Method Jacobi . Error: The variable x in a parfor cannot be classified.

Hello. I have a problem with function " parfor ". Please help, thank you!

A = [5 -2 3 0 2;-3 9 1 -2 3;2 -1 -7 1 4; 4 3 -5 7 1; 3 2 -4 5 -7]
b = [-1 2 3 0.5 4]'
x = zeros(1,5)';
n=size(x,1);
normVal=Inf; 
tol=0.001; itr=0;
tic
while normVal>tol
  xold=x;

    parfor i=1:n
        sigma=0;

       for j=1:n

            if j~=i
                sigma=sigma+A(i,j)*x(j);
            end            
       end      
        x(i)=(1/A(i,i))*(b(i)-sigma);
    end    
    itr=itr+1;
    normVal=abs(xold-x);
end
toc
fprintf('Solution of the system is : \n%f\n%f\n%f\n%f\n%f \n in %d iterations\n',x,itr);

Answer 1

[Edric Ellis]

parfor cannot run in this case because the iterations of your loop are order dependent. That is, to calculate a the value of x(i), you are using all the existing values of x that have been calculated in prior iterations.

To speed this code up, I would first look to vectorise all the operations. For instance, you can remove the inner loop by first creating a version of A with zero on the diagonal, and then using * to compute sigma in one go:

Azd = A - diag(diag(A));
...
    % instead of for j=1:n loop, simply compute
     sigma = Azd(i,:) * x;