MATLAB: For-loop order

for loopspeed

I am wondering whether the order of for-loop affects the speed. For example, I am running multiple for-loops and they have different number of elements.
for i=1:n
  for j=1:m
     for  k=1:p
        ....
       end
     end
  end
In this case, is it better to place the loop with the smallest number into the outer loop ? or doesn't it matter?

Best Answer

For the m-code loop itself it probably doesn't matter since the total number of iterations is the same. The stuff inside the for loops can easily dominate the run-time so it may be a moot point. But for memory access, it is often good practice to transverse an array in memory order to take advantage of memory caching. E.g.,
A = some MxN matrix
for i=1:M
    for j=1:N
        % some stuff involving A(i,j) here

    end
end
The above does not access the elements of A in linear order since A is stored in column order. So the memory access pattern for A jumps around in memory.
A = some MxN matrix
for j=1:N
    for i=1:M
        % some stuff involving A(i,j) here
    end
end
The above does access A in linear order in memory, so it would take better advantage of the memory cache.
All that being said, the m-code for-loop stuff and what you are doing inside the for-loops may easily dominate the A memory access times so in practice you may not see much difference between the two.
E.g., take this code
A = rand(5000);
disp('Access jumping around in memory');
tic
for i=1:5000
    for j=1:5000
        A(i,j);
    end
end
toc
disp('Access in linear order');
tic
for j=1:5000
    for i=1:5000
        A(i,j);
    end
end
toc
And run it:
Access jumping around in memory
Elapsed time is 1.542680 seconds.
Access in linear order
Elapsed time is 0.802103 seconds.
Related Question