I am trying to solve SBS equations but they are taking too much memory and hence the code is slow

globalize_vars;

p=zeros(Nz,Nt);

%% initial conditions
if Is_stationary
    EL=El_s.*ones(Nz,Nt);
    ES=Es_s.*ones(Nz,Nt);
else
    EL =El_s.*ones(Nz,Nt);
    ES = Es_s.*ones(Nz,Nt);
    EL(1,:)=El_s(1)*exp(1i*phi);
    ES(Nz,:)=zeros;
    roh=sqrt(n*Q/c/GAMMAb)*(randn(Nz,Nt)+1i*randn(Nz,Nt));
end
ES0_T=zeros(1,iterationsNum); %Es(0,t) Stokes field in z=0
EL_L_T=ES0_T; %El(L,t) Stokes field in z=L 

%% Numerical Process
ELnew=EL;
ESnew=ES;
rohnew=roh;
pnew=p;

for index=1:iterationsNum
     
    croh=conj(roh);  
    ELz=(EL(2:end,index)-EL(1:end-1,index))/dz;
    ESz=(ES(2:end,index)-ES(1:end-1,index))/dz;

    ELnew(2:end,index+1)=EL(2:end,index)+dt*c/n*(1i*sigma*roh(2:end,index).*ES(2:end,index)-ELz);  %final equation for EL
    ESnew(1:end-1,index+1)=ES(1:end-1,index)+dt*c/n*(1i*sigma*croh(1:end-1,index).*EL(1:end-1,index)+ESz);  %final equation for ES 
    
    rohnew(:,index)=roh(:,index)+(dt*p(:,index));  %substitution for second derivative p=droh/dt 
    pnew(:,index)=p(:,index)+dt*((-GAMMAb+2*1i*Omega)*p(:,index)+1i*Omega*GAMMAb*roh(:,index)+eps0*gammaE*q^2*EL(:,index).*conj(ES(:,index))-2*1i*Omega*f(index)); 

    EL=ELnew;
    ES=ESnew;
    roh=rohnew;
    pnew=p

In the above code each variable is defined for 10000*10000 matrix and hence the computation time is high.

I am looking to make the code efficient and hence less memory consuming.

[Shivam]

Hi Yogesh,

Could you attach your whole code snippet for me to debug it?

Thanks

Answer 1

[Umang Pandey]

Hi Yogesh,

Given the partial nature of the code you've provided, pinpointing specific bottlenecks is challenging. I can see that your code is vectorized, which is the recommended practice for faster performance.

For further optimization, you can consult the following MATLAB documentation on "Techniques to Improve Performance":

https://www.mathworks.com/help/matlab/matlab_prog/techniques-for-improving-performance.html

Additionally, profiling your code can offer valuable insights into which sections are running slower than others. This information can help you in making targeted modifications to boost performance. For more details on profiling, you can visit the following MATLAB documentation page highlighting the steps for the same:

https://www.mathworks.com/help/matlab/matlab_prog/profiling-for-improving-performance.html

Hope this helps!

Best,

Umang