How I can speed up My code that contain of 8 FOR nested loops ?

Hi every one , I have a code that contain of 7 nested FOR loops, each loop from 1:30 . My idea of this code is calculate many of a special functions for each value of these loops and many of files need to calling, for example :

A1= 1:30
A2= 1:30
A3=1:30
A4=1:30
A5=1:30
A6=1:30
A7=1:30
for b1=1:length(A1)
  for b2= 1: length(A2)
    for b3= 1:length(A3)
      for b4=1:length(A4)
        for b5= 1: length (A5)
           for b6=1:length(A6)
             for b7=1:length(A7)
               N(b1,b2,b3,b4,b5,b6,b7)=M(b1,b2,b3,b4,5b,b6,b7)*T(b1,b2,b3,b4,5b,b6,b7)
             end
           end
         end
       end
     end
   end
 end

where M and T are have a unique value for each iteration , for example M(1,1,1,1,1,1,1)=5 , M(1,2,1,1,1,1,1)=8 and so on , when I run my code its tack long time and then restart my computer without any result can you help me to speed up this code ? thank you in advance .

[James Tursa]

Are M and T variables, or are they functions? If they are variables use the .* operator. If they are functions, either vectorize the functions if you can, or use the arrayfun() function (which may not be much faster).

[Adam Danz]

So, M and T are both 7-dimensional arrays where each dimension contains 30 elements. Is that correct?

When I create such an array using rand()

M = rand(30,30,30,30,30,30,30);

Matlab throws the following error:

Error using rand
Requested 30x30x30x30x30x30x30 (162.9GB) array exceeds maximum array size preference. Creation of arrays greater than this limit
may take a long time and cause MATLAB to become unresponsive. See array size limit or preference panel for more information.

So before I dig any deeper, please provide more info about your variables M and T. Confirm their sizes, class, what's stored in them, how you created them, where they came from, etc.

Also, the idea here is for you to do most of the work and for us to do as little as possible. So when you provide code, make sure it's correct code ('for' does not have an upper case F and always ends with an 'end').

[A]

Thank you James and Adam , My code is long and contain of many function to calling so I but that just as example . when I use A1=A2=A3=A4=A5=A6=A7=1:3 all the functions run and give right result but if I increase the values of A1=A2=A2=A4=A5=A6=A7=1:30 the program take a long time and become unresponsive . How I can solve that problem ?

[dpb]

Buy more memory.

[Stephen23]

Or use tall arrays.

[Adam Danz]

You haven't answered the question as to whether 'A' is a function or a 7D array. If it's an array and this example really represents what you want to do you might be able to avoid loops and replace them with a vector method which may (or may not) speed things up.

Nevertheless, given the little I know about your problem, it seems that another solution may be to process your data in chunks. For example, you could save data to a file every time A=3 loop is complete and then free up the memory in matlab so it's available for the next series of loops.

[OCDER]

Even without knowing the class of M and T, it takes a while. 30^7 is 21,870,000,000 iterations. That's ~45s to just go through the for loop.

 tic
 for j = 1:30^7
 end
 toc %45s

Any math inside is just going to make the things slower. You may need to use parfor to divide up the compute time, or vectorize a segment of the loop to prevent memory error.

Answer 1

[David Goodmanson]

Hi A,

I am assuming that M,T and N are 7d arrays of the same size, n x n x n x n x n x n x n for some n. For n = 30 that's 30^7 = 2.1870e+10 elements per array. Not much to say about the memory requirements, they are what they are.

As far as speed, though, in place of all the for loops you can write

X = M(:).*T(:);
NN = reshape(X,n,n,n,n,n,n,n);

On my pc the for loops start to take significant time around n = 12. It's about 8 seconds for the for loop version, compared to .2 sec for the code just above, and the ratio will get more pronounced as n increases.

----------p.s. on for loops:

You have defined A1 = 1:n (1:30 in your case), so rather than write

for b1 = 1:length(A1) etc.

you can just write

for b1 = A1 etc.

Also it makes sense to preallocate N as

N = zeros(n,n,n,n,n,n,n)

[A]

Thank you David , I already determinant N=zeros(1:length(A1),1:length(A2),1:length(A3),1:length(A4),1:length(A5),1:length(A6)) to speed my code but I did not notice any change in speed. And for b1 = A1 etc it's give me error because I need all element in my code as for I want N if A1=1,A2=1,A3=1,A4=1,A5=1 and A6=1 to compare with N if A1=2,A2=1,A3=1,A4=1,A5=1 and A6=1 and so on . I can't know the code problem because its take a long time without give me any error message in command window :(