How I can speed up of the 8 nested FOR loops with high values in each loop ?

Hello everyone , I have a long code that using 8 nested FOR loops and 4 of these loops contain of 30 values while another 4 loops contain of 20 values as follows:

M1 = M2 = M3 = M4= 1:30 ;
M5 = M6 = M7 = M8= 1:20 ;
for n1=1:size(M1,2)
 for n2=1:size(M2,2)

   for n3=1:size(M3,2)

     for n4=1:size(M4,2)

        for n5=1:size(M5,2)

          for n6=1:size(M6,2)

             for n7=1:size(M7,2)

               for n8=1:size(M8,2)
                  My code

When I run this code its take long time and then restart my computer without any output, while if I use less value for example 3 for all 8 loops doesn't take long time and give me true result. can you help me to speed up my code to solve this problem please?

Answer 1

[Aquatris]

Depending on the problem you are trying to solve, you can convert the nested for loops into matrix algebra instead.

The reason why it is fast when you use 3 for all 8 loops is, the number of times the for loops run is around 3^8. When you use 20, it is 20^8 or so, which is a significant increase in the number of computations, hence time.

Otherwise, you might wanna explore Parallel Computing Toolbox if you have access to it.