# Make this matrix multiplication more efficient

1 view (last 30 days)
Ignacio Echeveste on 23 Nov 2015
Commented: Ignacio Echeveste on 26 Nov 2015
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

James Tursa on 25 Nov 2015
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 on 26 Nov 2015
Yes, the dimensions were wrong. Thank you, it is much more efficient.

Richa Gupta on 25 Nov 2015
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.

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