Vectorize operations referencing adjacent elements of a matrix

Question

Christopher 2014-2-18

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https://ww2.mathworks.cn/matlabcentral/answers/116535-vectorize-operations-referencing-adjacent-elements-of-a-matrix

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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Answer 1

Andrei Bobrov 2014-2-18

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https://ww2.mathworks.cn/matlabcentral/answers/116535-vectorize-operations-referencing-adjacent-elements-of-a-matrix#answer_124728

编辑：Andrei Bobrov 2014-2-18

在 MATLAB Online 中打开

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 2014-2-19

编辑：Christopher 2014-2-19

在 MATLAB Online 中打开

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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