Re: Re: plot thousands(?) of trajectories in single graph.

*To*: mathgroup at smc.vnet.net*Subject*: [mg50526] Re: [mg50494] Re: plot thousands(?) of trajectories in single graph.*From*: DrBob <drbob at bigfoot.com>*Date*: Thu, 9 Sep 2004 05:17:47 -0400 (EDT)*References*: <chk0es$so$1@smc.vnet.net> <200409080908.FAA08363@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Very nice, but I'd block y, g, and omega to avoid surprises, as follows: DoRandomSolution[i_Integer] := Block[{$DisplayFunction = Identity, sol, y, g, omega}, Table[sol = NDSolve[{y''[t] - g*y'[t] + (1 + Cos[omega*t])*y[ t] == 0, y[0] == Random[], y'[0] == Random[]} /. {g -> Random[], omega -> 2Pi*Random[]}, {y[t]}, {t, 0, 6Pi}]; Plot[Evaluate[y[t] /. sol[[1]]], {t, 0, 2Pi}], {i}]] Bobby On Wed, 8 Sep 2004 05:08:27 -0400 (EDT), Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote: > Hi, > > DoRandomSolution[i_Integer] := > Block[{$DisplayFunction = Identity, sol}, > Table[sol = NDSolve[{ > y''[t] - g*y'[t] + (1 + Cos[omega*t])*y[t] == 0, > y[0] == Random[], > y'[0] == Random[]} /. > {g -> Random[], > omega -> 2Pi*Random[]}, {y[t]}, {t, 0, 6Pi}]; > Plot[Evaluate[y[t] /. sol[[1]]], {t, 0, 2Pi}], {i}] > ] > > ss = DoRandomSolution[4000]; > Show[ss] > > Regards > Jens > > > sean kim wrote: >> >> hello group, >> >> I have a routein that solves a system of odes over a >> parameter space thousands of times while randomly >> varying the values. >> >> What I would like to do is take a variable and the >> resulting solutions(however many routine has generated >> over the course of evaluation) and plot them on single >> graph. >> >> So you will get rather messy graph, but nonetheless >> shows possible trajectories given system can yield. >> >> How do I go about doing this? >> >> I thought i could save the interpolating functions and >> then evaluate thousands at the end of a routine and >> show together. But How do I save the interpolating >> function? >> >> or do I plot with inside the module with >> DisplayFunction-> Identity and then save the plot and >> DisplayTogether the thousands of graphs at the end of >> the routine. >> >> if doing thousands isn't possible, is it possible to >> show hundreds of trajectories? >> >> thanks in advance for any insights. >> >> sean >> >> code below is a example skeletal code for running >> hundred random solutions of an ode system. >> >> Do[ >> Module[{}, >> k1 = Random[Real, {1/10, 5/10}]; >> k2 = Random[Real, {1/20, 5/20}]; >> ndsolution = >> NDSolve[{a'[t] == -k1 a[t] x[t], b'[t] == -k2 b[t] >> y[t], x'[t] == -k1 a[t] x[t] + k2 b[t] y[t], y'[t] == >> k1 a[t] x[t] - k2 b[t] y[t], a[0] == 1, b[0] == 1, >> x[0] == 1, y[0] == 0},{a, b, x, y}, {t, 0, 250}][[1]]; >> Plot[Evaluate[{a[t], b[t], x[t], y[t]} /. ndsolution], >> {t, 0, 250}, PlotRange -> All, PlotStyle -> >> {{AbsoluteThickness[2], RGBColor[0, 0, 0]}, >> {AbsoluteThickness[2], RGBColor[.7, 0, 0]}, >> {AbsoluteThickness[2], RGBColor[0, .7, 0]}, >> {AbsoluteThickness[2], RGBColor[0, 0, .7]}}, Axes -> >> False, Frame -> True, PlotLabel -> StyleForm[A >> StyleForm[" B", FontColor -> RGBColor[.7, 0, 0]] >> StyleForm[" X", FontColor -> RGBColor[0, .7, >> 0]]StyleForm[" Y", FontColor -> RGBColor[0, 0, .7]], >> FontFamily -> "Helvetica", FontWeight -> "Bold"]]; >> ] >> ,{i, 100}] >> >> >> _______________________________ >> Do you Yahoo!? >> Win 1 of 4,000 free domain names from Yahoo! Enter now. >> http://promotions.yahoo.com/goldrush > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Re: plot thousands(?) of trajectories in single graph.***From:*Jens-Peer Kuska <kuska@informatik.uni-leipzig.de>