Efficient way to multiply an cell matrix with a scaler?

Hi,

I have a for loop that multiplies a cell matrix with a scaler component. The size of K11{1,i} is never too big (maximum 50 by 50 matrix) and its a full matrix. What takes time is that sometimes the maximum value of "i" can go up to 10000 or more and I have to do it for many analysis. It would be very helpful if you could suggest a way to compute it faster by vectorizing the loop or any other way.

nonZeroDel = nnz(del);
delNonZero = nonzeros(del);

for i = 1:nonZeroDel
    KE = KE + K11{1,i}*delNonZero(i);
end

Answer 1

[Guillaume]

Since for your summation to succeed all the arrays in K11 must be the same size, convert that cell array to a 3D matrix. It will be a lot more efficient.

K11 = cat(3, K11{:});

delNonZero = permute(nonzeros(del), [3 2 1]);  %move the non-zeros in the 3rd dimension
KE = sum(K11 .* delNonZero, 3);

[Mohammod Minhajur Rahman]

Hi Guillaume, Thank you for your answer. I tried your code and the problem I am facing is that my "KE" matrix has become "32 by 2304 " where "32 by 32" is the size of each cell matrices "K11{:}" and there are 72 of these. So, in short the size of "KE" matrix and "K11{:}" should match. Thanks again.

[Guillaume]

I'd made a rather critical typo, it should have been K11{:} in the cat, not K11(:). It would have resulted in an error in the sum. Whatever you did to resolve the error was incorrect.

Fixed now.

Note that I assume that the number of nonzeros in del match the number of matrices in that K11 cell array. A more faithful version of the code, that only sum the first nnz(del) elements of K11 would be:

KE = sum(K11(:, :, numel(delNonZero)) .* delNonZero, 3);

[Mohammod Minhajur Rahman]

Much Thanks! It does give me the right answers, however, I am still struggling to have better results based on computational time. May be there is something in my code that I need to do in correct way.

[Guillaume]

Well, I don't know how you created that K11, but it shouldn't be a cell array in the first place. It should have been created as a 3D matrix from the beginning. Cell arrays are slower than matrices, often by a lot (as was your original code). In my answer, the slowest part will be the conversion from cell to matrix.