Starting diary file diary-08-May-2013.txt

A = grid5(100);
n = length(A)
n =
       10000
b = rand(n,1);
[x, flag, relres, iter, resvec] = pcg(A,b,1e-8,10*n);
iter
iter =
   302

semilogy(resvec / resvec(1)),shg


help luinc
 LUINC  Sparse Incomplete LU factorization.
 ...

help cholinc
 CHOLINC  Sparse Incomplete Cholesky and Cholesky-Infinity factorizations.
 ...

hold on

figure,spy(A)
nnz(A)
ans =
       49600
nnz(chol(A))
ans =
     1000099
R = cholinc(A,'0');
nnz(R)
ans =
       29800
nnz(tril(A))
ans =
       29800

figure,spy(R)

help pcg
 PCG   Preconditioned Conjugate Gradients Method.
 ...

[x,flag,relres,iter,resvec] = pcg(A,b,1e-8,n,R',R);

shg
semilogy(resvec / resvec(1),'r'),shg

opt.droptol=.1
opt = 
    droptol: 0.1000
R = cholinc(A,opt);
nnz(R)
ans =
       29800
nnz(triu(A))
ans =
       29800
opt.droptol=.05
opt = 
    droptol: 0.0500
R = cholinc(A,opt);
nnz(R)
ans =
       39601
nnz(chol(A))
ans =
     1000099

[x,flag,relres,iter,resvec] = pcg(A,b,1e-8,n,R',R);

semilogy(resvec / resvec(1),'g'),shg

diary off