Make this matrix multiplication more efficient

Hello,

I would like to do the following matrix multiplication much efficiently:

m=1000;n=500;
a=zeros(n,1);
b=rand(n,1);
A=rand(m,n);
B=rand(m,m);
for i=1:n
    a(i)=b'*(A'*B(i,:)'*B(i,:)*A)*b;
end

Thanks in advance

Answer 1

[James Tursa]

a = (B(1:n,:)*(A*b)).^2;

You dimensions for B look a little strange to me, since your calculations do not use all of the rows of B (hence the B(1:n,:) reduction above).

[Ignacio Echeveste]

Yes, the dimensions were wrong. Thank you, it is much more efficient.

Answer 2

[Richa Gupta]

Hi Ignacio,

The code below reduces the time from 2.6 secs to 0.06 secs on my machine:

m = 1000; n = 500;
a = zeros(n,1);
b = rand(n,1);
A = rand(m,n);
B = rand(m,m);
for i=1:n  
  temp =(B(i,:)*A)*b;
  a(i) = temp'*temp;
end

Hope this helps.