and jQueryUI have been loaded\n otherwise load with require.js */\n var jQuery = window.jQuery,\n // check for old versions of jQuery\n oldjQuery = jQuery && !!jQuery.fn.jquery.match(/^1\\.[0-4](\\.|$)/),\n jquery_path = '',\n paths = {},\n noConflict;\n var jQueryUI = jQuery.ui;\n // check for jQuery\n if (!jQuery || oldjQuery) {\n // load if it's not available or doesn't meet min standards\n paths.jQuery = jQuery;\n noConflict = !!oldjQuery;\n } else {\n // register the current jQuery\n define('jquery', [], function() { return jQuery; });\n }\n if (!jQueryUI) {\n paths.jQueryUI = jQueryUI_CDN.slice(null, -3);\n } else {\n define('jQueryUI', [], function() { return jQuery.ui; });\n }\n paths.underscore = UNDERSCORE_CDN.slice(null, -3);\n var jquery_require = {\n paths: paths,\n shim: {\n \"jQueryUI\": {\n exports:\"$\",\n deps: ['jquery']\n },\n \"underscore\": {\n exports: '_'\n }\n }\n }\n require.config(jquery_require);\n require([\"jQueryUI\", \"underscore\"], function(jUI, _){\n if (noConflict) $.noConflict(true);\n var vals = values;\n if (dynamic && vals.constructor === Array) {\n var default_value = parseFloat(value);\n var min = parseFloat(vals[0]);\n var max = parseFloat(vals[vals.length-1]);\n var wstep = step;\n var wlabels = [default_value];\n var init_label = default_value;\n } else {\n var min = 0;\n if (dynamic) {\n var max = Object.keys(vals).length - 1;\n var init_label = labels[value];\n var default_value = values[value];\n } else {\n var max = vals.length - 1;\n var init_label = labels[value];\n var default_value = value;\n }\n var wstep = 1;\n var wlabels = labels;\n }\n function adjustFontSize(text) {\n var width_ratio = (text.parent().width()/8)/text.val().length;\n var size = Math.min(0.9, Math.max(0.6, width_ratio))+'em';\n text.css('font-size', size);\n }\n var slider = $('#_anim_widget'+id+'_'+dim);\n slider.slider({\n animate: \"fast\",\n min: min,\n max: max,\n step: wstep,\n value: default_value,\n dim_vals: vals,\n dim_labels: wlabels,\n next_vals: next_vals,\n slide: function(event, ui) {\n var vals = slider.slider(\"option\", \"dim_vals\");\n var next_vals = slider.slider(\"option\", \"next_vals\");\n var dlabels = slider.slider(\"option\", \"dim_labels\");\n if (dynamic) {\n var dim_val = ui.value;\n if (vals.constructor === Array) {\n var label = ui.value;\n } else {\n var label = dlabels[ui.value];\n }\n } else {\n var dim_val = vals[ui.value];\n var label = dlabels[ui.value];\n }\n var text = $('#textInput'+id+'_'+dim);\n text.val(label);\n adjustFontSize(text);\n HoloViews.index[plot_id].set_frame(dim_val, dim_idx);\n if (Object.keys(next_vals).length > 0) {\n var new_vals = next_vals[dim_val];\n var next_widget = $('#_anim_widget'+id+'_'+next_dim);\n update_widget(next_widget, new_vals);\n }\n }\n });\n slider.keypress(function(event) {\n if (event.which == 80 || event.which == 112) {\n var start = slider.slider(\"option\", \"value\");\n var stop = slider.slider(\"option\", \"max\");\n for (var i=start; i<=stop; i++) {\n var delay = i*delay;\n $.proxy(function doSetTimeout(i) { setTimeout($.proxy(function() {\n var val = {value:i};\n slider.slider('value',i);\n slider.slider(\"option\", \"slide\")(null, val);\n }, slider), delay);}, slider)(i);\n }\n }\n if (event.which == 82 || event.which == 114) {\n var start = slider.slider(\"option\", \"value\");\n var stop = slider.slider(\"option\", \"min\");\n var count = 0;\n for (var i=start; i>=stop; i--) {\n var delay = count*delay;\n count = count + 1;\n $.proxy(function doSetTimeout(i) { setTimeout($.proxy(function() {\n var val = {value:i};\n slider.slider('value',i);\n slider.slider(\"option\", \"slide\")(null, val);\n }, slider), delay);}, slider)(i);\n }\n }\n });\n var textInput = $('#textInput'+id+'_'+dim)\n textInput.val(init_label);\n adjustFontSize(textInput);\n });\n}\n\nfunction init_dropdown(id, plot_id, dim, vals, value, next_vals, labels, next_dim, dim_idx, dynamic) {\n var widget = $(\"#_anim_widget\"+id+'_'+dim);\n widget.data('values', vals)\n for (var i=0; i\", {\n value: val,\n text: labels[i]\n }));\n };\n widget.data(\"next_vals\", next_vals);\n widget.val(value);\n widget.on('change', function(event, ui) {\n if (dynamic) {\n var dim_val = parseInt(this.value);\n } else {\n var dim_val = $.data(this, 'values')[this.value];\n }\n var next_vals = $.data(this, \"next_vals\");\n if (Object.keys(next_vals).length > 0) {\n var new_vals = next_vals[dim_val];\n var next_widget = $('#_anim_widget'+id+'_'+next_dim);\n update_widget(next_widget, new_vals);\n }\n var widgets = HoloViews.index[plot_id]\n if (widgets) {\n widgets.set_frame(dim_val, dim_idx);\n }\n });\n}\n\n\nif (window.HoloViews === undefined) {\n window.HoloViews = {}\n window.PyViz = window.HoloViews\n} else if (window.PyViz === undefined) {\n window.PyViz = window.HoloViews\n}\n\n\nvar _namespace = {\n init_slider: init_slider,\n init_dropdown: init_dropdown,\n comms: {},\n comm_status: {},\n index: {},\n plot_index: {},\n kernels: {},\n receivers: {}\n}\n\nfor (var k in _namespace) {\n if (!(k in window.HoloViews)) {\n window.HoloViews[k] = _namespace[k];\n }\n}\n\n// Define Bokeh specific subclasses\nfunction BokehSelectionWidget() {\n SelectionWidget.apply(this, arguments);\n}\n\nfunction BokehScrubberWidget() {\n ScrubberWidget.apply(this, arguments);\n}\n\n// Let them inherit from the baseclasses\nBokehSelectionWidget.prototype = Object.create(SelectionWidget.prototype);\nBokehScrubberWidget.prototype = Object.create(ScrubberWidget.prototype);\n\n// Define methods to override on widgets\nvar BokehMethods = {\n update_cache : function(){\n for (var index in this.frames) {\n this.frames[index] = JSON.parse(this.frames[index]);\n }\n },\n update : function(current){\n if (current === undefined) {\n return;\n }\n var data = this.frames[current];\n if (data !== undefined) {\n if (data.root in HoloViews.plot_index) {\n var doc = HoloViews.plot_index[data.root].model.document;\n } else {\n var doc = Bokeh.index[data.root].model.document;\n }\n doc.apply_json_patch(data.content);\n }\n },\n init_comms: function() {\n if (Bokeh.protocol !== undefined) {\n this.receiver = new Bokeh.protocol.Receiver()\n } else {\n this.receiver = null;\n }\n return HoloViewsWidget.prototype.init_comms.call(this);\n },\n process_msg : function(msg) {\n if (this.plot_id in HoloViews.plot_index) {\n var doc = HoloViews.plot_index[this.plot_id].model.document;\n } else {\n var doc = Bokeh.index[this.plot_id].model.document;\n }\n if (this.receiver === null) { return }\n var receiver = this.receiver;\n if (msg.buffers.length > 0) {\n receiver.consume(msg.buffers[0].buffer)\n } else {\n receiver.consume(msg.content.data)\n }\n const comm_msg = receiver.message;\n if ((comm_msg != null) && (doc != null)) {\n doc.apply_json_patch(comm_msg.content, comm_msg.buffers)\n }\n }\n}\n\n// Extend Bokeh widgets with backend specific methods\nextend(BokehSelectionWidget.prototype, BokehMethods);\nextend(BokehScrubberWidget.prototype, BokehMethods);\n\nwindow.HoloViews.BokehSelectionWidget = BokehSelectionWidget\nwindow.HoloViews.BokehScrubberWidget = BokehScrubberWidget\n\n function JupyterCommManager() {\n }\n\n JupyterCommManager.prototype.register_target = function(plot_id, comm_id, msg_handler) {\n if (window.comm_manager || ((window.Jupyter !== undefined) && (Jupyter.notebook.kernel != null))) {\n var comm_manager = window.comm_manager || Jupyter.notebook.kernel.comm_manager;\n comm_manager.register_target(comm_id, function(comm) {\n comm.on_msg(msg_handler);\n });\n } else if ((plot_id in window.PyViz.kernels) && (window.PyViz.kernels[plot_id])) {\n window.PyViz.kernels[plot_id].registerCommTarget(comm_id, function(comm) {\n comm.onMsg = msg_handler;\n });\n }\n }\n\n JupyterCommManager.prototype.get_client_comm = function(plot_id, comm_id, msg_handler) {\n if (comm_id in window.PyViz.comms) {\n return window.PyViz.comms[comm_id];\n } else if (window.comm_manager || ((window.Jupyter !== undefined) && (Jupyter.notebook.kernel != null))) {\n var comm_manager = window.comm_manager || Jupyter.notebook.kernel.comm_manager;\n var comm = comm_manager.new_comm(comm_id, {}, {}, {}, comm_id);\n if (msg_handler) {\n comm.on_msg(msg_handler);\n }\n } else if ((plot_id in window.PyViz.kernels) && (window.PyViz.kernels[plot_id])) {\n var comm = window.PyViz.kernels[plot_id].connectToComm(comm_id);\n comm.open();\n if (msg_handler) {\n comm.onMsg = msg_handler;\n }\n }\n\n window.PyViz.comms[comm_id] = comm;\n return comm;\n }\n\n window.PyViz.comm_manager = new JupyterCommManager();\n \n\nvar JS_MIME_TYPE = 'application/javascript';\nvar HTML_MIME_TYPE = 'text/html';\nvar EXEC_MIME_TYPE = 'application/vnd.holoviews_exec.v0+json';\nvar CLASS_NAME = 'output';\n\n/**\n * Render data to the DOM node\n */\nfunction render(props, node) {\n var div = document.createElement(\"div\");\n var script = document.createElement(\"script\");\n node.appendChild(div);\n node.appendChild(script);\n}\n\n/**\n * Handle when a new output is added\n */\nfunction handle_add_output(event, handle) {\n var output_area = handle.output_area;\n var output = handle.output;\n if ((output.data == undefined) || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n return\n }\n var id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n if (id !== undefined) {\n var nchildren = toinsert.length;\n toinsert[nchildren-1].children[0].innerHTML = output.data[HTML_MIME_TYPE];\n toinsert[nchildren-1].children[1].textContent = output.data[JS_MIME_TYPE];\n output_area._hv_plot_id = id;\n if ((window.Bokeh !== undefined) && (id in Bokeh.index)) {\n window.PyViz.plot_index[id] = Bokeh.index[id];\n } else {\n window.PyViz.plot_index[id] = null;\n }\n }\n}\n\n/**\n * Handle when an output is cleared or removed\n */\nfunction handle_clear_output(event, handle) {\n var id = handle.cell.output_area._hv_plot_id;\n if ((id === undefined) || !(id in PyViz.plot_index)) { return; }\n var comm = window.PyViz.comm_manager.get_client_comm(\"hv-extension-comm\", \"hv-extension-comm\", function () {});\n if (comm !== null) {\n comm.send({event_type: 'delete', 'id': id});\n }\n delete PyViz.plot_index[id];\n if ((window.Bokeh !== undefined) & (id in window.Bokeh.index)) {\n var doc = window.Bokeh.index[id].model.document\n doc.clear();\n const i = window.Bokeh.documents.indexOf(doc);\n if (i > -1) {\n window.Bokeh.documents.splice(i, 1);\n }\n }\n}\n\n/**\n * Handle kernel restart event\n */\nfunction handle_kernel_cleanup(event, handle) {\n delete PyViz.comms[\"hv-extension-comm\"];\n window.PyViz.plot_index = {}\n}\n\n/**\n * Handle update_display_data messages\n */\nfunction handle_update_output(event, handle) {\n handle_clear_output(event, {cell: {output_area: handle.output_area}})\n handle_add_output(event, handle)\n}\n\nfunction register_renderer(events, OutputArea) {\n function append_mime(data, metadata, element) {\n // create a DOM node to render to\n var toinsert = this.create_output_subarea(\n metadata,\n CLASS_NAME,\n EXEC_MIME_TYPE\n );\n this.keyboard_manager.register_events(toinsert);\n // Render to node\n var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n render(props, toinsert[0]);\n element.append(toinsert);\n return toinsert\n }\n\n events.on('output_added.OutputArea', handle_add_output);\n events.on('output_updated.OutputArea', handle_update_output);\n events.on('clear_output.CodeCell', handle_clear_output);\n events.on('delete.Cell', handle_clear_output);\n events.on('kernel_ready.Kernel', handle_kernel_cleanup);\n\n OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n safe: true,\n index: 0\n });\n}\n\nif (window.Jupyter !== undefined) {\n try {\n var events = require('base/js/events');\n var OutputArea = require('notebook/js/outputarea').OutputArea;\n if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n register_renderer(events, OutputArea);\n }\n } catch(err) {\n }\n}\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import holoviews as hv\n", "hv.extension('bokeh')\n", "hv.opts.defaults(hv.opts.Curve(width=500))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "\n", "// Ugly hack 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To generate clean HTML output set HV_DOC_HTML as an environment variable.\")\n", " var htmlObject = document.createElement('div');\n", " htmlObject.innerHTML = `
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" ], "text/plain": [ ":Curve [x] (y)" ] }, "execution_count": 5, "metadata": { "application/vnd.holoviews_exec.v0+json": { "id": "1114" } }, "output_type": "execute_result" } ], "source": [ "td_solver.steps(10)\n", "\n", "hv.Curve((td_solver.x, td_solver.ucurr)).redim.range(y=(-1, 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's animate this:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "\n", "// Ugly hack - see HoloViews #2574 for more information\n", "if (!(document.getElementById('1224')) && !(document.getElementById('_anim_imgdb5cce439df648c5aa16306c183fb3b9'))) {\n", " console.log(\"Creating DOM nodes dynamically for assumed nbconvert export. To generate clean HTML output set HV_DOC_HTML as an environment variable.\")\n", " var htmlObject = document.createElement('div');\n", " htmlObject.innerHTML = `
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" ], "text/plain": [ ":HoloMap [snapshot]\n", " :Curve [x] (y)" ] }, "execution_count": 6, "metadata": { "application/vnd.holoviews_exec.v0+json": { "id": "1224" } }, "output_type": "execute_result" } ], "source": [ "%%output holomap='scrubber'\n", "snapshots = []\n", "td_solver = TimeDomainSolver(L, 200, T, m, triangle)\n", "for _ in range(41):\n", " snapshots.append(td_solver.ucurr.copy())\n", " td_solver.steps(10)\n", "\n", "td_hmap = hv.HoloMap({i: hv.Curve((td_solver.x, snapshots[i]), label='time domain') for i in range(len(snapshots))}, kdims=['snapshot'])\n", "td_hmap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can observe that the vibrations of the string keeps the initial triangular shape and that this shape repeats after some time. In fact, this is a particular wave we are observing: a [standing wave](https://en.wikipedia.org/wiki/Standing_wave). This is due to the symmetry in the way we have formulated this problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now on to the frequency domain solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Frequency domain solution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the frequency domain, the solution is written as follows: \n", "$$\n", "y(x,t)=\\sum_{n=0}^\\infty B_{n}\\sin \\left(n\\pi {x \\over L}\\right)\\cos \\left(n\\pi {c t \\over L}\\right)\n", "$$\n", "where \n", "$$\n", "B_{n}={2 \\over L}\\int _{{0}}^{{L}}f(x)\\sin \\left(n\\pi {x \\over L}\\right){\\mathrm d}x.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use this to compute a frequency domain solver that operates with a truncated number of modes. We will keep a similar time step for animation since this will allow us to exactly compare the outcome of the simulation between our two solvers." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "class FrequencyDomainSolver:\n", " \n", " def __init__(self, L, nx, T, m, y0, nmodes):\n", " \"\"\"Setup of the time domain solver.\"\"\"\n", " self.x = np.linspace(0, L, num=nx)\n", " self.L = L\n", " self.dx = self.x[1] - self.x[0]\n", " c = np.sqrt(T/m)\n", " self.c = c\n", " self.dt = self.dx / c\n", " self.t = 0.\n", " self.uprev = y0(self.x)\n", " self.ucurr = y0(self.x)\n", " self.alpha = T / m * self.dt ** 2 / self.dx **2\n", " self.nmodes = nmodes\n", " self.Bn = []\n", " for n in range(nmodes):\n", " self.Bn.append(2/L * np.trapz(y0(self.x) * np.sin(n * np.pi * self.x / L), self.x))\n", " \n", " \n", " def step(self):\n", " \"\"\"Steps the system forward in time.\"\"\"\n", " unext = np.zeros_like(self.ucurr)\n", " self.t += self.dt\n", " for n, Bn in zip(range(self.nmodes), self.Bn):\n", " unext += Bn * np.sin(n * np.pi * self.x / self.L) * np.cos(n * np.pi * self.c / self.L * self.t)\n", " self.ucurr, self.uprev = unext, self.ucurr\n", " \n", " def steps(self, n):\n", " for _ in range(n):\n", " self.step()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "\n", "// Ugly hack - see HoloViews #2574 for more information\n", "if (!(document.getElementById('1547')) && !(document.getElementById('_anim_imgNone'))) {\n", " console.log(\"Creating DOM nodes dynamically for assumed nbconvert export. To generate clean HTML output set HV_DOC_HTML as an environment variable.\")\n", " var htmlObject = document.createElement('div');\n", " htmlObject.innerHTML = `
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" ], "text/plain": [ ":HoloMap [snapshot]\n", " :Curve [x] (y)" ] }, "execution_count": 11, "metadata": { "application/vnd.holoviews_exec.v0+json": { "id": "1657" } }, "output_type": "execute_result" } ], "source": [ "%%output holomap='scrubber'\n", "snapshots = []\n", "fd_solver = FrequencyDomainSolver(L, 200, T, m, triangle, nmodes=10)\n", "for _ in range(41):\n", " snapshots.append(fd_solver.ucurr.copy())\n", " fd_solver.steps(10)\n", "\n", "fd_hmap = hv.HoloMap({i: hv.Curve((fd_solver.x, snapshots[i]), label='frequency domain') for i in range(len(snapshots))}, kdims=['snapshot'])\n", "fd_hmap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution obtained with this approach looks a lot like the previous. Except for the fact that the string looks less triangular than before! This is due to the fact that the infinite sum of modes has been replaced by a truncated sum.\n", "\n", "Let's superpose the obtained figures for comparison." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Comparison of both methods " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "\n", "// Ugly hack - see HoloViews #2574 for more information\n", "if (!(document.getElementById('1980')) && !(document.getElementById('_anim_img601cad669b0b495c94f13d2adfa380fa'))) {\n", " console.log(\"Creating DOM nodes dynamically for assumed nbconvert export. To generate clean HTML output set HV_DOC_HTML as an environment variable.\")\n", " var htmlObject = document.createElement('div');\n", " htmlObject.innerHTML = `
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" ], "text/plain": [ ":Overlay\n", " .Curve.Time_domain :Curve [x] (y)\n", " .Curve.Frequency_domain :Curve [x] (y)" ] }, "execution_count": 17, "metadata": { "application/vnd.holoviews_exec.v0+json": { "id": "2848" } }, "output_type": "execute_result" } ], "source": [ "hv.Curve((td_solver.x, td_solver.ucurr), label='time domain').redim.range(y=(0, .6)) * \\\n", " hv.Curve((fd_solver.x, fd_solver.ucurr), label='frequency domain')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above plot, we see that the time domain solution is now pretty wigly. This phenomenom is a natural artifact of the simulated string and is called *numerical dispersion*. Here, the frequency domain solution is more trustworthy since it is a closed-form sum and does not accumulate small errors due to many updates of a numerical value. \n", "\n", "This is an important argument for choosing one or the other model in engineering applications. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's all about tradeoffs. In the physics application that I use every day at work, it seems that each community has its preferred method and numerical strategy, which in a very broad way boils down to choosing time-domain or frequency-domain as your method to solve a wave propagation problem. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another question is: is this realistic? That is a difficult question, and to try to answer that we could have a look at YouTube, where one can find some realistic videos from guitars." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "from IPython.display import YouTubeVideo" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "YouTubeVideo('MZ1O1JkL5Dw')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bonus " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What happens if we excite the string with \"half a triangle\", a triangle on half of its side?" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "half_triangle = lambda x: (x * 4 / L) * (x < L/4) + (-x * 4 / L + 2) * (x >= L/4) + -(-x * 4 / L + 2) * (x >= L/2)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "\n", "// Ugly hack - see HoloViews #2574 for more information\n", "if (!(document.getElementById('3069')) && !(document.getElementById('_anim_imgf448c1d9b1894f50a7ee668d7935c926'))) {\n", " console.log(\"Creating DOM nodes dynamically for assumed nbconvert export. To generate clean HTML output set HV_DOC_HTML as an environment variable.\")\n", " var htmlObject = document.createElement('div');\n", " htmlObject.innerHTML = `
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" ], "text/plain": [ ":HoloMap [snapshot]\n", " :Curve [x] (y)" ] }, "execution_count": 21, "metadata": { "application/vnd.holoviews_exec.v0+json": { "id": "3069" } }, "output_type": "execute_result" } ], "source": [ "%%output holomap='scrubber'\n", "snapshots = []\n", "td_solver = TimeDomainSolver(L, 400, T, m, half_triangle)\n", "for _ in range(80):\n", " snapshots.append(td_solver.ucurr.copy())\n", " td_solver.steps(20)\n", "\n", "td_hmap = hv.HoloMap({i: hv.Curve((td_solver.x, snapshots[i]), label='time domain') for i in range(len(snapshots))}, kdims=['snapshot'])\n", "td_hmap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*This post was entirely written using the IPython notebook. Its content is BSD-licensed. You can see a static view or download this notebook with the help of nbviewer at [20190328_vibratingStringTimeFrequency.ipynb](http://nbviewer.ipython.org/urls/raw.github.com/flothesof/posts/master/20190328_vibratingStringTimeFrequency.ipynb).*" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.7" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }