Explicit multiplication of matrices using for loops

Hi, I'm just getting to grips with for loops in Matlab, and I encountered a problem in understanding this specific code:

x = [4; 0.5 ; 1];
A = [6 8 1 ; 3 10 1 ; 1 0.5 12.5];
B = [2 0.5 1 ; 0 0.75 0.5 ; 0.5 4 1.5];
for ix = 1:3;
    yex(ix)=0;
    for jx = 1:3;
        yex(ix) = yex(ix) + A(ix,jx) * x(jx);
    end
end

for ix = 1:3;
    for jx = 1:3;
        Cex(ix,jx) = 0;
        for kx = 1:3 ;
            Cex(ix,jx) = Cex(ix,jx) + A(ix,kx) * B(kx,jx);
        end
    end
end

As you can see, it's a way of explicitly multiplying matrices using for loops. My problem is understanding the explicit part, and what each line of code is doing. Help in understanding this would be much appreciated. Thanks.

[dpb]

What, specifically don't you understand?

BTW, it would be more efficient to move the initializations outside the loops --

yex=zeros(1,3);
for ix = 1:3;
  ...

and

Cex=zeros(3);
for ix = 1:3;
  for jx = 1:3;
    ...

respectively.

Not sure what your question is really asking -- they compute two different sums, the latter one of which is the formal definition of a matrix multiplication. What do you consider 'explicit' as opposed to the rest, maybe?

[Image Analyst]

And FYI, you don't need a semicolon at the end of a "for" line of code.

Answer 1

[David Sanchez]

 for ix = 1:3; % loop along the elements of yex

      yex(ix)=0; % initialization of ix-th element of yex to zero

      for jx = 1:3; % iterate along the column elements of A in the ix-th row
          yex(ix) = yex(ix) + A(ix,jx) * x(jx); % update the value of yex, the yex previous value is added to the jx-th column element of A plus the jx-th value of x
      end
  end

The other for-loop is the same but with an extra dimension.