Vectorize operations referencing adjacent elements of a matrix

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Christopher
Christopher 2014-2-18
编辑： Christopher 2014-2-19
I have made the simple code:
for i=2:xsize-1
for j=2:ysize-1
for n=2:zsize-1
matrix(i,j,n)=matrix(i,j,n)+0.2*(matrix(i,j,n)*6-matrix(i-1,j,n)-matrix(i+1,j,n)-matrix(i,j-1,n)-matrix(i,j+1,n)-matrix(i,j,n-1)-matrix(i,j,n+1));
end
end
end
This is part of a diffusion problem and it is particularly slow because the 3D matrix is large. Is it possible to vectorize an operation like this? How do you vectorize references to the matrix like this?

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Andrei Bobrov
Andrei Bobrov 2014-2-18
编辑：Andrei Bobrov 2014-2-18
out = convn(matrix,cat(3,[0 0 0;0 -1 0;0 0 0],...
[0 -1 0;-1 1 -1;0 -1 0],...
[0 0 0;0 -1 0;0 0 0]),'valid');
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Christopher
Christopher 2014-2-19
编辑：Christopher 2014-2-19
Thanks! This gives about a factor of 20 speedup. The form I used is
newmatrix = convn(matrix,cat(3,[0 0 0; 0 rt 0; 0 0 0],...
[0 rt 0; rt 1-rt*6 rt; 0 rt 0],...
[0 0 0; 0 rt 0; 0 0 0]),'same');
where rt=0.2

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