Explicit multiplication of matrices using for loops

Question

Chris 2013-11-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/105955-explicit-multiplication-of-matrices-using-for-loops

回答： David Sanchez 2013-11-13

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.

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dpb 2013-11-13

在 MATLAB Online 中打开

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 2013-11-13

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

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Answer 1

David Sanchez 2013-11-13

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/105955-explicit-multiplication-of-matrices-using-for-loops#answer_115081

在 MATLAB Online 中打开

 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