How can i use symbolic variables in a parallel Computing (parfor)?

Hi guys,

I'm using 'parfor' instead of 'for' and performing some calculations with symbolic variables and matrices. However, I encountered some errors when using this function (figs belos).

Are there any solutions for this?

I attached the code.

thanks so much

Answer 1

[Matt J]

Dlu_11_1= zeros([M,N,N,M], 'sym') ;

parfor t=1:(M*N)^2
    
    [ki,kj,j,i]=ind2sub([M,N,N,M],t);
    
     Dlu_11_1(t)=diff(dlU_11(ki,kj),U1(i,j));
    
end

Dlu_11_1=reshape( Dlu_11_1 , M*N, []);

[asad]

Dear Matt,

Thanks for your response.

I actually made a mistake in the size of the matrix 'Dlu_11'. It should be:

dlU_11= zeros([M*N,1], 'sym') ;

However, there is a problem—the matrix 'Dlu_11_1' obtained from the old code is different from the one generated by the code you proposed.

I have attached the results here for you.

[asad]

I really appreciate your help, Matt.

I have solved the problem by changing the code to the following form:

Dlu_11_1= zeros([M*N,N,M], 'sym') ;

parfor t=1:(M*N)^2
    
    [s,j,i]=ind2sub([M*N,N,M],t);
    
     Dlu_11_1(t)=diff(dlU_11(s),U1(i,j));
end

Dlu_11_1=reshape( Dlu_11_1 , M*N, []);

Thanks a lot!

[Matt J]

This might be a little bit faster,

MN=M*N;

Dlu_11_1= zeros(MN, 'sym') ;

U1=U1.';

parfor t=1:(MN)^2
    
    [I,J]=ind2sub([MN,MN],t);
    
     Dlu_11_1(t)=diff(dlU_11(I),U1(J));
end

U1=U1.';

Dlu_11_1=reshape( Dlu_11_1 , MN, []);

[asad]

Thanks again Matt.

Answer 2

[Catalytic]

Why not simply -

Dlu_11_1 = reshape( jacobian(dlU_11, U1)   , M*N,N,M);