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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: [mg50596] Re: [mg50489] plot thousands(?) of trajectories in single graph.
  • From: sean kim <sean_incali at yahoo.com>
  • Date: Sat, 11 Sep 2004 06:45:14 -0400 (EDT)
  • Reply-to: sean_incali at yahoo.com
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Bob. 

I have tried this for few times now, but I just can;t
seem to get the array thing to work...

it will display blank graphics... 


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]; 


I tought I wold be clever and do Show...
but that just brings back two blank graphics.

Show[
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]; 
]


So I thought I need to add displayfunction statements 

Show[
DisplayTogetherArray[ Partition[ Table[ Plot[
Evaluate[ndsoln[[k]]], {t, 0, 250}, PlotRange -> All,
PlotStyle -> ps[[k]], DisplayFunction -> Identity,
PlotLabel -> StyleForm[ expr[[k]], FontColor ->
ps[[k]], FontFamily -> "Helvetica", FontWeight ->
"Bold", FontSize -> 12], DisplayFunction ->
$DisplayFunction], {k, 4}], 2], ImageSize -> 500]
];

still nothing...

Maybe it's some type of modification setting you have
that i don't?  

thanks in advance for any insights 


sean 

--- Bob Hanlon <hanlonr at cox.net> wrote:

> 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: [mg50596] [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}]
> > 
> > 
> > 
> > 
> > 		
> > _______________________________
> > Do you Yahoo!?
> > Win 1 of 4,000 free domain names from Yahoo! Enter
> now.
> > http://promotions.yahoo.com/goldrush
> > 
> > 
> 
> 



		
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