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MathGroup Archive 2004

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50608] Re: Re: [mg50489] plot thousands(?) of trajectories in single graph.
  • From: sean kim <sean_incali at yahoo.com>
  • Date: Sun, 12 Sep 2004 04:42:22 -0400 (EDT)
  • Reply-to: sean_incali at yahoo.com
  • Sender: owner-wri-mathgroup at wolfram.com

hm... i think my install is bad? 

I tried it with fresh kernel with Graphics preloaded. 


DisplayTogetherArray[ 
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}], ImageSize -> 500]

works as expected with an GraphicsArray object with f
plots in a row.

but if i add Partition, it still brings back a blank
GraphicsArray object.

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'm using Windows version 5.0.  I have tried the
Examples that use similar format of commands in the
Help and they seem to work fine. I wonder what's going
on?  

Does anyone else have similar problems? ( someone
using windows? ) 

Thanks in advance for any thoughts 


sean 

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

> Works fine in version 5.0.1 under Mac OS X.
> 
> Start with a fresh kernel and make sure that you
> load the Graphics packages 
> first.
> 
> Needs["Graphics`"];
> 
> 
> Bob Hanlon
> 
> > 
> > From: sean kim <sean_incali at yahoo.com>
To: mathgroup at smc.vnet.net
> > Date: 2004/09/10 Fri PM 07:30:41 EDT
> > To: hanlonr at cox.net
> > CC: mathgroup at smc.vnet.net
> > Subject: [mg50608] Re: [mg50489] plot thousands(?) of
> trajectories in single graph.
> > 
> > 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: [mg50608] [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!
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> > > now.
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> > > > 
> > > > 
> > > 
> > > 
> > 
> > 
> > 
> > 		
> > _______________________________
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> > Shop for Back-to-School deals on Yahoo! Shopping.
> > http://shopping.yahoo.com/backtoschool
> > 
> 
> 



		
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