my_cocg.asv

求解线性系统的Krylov方法的工具箱

function [x,iter,flg,res]=my_cocg(A,b,tol,maxit,M1,D,M2,x0)
% [x,iter,flg,res]=my_cocg(A,b,tol,maxit,M1,D,M2,x0)
% This code implements cocg algorithm with preconditioners M1 and M2, D if
% necessary
% flg=0 success; flg=1 failed to ;

% Developed by: Plum_Liliang UESTC China
% Date        : 2006-05-13
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Check the dimension of A and the right-hand vector b
[m,n]=size(A);
if m~=n
    error('The coefficient matrix must be square!')
end
[m_b,n_b]=size(b);
if n_b~=1
    error('b must be a vector!')
end
nz=nnz(A);
if m~=m_b
    error('The right-hand vecotor must have the same length of A!')
end

% Check the input arguments and assign the default value
if nargin<2
    error('Not enough input arguments!');
end

if (nargin < 3) | isempty(tol)
   tol = 1e-6;
end
if (nargin < 4) | isempty(maxit)
   maxit = min(n,20);
end

% if 'b' is zero then the solution is zero
norm_b=norm(b);
if norm_b==0
    x=0;
    iter=0;
    return;
end

% Check the preconditioners
if nargin>=5 & ~isempty(M1)
    existM1=1;
    if ~isequal(size(M1),[m,n])
        error('The preconditioners M1 should match the size of A!')
    end
else
    existM1=0;
end
if nargin>=6 & ~isempty(D)
    existD=1;
    if ~isequal(size(D),[m,n])
        error('The preconditioners D should match the size of A!')
    end
else
    existD=0;
end
if nargin>=7 & ~isempty(M2)
    existM2=1;
    if ~isequal(size(M2),[m,n])
        error('The preconditioners M2 should match the size of A!')
    end
else
    existM2=0;
end

% Check the initial guess x0
if nargin==8 & ~isempty(x0)
    if ~isequal(size(x0),[m,1])
        error('The initial guess x0 must have the same length of A')
    end
else
    x0=zeros(m,1);
end

if nargin>8
    error('Too many input arguments!')
end

% set up for the PCG method
flg = 1;
x=x0;
v=b-A*x;
tol = tol*norm_b;
p = zeros(n,1);
beta = 0;
w = v;
if existM1
    w = M1 \ w;
end
if existD
    w = D \ w;
end  
if existM2
    w = M2 \ w; 
end
rho1 = v.'*w;
res(1) = 0;
for iter = 1:maxit
    p = w + beta*p;
    u = A*p;
    mu = u.'*p;
    if mu == 0
        flg = 2;
        return;
    end
    alf = rho1 / mu;
    x = x + alf*p;
    v = v - alf*u;
    res(iter) = norm(v);
    if res(iter) < tol
        flg = 0;
        return;
    end
    w = v;
    if existM1
        w = M1 \ w;
    end
    if existD
        w = D \ w;
    end  
    if existM2
        w = M2 \ w; 
    end
    rho2 = v.'*w;
    if abs(rho2) < 1e-16
        flg = 3;
        return;
    end
    beta = rho2 / rho1;
end