Vectorize operations referencing adjacent elements of a matrix

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?

Answer 1

[Andrei Bobrov]

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');

[Christopher]

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