This is /Users/gilbert/219/Matlab/startup.m
Starting diary file diary-25-Apr-2018.txt

A = grid5(100);
n = length(A)
n =
       10000
spy(A)
b = rand(n,1);

[x, flag, relres, iter, resvec] = pcg(A,b,1e-8,10*n);
flag
flag =
     0
iter
iter =
   301
semilogy(resvec / resvec(1))
hold on

help ichol
 <strong>ichol</strong>  Sparse Incomplete Cholesky factorization 
    ...

opt1.type = 'nofill'
opt1 = 
    type: 'nofill'
L = ichol(A,opt1);
nnz(L)
ans =
       29800
nnz(tril(A))
ans =
       29800
figure,spy(L)

[x, flag, relres, iter, resvec] = pcg(A,b,1e-8,10*n,L,L');
flag
flag =
     0
iter
iter =
    98
figure(1),hold on

semilogy(resvec / resvec(1),'r')
opt2.type = 'ict'
opt2 = 
    type: 'ict'
opt2.droptol = 1;
L = ichol(A,opt2);
nnz(L)
ans =
       10000
[x, flag, relres, iter, resvec] = pcg(A,b,1e-8,10*n,L,L');
iter
iter =
   301
max(diag(L))
ans =
   (1,1)        2
min(diag(L))
ans =
   (1,1)        2

opt2.droptol = .01;
L = ichol(A,opt2);
nnz(L)
ans =
       49303
nnz(tril(A))
ans =
       29800
figure,spy(L)

[x, flag, relres, iter, resvec] = pcg(A,b,1e-8,10*n,L,L');
iter
iter =
    51
figure(1),hold on
semilogy(resvec / resvec(1),'g')

load bcsstk08
A = BCSSTK08;
n = length(A)
n =
        1074
b = rand(n,1);

[x, flag, relres, iter, resvec] = pcg(A,b,1e-8,10*n);
semilogy(resvec / resvec(1));

L = ichol(A,opt1);
[x, flag, relres, iter, resvec] = pcg(A,b,1e-8,10*n,L,L');
figure(1),hold on
semilogy(resvec / resvec(1),'r')
iter
iter =
    33

cond(full(A))
ans =
   2.5988e+07
cond (full((L\A)/L'))
ans =
   82.8415

nnz(L)
ans =
        7017
nnz(tril(A))
ans =
        7017
nnz(chol(A))
ans =
      234160

clear

load nonsymmats.mat
whos
  Name                  Size                 Bytes  Class     Attributes

  arc130              130x130                17640  double    sparse    
  badA                100x100                 2552  double    sparse    
  badb                100x1                    800  double              
  mult_dcop_03      25187x25187            3292960  double    sparse    
  sinc12             7500x7500             4603880  double    sparse    
  watt1              1856x1856              196616  double    sparse    
  west0479            479x479                34400  double    sparse    

A = badA;
spy(A)
n = length(A)
n =
   100
b = badb;

spy(A)

badb
badb =
     1
     0
     0
     0
     ...
     0
     0

x = A \ b
x =
     0
     0
     0
     0
     ...
     0
     1

[x, flag, relres, iter, resvec] = gmres(A,b,[],1e-8,n);
x 
x =
     0
     0
     0
     0
     ...
     0
     1

iter
iter =
     1   100
figure
semilogy(resvec / resvec(1),'r')

[x, flag, relres, iter, resvec] = bicgstab(A,b,1e-8,n);
x
x =
     0
     0
     0
     0
     ...
     0
     0
flag
flag =
     4
iter
iter =
     0

spy(west0479)
diary off