MATLAB: Fast matrix multiplication in loop

loopmatrix multiplication

Dear All,

I have two matrices with dimensions 3×3 and E6x3. I need to multiply each row of the latter with the former. It's like

a=rand(3,3);
b=(1000000,3);
for i=1:size(b,1)
   c=a*b(i,:)';
end

However, this step takes hours to be done. I wonder if there is any faster way to do this.

Cheers.

a=rand(3,3);
b=rand(100,3);
n=size(a,2);
m=size(b,1);
c=zeros(m,n);
for i=1:size(b,1)
 c(i,:)=a*b(i,:)';
end

%or simply

c=(a*b')'

a=rand(4,3)
b=rand(1,6)
[n,m]=size(a)
p=numel(b);
c=reshape(bsxfun(@times, repmat(a(:)',numel(b),1),b')',n,m,p)

Horizontal concatenation

 c=[a b]

example

for horizontal concatenation

 a=rand(20,6);
 b=rand(20,3);
 c=[a b]

for vertical concatenation

 a=rand(6,20)
 b=rand(3,20)
 c=[a;b]