
How to speed up this inner loop?
Posted:
Oct 1, 2012 2:19 AM


Can someone suggest how I might optimize the For loop below for speed? I can think of various optimizations to try, but I would like to see what an experienced coder would do before trying to reinvent something well known.
This is tested code, which accomplishes the basics of what I want, but which needs to run faster.
Using Compile would be fine, but I don't yet understand how to set it up properly.
As an aside, I found the details of calling ListConvolve difficult to grasp from the documentation.
Thank you in advance.
Ralph Dratman 
(* Size of arrays *) xSize = ySize = 40;
(* The mass at a location, not used yet. *) mfunc[x_, y_] := 1.0;
(* Initial conditions are products of eigenfunctions in x and y. *)
zpos = Table[ Sin[3 (x/(xSize + 1)) Pi] Sin[2 (y/(ySize + 1)) Pi], {y, ySize}, {x, xSize}];
(* Zero initial velocity. *) zvel = Table[0, {y, ySize}, {x, xSize}];
(* Mass does not vary here but may later vary with position via mfunc.*) m = Table[1., {y, ySize}, {x, xSize}];
(* Spring constant when viewing this as an array of coupled oscillators. *) k = .05;
damp = .001; dt = .1;
(* Discrete second derivative in PDE interpretation; *) (* spring coupling arrangement in coupled oscillator view. *)
convKernel = {{0., 1., 0.}, {1., 4., 1.}, {0., 1., 0.}};
timeEvolve[cycles_] := Module[{},
For[i = 1, i <= cycles, i++, zpos = zpos + zvel dt; zvel = (1.damp) zvel + (k/m) ListConvolve[convKernel, zpos, {{2, 2}, {2, 2}}, 0.] dt ];
Print@ListPlot3D[zpos, PlotRange > {1., 1.}, ImageSize > {200}]];
Table[timeEvolve[cycles], {cycles, {0, 120, 150, 500, 600}}]

