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Avoid for following loops

Hello everyone,

Can anyone show me how I can avoid following for loops. Thanks!

l1 = 100;
l2 = 100;
n1 = [1:10];
n2 = [1:10];
x3 = rand(N3,1);
for ik1=1:N1
    for ik2=1:N2
        for ix3=1:N3
            k1= 2*pi*n1(ik1)/l1;
            k2= 2*pi*n2(ik2)/l2;
            s = sqrt(k1^2+k2^2);
            if s~=0

  1 Comment

Perhaps, but it could get a little complicated-- you will need to use meshgrid() to define k1 and k2 over the full n1xn2 (10x10) grid, and defining the third dimension in R11 could get a bit complicated using purely vector operations.

Why are you doing this? Are you doing this for speed reasons? Oftentimes, for loops are actually faster than vectorized loops. Your best bet to improve speed is to preallocate R11 prior to entering the loop. That is, add this line to right before your for loop:

R11 = NaN(N1, N2, N3);   %this preallocates memory for R11

Now each iteration of the loop just fills in data in the already existing R11 variable.

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2 Answers

Answer by Sean de Wolski
on 18 Oct 2012
Edited by Sean de Wolski
on 18 Oct 2012
 Accepted Answer

How about this beauty?

k1 = (2*pi.*n1(1:N1).')./l1;
R22 = bsxfun(@times,k1,P);

Check to make sure it's close:


The difference arises because I used hypot in places of sqrt(x^2+y^2), it's a more numerically stable implementation of this.

Also note, that just redoing your for loops with some simple preallocation and calculation rearranging would help a lot.

preallocate R11 before the loop:

R11 = zeros(N1,N2,N3);

And move things that don't change into their respective loops

for ix1 = etc
   k1 = etc.
   for ix2 = etc.
      k2 = etc.

Since k1 and k2 are independent of the inner loops.

  1 Comment

Thanks again Sean de Wolski for your answer.

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Answer by Matt J
on 18 Oct 2012

              k1= 2*pi*n1(ik1)/l1;
              k2= 2*pi*n2(ik2)/l2;
              s = sqrt(k1.^2+k2.^2);


Matt's solution is certainly easier to understand. However, it will be slower, especially when N1,N2,N3 get large

As I said, that's probably true unless possibly, the ngrid output will be recycled later for further operations. Once you've paid the overhead of ndgrid execution time, further operations tend to be fast element-wise operations on the grid variables.

Also, you have not one but several calls to BSXFUN. Not sure how that adds up...

Well, I stand corrected, the ndgrid solution is still faster up to 150. At this point a smart for-loop wins:

    tau = 2*pi;
    R11 = zeros(N1,N2,N3);
    for ik1=1:N1
        k1= tau*n1(ik1)/l1;
        for ik2=1:N2
            k2 = tau*n2(ik2)/l2;
            s = sqrt(k1^2+k2^2);
            st = s*t;

Thanks for all your comments.

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