Creating function to use pcg

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Samuel Martinez 2021-6-26

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/865970-creating-function-to-use-pcg

Hello, I am solving a problem that involves matrices of

per side, but they are matrices that only have 4 different diagonals of 0, so I am looking to implement what you mention in the following link in the part of Using Function Handle Instead of Numeric Matrix.

I'm going to show you the structure that I have in the matrix for the case of

I get this from here. Well what I tried to do was the following:

function y=afun(x)
nx = 5;
N = nx*nx;
x1 = linspace(0,1,nx);
y1 = x1;
[X,Y] = ndgrid(x1,y1);
dx = x1(2)-x1(1);
k=@(x,y) 1+x.^2+y.^2;
isDirichlet = (X==0) | (X==1) | (Y==0) | (Y==1);
Ad = zeros(N,5);
Ad(:,1) = -k(X(:),Y(:)+dx/2); 
Ad(:,2) = -k(X(:)+dx*0.5,Y(:)); 
Ad(:,4) = -k(X(:)-dx*0.5,Y(:)); 
Ad(:,5) =  -k( X(:), Y(:)-dx/2 );
Ad(:,3) = -sum( Ad(:,[1,2,4,5]), 2 ); 
idx = find(isDirichlet(:)); 
L=Ad(:,1);L(idx)=[];B=Ad(:,2);B(idx)=[];
C=Ad(:,3);C(idx)=[];U=Ad(:,4);
U(idx)=[];UP=Ad(:,5);UP(idx)=[];
n=sqrt(size(C,1));
l=B(1:end-1);s=U(2:end);
for i=n:n:(n-1)*n
l(i)=0;s(i)=0;
end
y=([[diag(zeros(n));L(1:(n-1)*n)] +[0;l] +[C] +[s;0] +[UP(n+1:end);diag(zeros(n))]]).*x;
end

but when I apply pcg it does not solve the system correctly. I do not know if my code has any logic errors or if I am not understanding how the implementation works with afun.

I hope you can help me, thank you very much.