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}]
> > > >
> > > >
> > > >
> > > >
> > > >
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