optimise nested for-loop

I have this function (test) which uses nested-for loops, usually the function takes 75 seconds (interested in <4 seconds).

function l1=test(a,z)
f=zeros(size(z));
[ep,u,lam]=ndgrid(1e-3:1e-2:0.99,1e-3:1e-2:0.99,1e-3:1e-2:0.99);

l1=zeros(size(ep));
 for i=1:size(ep,1)
         for p=1:size(ep,2)
             for o=1:size(ep,3)                                                                                                                                      
                l1(i,p,o)=ep(i,p,o)*lam(i,p,o)+sum(a*u(i,p,o)*exp(-z));
             end
         end 
 end
end

z is an array of data (size >4000)

I tried to use bsxfun and vectorize the code by appending zeros to z and reshaping ep,lam and u, but I am faced with MATLAB limitations (required memory 70 GB of RAM). To vectorize it, I appneded zeros to array z then with multiplication I got the following:

l1=(ep.*lam)+sum(a*u.'.*z);

the multiplication of a*u.'.*z results in (1e6,1e6) matrix. How can I solve this problem?

I tried also using tall array but no sucess. Is there a method I can use that can speedup this function

I also looked up the below link for solutions to memory out of bound.

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

Answer 1

[sushanth govinahallisathyanarayana]

Is a a constant? You can pre-calculate ep(i,p,o)*lam(i,p,o) outside the loop as

ep(i,p,o).*lam(i,p,o). Then you only have a loop over z to work with. What is the dimensions of z? ep, u and lam are 99x99x99 cubes. You can replicate z in one of the directions and make it simpler to compute.