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MathGroup Archive 2004

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50521] Re: [mg50489] plot thousands(?) of trajectories in single graph.
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 9 Sep 2004 05:17:33 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

I recommend that you break it into an array of four plots.  Increase the value 
of n for more cases of each plot.

Needs["Graphics`"];

n=20;
expr={a[t],b[t],x[t],y[t]};
ps = {RGBColor[0,0,0],RGBColor[.7,0,0],
      RGBColor[0,.7,0],RGBColor[0,0,.7]};
ndsoln = Transpose[
      Table[(
          k1=Random[Real,{1/10,5/10}];
          k2=Random[Real,{1/20,5/20}];
          expr /.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]]),
        {k,n}]];
DisplayTogetherArray[
    Partition[
      Table[
        Plot[
          Evaluate[ndsoln[[k]]], 
          {t,0,250},
          PlotRange->All,
          PlotStyle->ps[[k]],
          PlotLabel->StyleForm[
              expr[[k]], 
              FontColor->ps[[k]], 
              FontFamily->"Helvetica", 
              FontWeight->"Bold",
              FontSize->12]],
        {k,4}],
      2],
    ImageSize->500];


Bob Hanlon

> 
> From: sean kim <sean_incali at yahoo.com>
To: mathgroup at smc.vnet.net
> Date: 2004/09/07 Tue AM 05:43:50 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg50521] [mg50489] plot thousands(?) of trajectories in single graph.
> 
> 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}]
> 
> 
> 
> 
> 		
> _______________________________
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> http://promotions.yahoo.com/goldrush
> 
> 


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