MATLAB: Conv a matrix multiple times

MATLABmatricesmatrixmatrix arraymatrix manipulation

Hello
I have a rectangular matrix and i want to convolve it to some power of that matrix times. e.g.
a = [1 1 0; 1 0 1]^5
convolve the 1st row with the 1st row 5 times and then the row with the 2nd row 5 times.
Any help!

Best Answer

a1 = [1 1 0; 
      1 0 1]; % rand(2,3);
p = 5; % power
[m,n] = size(a1);
%% Method 1, straighforward double for-loops
ap = a1;
for p=2:p
    temp = zeros(m,n+size(ap,2)-1);
    for i=1:m
        temp(i,:) = conv(a1(i,:),ap(i,:));
    end
    ap = temp;
end
ap
%% Method 2 single for-loop
ap = a1;
i = 0:n-1;
k = n;
A1 = reshape(a1,[m 1 n]);
for p=2:p
    c = i+(1:k)';
    [r,c] = ndgrid(1:m,c(:));
    ap = A1.*ap;
    k = n+k-1;
    ap = accumarray([r(:) c(:)], ap(:), [m, k]); 
end
ap
You might try to improve by using a "smart" of power raising, by using the binary decomposition of p.
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