MATLAB: X’SX were X is a column vector and S is a matrix.

arrayfungpuMATLABparallel computing

I'm trying to do X'SX N times and store the results in a matrix that is N long.
Remembering this is an inner product so the output is 1xN. X is (dx1) and S is (dxd), Where d is on the order of 10 and N is large.
I currently have the for loop below:
X = (X-mu);
N = length(X)
z = zeros(length(X),1);
for i = 1:N
z(i) = X(:,i)'*S*X(:,i);
end
I want to run the loop faster(more parallel) as N can be upwards of 1,000,000. Optimally I would use gpuArrays, but I ran into the problem that I don't know how to work on the rows element-wise and the columns matrix wise. Any help would be great.

Best Answer

I suppose what you mean is that X is d-by-N, not d-by-1? So it seems like what you want is
SX = S * X;
for i = 1:N
    z(i) = X(:,i).'*SX(:,i);
end
So you can vectorize this with
z = sum(X.*(S*X), 1).';
Actually, your code is quite explicit that X is a vector, but then saying that X'*S*X produces a vector rather than a scalar makes no sense, so perhaps you should clarify exactly what these shapes are.
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