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MathGroup Archive 2006

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Re: ndsolve & compile

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64912] Re: ndsolve & compile
  • From: Peter Pein <petsie at dordos.net>
  • Date: Tue, 7 Mar 2006 06:12:13 -0500 (EST)
  • References: <duh3bs$5ut$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Christopher Klausmeier schrieb:
> Hi folks --
> 
> Recently Rob Knapp helped greatly speed up Alberto Verga's code to  
> solve a large set of ODEs by using Compile with NDSolve ("  
> Re: NDSolve useless?" of 21 Jan 2006).  I was hoping to see such a  
> speedup myself, but got a big  slowdown instead.  Any ideas what is  
> different?
> 
> thanks -- Chris
> 
> In[213]:=
> r=1;
> k=2;
> kp=1;
> c=1;
> m=0.1;
> 
> nx=128;
> 
> cf=Compile[{{n,_Real,1},{p,_Real,1}},
>        Module[{dndt,dpdt,nx=Length[n]},Transpose[
>            Table[
>              dndt=r*n[[x]]*(1-n[[x]]/k)-c*n[[x]]*p[[x]]/(n[[x]]+kp);
>              dpdt=c*n[[x]]*p[[x]]/(n[[x]]+kp)-m*p[[x]];
>              {dndt,dpdt},{x,1,nx}]]]
>        ];
> 
> g[{n_?VectorQ,p_?VectorQ}]:=cf[n,p];
> 
> First[Timing[
>      sol=First[NDSolve[{np'[t]  == g[np[t]],np[0] == {Table[0.69807, 
> {x,1,nx}],
>                  Table[0.32324,{x,1,nx}]}},np,{t,0,tmax}]]]]
> Out[221]=
> 26.2489 Second
> 
> 
> In[222]:=
> eqns=Flatten[Table[{
> 
>            n[x]'[t]\[Equal]
>              r*n[x][t]*(1-n[x][t]/k)-c*n[x][t]*p[x][t]/(n[x][t]+kp),
>            p[x]'[t]\[Equal]c*n[x][t]*p[x][t]/(n[x][t]+kp)-m*p[x][t]}, 
> {x,1,
>            nx}]];
> 
> ics=Flatten[Table[{n[x][0]\[Equal]0.69807,p[x][0]\[Equal]0.32324},{x, 
> 1,nx}]];
> 
> unks=Flatten[Table[{n[x],p[x]},{x,1,nx}]];
> 
> First[Timing[NDSolve[Flatten[Join[eqns,ics]],unks,{t,0,tmax}]]]
> Out[225]=
> 1.50484 Second
> --
> Christopher Klausmeier
> Kellogg Biological Station
> Michigan State University
> Hickory Corners MI 49060
> 
> Web: http://www.kbs.msu.edu/Faculty/Klausmeier/Index.htm
> Email: klausme1 at msu.edu
> Phone: (269) 671-4987
> 
> 
> 
> 
Hi Christopher,

  I guess this has to do with
Cases[Options@NDSolve,HoldPattern[Compiled->_]]
{Compiled->True}
and NDSolve tries to compile a compiled function.
As I said: just a guess...

Peter


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