Re: Re: Speeding Up Realtime Visualization

*To*: mathgroup at smc.vnet.net*Subject*: [mg84367] Re: Re: Speeding Up Realtime Visualization*From*: Will <secandum.oculi at gmail.com>*Date*: Thu, 20 Dec 2007 00:11:34 -0500 (EST)

Since I haven't mentioned this before, I'm trying to make a two species reaction diffusion simulator by approximating the associated PDE using finite difference integration. These 'rough' simulators, e.g. http://texturegarden.com/java/rd/index.html, are typically very fast. I'm going for something with this speed. In my code, I've compiled a function which performs the 'next-time-interval' finite difference calculation. Using the Timing function, I found this calculation takes essentially no time. Mathematica usually says 0. sec. However, when I perform this calculation across the entire 100x100 grid, i.e. ~99^2 calcuations, it takes 0.45 sec. I originally computed the entire grid using For loops, which required ~0.5-0.6 sec. Figuring that Mathematica doesn't like procedural programming, I tried implementing a Threading technique to apply the finite difference calculation across the grid, which takes 0.45. Of course, this is way to slow for a 'fast' simulator. Again, I can speed things up by lowering my grid size, or keeping the grid size and increasing the spatial interval in the integrator, but I'll be losing significant quality. I still think the sluggishness has something to do with the way I'm setting up my matrices, which are used to read/write during the finite difference calculation. I figure I'm forgetting something huge Ok, here's my code: Clear["Global`*"]; N[ L=100; ds=1; length=L/ds; dt=0.5; a=0.082;(*u diffusion*) b=0.041;(*v diffusion*) f=0.035;(*u feed/rxn rate*) k=0.0625;(*v death rate*) dtf=dt f; dtfk=dt(f+k); e=a dt/(ds)^2; g=b dt/(ds)^2; uP=Table[1,{i,1,length},{j,1,length}];(*previous u state*) uC=Table[0,{i,1,length},{j,1,length}];(*current u state*) vP=Table[0,{i,1,length},{j,1,length}];(*previous v state*) vC=Table[0,{i,1,length},{j,1,length}];(*current v state*) c=2;p=1;(*for double buffer*) u={uP,uC};(*u[[1]] is previous, u[[2]] is current*) v={vP,vC};(*v[[1]] is previous, v[[2]] is current*) (*initial conditions, small square of altered conc values*) Do[u[[1,i,j]]=0.35,{i,0.4length,0.6length},{j,0.40length,0.6length}]; Do[v[[1,i,j]]= Sin[0.1i-0.5length]Cos[0.1j-0.5length]^2,{i,1,length},{j,1,length}]; ]; (*finite difference/rxn diffusion calculation*) Rxn=Compile[{{c,_Integer},{p,_Integer},{i,_Integer},{j,_Integer}}, u[[c,i,j]]=u[[p,i,j]](1-4*e-dt*(v[[p,i,j]])^2-dtf)+dtf+e*(u[[p,i+1,j]]+u[[p,i-1,j]]+u[[p,i,j+1]]+u[[p,i,j-1]])//N; v[[c,i,j]]=v[[p,i,j]](1-4*g+dt*u[[p,i,j]]*v[[p,i,j]])-dtfk+ g*(v[[p,i+1,j]]+v[[p,i-1,j]]+v[[p,i,j+1]]+v[[p,i,j-1]])//N; ]; (*Rxn Diffusion*) While[True, Outer[ Thread[Rxn[c,p,#1,#2]]&,Range[2,length-1],Range[2,length-1] ]; If[p==1,c=1;p=2,c=2;p=1] ; (*c/p inverter*) ugrid=u[[2]]; vgrid=v[[2]]; ] Then I Dynamically visualize either ugrid or vgrid using ArrayPlot or Graphics[Raster[]] , which seem take take the same time. Any ideas? Thanks.