How to reduce number of loops

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David Kusnirak
David Kusnirak 2013-4-19
Hello,
I have code, which assembles coefficients into large sparse matrix. My coding seems to be inefficient as I use 3 loops, so I'm trying to improve the code to get better pefromance. I think it would be nice to reduce the number of loops to single loop and run it parallel (parfor), but I'm struggling to do that..
The main matrix sig is a matrix of size LX,LY,LZ and vectors dx, dy, dz holds the distances between nods along the diretion X, Y an Z.
for i = 2:LX-1
for j = 2:LY-1
for k = 2:LZ-1
Ctop(i,j,k) = (-1/dz(k-1))*((sig(i-1,j ,k-1)*((dx(i-1)*dy(j ))/4))+...
(sig(i ,j ,k-1)*((dx(i )*dy(j ))/4))+...
(sig(i-1,j-1,k-1)*((dx(i-1)*dy(j-1))/4))+...
(sig(i ,j-1,k-1)*((dx(i )*dy(j-1))/4)));
end
end
end
C1v=reshape(Ctop,[],1);
thanks for help!
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Cedric
Cedric 2013-4-19
And actually this is correct that Ctop has the size of sig and that Ctop(LX,:,:), Ctop(:,LY,:), Ctop(:,:,LZ), Ctop(1,:,:), Ctop(:,1,:), and Ctop(:,:,1) are 0's ?
David Kusnirak
David Kusnirak 2013-4-19
Values assigned to those matrix positions are evaluated separately by another code as the boundary conditions are applied there.

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Cedric
Cedric 2013-4-19
Ok, well, you could adapt the following to your case then. I am not checking in-depth that it is working though, and there is room for improvement as I didn't optimize indexing for managing properly boundaries..
n = 100 ;
sig = 20 * rand(n,n,n) ;
LX = size(sig,1) ;
LY = size(sig,2) ;
LZ = size(sig,3) ;
dx = 0.1 + rand(LX, 1) ; % Made irregular for testing..
dy = 0.8 + zeros(LY, 1) ;
dz = 0.3 + zeros(LZ, 1) ;
Ctop = zeros(size(sig)) ;
% - Your code.
tic ;
for i = 2:LX-1
for j = 2:LY-1
for k = 2:LZ-1
Ctop(i,j,k) = (-1/dz(k-1))*((sig(i-1,j ,k-1)*((dx(i-1)*dy(j ))/4))+...
(sig(i ,j ,k-1)*((dx(i )*dy(j ))/4))+...
(sig(i-1,j-1,k-1)*((dx(i-1)*dy(j-1))/4))+...
(sig(i ,j-1,k-1)*((dx(i )*dy(j-1))/4)));
end
end
end
toc
% - Meshgrid based code.
Ctop_mesh = zeros(size(Ctop)) ;
tic ;
[dy_m0, dx_m0] = meshgrid(dy(2:end-1), dx(2:end-1)) ;
[dy_m1, dx_m1] = meshgrid(dy(1:end-2), dx(1:end-2)) ;
sig_m00 = sig(2:end-1,2:end-1,:) ;
sig_m10 = sig(1:end-2,2:end-1,:) ;
sig_m01 = sig(2:end-1,1:end-2,:) ;
sig_m11 = sig(1:end-2,1:end-2,:) ;
for k = 2 : LZ-1
Ctop_mesh(2:end-1,2:end-1,k) = (-1/dz(k-1)) / 4 * ...
(sig_m10(:,:,k-1) .* dx_m1 .* dy_m0 + ...
sig_m00(:,:,k-1) .* dx_m0 .* dy_m0 +...
sig_m11(:,:,k-1) .* dx_m1 .* dy_m1 +...
sig_m01(:,:,k-1) .* dx_m0 .* dy_m1) ;
end
toc
% - Check.
tmp = abs(Ctop_mesh(2:end-1,2:end-1,2:end-1)-Ctop(2:end-1,2:end-1,2:end-1)) ;
all(tmp(:) < 1e-12)
This code outputs:
Elapsed time is 6.281855 seconds. % 3 nested loops
Elapsed time is 0.408983 seconds. % meshgrid
ans = % check
1
Note that it is possible to get rid of the last FOR loop and work with a 3D array for dz built this way:
dz_m1 = permute(repmat(dz(1:end-1),[1,LX-1,LY-1]), [2,3,1]) ;
but I am not sure that it is more efficient (especially if you want to PARFOR the remaining loop).

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