Faster projected-norm (quadratic-form, metric-matrix...) style computations
- by thekindamzkyoulike
I need to perform lots of evaluations of the form
X(:,i)' * A * X(:,i) i = 1...n
where X(:,i) is a vector and A is a symmetric matrix. Ostensibly, I can either do this in a loop
for i=1:n
z(i) = X(:,i)' * A * X(:,i)
end
which is slow, or vectorise it as
z = diag(X' * A * X)
which wastes RAM unacceptably when X has a lot of columns. Currently I am compromising on
Y = A * X
for i=1:n
z(i) = Y(:,i)' * X(:,i)
end
which is a little faster/lighter but still seems unsatisfactory.
I was hoping there might be some matlab/scilab idiom or trick to achieve this result more efficiently?
