Vectorizing for loops

Question

Andreas 2011-1-21

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/248-vectorizing-for-loops

I have a function with 3 for loops and wondered if:

Can these for loops be vectorized?
If yes, could I get some guidance vectorizing them?
If no, why not?
As a newbie to this forum and MatLab, does the forum consider these appropriate questions to ask?

Function follows:

function[E, L, G] = SetPrincipalComponentBasis(S, A)
% S : covariance matrix
% A : conditioning matrix
if isempty (A)
    N = size (S, 1);
    K = 0;
    [E_, L_] = eig (S);
    E = E_;
      for n = 1 : N
         E (: , n) = E_ (: , N - n + 1);
         L (n) = L_ (N - n + 1, N - n + 1);
      end
else
   [K,N]=size(A);
    E=[];
    B=A;
      for n=1:N-K
          if ~isempty(E) 
              B=[A
                  E'*S];
          end
          e=SetFirstEigenVectors(S,B);
          E=[E e];
      end
      for n=N-K+1:N
          B=E'*S;
          e=SetFirstEigenVectors(S,B);
          E=[E e];
      end
      E=[E(:,N-K+1:N) E(:,1:N-K)];
  end
  L=diag(E'*S*E);
  G=diag(sqrt(L))*inv(E);
  G=G(K+1:N,:);

Some additional info as requested by Walter and Matt...

Sizes of S and A typically less than 30 x 30. Sometimes only 5 X 5. As you discerned they are regular matrices. S & A will always have the same dimensions.

SetFirstEigenVectors code follows:

function e = SetFirstEigenVectors(S,A) N=size(S,1); P=eye(N); if rank(A)>0 P=eye(N)-A'*inv(A*A')*A; end [E_,L_]=eig(P*S*P'); [m,I]=max(diag(L_)); e=E_(:,I);

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Andreas 2011-1-21

Doug's comments led me do some digging through my sources. The code came to me from a friend, who just advised me he got it from: http://www.mathworks.com/matlabcentral/fileexchange/23271

So anyone can look at the original and the zip file has a data.mat file to run an example.

I agree with Doug. The N-K looks funny. Note that the original version has slightly different names for the functions I supplied, GenPCBasis and GenFirstEigVect. You guys go well beyond the call of duty on this forum. Many thanks for any guidance. -- A

Andreas 2011-1-21

One more quick comment. At this stage of my learning MatLab, I'm more interested in getting a clearer idea of how to go about converting for loops into more vectorized solutions than making this particular set of code work (that may come latter ;-)

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Answer 1

Walter Roberson 2011-1-21

2
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https://ww2.mathworks.cn/matlabcentral/answers/248-vectorizing-for-loops#answer_327

在 MATLAB Online 中打开

Your loop

      for n = 1 : N
         E (: , n) = E_ (: , N - n + 1);
         L (n) = L_ (N - n + 1, N - n + 1);
      end

is equivalent to

E = fliplr(E_);
L = flipud(fliplr(L_));

provided that your covariance matrix is square. (The square constraint comes out of the fact that you defined N as size(S,1) but use N in the second index rather than the first; defining N as size(S,2) would remove this constraint.)

We cannot determine whether the loops in your "else" condition can be vectorized without seeing the code for SetFirstEigenVectors()