Vectorization or for loop (speedup)

I have a function the do operations on 3 dimensional matrix like this: user_defined_function is a function that does the calculations

a=rand(100,100,100);
b=rand(100,100,100);
c=rand(1,1000);
l11=zeros(size(a))
for i=1:1:100
    for j=1:1:100
        for o=1:1:100
            l11=user_defined_fnuction (a(o,j,i),b(o,j,i));
        end 
     end
end 

Basically the for-loop is slow so I tried to vectrize it. Using vectorization, I end up having a matrix of size (1e6,1e6) which exceeded maximum array size (requires 7320 GB). So I looked over the internet and I found this:

https://www.mathworks.com/help/matlab/matlab_prog/resolving-out-of-memory-errors.html

I tried the tall array but still I got the same problem. How I could solve this problem of maximum array size ( without the need to use spmd or for-drange since I am using parfor in the main program and the for loop is part of a function that does calculations).

Does deploying this code to MATALB server speedup the code

[Matt J]

There is no need to have 3 loops. You could just have,

a=rand(100,100,100);
b=rand(100,100,100);
c=rand(1,1000);
l11=zeros(size(a));
for k=1:1e6
            l11(k)=user_defined_fnuction (a(k),b(k));
end 

In any case, I doubt your example code is representative of what you are actually doing. Your loops contain only 1e6 iterations, so there is no way they should be able to fill a 1e6 x 1e6 matrix.

[Muna Tageldin]

yes you are right. My mistake:

Actually the simplified code is like this

for i=1:1:100
    for j=1:1:100
        for o=1:1:100
            l11=a(o,j,i)*b(o,j,i)*exp(-a(o,j,i)*c);
        end 
     end
end 

[Matt J]

Fine, but it is still not clear how this results in a 1e6 x1e6 matrix. Your loops are still performing only 1e6 calculations.

[Muna Tageldin]

so basically l1 has a size of 100*100*100. if I want to vectorize the above code the following is done:

a=reshape(a,[1,size(a,1)*size(a,2),size(a,3)];
b=reshape(b,[1,size(b,1)*size(a,2),size(b,3)];
sz=size(a,1)*size(a,2),size(a,3)-size(c,2);
c=[c  zeros(1,sz)];
l1=(a.'.*c.').*exp(-b)

Eventually using the above code, l1 is a mtrix of size 1e6*1e6 (error maximum array size reaced: out of memory)

Answer 1

[Matt J]

Your vectorized code doesn't resemble at all what your for-looped code is computing. The vectorized implementation of your for-loops would be,

a=a(:);
b=b(:); 
c=c(:).';

l1=(a.*b).*exp(-c.*a);

This will be a 1e6 x 1e3 matrix, which will be 4GB in single floats. A large matrix to be sure, but possible on a 32GB RAM machine. Why though do you need so much data in memory at the same time?

[Muna Tageldin]

yes you are correct. I was trying to vectorise the code by appending zeros to the array z to match the sizes of a, b and c and then do multiplication. But in some cases, I would need to operate on large data sets. For example, c could be of size 1*1e10. then resulting matrix would be of size 1e10*1e6. In this case, I get memory out of bounds error. How can I solve this problem ?

[Matt J]

I can't say what the solution would be because I don't know how l11 is being used. It's hard to image why a 1e10 x 1e6 matrix would need all of its data in RAM simultaneously.