Most efficient way to do matrix operation v'*M*v

Hi all,

i have a problem where I need to do the following operation:

R is a square matrix
V is a nonsquare matrix

The operation is to multiply 1 - V(i, :)*inv( R )*V(i, :)', and store the result for each i.

Right now I'm doing it using a for loop:

Rinv = inv( R );
for i=1:n
  val(i) = 1 - Z(i, :)*Rinv*Z(i, :)';
end

My problem requires performing this calculation a few million times and I'm trying to optimize it as much as possible. Is there a way to get rid of the for loop? I could do V*inv( R )*V', but that performs a lot more inner products than I actually need.

Thanks for the help.

Answer 1

[Roger Stafford]

Assuming the values in V are real,

   val = 1-sum((V/R).*V,2);

If V has complex-valued elements, change that to

   val = 1-sum((V/R).*conj(V),2);

Note that V must have the same number of columns as R has rows and columns.