Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Do I need MathLink to run finite-difference fast enough

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115783] Re: Do I need MathLink to run finite-difference fast enough
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Thu, 20 Jan 2011 06:32:58 -0500 (EST)

James wrote:
> Hello guys,
> 
> I would like to create a Manipulate for a finite-difference on a system 
> of PDEs using a 100x100 array that is processed about 10,000 times.  Is 
> it possible to code this in native Mathematica, for example using 
> Compile, fast enough to be reasonably used by Manipulate (under 3 or 4 
> seconds)?  The C++ code is below and with the Compiler set to optimize 
> speed, it runs in approximately 1.5 seconds.  However, if I attempt to 
> just code it in Mathematica using arrays, it takes much too long to 
> execute.
> 
> Can someone help me decide if the only reasonable option is to use 
> MathLink or can I even use MathLink in a Manipulate? 
> 
> Thanks Guys.  Here's the C++ code.  The variables u, v, and lap 
> are all 100x100 arrays.
> 
> startt=clock();
> 
>   for(p=1;p<=10000;p++){
> 
> 
>      lap[0][0]=(u[0][1]-4*u[0][0]+u[0][M-1]+u[1][0]+u[N-1][0]);
> 
>     for(j=1;j<=M-2;j++)
>     {
>         lap[0][j]=(u[0][j+1]-4*u[0][j]+u[0][j-1]+u[1][j]+u[N-1][j]);
>     }
> 
>     lap[0][M-1]=(u[0][0]-4*u[0][M-1]+u[0][M-2]+u[1][M-1]+u[N-1][M-1]);
>    
>     for(i=1;i<=N-2;i++)
>     {
>         lap[i][0]=(u[i][1]-4*u[i][0]+u[i][M-1]+u[i+1][0]+u[i-1][0]);
>     }
> 
>     for(i=1;i<=N-2;i++)
>     {
>         
> lap[i][M-1]=(u[i][0]-4*u[i][M-1]+u[i][M-2]+u[i+1][M-1]+u[i-1][M-1]);
>     }
> 
>     lap[N-1][0]=(u[N-1][1]-4*u[N-1][0]+u[N-1][M-1]+u[0][0]+u[N-2][0]);
> 
>     
> lap[N-1][M-1]=(u[N-1][0]-4*u[N-1][M-1]+u[N-1][M-2]+u[0][M-1]+u[N-2][M-1]);
> 
>     for(j=1;j<=M-2;j++)
>     {
>         
> lap[N-1][j]=(u[N-1][j+1]-4*u[N-1][j]+u[N-1][j-1]+u[0][j]+u[N-2][j]);
>     }
> 
>     for(i=1;i<=N-2;i++)
>         for(j=1;j<=M-2;j++)
>     {
>         lap[i][j]=(u[i][j+1]-4*u[i][j]+u[i][j-1]+u[i+1][j]+u[i-1][j]);
>     }
>       
>     for(i=0;i<M;i++)
>       for(j=0;j<N;j++){
>            
>         u[i][j] =
> =u[i][j]+dt*(D_u*lap[i][j]+(a-(b+1)*u[i][j]+v[i][j]*u[i][j]*u[i][j]));
> 
>       }
> 
> 
>       lap[0][0]=(v[0][1]-4*v[0][0]+v[0][M-1]+v[1][0]+v[N-1][0]);
> 
>     for(j=1;j<=M-2;j++)
>     {
>         lap[0][j]=(v[0][j+1]-4*v[0][j]+v[0][j-1]+v[1][j]+v[N-1][j]);
>     }
> 
>     lap[0][M-1]=(v[0][0]-4*v[0][M-1]+v[0][M-2]+v[1][M-1]+v[N-1][M-1]);
>    
>     for(i=1;i<=N-2;i++)
>     {
>         lap[i][0]=(v[i][1]-4*v[i][0]+v[i][M-1]+v[i+1][0]+v[i-1][0]);
>     }
> 
>     for(i=1;i<=N-2;i++)
>     {
>         
> lap[i][M-1]=(v[i][0]-4*v[i][M-1]+v[i][M-2]+v[i+1][M-1]+v[i-1][M-1]);
>     }
> 
>     lap[N-1][0]=(v[N-1][1]-4*v[N-1][0]+v[N-1][M-1]+v[0][0]+v[N-2][0]);
> 
>     
> lap[N-1][M-1]=(v[N-1][0]-4*v[N-1][M-1]+v[N-1][M-2]+v[0][M-1]+v[N-2][M-1]);
> 
>     for(j=1;j<=M-2;j++)
>     {
>         
> lap[N-1][j]=(v[N-1][j+1]-4*v[N-1][j]+v[N-1][j-1]+v[0][j]+v[N-2][j]);
>     }
> 
>     for(i=2;i<=N-2;i++)
>         for(j=2;j<=M-2;j++)
>     {
>         lap[i][j]=(v[i][j+1]-4*v[i][j]+v[i][j-1]+v[i+1][j]+v[i-1][j]);
>     }
>    
>       for(i=0;i<M;i++)
>       for(j=0;j<N;j++){
>          v[i][j] =
> =v[i][j]+dt*(D_v*lap[i][j]+(b*u[i][j]-v[i][j]*u[i][j]*u[i][j]));
>     }
>     
>   endt=clock();
> 
>   fprintf(stderr,"%d\n",endt-startt);

Not certain, but these operations look like the sort of thing that might 
be accomplished with ListConvolve. If so, that would probably be 
comparable to a C/C++ coding.

Daniel Lichtblau
Wolfram Research


  • Prev by Date: Re: Using FindRoot on an equation involving Log terms
  • Next by Date: Re: avoiding non-machine numbers
  • Previous by thread: Re: The new (v.8.0) distribution plots using a numerical
  • Next by thread: problem with LessEqual::nord: