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Verlet ODE Integrators
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VerletODEIntegrator
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Verlet ODE Integrators\n",
"*note: this was transcribed from <http://www.physics.drexel.edu/~valliere/PHYS305/Diff_Eq_Integrators/Verlet_Methods/Verlet/>*\n",
"\n",
"The *Leapfrog integrator* belongs to a class of integrators commonly known as the Verlet ODE integration schemes. They are popular integrators that are widely used in Molecular Dynamics simulations. These are *N-body* simulations to model various systems from solids and gases to proteins. Electrons, atoms or molecules might constitute the building blocks in these models. Often, quantum effects are neglected for simplicity. Newton equations of motion, derived from his laws, are then solved for the motion of the N bodies under the influence of pair-wise (or more complicated) interactions.\n",
"\n",
"The motion of the individual atoms or molecules is likely to be chaotic. This demands accurate and stable ODE integration schemes. The calculations can also be very time consuming. This is so since the number of ODEs to solve ( $ x, y, z, v_x, v_y, v_z$ for each particle, or $ 6 N$ in total) can be very large. Furthermore the number of interaction terms to calculate also increases very rapidly with $ N$ ( $ N(N-1)/2$ for pair-wise interactions). This demands an ODE integrator that minimizes the number of evaluations of the ODE RHS.\n",
"\n",
"The Verlet integration schemes are ODE integrators which satisfy these requirements. They are time reversible, which insures conservation of energy, and are found to be very stable.\n",
"\n",
"There are three common formulations of the Verlet integration schemes: the *Basic Verlet Algorithm*, the *Verlet Leapfrog Algorithm* and the *Velocity Verlet Algorithm*.\n",
"\n",
"###Basic Verlet Algorithm\n",
"\n",
"The *Basic Verlet Algorithm* takes the form \n",
"\n",
"\\begin{eqnarray}\n",
" x_{n+1} = 2 x_n - x_{n-1} + \\frac{ f_n}{m} \\Delta t^2 +\n",
" O(\\Delta t^4) \\nonumber \\\\\n",
" v_n = \\frac{1}{2 \\Delta t} [ x_{n+1} - x_{n-1} ] + O(\\Delta t^2 ) \\nonumber\n",
"\\end{eqnarray}\n",
"\n",
"where $ n$ denotes a time slice on a time grid with spacing $ \\Delta t$ . This scheme is simple and robust. But it suffers from needing to compute the velocity as a separate step with a less accurate expression since only the position is predicted by the integrator. It also requires the position at the previous time slice, $ t-\\Delta t$ , which requires the use of another integration scheme to start the integration.\n",
"\n",
"###Verlet Leapfrog Algorithm\n",
"\n",
"The *Verlet Leapfrog Algorithm* is written as\n",
"\n",
" \\begin{eqnarray}\n",
" v_{n+1/2} = v_{n-1/2} + \\frac{f_n}{m} \\Delta t +\n",
" O(\\Delta t^3) \\nonumber \\\\\n",
" x_{n+1} = x_n + v_{n+1/2} \\Delta t + O(\\Delta t^4) \\nonumber \\\\\n",
" v_n = \\frac{1}{2} [ v_{n+1/2} + v_{n-1/2} ] + O(\\Delta t^2). \\nonumber \n",
"\\end{eqnarray}\n",
"\n",
"This last equation for $ v_n$ could be replaced by a *Euler Step* or a more accurate integration half step. This algorithm was described in details in a previous section.\n",
"\n",
"###Velocity Verlet Algorithm\n",
"\n",
"The most popular scheme is the *Velocity Verlet Algorithm*.\n",
"\n",
"\\begin{eqnarray}\n",
" x_{n+1} = x_n + v_n \\Delta t + \\frac{f_n}{2 m} \\Delta t^2 +\n",
" O(\\Delta t^3) \\nonumber \\\\\n",
" v_{n+1} = v_n + \\frac{\\Delta t}{2m} [ f_{n+1} + f_n ] +\n",
" O(\\Delta t^3). \\nonumber \n",
"\\end{eqnarray}\n",
"\n",
"\n",
"This algorithm only requires $ x_n$ and $ v_n$ to get started. Positions and velocities are generated on a single time grid. These equations can be written as\n",
"\n",
"\\begin{eqnarray}\n",
" v_{n+1/2} = v_n + \\frac{f_n}{2 m} \\Delta t \\nonumber \\\\\n",
" x_{n+1} = x_n + v_{n+1/2} \\Delta t \\nonumber \\\\\n",
" v_{n+1} = v_{n+1/2} + \\frac{\\Delta t}{2m} f_{n+1} \\nonumber\n",
"\\end{eqnarray}\n",
"\n",
"The following are time step functions implementing the *Velocity Verlet* ODE integrator for 1D problems. ~~They are interchangeable with the previous functions (i.e., euler_step.c, mid_step.c, RK4_step.c, ...).~~\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"type Particle\n",
" x :: Real\n",
" v :: Real\n",
"end\n",
"\n",
"#here we define the spring\n",
"k = 1.0\n",
"m = 1.0\n",
"\n",
"function force(s) #actually acceleration\n",
" return - (k / m) * s.x\n",
"end\n",
"\n",
"# Purely functional, takes a particle, returns a particle\n",
"# Works for particle of arbitrary dimension\n",
"function velocity_verlet_step ( t, dt, s )\n",
" rhsv = force(s)\n",
" v_half = s.v + 0.5*dt*rhsv\n",
" rhsx = v_half\n",
" x = s.x + dt*rhsx\n",
" rhsv = force(Particle(x,s.v))\n",
" v = v_half + 0.5*dt*rhsv\n",
" return x, v\n",
"end;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"In n-dimensions, this scheme becomes\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"type ParticleND\n",
" x :: Array{Float64,1}\n",
" v :: Array{Float64,1}\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"The Velocity Verlet method applies to mechanics problems and so are these functions. Furthermore, these functions assume a one body problem in 1-Dimension or 2-Dimension. Writing it more generally would be easy once we agree on the proper way to store the position and velocity components of the particles in the unknown function and ODE RHS arrays.\n",
"\n",
"Many references can be found that describe or derive the Verlet Algorithms, specially in the context of Molecular Dynamics. \n",
"\n",
"[Verlet algorithms\n",
"description](http://www.compsoc.man.ac.uk/~lucky/Democritus/Theory/verlet.html)\\\n",
" [Verlet algorithms derivation from Taylor Series](http://www.physics.drexel.edu/~valliere/PHYS305/Diff_Eq_Integrators/Verlet_Methods/Diffrntleqn3.pdf)\\\n",
" [Introduction to\n",
"MD](http://www.fz-juelich.de/nic-series/volume23/allen.pdf)\\\n",
"\n",
"#Code Examples\n",
"\n",
"Recommended resources for learning Julia:\n",
"\n",
"* <http://learnxinyminutes.com/docs/julia/>\n",
"* <https://julia.readthedocs.org/en/release-0.3/>\n",
"* <https://en.wikibooks.org/wiki/Introducing_Julia>"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"using Gadfly\n",
"using Iterators"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"matrix\" values=\"{a} {b} {c} 0 0 {d} {e} {f} 0 0 {g} {h} {i} 0 0 0 0 0 1 0\"/>',{a:0.393+0.607*(1-d),b:0.769-0.769*(1-d),c:0.189-0.189*(1-d),d:0.349-0.349*(1-d),e:0.686+0.314*(1-d),f:0.168-0.168*(1-d),g:0.272-0.272*(1-d),h:0.534-0.534*(1-d),i:0.131+0.869*(1-d)})};a.filter.sepia.toString=function(){return this()};a.filter.saturate=function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"saturate\" values=\"{amount}\"/>',{amount:1-\n",
"d})};a.filter.saturate.toString=function(){return this()};a.filter.hueRotate=function(d){return a.format('<feColorMatrix type=\"hueRotate\" values=\"{angle}\"/>',{angle:d||0})};a.filter.hueRotate.toString=function(){return this()};a.filter.invert=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncG type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncB type=\"table\" tableValues=\"{amount} {amount2}\"/></feComponentTransfer>',{amount:d,\n",
"amount2:1-d})};a.filter.invert.toString=function(){return this()};a.filter.brightness=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\"/><feFuncG type=\"linear\" slope=\"{amount}\"/><feFuncB type=\"linear\" slope=\"{amount}\"/></feComponentTransfer>',{amount:d})};a.filter.brightness.toString=function(){return this()};a.filter.contrast=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncG type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncB type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/></feComponentTransfer>',\n",
"{amount:d,amount2:0.5-d/2})};a.filter.contrast.toString=function(){return this()}});return C});\n",
"\n",
"]]> </script>\n",
"<script> <![CDATA[\n",
"\n",
"(function (glob, factory) {\n",
" // AMD support\n",
" if (typeof define === \"function\" && define.amd) {\n",
" // Define as an anonymous module\n",
" define(\"Gadfly\", [\"Snap.svg\"], function (Snap) {\n",
" return factory(Snap);\n",
" });\n",
" } else {\n",
" // Browser globals (glob is window)\n",
" // Snap adds itself to window\n",
" glob.Gadfly = factory(glob.Snap);\n",
" }\n",
"}(this, function (Snap) {\n",
"\n",
"var Gadfly = {};\n",
"\n",
"// Get an x/y coordinate value in pixels\n",
"var xPX = function(fig, x) {\n",
" var client_box = fig.node.getBoundingClientRect();\n",
" return x * fig.node.viewBox.baseVal.width / client_box.width;\n",
"};\n",
"\n",
"var yPX = function(fig, y) {\n",
" var client_box = fig.node.getBoundingClientRect();\n",
" return y * fig.node.viewBox.baseVal.height / client_box.height;\n",
"};\n",
"\n",
"\n",
"Snap.plugin(function (Snap, Element, Paper, global) {\n",
" // Traverse upwards from a snap element to find and return the first\n",
" // note with the \"plotroot\" class.\n",
" Element.prototype.plotroot = function () {\n",
" var element = this;\n",
" while (!element.hasClass(\"plotroot\") && element.parent() != null) {\n",
" element = element.parent();\n",
" }\n",
" return element;\n",
" };\n",
"\n",
" Element.prototype.svgroot = function () {\n",
" var element = this;\n",
" while (element.node.nodeName != \"svg\" && element.parent() != null) {\n",
" element = element.parent();\n",
" }\n",
" return element;\n",
" };\n",
"\n",
" Element.prototype.plotbounds = function () {\n",
" var root = this.plotroot()\n",
" var bbox = root.select(\".guide.background\").node.getBBox();\n",
" return {\n",
" x0: bbox.x,\n",
" x1: bbox.x + bbox.width,\n",
" y0: bbox.y,\n",
" y1: bbox.y + bbox.height\n",
" };\n",
" };\n",
"\n",
" Element.prototype.plotcenter = function () {\n",
" var root = this.plotroot()\n",
" var bbox = root.select(\".guide.background\").node.getBBox();\n",
" return {\n",
" x: bbox.x + bbox.width / 2,\n",
" y: bbox.y + bbox.height / 2\n",
" };\n",
" };\n",
"\n",
" // Emulate IE style mouseenter/mouseleave events, since Microsoft always\n",
" // does everything right.\n",
" // See: http://www.dynamic-tools.net/toolbox/isMouseLeaveOrEnter/\n",
" var events = [\"mouseenter\", \"mouseleave\"];\n",
"\n",
" for (i in events) {\n",
" (function (event_name) {\n",
" var event_name = events[i];\n",
" Element.prototype[event_name] = function (fn, scope) {\n",
" if (Snap.is(fn, \"function\")) {\n",
" var fn2 = function (event) {\n",
" if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
" return;\n",
" }\n",
"\n",
" var reltg = event.relatedTarget ? event.relatedTarget :\n",
" event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
" while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
"\n",
" if (reltg != this.node) {\n",
" return fn.apply(this, event);\n",
" }\n",
" };\n",
"\n",
" if (event_name == \"mouseenter\") {\n",
" this.mouseover(fn2, scope);\n",
" } else {\n",
" this.mouseout(fn2, scope);\n",
" }\n",
" }\n",
" return this;\n",
" };\n",
" })(events[i]);\n",
" }\n",
"\n",
"\n",
" Element.prototype.mousewheel = function (fn, scope) {\n",
" if (Snap.is(fn, \"function\")) {\n",
" var el = this;\n",
" var fn2 = function (event) {\n",
" fn.apply(el, [event]);\n",
" };\n",
" }\n",
"\n",
" this.node.addEventListener(\n",
" /Firefox/i.test(navigator.userAgent) ? \"DOMMouseScroll\" : \"mousewheel\",\n",
" fn2);\n",
"\n",
" return this;\n",
" };\n",
"\n",
"\n",
" // Snap's attr function can be too slow for things like panning/zooming.\n",
" // This is a function to directly update element attributes without going\n",
" // through eve.\n",
" Element.prototype.attribute = function(key, val) {\n",
" if (val === undefined) {\n",
" return this.node.getAttribute(key, val);\n",
" } else {\n",
" return this.node.setAttribute(key, val);\n",
" }\n",
" };\n",
"});\n",
"\n",
"\n",
"// When the plot is moused over, emphasize the grid lines.\n",
"Gadfly.plot_mouseover = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
"\n",
" var xgridlines = root.select(\".xgridlines\"),\n",
" ygridlines = root.select(\".ygridlines\");\n",
"\n",
" xgridlines.data(\"unfocused_strokedash\",\n",
" xgridlines.attr(\"stroke-dasharray\").replace(/px/g, \"mm\"))\n",
" ygridlines.data(\"unfocused_strokedash\",\n",
" ygridlines.attr(\"stroke-dasharray\").replace(/px/g, \"mm\"))\n",
"\n",
" // emphasize grid lines\n",
" var destcolor = root.data(\"focused_xgrid_color\");\n",
" xgridlines.attr(\"stroke-dasharray\", \"none\")\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" destcolor = root.data(\"focused_ygrid_color\");\n",
" ygridlines.attr(\"stroke-dasharray\", \"none\")\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" // reveal zoom slider\n",
" root.select(\".zoomslider\")\n",
" .animate({opacity: 1.0}, 250);\n",
"};\n",
"\n",
"\n",
"// Unemphasize grid lines on mouse out.\n",
"Gadfly.plot_mouseout = function(event) {\n",
" var root = this.plotroot();\n",
" var xgridlines = root.select(\".xgridlines\"),\n",
" ygridlines = root.select(\".ygridlines\");\n",
"\n",
" var destcolor = root.data(\"unfocused_xgrid_color\");\n",
"\n",
" xgridlines.attr(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" destcolor = root.data(\"unfocused_ygrid_color\");\n",
" ygridlines.attr(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" // hide zoom slider\n",
" root.select(\".zoomslider\")\n",
" .animate({opacity: 0.0}, 250);\n",
"};\n",
"\n",
"\n",
"var set_geometry_transform = function(root, tx, ty, scale) {\n",
" var xscalable = root.hasClass(\"xscalable\"),\n",
" yscalable = root.hasClass(\"yscalable\");\n",
"\n",
" var old_scale = root.data(\"scale\");\n",
"\n",
" var xscale = xscalable ? scale : 1.0,\n",
" yscale = yscalable ? scale : 1.0;\n",
"\n",
" tx = xscalable ? tx : 0.0;\n",
" ty = yscalable ? ty : 0.0;\n",
"\n",
" var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
"\n",
" root.selectAll(\".geometry, image\")\n",
" .forEach(function (element, i) {\n",
" element.transform(t);\n",
" });\n",
"\n",
" bounds = root.plotbounds();\n",
"\n",
" if (yscalable) {\n",
" var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
" root.selectAll(\".xfixed\")\n",
" .forEach(function (element, i) {\n",
" element.transform(xfixed_t);\n",
" });\n",
"\n",
" root.select(\".ylabels\")\n",
" .transform(xfixed_t)\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var cx = element.asPX(\"x\"),\n",
" cy = element.asPX(\"y\");\n",
" var st = element.data(\"static_transform\");\n",
" unscale_t = new Snap.Matrix();\n",
" unscale_t.scale(1, 1/scale, cx, cy).add(st);\n",
" element.transform(unscale_t);\n",
"\n",
" var y = cy * scale + ty;\n",
" element.attr(\"visibility\",\n",
" bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" if (xscalable) {\n",
" var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
" var xtrans = new Snap.Matrix().translate(tx, 0);\n",
" root.selectAll(\".yfixed\")\n",
" .forEach(function (element, i) {\n",
" element.transform(yfixed_t);\n",
" });\n",
"\n",
" root.select(\".xlabels\")\n",
" .transform(yfixed_t)\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var cx = element.asPX(\"x\"),\n",
" cy = element.asPX(\"y\");\n",
" var st = element.data(\"static_transform\");\n",
" unscale_t = new Snap.Matrix();\n",
" unscale_t.scale(1/scale, 1, cx, cy).add(st);\n",
"\n",
" element.transform(unscale_t);\n",
"\n",
" var x = cx * scale + tx;\n",
" element.attr(\"visibility\",\n",
" bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" // we must unscale anything that is scale invariance: widths, raiduses, etc.\n",
" var size_attribs = [\"font-size\"];\n",
" var unscaled_selection = \".geometry, .geometry *\";\n",
" if (xscalable) {\n",
" size_attribs.push(\"rx\");\n",
" unscaled_selection += \", .xgridlines\";\n",
" }\n",
" if (yscalable) {\n",
" size_attribs.push(\"ry\");\n",
" unscaled_selection += \", .ygridlines\";\n",
" }\n",
"\n",
" root.selectAll(unscaled_selection)\n",
" .forEach(function (element, i) {\n",
" // circle need special help\n",
" if (element.node.nodeName == \"circle\") {\n",
" var cx = element.attribute(\"cx\"),\n",
" cy = element.attribute(\"cy\");\n",
" unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,\n",
" cx, cy);\n",
" element.transform(unscale_t);\n",
" return;\n",
" }\n",
"\n",
" for (i in size_attribs) {\n",
" var key = size_attribs[i];\n",
" var val = parseFloat(element.attribute(key));\n",
" if (val !== undefined && val != 0 && !isNaN(val)) {\n",
" element.attribute(key, val * old_scale / scale);\n",
" }\n",
" }\n",
" });\n",
"};\n",
"\n",
"\n",
"// Find the most appropriate tick scale and update label visibility.\n",
"var update_tickscale = function(root, scale, axis) {\n",
" if (!root.hasClass(axis + \"scalable\")) return;\n",
"\n",
" var tickscales = root.data(axis + \"tickscales\");\n",
" var best_tickscale = 1.0;\n",
" var best_tickscale_dist = Infinity;\n",
" for (tickscale in tickscales) {\n",
" var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
" if (dist < best_tickscale_dist) {\n",
" best_tickscale_dist = dist;\n",
" best_tickscale = tickscale;\n",
" }\n",
" }\n",
"\n",
" if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
" root.data(axis + \"tickscale\", best_tickscale);\n",
" var mark_inscale_gridlines = function (element, i) {\n",
" var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
" element.attribute(\"gadfly:inscale\", inscale);\n",
" element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
" };\n",
"\n",
" var mark_inscale_labels = function (element, i) {\n",
" var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
" element.attribute(\"gadfly:inscale\", inscale);\n",
" element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
" };\n",
"\n",
" root.select(\".\" + axis + \"gridlines\").selectAll(\"path\").forEach(mark_inscale_gridlines);\n",
" root.select(\".\" + axis + \"labels\").selectAll(\"text\").forEach(mark_inscale_labels);\n",
" }\n",
"};\n",
"\n",
"\n",
"var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
" var old_scale = root.data(\"scale\");\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" // compute the viewport derived from tx, ty, and scale\n",
" var x_min = -width * scale - (scale * width - width),\n",
" x_max = width * scale,\n",
" y_min = -height * scale - (scale * height - height),\n",
" y_max = height * scale;\n",
"\n",
" var x0 = bounds.x0 - scale * bounds.x0,\n",
" y0 = bounds.y0 - scale * bounds.y0;\n",
"\n",
" var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
" ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
"\n",
" tx += x0;\n",
" ty += y0;\n",
"\n",
" // when the scale change, we may need to alter which set of\n",
" // ticks is being displayed\n",
" if (scale != old_scale) {\n",
" update_tickscale(root, scale, \"x\");\n",
" update_tickscale(root, scale, \"y\");\n",
" }\n",
"\n",
" set_geometry_transform(root, tx, ty, scale);\n",
"\n",
" root.data(\"scale\", scale);\n",
" root.data(\"tx\", tx);\n",
" root.data(\"ty\", ty);\n",
"};\n",
"\n",
"\n",
"var scale_centered_translation = function(root, scale) {\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var scale0 = root.data(\"scale\");\n",
"\n",
" // how off from center the current view is\n",
" var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
" yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
"\n",
" // rescale offsets\n",
" xoff = xoff * scale / scale0;\n",
" yoff = yoff * scale / scale0;\n",
"\n",
" // adjust for the panel position being scaled\n",
" var x_edge_adjust = bounds.x0 * (1 - scale),\n",
" y_edge_adjust = bounds.y0 * (1 - scale);\n",
"\n",
" return {\n",
" x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
" y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
" };\n",
"};\n",
"\n",
"\n",
"// Initialize data for panning zooming if it isn't already.\n",
"var init_pan_zoom = function(root) {\n",
" if (root.data(\"zoompan-ready\")) {\n",
" return;\n",
" }\n",
"\n",
" // The non-scaling-stroke trick. Rather than try to correct for the\n",
" // stroke-width when zooming, we force it to a fixed value.\n",
" var px_per_mm = root.node.getCTM().a;\n",
"\n",
" // Drag events report deltas in pixels, which we'd like to convert to\n",
" // millimeters.\n",
" root.data(\"px_per_mm\", px_per_mm);\n",
"\n",
" root.selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
" if (sw > 0) {\n",
" element.attribute(\"stroke-width\", sw);\n",
" element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
" }\n",
" });\n",
"\n",
" // Store ticks labels original tranformation\n",
" root.selectAll(\".xlabels > text, .ylabels > text\")\n",
" .forEach(function (element, i) {\n",
" var lm = element.transform().localMatrix;\n",
" element.data(\"static_transform\",\n",
" new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
" });\n",
"\n",
" if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
" if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
" if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
" if (root.data(\"xtickscales\") === undefined) {\n",
"\n",
" // index all the tick scales that are listed\n",
" var xtickscales = {};\n",
" var ytickscales = {};\n",
" var add_x_tick_scales = function (element, i) {\n",
" xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
" var add_y_tick_scales = function (element, i) {\n",
" ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
"\n",
" root.select(\".xgridlines\").selectAll(\"path\").forEach(add_x_tick_scales);\n",
" root.select(\".ygridlines\").selectAll(\"path\").forEach(add_y_tick_scales);\n",
" root.select(\".xlabels\").selectAll(\"text\").forEach(add_x_tick_scales);\n",
" root.select(\".ylabels\").selectAll(\"text\").forEach(add_y_tick_scales);\n",
"\n",
" root.data(\"xtickscales\", xtickscales);\n",
" root.data(\"ytickscales\", ytickscales);\n",
" root.data(\"xtickscale\", 1.0);\n",
" }\n",
"\n",
" var min_scale = 1.0, max_scale = 1.0;\n",
" for (scale in xtickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" for (scale in ytickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" root.data(\"min_scale\", min_scale);\n",
" root.data(\"max_scale\", max_scale);\n",
"\n",
" // store the original positions of labels\n",
" root.select(\".xlabels\")\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"x\", element.asPX(\"x\"));\n",
" });\n",
"\n",
" root.select(\".ylabels\")\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"y\", element.asPX(\"y\"));\n",
" });\n",
"\n",
" // mark grid lines and ticks as in or out of scale.\n",
" var mark_inscale = function (element, i) {\n",
" element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
" };\n",
"\n",
" root.select(\".xgridlines\").selectAll(\"path\").forEach(mark_inscale);\n",
" root.select(\".ygridlines\").selectAll(\"path\").forEach(mark_inscale);\n",
" root.select(\".xlabels\").selectAll(\"text\").forEach(mark_inscale);\n",
" root.select(\".ylabels\").selectAll(\"text\").forEach(mark_inscale);\n",
"\n",
" // figure out the upper ond lower bounds on panning using the maximum\n",
" // and minum grid lines\n",
" var bounds = root.plotbounds();\n",
" var pan_bounds = {\n",
" x0: 0.0,\n",
" y0: 0.0,\n",
" x1: 0.0,\n",
" y1: 0.0\n",
" };\n",
"\n",
" root.select(\".xgridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
" pan_bounds.x0 = bounds.x1 - bbox.x;\n",
" }\n",
" if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
" pan_bounds.x1 = bounds.x0 - bbox.x;\n",
" }\n",
" }\n",
" });\n",
"\n",
" root.select(\".ygridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
" pan_bounds.y0 = bounds.y1 - bbox.y;\n",
" }\n",
" if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
" pan_bounds.y1 = bounds.y0 - bbox.y;\n",
" }\n",
" }\n",
" });\n",
"\n",
" // nudge these values a little\n",
" pan_bounds.x0 -= 5;\n",
" pan_bounds.x1 += 5;\n",
" pan_bounds.y0 -= 5;\n",
" pan_bounds.y1 += 5;\n",
" root.data(\"pan_bounds\", pan_bounds);\n",
"\n",
" // Set all grid lines at scale 1.0 to visible. Out of bounds lines\n",
" // will be clipped.\n",
" root.select(\".xgridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
"\n",
" root.select(\".ygridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
"\n",
" root.data(\"zoompan-ready\", true)\n",
"};\n",
"\n",
"\n",
"// Panning\n",
"Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
" var root = this.plotroot();\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var dx0 = root.data(\"dx\"),\n",
" dy0 = root.data(\"dy\");\n",
"\n",
" root.data(\"dx\", dx);\n",
" root.data(\"dy\", dy);\n",
"\n",
" dx = dx - dx0;\n",
" dy = dy - dy0;\n",
"\n",
" var tx = tx0 + dx,\n",
" ty = ty0 + dy;\n",
"\n",
" set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
" var root = this.plotroot();\n",
" root.data(\"dx\", 0);\n",
" root.data(\"dy\", 0);\n",
" init_pan_zoom(root);\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onend = function(event) {\n",
" var root = this.plotroot();\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_scroll = function(event) {\n",
" if (event.shiftKey) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var new_scale = root.data(\"scale\") * Math.pow(2, 0.002 * event.wheelDelta);\n",
" new_scale = Math.max(\n",
" root.data(\"min_scale\"),\n",
" Math.min(root.data(\"max_scale\"), new_scale))\n",
" update_plot_scale(root, new_scale);\n",
" event.stopPropagation();\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseover = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseout = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomout_click = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var min_scale = root.data(\"min_scale\"),\n",
" scale = root.data(\"scale\");\n",
" Snap.animate(\n",
" scale,\n",
" Math.max(min_scale, scale / 1.5),\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomin_click = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var max_scale = root.data(\"max_scale\"),\n",
" scale = root.data(\"scale\");\n",
"\n",
" Snap.animate(\n",
" scale,\n",
" Math.min(max_scale, scale * 1.5),\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_track_click = function(event) {\n",
" // TODO\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_mousedown = function(event) {\n",
" this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_mouseup = function(event) {\n",
" this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"// compute the position in [0, 1] of the zoom slider thumb from the current scale\n",
"var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
" if (scale >= 1.0) {\n",
" return 0.5 + 0.5 * (Math.log(scale) / Math.log(max_scale));\n",
" }\n",
" else {\n",
" return 0.5 * (Math.log(scale) - Math.log(min_scale)) / (0 - Math.log(min_scale));\n",
" }\n",
"}\n",
"\n",
"\n",
"var update_plot_scale = function(root, new_scale) {\n",
" var trans = scale_centered_translation(root, new_scale);\n",
" set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
"\n",
" root.selectAll(\".zoomslider_thumb\")\n",
" .forEach(function (element, i) {\n",
" var min_pos = element.data(\"min_pos\"),\n",
" max_pos = element.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\");\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
" element.transform(new Snap.Matrix().translate(\n",
" Math.max(min_pos, Math.min(\n",
" max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
" });\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y) {\n",
" var root = this.plotroot();\n",
" var min_pos = this.data(\"min_pos\"),\n",
" max_pos = this.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\"),\n",
" old_scale = root.data(\"old_scale\");\n",
"\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
" dx / (max_pos - min_pos);\n",
"\n",
" // compute the new scale\n",
" var new_scale;\n",
" if (xpos >= 0.5) {\n",
" new_scale = Math.exp(2.0 * (xpos - 0.5) * Math.log(max_scale));\n",
" }\n",
" else {\n",
" new_scale = Math.exp(2.0 * xpos * (0 - Math.log(min_scale)) +\n",
" Math.log(min_scale));\n",
" }\n",
" new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
"\n",
" update_plot_scale(root, new_scale);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragstart = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
"\n",
" // keep track of what the scale was when we started dragging\n",
" root.data(\"old_scale\", root.data(\"scale\"));\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragend = function(event) {\n",
"};\n",
"\n",
"\n",
"var toggle_color_class = function(root, color_class, ison) {\n",
" var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
" var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
" if (ison) {\n",
" guides.animate({opacity: 0.5}, 250);\n",
" geoms.animate({opacity: 0.0}, 250);\n",
" } else {\n",
" guides.animate({opacity: 1.0}, 250);\n",
" geoms.animate({opacity: 1.0}, 250);\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.colorkey_swatch_click = function(event) {\n",
" var root = this.plotroot();\n",
" var color_class = this.data(\"color_class\");\n",
"\n",
" if (event.shiftKey) {\n",
" root.selectAll(\".colorkey text\")\n",
" .forEach(function (element) {\n",
" var other_color_class = element.data(\"color_class\");\n",
" if (other_color_class != color_class) {\n",
" toggle_color_class(root, other_color_class,\n",
" element.attr(\"opacity\") == 1.0);\n",
" }\n",
" });\n",
" } else {\n",
" toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
" }\n",
"};\n",
"\n",
"\n",
"return Gadfly;\n",
"\n",
"}));\n",
"\n",
"\n",
"//@ sourceURL=gadfly.js\n",
"\n",
"(function (glob, factory) {\n",
" // AMD support\n",
" if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
" require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
" factory(Snap, Gadfly);\n",
" });\n",
" } else {\n",
" factory(glob.Snap, glob.Gadfly);\n",
" }\n",
"})(window, function (Snap, Gadfly) {\n",
" var fig = Snap(\"#fig-abdb6a2fa6fa4f62ba063435a589e866\");\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-4\")\n",
" .mouseenter(Gadfly.plot_mouseover)\n",
".mouseleave(Gadfly.plot_mouseout)\n",
".mousewheel(Gadfly.guide_background_scroll)\n",
".drag(Gadfly.guide_background_drag_onmove,\n",
" Gadfly.guide_background_drag_onstart,\n",
" Gadfly.guide_background_drag_onend)\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-7\")\n",
" .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-7\")\n",
" .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-8\")\n",
" .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-8\")\n",
" .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-12\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-12\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-12\")\n",
" .click(Gadfly.zoomslider_zoomin_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-14\")\n",
" .data(\"max_pos\", 120.42)\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-14\")\n",
" .data(\"min_pos\", 103.42)\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-14\")\n",
" .click(Gadfly.zoomslider_track_click);\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-15\")\n",
" .data(\"max_pos\", 120.42)\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-15\")\n",
" .data(\"min_pos\", 103.42)\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-15\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-15\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-15\")\n",
" .drag(Gadfly.zoomslider_thumb_dragmove,\n",
" Gadfly.zoomslider_thumb_dragstart,\n",
" Gadfly.zoomslider_thumb_dragend)\n",
".mousedown(Gadfly.zoomslider_thumb_mousedown)\n",
".mouseup(Gadfly.zoomslider_thumb_mouseup)\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-16\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-16\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-abdb6a2fa6fa4f62ba063435a589e866-element-16\")\n",
" .click(Gadfly.zoomslider_zoomout_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
" });\n",
"]]> </script>\n",
"</svg>\n"
],
"text/plain": [
"Plot(...)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sys = Particle(5.0,0)\n",
"δt = 0.01\n",
"N = 500\n",
"t_range = range(0.0,δt,N)\n",
"\n",
"history = Particle[]\n",
"\n",
"for t in t_range\n",
" push!(history,sys)\n",
" x, v = velocity_verlet_step(t,δt,sys)\n",
" sys = Particle(x, v)\n",
"end\n",
"\n",
"x_range = map(s->s.x,history)\n",
"y_range = map(s->s.v,history)\n",
"\n",
"function energy(s)\n",
" return (m * s.v * s.v + (k/m) * s.x * s.x) / 2 \n",
"end\n",
"\n",
"e_range = map(s->energy(s),history)\n",
"\n",
"\n",
"plot(x=t_range,y=e_range,Geom.line)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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" if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
" root.data(axis + \"tickscale\", best_tickscale);\n",
" var mark_inscale_gridlines = function (element, i) {\n",
" var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
" element.attribute(\"gadfly:inscale\", inscale);\n",
" element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
" };\n",
"\n",
" var mark_inscale_labels = function (element, i) {\n",
" var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
" element.attribute(\"gadfly:inscale\", inscale);\n",
" element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
" };\n",
"\n",
" root.select(\".\" + axis + \"gridlines\").selectAll(\"path\").forEach(mark_inscale_gridlines);\n",
" root.select(\".\" + axis + \"labels\").selectAll(\"text\").forEach(mark_inscale_labels);\n",
" }\n",
"};\n",
"\n",
"\n",
"var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
" var old_scale = root.data(\"scale\");\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" // compute the viewport derived from tx, ty, and scale\n",
" var x_min = -width * scale - (scale * width - width),\n",
" x_max = width * scale,\n",
" y_min = -height * scale - (scale * height - height),\n",
" y_max = height * scale;\n",
"\n",
" var x0 = bounds.x0 - scale * bounds.x0,\n",
" y0 = bounds.y0 - scale * bounds.y0;\n",
"\n",
" var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
" ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
"\n",
" tx += x0;\n",
" ty += y0;\n",
"\n",
" // when the scale change, we may need to alter which set of\n",
" // ticks is being displayed\n",
" if (scale != old_scale) {\n",
" update_tickscale(root, scale, \"x\");\n",
" update_tickscale(root, scale, \"y\");\n",
" }\n",
"\n",
" set_geometry_transform(root, tx, ty, scale);\n",
"\n",
" root.data(\"scale\", scale);\n",
" root.data(\"tx\", tx);\n",
" root.data(\"ty\", ty);\n",
"};\n",
"\n",
"\n",
"var scale_centered_translation = function(root, scale) {\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var scale0 = root.data(\"scale\");\n",
"\n",
" // how off from center the current view is\n",
" var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
" yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
"\n",
" // rescale offsets\n",
" xoff = xoff * scale / scale0;\n",
" yoff = yoff * scale / scale0;\n",
"\n",
" // adjust for the panel position being scaled\n",
" var x_edge_adjust = bounds.x0 * (1 - scale),\n",
" y_edge_adjust = bounds.y0 * (1 - scale);\n",
"\n",
" return {\n",
" x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
" y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
" };\n",
"};\n",
"\n",
"\n",
"// Initialize data for panning zooming if it isn't already.\n",
"var init_pan_zoom = function(root) {\n",
" if (root.data(\"zoompan-ready\")) {\n",
" return;\n",
" }\n",
"\n",
" // The non-scaling-stroke trick. Rather than try to correct for the\n",
" // stroke-width when zooming, we force it to a fixed value.\n",
" var px_per_mm = root.node.getCTM().a;\n",
"\n",
" // Drag events report deltas in pixels, which we'd like to convert to\n",
" // millimeters.\n",
" root.data(\"px_per_mm\", px_per_mm);\n",
"\n",
" root.selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
" if (sw > 0) {\n",
" element.attribute(\"stroke-width\", sw);\n",
" element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
" }\n",
" });\n",
"\n",
" // Store ticks labels original tranformation\n",
" root.selectAll(\".xlabels > text, .ylabels > text\")\n",
" .forEach(function (element, i) {\n",
" var lm = element.transform().localMatrix;\n",
" element.data(\"static_transform\",\n",
" new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
" });\n",
"\n",
" if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
" if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
" if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
" if (root.data(\"xtickscales\") === undefined) {\n",
"\n",
" // index all the tick scales that are listed\n",
" var xtickscales = {};\n",
" var ytickscales = {};\n",
" var add_x_tick_scales = function (element, i) {\n",
" xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
" var add_y_tick_scales = function (element, i) {\n",
" ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
"\n",
" root.select(\".xgridlines\").selectAll(\"path\").forEach(add_x_tick_scales);\n",
" root.select(\".ygridlines\").selectAll(\"path\").forEach(add_y_tick_scales);\n",
" root.select(\".xlabels\").selectAll(\"text\").forEach(add_x_tick_scales);\n",
" root.select(\".ylabels\").selectAll(\"text\").forEach(add_y_tick_scales);\n",
"\n",
" root.data(\"xtickscales\", xtickscales);\n",
" root.data(\"ytickscales\", ytickscales);\n",
" root.data(\"xtickscale\", 1.0);\n",
" }\n",
"\n",
" var min_scale = 1.0, max_scale = 1.0;\n",
" for (scale in xtickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" for (scale in ytickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" root.data(\"min_scale\", min_scale);\n",
" root.data(\"max_scale\", max_scale);\n",
"\n",
" // store the original positions of labels\n",
" root.select(\".xlabels\")\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"x\", element.asPX(\"x\"));\n",
" });\n",
"\n",
" root.select(\".ylabels\")\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"y\", element.asPX(\"y\"));\n",
" });\n",
"\n",
" // mark grid lines and ticks as in or out of scale.\n",
" var mark_inscale = function (element, i) {\n",
" element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
" };\n",
"\n",
" root.select(\".xgridlines\").selectAll(\"path\").forEach(mark_inscale);\n",
" root.select(\".ygridlines\").selectAll(\"path\").forEach(mark_inscale);\n",
" root.select(\".xlabels\").selectAll(\"text\").forEach(mark_inscale);\n",
" root.select(\".ylabels\").selectAll(\"text\").forEach(mark_inscale);\n",
"\n",
" // figure out the upper ond lower bounds on panning using the maximum\n",
" // and minum grid lines\n",
" var bounds = root.plotbounds();\n",
" var pan_bounds = {\n",
" x0: 0.0,\n",
" y0: 0.0,\n",
" x1: 0.0,\n",
" y1: 0.0\n",
" };\n",
"\n",
" root.select(\".xgridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
" pan_bounds.x0 = bounds.x1 - bbox.x;\n",
" }\n",
" if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
" pan_bounds.x1 = bounds.x0 - bbox.x;\n",
" }\n",
" }\n",
" });\n",
"\n",
" root.select(\".ygridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
" pan_bounds.y0 = bounds.y1 - bbox.y;\n",
" }\n",
" if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
" pan_bounds.y1 = bounds.y0 - bbox.y;\n",
" }\n",
" }\n",
" });\n",
"\n",
" // nudge these values a little\n",
" pan_bounds.x0 -= 5;\n",
" pan_bounds.x1 += 5;\n",
" pan_bounds.y0 -= 5;\n",
" pan_bounds.y1 += 5;\n",
" root.data(\"pan_bounds\", pan_bounds);\n",
"\n",
" // Set all grid lines at scale 1.0 to visible. Out of bounds lines\n",
" // will be clipped.\n",
" root.select(\".xgridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
"\n",
" root.select(\".ygridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
"\n",
" root.data(\"zoompan-ready\", true)\n",
"};\n",
"\n",
"\n",
"// Panning\n",
"Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
" var root = this.plotroot();\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var dx0 = root.data(\"dx\"),\n",
" dy0 = root.data(\"dy\");\n",
"\n",
" root.data(\"dx\", dx);\n",
" root.data(\"dy\", dy);\n",
"\n",
" dx = dx - dx0;\n",
" dy = dy - dy0;\n",
"\n",
" var tx = tx0 + dx,\n",
" ty = ty0 + dy;\n",
"\n",
" set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
" var root = this.plotroot();\n",
" root.data(\"dx\", 0);\n",
" root.data(\"dy\", 0);\n",
" init_pan_zoom(root);\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onend = function(event) {\n",
" var root = this.plotroot();\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_scroll = function(event) {\n",
" if (event.shiftKey) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var new_scale = root.data(\"scale\") * Math.pow(2, 0.002 * event.wheelDelta);\n",
" new_scale = Math.max(\n",
" root.data(\"min_scale\"),\n",
" Math.min(root.data(\"max_scale\"), new_scale))\n",
" update_plot_scale(root, new_scale);\n",
" event.stopPropagation();\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseover = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseout = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomout_click = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var min_scale = root.data(\"min_scale\"),\n",
" scale = root.data(\"scale\");\n",
" Snap.animate(\n",
" scale,\n",
" Math.max(min_scale, scale / 1.5),\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomin_click = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var max_scale = root.data(\"max_scale\"),\n",
" scale = root.data(\"scale\");\n",
"\n",
" Snap.animate(\n",
" scale,\n",
" Math.min(max_scale, scale * 1.5),\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_track_click = function(event) {\n",
" // TODO\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_mousedown = function(event) {\n",
" this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_mouseup = function(event) {\n",
" this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"// compute the position in [0, 1] of the zoom slider thumb from the current scale\n",
"var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
" if (scale >= 1.0) {\n",
" return 0.5 + 0.5 * (Math.log(scale) / Math.log(max_scale));\n",
" }\n",
" else {\n",
" return 0.5 * (Math.log(scale) - Math.log(min_scale)) / (0 - Math.log(min_scale));\n",
" }\n",
"}\n",
"\n",
"\n",
"var update_plot_scale = function(root, new_scale) {\n",
" var trans = scale_centered_translation(root, new_scale);\n",
" set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
"\n",
" root.selectAll(\".zoomslider_thumb\")\n",
" .forEach(function (element, i) {\n",
" var min_pos = element.data(\"min_pos\"),\n",
" max_pos = element.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\");\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
" element.transform(new Snap.Matrix().translate(\n",
" Math.max(min_pos, Math.min(\n",
" max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
" });\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y) {\n",
" var root = this.plotroot();\n",
" var min_pos = this.data(\"min_pos\"),\n",
" max_pos = this.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\"),\n",
" old_scale = root.data(\"old_scale\");\n",
"\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
" dx / (max_pos - min_pos);\n",
"\n",
" // compute the new scale\n",
" var new_scale;\n",
" if (xpos >= 0.5) {\n",
" new_scale = Math.exp(2.0 * (xpos - 0.5) * Math.log(max_scale));\n",
" }\n",
" else {\n",
" new_scale = Math.exp(2.0 * xpos * (0 - Math.log(min_scale)) +\n",
" Math.log(min_scale));\n",
" }\n",
" new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
"\n",
" update_plot_scale(root, new_scale);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragstart = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
"\n",
" // keep track of what the scale was when we started dragging\n",
" root.data(\"old_scale\", root.data(\"scale\"));\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragend = function(event) {\n",
"};\n",
"\n",
"\n",
"var toggle_color_class = function(root, color_class, ison) {\n",
" var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
" var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
" if (ison) {\n",
" guides.animate({opacity: 0.5}, 250);\n",
" geoms.animate({opacity: 0.0}, 250);\n",
" } else {\n",
" guides.animate({opacity: 1.0}, 250);\n",
" geoms.animate({opacity: 1.0}, 250);\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.colorkey_swatch_click = function(event) {\n",
" var root = this.plotroot();\n",
" var color_class = this.data(\"color_class\");\n",
"\n",
" if (event.shiftKey) {\n",
" root.selectAll(\".colorkey text\")\n",
" .forEach(function (element) {\n",
" var other_color_class = element.data(\"color_class\");\n",
" if (other_color_class != color_class) {\n",
" toggle_color_class(root, other_color_class,\n",
" element.attr(\"opacity\") == 1.0);\n",
" }\n",
" });\n",
" } else {\n",
" toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
" }\n",
"};\n",
"\n",
"\n",
"return Gadfly;\n",
"\n",
"}));\n",
"\n",
"\n",
"//@ sourceURL=gadfly.js\n",
"\n",
"(function (glob, factory) {\n",
" // AMD support\n",
" if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
" require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
" factory(Snap, Gadfly);\n",
" });\n",
" } else {\n",
" factory(glob.Snap, glob.Gadfly);\n",
" }\n",
"})(window, function (Snap, Gadfly) {\n",
" var fig = Snap(\"#fig-e798002e428444eba6b60f8cf8e85683\");\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-4\")\n",
" .mouseenter(Gadfly.plot_mouseover)\n",
".mouseleave(Gadfly.plot_mouseout)\n",
".mousewheel(Gadfly.guide_background_scroll)\n",
".drag(Gadfly.guide_background_drag_onmove,\n",
" Gadfly.guide_background_drag_onstart,\n",
" Gadfly.guide_background_drag_onend)\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-7\")\n",
" .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-7\")\n",
" .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-8\")\n",
" .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-8\")\n",
" .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-12\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-12\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-12\")\n",
" .click(Gadfly.zoomslider_zoomin_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-14\")\n",
" .data(\"max_pos\", 120.42)\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-14\")\n",
" .data(\"min_pos\", 103.42)\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-14\")\n",
" .click(Gadfly.zoomslider_track_click);\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-15\")\n",
" .data(\"max_pos\", 120.42)\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-15\")\n",
" .data(\"min_pos\", 103.42)\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-15\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-15\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-15\")\n",
" .drag(Gadfly.zoomslider_thumb_dragmove,\n",
" Gadfly.zoomslider_thumb_dragstart,\n",
" Gadfly.zoomslider_thumb_dragend)\n",
".mousedown(Gadfly.zoomslider_thumb_mousedown)\n",
".mouseup(Gadfly.zoomslider_thumb_mouseup)\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-16\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-16\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-e798002e428444eba6b60f8cf8e85683-element-16\")\n",
" .click(Gadfly.zoomslider_zoomout_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
" });\n",
"]]> </script>\n",
"</svg>\n"
],
"text/plain": [
"Plot(...)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function euler_step ( t :: Real, dt :: Real, s )\n",
" rhsv = force(s)\n",
" v = s.v + dt*rhsv\n",
" rhsx = v\n",
" x = s.x + dt*rhsx\n",
" return x, v\n",
"end\n",
"\n",
"function midpoint_step ( t :: Real, dt :: Real, s )\n",
" v_half = s.v + 0.5*dt*force(s)\n",
" x_half = s.x + 0.5*dt*s.v \n",
" x = s.x + dt*v_half\n",
" v = s.v + dt*force(Particle(x_half,v_half))\n",
" return x, v\n",
"end\n",
"\n",
"sys = Particle(5.0,0)\n",
"\n",
"history = Particle[]\n",
"for t in t_range\n",
" push!(history,sys)\n",
" x, v = midpoint_step(t,δt,sys)\n",
" sys = Particle(x,v)\n",
"end\n",
"\n",
"x_range = map(s->s.x,history)\n",
"y_range = map(s->s.v,history)\n",
"e_range = map(s->energy(s),history)\n",
"\n",
"plot(x=t_range,y=e_range,Geom.line)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"matrix\" values=\"{a} {b} {c} 0 0 {d} {e} {f} 0 0 {g} {h} {i} 0 0 0 0 0 1 0\"/>',{a:0.393+0.607*(1-d),b:0.769-0.769*(1-d),c:0.189-0.189*(1-d),d:0.349-0.349*(1-d),e:0.686+0.314*(1-d),f:0.168-0.168*(1-d),g:0.272-0.272*(1-d),h:0.534-0.534*(1-d),i:0.131+0.869*(1-d)})};a.filter.sepia.toString=function(){return this()};a.filter.saturate=function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"saturate\" values=\"{amount}\"/>',{amount:1-\n",
"d})};a.filter.saturate.toString=function(){return this()};a.filter.hueRotate=function(d){return a.format('<feColorMatrix type=\"hueRotate\" values=\"{angle}\"/>',{angle:d||0})};a.filter.hueRotate.toString=function(){return this()};a.filter.invert=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncG type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncB type=\"table\" tableValues=\"{amount} {amount2}\"/></feComponentTransfer>',{amount:d,\n",
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"]]> </script>\n",
"<script> <![CDATA[\n",
"\n",
"(function (glob, factory) {\n",
" // AMD support\n",
" if (typeof define === \"function\" && define.amd) {\n",
" // Define as an anonymous module\n",
" define(\"Gadfly\", [\"Snap.svg\"], function (Snap) {\n",
" return factory(Snap);\n",
" });\n",
" } else {\n",
" // Browser globals (glob is window)\n",
" // Snap adds itself to window\n",
" glob.Gadfly = factory(glob.Snap);\n",
" }\n",
"}(this, function (Snap) {\n",
"\n",
"var Gadfly = {};\n",
"\n",
"// Get an x/y coordinate value in pixels\n",
"var xPX = function(fig, x) {\n",
" var client_box = fig.node.getBoundingClientRect();\n",
" return x * fig.node.viewBox.baseVal.width / client_box.width;\n",
"};\n",
"\n",
"var yPX = function(fig, y) {\n",
" var client_box = fig.node.getBoundingClientRect();\n",
" return y * fig.node.viewBox.baseVal.height / client_box.height;\n",
"};\n",
"\n",
"\n",
"Snap.plugin(function (Snap, Element, Paper, global) {\n",
" // Traverse upwards from a snap element to find and return the first\n",
" // note with the \"plotroot\" class.\n",
" Element.prototype.plotroot = function () {\n",
" var element = this;\n",
" while (!element.hasClass(\"plotroot\") && element.parent() != null) {\n",
" element = element.parent();\n",
" }\n",
" return element;\n",
" };\n",
"\n",
" Element.prototype.svgroot = function () {\n",
" var element = this;\n",
" while (element.node.nodeName != \"svg\" && element.parent() != null) {\n",
" element = element.parent();\n",
" }\n",
" return element;\n",
" };\n",
"\n",
" Element.prototype.plotbounds = function () {\n",
" var root = this.plotroot()\n",
" var bbox = root.select(\".guide.background\").node.getBBox();\n",
" return {\n",
" x0: bbox.x,\n",
" x1: bbox.x + bbox.width,\n",
" y0: bbox.y,\n",
" y1: bbox.y + bbox.height\n",
" };\n",
" };\n",
"\n",
" Element.prototype.plotcenter = function () {\n",
" var root = this.plotroot()\n",
" var bbox = root.select(\".guide.background\").node.getBBox();\n",
" return {\n",
" x: bbox.x + bbox.width / 2,\n",
" y: bbox.y + bbox.height / 2\n",
" };\n",
" };\n",
"\n",
" // Emulate IE style mouseenter/mouseleave events, since Microsoft always\n",
" // does everything right.\n",
" // See: http://www.dynamic-tools.net/toolbox/isMouseLeaveOrEnter/\n",
" var events = [\"mouseenter\", \"mouseleave\"];\n",
"\n",
" for (i in events) {\n",
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" var event_name = events[i];\n",
" Element.prototype[event_name] = function (fn, scope) {\n",
" if (Snap.is(fn, \"function\")) {\n",
" var fn2 = function (event) {\n",
" if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
" return;\n",
" }\n",
"\n",
" var reltg = event.relatedTarget ? event.relatedTarget :\n",
" event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
" while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
"\n",
" if (reltg != this.node) {\n",
" return fn.apply(this, event);\n",
" }\n",
" };\n",
"\n",
" if (event_name == \"mouseenter\") {\n",
" this.mouseover(fn2, scope);\n",
" } else {\n",
" this.mouseout(fn2, scope);\n",
" }\n",
" }\n",
" return this;\n",
" };\n",
" })(events[i]);\n",
" }\n",
"\n",
"\n",
" Element.prototype.mousewheel = function (fn, scope) {\n",
" if (Snap.is(fn, \"function\")) {\n",
" var el = this;\n",
" var fn2 = function (event) {\n",
" fn.apply(el, [event]);\n",
" };\n",
" }\n",
"\n",
" this.node.addEventListener(\n",
" /Firefox/i.test(navigator.userAgent) ? \"DOMMouseScroll\" : \"mousewheel\",\n",
" fn2);\n",
"\n",
" return this;\n",
" };\n",
"\n",
"\n",
" // Snap's attr function can be too slow for things like panning/zooming.\n",
" // This is a function to directly update element attributes without going\n",
" // through eve.\n",
" Element.prototype.attribute = function(key, val) {\n",
" if (val === undefined) {\n",
" return this.node.getAttribute(key, val);\n",
" } else {\n",
" return this.node.setAttribute(key, val);\n",
" }\n",
" };\n",
"});\n",
"\n",
"\n",
"// When the plot is moused over, emphasize the grid lines.\n",
"Gadfly.plot_mouseover = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
"\n",
" var xgridlines = root.select(\".xgridlines\"),\n",
" ygridlines = root.select(\".ygridlines\");\n",
"\n",
" xgridlines.data(\"unfocused_strokedash\",\n",
" xgridlines.attr(\"stroke-dasharray\").replace(/px/g, \"mm\"))\n",
" ygridlines.data(\"unfocused_strokedash\",\n",
" ygridlines.attr(\"stroke-dasharray\").replace(/px/g, \"mm\"))\n",
"\n",
" // emphasize grid lines\n",
" var destcolor = root.data(\"focused_xgrid_color\");\n",
" xgridlines.attr(\"stroke-dasharray\", \"none\")\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" destcolor = root.data(\"focused_ygrid_color\");\n",
" ygridlines.attr(\"stroke-dasharray\", \"none\")\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" // reveal zoom slider\n",
" root.select(\".zoomslider\")\n",
" .animate({opacity: 1.0}, 250);\n",
"};\n",
"\n",
"\n",
"// Unemphasize grid lines on mouse out.\n",
"Gadfly.plot_mouseout = function(event) {\n",
" var root = this.plotroot();\n",
" var xgridlines = root.select(\".xgridlines\"),\n",
" ygridlines = root.select(\".ygridlines\");\n",
"\n",
" var destcolor = root.data(\"unfocused_xgrid_color\");\n",
"\n",
" xgridlines.attr(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" destcolor = root.data(\"unfocused_ygrid_color\");\n",
" ygridlines.attr(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
" .selectAll(\"path\")\n",
" .animate({stroke: destcolor}, 250);\n",
"\n",
" // hide zoom slider\n",
" root.select(\".zoomslider\")\n",
" .animate({opacity: 0.0}, 250);\n",
"};\n",
"\n",
"\n",
"var set_geometry_transform = function(root, tx, ty, scale) {\n",
" var xscalable = root.hasClass(\"xscalable\"),\n",
" yscalable = root.hasClass(\"yscalable\");\n",
"\n",
" var old_scale = root.data(\"scale\");\n",
"\n",
" var xscale = xscalable ? scale : 1.0,\n",
" yscale = yscalable ? scale : 1.0;\n",
"\n",
" tx = xscalable ? tx : 0.0;\n",
" ty = yscalable ? ty : 0.0;\n",
"\n",
" var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
"\n",
" root.selectAll(\".geometry, image\")\n",
" .forEach(function (element, i) {\n",
" element.transform(t);\n",
" });\n",
"\n",
" bounds = root.plotbounds();\n",
"\n",
" if (yscalable) {\n",
" var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
" root.selectAll(\".xfixed\")\n",
" .forEach(function (element, i) {\n",
" element.transform(xfixed_t);\n",
" });\n",
"\n",
" root.select(\".ylabels\")\n",
" .transform(xfixed_t)\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var cx = element.asPX(\"x\"),\n",
" cy = element.asPX(\"y\");\n",
" var st = element.data(\"static_transform\");\n",
" unscale_t = new Snap.Matrix();\n",
" unscale_t.scale(1, 1/scale, cx, cy).add(st);\n",
" element.transform(unscale_t);\n",
"\n",
" var y = cy * scale + ty;\n",
" element.attr(\"visibility\",\n",
" bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" if (xscalable) {\n",
" var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
" var xtrans = new Snap.Matrix().translate(tx, 0);\n",
" root.selectAll(\".yfixed\")\n",
" .forEach(function (element, i) {\n",
" element.transform(yfixed_t);\n",
" });\n",
"\n",
" root.select(\".xlabels\")\n",
" .transform(yfixed_t)\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var cx = element.asPX(\"x\"),\n",
" cy = element.asPX(\"y\");\n",
" var st = element.data(\"static_transform\");\n",
" unscale_t = new Snap.Matrix();\n",
" unscale_t.scale(1/scale, 1, cx, cy).add(st);\n",
"\n",
" element.transform(unscale_t);\n",
"\n",
" var x = cx * scale + tx;\n",
" element.attr(\"visibility\",\n",
" bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
" }\n",
" });\n",
" }\n",
"\n",
" // we must unscale anything that is scale invariance: widths, raiduses, etc.\n",
" var size_attribs = [\"font-size\"];\n",
" var unscaled_selection = \".geometry, .geometry *\";\n",
" if (xscalable) {\n",
" size_attribs.push(\"rx\");\n",
" unscaled_selection += \", .xgridlines\";\n",
" }\n",
" if (yscalable) {\n",
" size_attribs.push(\"ry\");\n",
" unscaled_selection += \", .ygridlines\";\n",
" }\n",
"\n",
" root.selectAll(unscaled_selection)\n",
" .forEach(function (element, i) {\n",
" // circle need special help\n",
" if (element.node.nodeName == \"circle\") {\n",
" var cx = element.attribute(\"cx\"),\n",
" cy = element.attribute(\"cy\");\n",
" unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,\n",
" cx, cy);\n",
" element.transform(unscale_t);\n",
" return;\n",
" }\n",
"\n",
" for (i in size_attribs) {\n",
" var key = size_attribs[i];\n",
" var val = parseFloat(element.attribute(key));\n",
" if (val !== undefined && val != 0 && !isNaN(val)) {\n",
" element.attribute(key, val * old_scale / scale);\n",
" }\n",
" }\n",
" });\n",
"};\n",
"\n",
"\n",
"// Find the most appropriate tick scale and update label visibility.\n",
"var update_tickscale = function(root, scale, axis) {\n",
" if (!root.hasClass(axis + \"scalable\")) return;\n",
"\n",
" var tickscales = root.data(axis + \"tickscales\");\n",
" var best_tickscale = 1.0;\n",
" var best_tickscale_dist = Infinity;\n",
" for (tickscale in tickscales) {\n",
" var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
" if (dist < best_tickscale_dist) {\n",
" best_tickscale_dist = dist;\n",
" best_tickscale = tickscale;\n",
" }\n",
" }\n",
"\n",
" if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
" root.data(axis + \"tickscale\", best_tickscale);\n",
" var mark_inscale_gridlines = function (element, i) {\n",
" var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
" element.attribute(\"gadfly:inscale\", inscale);\n",
" element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
" };\n",
"\n",
" var mark_inscale_labels = function (element, i) {\n",
" var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
" element.attribute(\"gadfly:inscale\", inscale);\n",
" element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
" };\n",
"\n",
" root.select(\".\" + axis + \"gridlines\").selectAll(\"path\").forEach(mark_inscale_gridlines);\n",
" root.select(\".\" + axis + \"labels\").selectAll(\"text\").forEach(mark_inscale_labels);\n",
" }\n",
"};\n",
"\n",
"\n",
"var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
" var old_scale = root.data(\"scale\");\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" // compute the viewport derived from tx, ty, and scale\n",
" var x_min = -width * scale - (scale * width - width),\n",
" x_max = width * scale,\n",
" y_min = -height * scale - (scale * height - height),\n",
" y_max = height * scale;\n",
"\n",
" var x0 = bounds.x0 - scale * bounds.x0,\n",
" y0 = bounds.y0 - scale * bounds.y0;\n",
"\n",
" var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
" ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
"\n",
" tx += x0;\n",
" ty += y0;\n",
"\n",
" // when the scale change, we may need to alter which set of\n",
" // ticks is being displayed\n",
" if (scale != old_scale) {\n",
" update_tickscale(root, scale, \"x\");\n",
" update_tickscale(root, scale, \"y\");\n",
" }\n",
"\n",
" set_geometry_transform(root, tx, ty, scale);\n",
"\n",
" root.data(\"scale\", scale);\n",
" root.data(\"tx\", tx);\n",
" root.data(\"ty\", ty);\n",
"};\n",
"\n",
"\n",
"var scale_centered_translation = function(root, scale) {\n",
" var bounds = root.plotbounds();\n",
"\n",
" var width = bounds.x1 - bounds.x0,\n",
" height = bounds.y1 - bounds.y0;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var scale0 = root.data(\"scale\");\n",
"\n",
" // how off from center the current view is\n",
" var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
" yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
"\n",
" // rescale offsets\n",
" xoff = xoff * scale / scale0;\n",
" yoff = yoff * scale / scale0;\n",
"\n",
" // adjust for the panel position being scaled\n",
" var x_edge_adjust = bounds.x0 * (1 - scale),\n",
" y_edge_adjust = bounds.y0 * (1 - scale);\n",
"\n",
" return {\n",
" x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
" y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
" };\n",
"};\n",
"\n",
"\n",
"// Initialize data for panning zooming if it isn't already.\n",
"var init_pan_zoom = function(root) {\n",
" if (root.data(\"zoompan-ready\")) {\n",
" return;\n",
" }\n",
"\n",
" // The non-scaling-stroke trick. Rather than try to correct for the\n",
" // stroke-width when zooming, we force it to a fixed value.\n",
" var px_per_mm = root.node.getCTM().a;\n",
"\n",
" // Drag events report deltas in pixels, which we'd like to convert to\n",
" // millimeters.\n",
" root.data(\"px_per_mm\", px_per_mm);\n",
"\n",
" root.selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
" if (sw > 0) {\n",
" element.attribute(\"stroke-width\", sw);\n",
" element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
" }\n",
" });\n",
"\n",
" // Store ticks labels original tranformation\n",
" root.selectAll(\".xlabels > text, .ylabels > text\")\n",
" .forEach(function (element, i) {\n",
" var lm = element.transform().localMatrix;\n",
" element.data(\"static_transform\",\n",
" new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
" });\n",
"\n",
" if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
" if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
" if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
" if (root.data(\"xtickscales\") === undefined) {\n",
"\n",
" // index all the tick scales that are listed\n",
" var xtickscales = {};\n",
" var ytickscales = {};\n",
" var add_x_tick_scales = function (element, i) {\n",
" xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
" var add_y_tick_scales = function (element, i) {\n",
" ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
" };\n",
"\n",
" root.select(\".xgridlines\").selectAll(\"path\").forEach(add_x_tick_scales);\n",
" root.select(\".ygridlines\").selectAll(\"path\").forEach(add_y_tick_scales);\n",
" root.select(\".xlabels\").selectAll(\"text\").forEach(add_x_tick_scales);\n",
" root.select(\".ylabels\").selectAll(\"text\").forEach(add_y_tick_scales);\n",
"\n",
" root.data(\"xtickscales\", xtickscales);\n",
" root.data(\"ytickscales\", ytickscales);\n",
" root.data(\"xtickscale\", 1.0);\n",
" }\n",
"\n",
" var min_scale = 1.0, max_scale = 1.0;\n",
" for (scale in xtickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" for (scale in ytickscales) {\n",
" min_scale = Math.min(min_scale, scale);\n",
" max_scale = Math.max(max_scale, scale);\n",
" }\n",
" root.data(\"min_scale\", min_scale);\n",
" root.data(\"max_scale\", max_scale);\n",
"\n",
" // store the original positions of labels\n",
" root.select(\".xlabels\")\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"x\", element.asPX(\"x\"));\n",
" });\n",
"\n",
" root.select(\".ylabels\")\n",
" .selectAll(\"text\")\n",
" .forEach(function (element, i) {\n",
" element.data(\"y\", element.asPX(\"y\"));\n",
" });\n",
"\n",
" // mark grid lines and ticks as in or out of scale.\n",
" var mark_inscale = function (element, i) {\n",
" element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
" };\n",
"\n",
" root.select(\".xgridlines\").selectAll(\"path\").forEach(mark_inscale);\n",
" root.select(\".ygridlines\").selectAll(\"path\").forEach(mark_inscale);\n",
" root.select(\".xlabels\").selectAll(\"text\").forEach(mark_inscale);\n",
" root.select(\".ylabels\").selectAll(\"text\").forEach(mark_inscale);\n",
"\n",
" // figure out the upper ond lower bounds on panning using the maximum\n",
" // and minum grid lines\n",
" var bounds = root.plotbounds();\n",
" var pan_bounds = {\n",
" x0: 0.0,\n",
" y0: 0.0,\n",
" x1: 0.0,\n",
" y1: 0.0\n",
" };\n",
"\n",
" root.select(\".xgridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
" pan_bounds.x0 = bounds.x1 - bbox.x;\n",
" }\n",
" if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
" pan_bounds.x1 = bounds.x0 - bbox.x;\n",
" }\n",
" }\n",
" });\n",
"\n",
" root.select(\".ygridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" var bbox = element.node.getBBox();\n",
" if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
" pan_bounds.y0 = bounds.y1 - bbox.y;\n",
" }\n",
" if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
" pan_bounds.y1 = bounds.y0 - bbox.y;\n",
" }\n",
" }\n",
" });\n",
"\n",
" // nudge these values a little\n",
" pan_bounds.x0 -= 5;\n",
" pan_bounds.x1 += 5;\n",
" pan_bounds.y0 -= 5;\n",
" pan_bounds.y1 += 5;\n",
" root.data(\"pan_bounds\", pan_bounds);\n",
"\n",
" // Set all grid lines at scale 1.0 to visible. Out of bounds lines\n",
" // will be clipped.\n",
" root.select(\".xgridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
"\n",
" root.select(\".ygridlines\")\n",
" .selectAll(\"path\")\n",
" .forEach(function (element, i) {\n",
" if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
" element.attr(\"visibility\", \"visible\");\n",
" }\n",
" });\n",
"\n",
" root.data(\"zoompan-ready\", true)\n",
"};\n",
"\n",
"\n",
"// Panning\n",
"Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
" var root = this.plotroot();\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var tx0 = root.data(\"tx\"),\n",
" ty0 = root.data(\"ty\");\n",
"\n",
" var dx0 = root.data(\"dx\"),\n",
" dy0 = root.data(\"dy\");\n",
"\n",
" root.data(\"dx\", dx);\n",
" root.data(\"dy\", dy);\n",
"\n",
" dx = dx - dx0;\n",
" dy = dy - dy0;\n",
"\n",
" var tx = tx0 + dx,\n",
" ty = ty0 + dy;\n",
"\n",
" set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
" var root = this.plotroot();\n",
" root.data(\"dx\", 0);\n",
" root.data(\"dy\", 0);\n",
" init_pan_zoom(root);\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_drag_onend = function(event) {\n",
" var root = this.plotroot();\n",
"};\n",
"\n",
"\n",
"Gadfly.guide_background_scroll = function(event) {\n",
" if (event.shiftKey) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var new_scale = root.data(\"scale\") * Math.pow(2, 0.002 * event.wheelDelta);\n",
" new_scale = Math.max(\n",
" root.data(\"min_scale\"),\n",
" Math.min(root.data(\"max_scale\"), new_scale))\n",
" update_plot_scale(root, new_scale);\n",
" event.stopPropagation();\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseover = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_button_mouseout = function(event) {\n",
" this.select(\".button_logo\")\n",
" .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomout_click = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var min_scale = root.data(\"min_scale\"),\n",
" scale = root.data(\"scale\");\n",
" Snap.animate(\n",
" scale,\n",
" Math.max(min_scale, scale / 1.5),\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_zoomin_click = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
" var max_scale = root.data(\"max_scale\"),\n",
" scale = root.data(\"scale\");\n",
"\n",
" Snap.animate(\n",
" scale,\n",
" Math.min(max_scale, scale * 1.5),\n",
" function (new_scale) {\n",
" update_plot_scale(root, new_scale);\n",
" },\n",
" 200);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_track_click = function(event) {\n",
" // TODO\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_mousedown = function(event) {\n",
" this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_mouseup = function(event) {\n",
" this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
"};\n",
"\n",
"\n",
"// compute the position in [0, 1] of the zoom slider thumb from the current scale\n",
"var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
" if (scale >= 1.0) {\n",
" return 0.5 + 0.5 * (Math.log(scale) / Math.log(max_scale));\n",
" }\n",
" else {\n",
" return 0.5 * (Math.log(scale) - Math.log(min_scale)) / (0 - Math.log(min_scale));\n",
" }\n",
"}\n",
"\n",
"\n",
"var update_plot_scale = function(root, new_scale) {\n",
" var trans = scale_centered_translation(root, new_scale);\n",
" set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
"\n",
" root.selectAll(\".zoomslider_thumb\")\n",
" .forEach(function (element, i) {\n",
" var min_pos = element.data(\"min_pos\"),\n",
" max_pos = element.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\");\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
" element.transform(new Snap.Matrix().translate(\n",
" Math.max(min_pos, Math.min(\n",
" max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
" });\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y) {\n",
" var root = this.plotroot();\n",
" var min_pos = this.data(\"min_pos\"),\n",
" max_pos = this.data(\"max_pos\"),\n",
" min_scale = root.data(\"min_scale\"),\n",
" max_scale = root.data(\"max_scale\"),\n",
" old_scale = root.data(\"old_scale\");\n",
"\n",
" var px_per_mm = root.data(\"px_per_mm\");\n",
" dx /= px_per_mm;\n",
" dy /= px_per_mm;\n",
"\n",
" var xmid = (min_pos + max_pos) / 2;\n",
" var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
" dx / (max_pos - min_pos);\n",
"\n",
" // compute the new scale\n",
" var new_scale;\n",
" if (xpos >= 0.5) {\n",
" new_scale = Math.exp(2.0 * (xpos - 0.5) * Math.log(max_scale));\n",
" }\n",
" else {\n",
" new_scale = Math.exp(2.0 * xpos * (0 - Math.log(min_scale)) +\n",
" Math.log(min_scale));\n",
" }\n",
" new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
"\n",
" update_plot_scale(root, new_scale);\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragstart = function(event) {\n",
" var root = this.plotroot();\n",
" init_pan_zoom(root);\n",
"\n",
" // keep track of what the scale was when we started dragging\n",
" root.data(\"old_scale\", root.data(\"scale\"));\n",
"};\n",
"\n",
"\n",
"Gadfly.zoomslider_thumb_dragend = function(event) {\n",
"};\n",
"\n",
"\n",
"var toggle_color_class = function(root, color_class, ison) {\n",
" var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
" var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
" if (ison) {\n",
" guides.animate({opacity: 0.5}, 250);\n",
" geoms.animate({opacity: 0.0}, 250);\n",
" } else {\n",
" guides.animate({opacity: 1.0}, 250);\n",
" geoms.animate({opacity: 1.0}, 250);\n",
" }\n",
"};\n",
"\n",
"\n",
"Gadfly.colorkey_swatch_click = function(event) {\n",
" var root = this.plotroot();\n",
" var color_class = this.data(\"color_class\");\n",
"\n",
" if (event.shiftKey) {\n",
" root.selectAll(\".colorkey text\")\n",
" .forEach(function (element) {\n",
" var other_color_class = element.data(\"color_class\");\n",
" if (other_color_class != color_class) {\n",
" toggle_color_class(root, other_color_class,\n",
" element.attr(\"opacity\") == 1.0);\n",
" }\n",
" });\n",
" } else {\n",
" toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
" }\n",
"};\n",
"\n",
"\n",
"return Gadfly;\n",
"\n",
"}));\n",
"\n",
"\n",
"//@ sourceURL=gadfly.js\n",
"\n",
"(function (glob, factory) {\n",
" // AMD support\n",
" if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
" require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
" factory(Snap, Gadfly);\n",
" });\n",
" } else {\n",
" factory(glob.Snap, glob.Gadfly);\n",
" }\n",
"})(window, function (Snap, Gadfly) {\n",
" var fig = Snap(\"#fig-da97e4c770454e539c367152585654cc\");\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-4\")\n",
" .mouseenter(Gadfly.plot_mouseover)\n",
".mouseleave(Gadfly.plot_mouseout)\n",
".mousewheel(Gadfly.guide_background_scroll)\n",
".drag(Gadfly.guide_background_drag_onmove,\n",
" Gadfly.guide_background_drag_onstart,\n",
" Gadfly.guide_background_drag_onend)\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-7\")\n",
" .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-7\")\n",
" .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-8\")\n",
" .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-8\")\n",
" .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-12\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-12\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-12\")\n",
" .click(Gadfly.zoomslider_zoomin_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-14\")\n",
" .data(\"max_pos\", 120.42)\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-14\")\n",
" .data(\"min_pos\", 103.42)\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-14\")\n",
" .click(Gadfly.zoomslider_track_click);\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-15\")\n",
" .data(\"max_pos\", 120.42)\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-15\")\n",
" .data(\"min_pos\", 103.42)\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-15\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-15\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-15\")\n",
" .drag(Gadfly.zoomslider_thumb_dragmove,\n",
" Gadfly.zoomslider_thumb_dragstart,\n",
" Gadfly.zoomslider_thumb_dragend)\n",
".mousedown(Gadfly.zoomslider_thumb_mousedown)\n",
".mouseup(Gadfly.zoomslider_thumb_mouseup)\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-16\")\n",
" .data(\"mouseover_color\", \"#cd5c5c\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-16\")\n",
" .data(\"mouseout_color\", \"#6a6a6a\")\n",
";\n",
"fig.select(\"#fig-da97e4c770454e539c367152585654cc-element-16\")\n",
" .click(Gadfly.zoomslider_zoomout_click)\n",
".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
";\n",
" });\n",
"]]> </script>\n",
"</svg>\n"
],
"text/plain": [
"Plot(...)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sys = Particle(5.0,0)\n",
"\n",
"history = Particle[]\n",
"for t in t_range\n",
" push!(history,sys)\n",
" x, v = euler_step(t,δt,sys)\n",
" sys = Particle(x,v)\n",
"end\n",
"\n",
"x_range = map(s->s.x,history)\n",
"y_range = map(s->s.v,history)\n",
"e_range = map(s->energy(s),history)\n",
"\n",
"plot(x=t_range,y=e_range,Geom.line)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{0.5,0.92,0.27084799999999987,0.7267608480972798,0.7307726253943448,0.7240179029564531,0.7353228032903749,0.7162132959657391,0.7479666631832848,0.6937261249350705}\n",
"[0.5,0.92,0.27084799999999987,0.7267608480972798,0.7307726253943448,0.7240179029564531,0.7353228032903749,0.7162132959657391,0.7479666631832848,0.6937261249350705]\n"
]
}
],
"source": [
"f(c,x)= c * x * (1 - x) # logistic map test\n",
"\n",
"x0 = 0.5\n",
"num_iterations = 10\n",
"\n",
"# functional one-liner\n",
"states = collect(take(iterate(x->f(3.68,x),x0),num_iterations))\n",
"\n",
"println(states)\n",
"\n",
"#or if you like procedural-style (for comfort or pedagogical reasons)\n",
"\n",
"states = Float64[]\n",
"z = 0.5\n",
"for i in range(0,num_iterations)\n",
" push!(states,z)\n",
" z = f(3.68,z)\n",
"end\n",
"println(states)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The original [about this document ... ](http://www.physics.drexel.edu/~valliere/PHYS305/Diff_Eq_Integrators/Verlet_Methods/Verlet/node1.html)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.3.7",
"language": "julia",
"name": "julia 0.3"
},
"language_info": {
"name": "julia",
"version": "0.3.7"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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