a simpler way of doing a nested loop

Hello,

Is there a more efficient alternative way that does the same function as:

V=[1+1i +1-1i -1+1i -1-1i];
for m1=1:length(V)
  a=V(m1);
  for m2=1:length(V)
    b=V(m2);
    for m3=1:length(V)
      c=V(m3);
      for m4=1:length(V)
        d=V(m4);
        h=[.3 .2]*[a b].'+[.5 .8]*[c d].';
        h1(m1,m2,m3,m4)=h;
      end
    end
  end
end

Thanks.

[Stephen23]

This is what you need to read and understand:

http://www.mathworks.com/help/matlab/matlab_prog/vectorization.html

[Mnr]

Thanks.

[Stephen23]

The question is continued here:

http://www.mathworks.com/matlabcentral/answers/252250-how-to-generalize-a-nested-for-loop-2

Answer 1

[Walter Roberson]

V=[1+1i +1-1i -1+1i -1-1i];
[A,B,C,D] = ndgrid(V);
h1 = 0.3*A + 0.2*B + 0.5*C + 0.8*D;

[Mnr]

Thank you, but does not give the same answer.

[Walter Roberson]

I just tried it and it gives an exact identical answer, not a single bit difference.

[Mnr]

oh sorry. I did not clear the memory. Thank you for your help.

[Mnr]

Is there is a way of writing this code in a more general form such that it works for different sizes of V? Thank you.

[Stephen23]

@Mnr: try this:

V = [1+1i,+1-1i,-1+1i,-1-1i];
W = [0.3,0.2,0.5,0.8];
N = numel(V);
X = cell(1,N);
[X{:}] = ndgrid(V);
Y = cat(N+1,X{:});
S = [ones(1,N),N];
Z = sum(bsxfun(@times,reshape(W,S),Y),N+1);

Answer 2

[Jan]

I prefer Walter's solution, because it is nice. But it is worth to mention, that a pre-allocation improves the loop version. Replacing the dot-product by direct algebra and avoiding repeated calculations improves the speed also:

V = [1+1i, 1-1i, -1+1i, -1-1i];
n = length(V);
h1 = zeros(n, n, n, n);
for m1 = 1:n
  c = 0.3 * V(m1);
  for m2 = 1:n
    c = c + 0.2 * V(m2);
    for m3 = 1:n
      c = c + 0.5 * V(m3);
      for m4 = 1:n
        h1(m1,m2,m3,m4) = c + 0.8 * V(m4);
      end
    end
  end
end

Timings for 5000 repetitions, Matlab R2011b/64/Win7:

 Original:  8.90 sec
 Walters ndgrid: 1.47 sec
 Loop, pre-allocation, inlined dot products: 0.34 sec

[Mnr]

Thank you so much!

[Mnr]

Is there is a way of writing this code in a more general form such that it works for different sizes of V? Thank you.