MATLAB: Problem in Using Parallel Feature for a “For Loop”!

parallel

I have written a code for Newton Raphson which includes two "for loops" inside of each other. Basically, I have a 1000 nonlinear equations, which are in a function called "f_int". In the "for loop" I try to construct tangent stiffness of these 1000 equations by finite difference, which is as below:
f_int = internal_eqns1000(X);
for i=1:1000
    for j=1:nvar
        X(j)=X(j)+h;
        f_intp1 = internal_eqns1000(X);
        k_k(i,j)=(f_intp1(i)-f_int(i))/h;
        X(j)=X(j)-h;
    end
end
After the completion of tangent stiffness, another "X" will be created and the loop will run again until convergence. This for loop might be required to run more than 100 times, and each time it takes 30 minutes average. I would like to use parallel to decrease the computational timing, but I was not successful. The change I made is as below:
f_int = internal_eqns1000(X);
parfor i=1:1000
    for j=1:nvar
        X(j)=X(j)+h;
        f_intp1 = internal_eqns1000(X);
        k_k(i,j)=(f_intp1(i)-f_int(i))/h;
        X(j)=X(j)-h;
    end
end
But this does not work and gives me an error: "due to the way "X" is defined, parallel computation cannot be used here".
Please let me know how can I write the code such that it will be run with parallel feature. Thank you.

Best Answer

X has to be sliced correctly. https://www.mathworks.com/help/distcomp/sliced-variable.html
But I didn't realize Newton Raphson iterations can be done in parallel. Or are you doing independent NR calc for many situations?
X = zeros(1000, nvar);
f_int = internal_eqns1000(X); 
parfor i=1:1000 
    for j=1:nvar 
        X(i,j)=X(i,j)+h; 
        f_intp1 = internal_eqns1000(X(i,j)); 
        k_k(i,j)=(f_intp1(i)-f_int(i))/h; 
        X(i,j)=X(i,j)-h; 
    end
end
Related Question