my_fgmres.m

求解线性系统的Krylov方法的工具箱

function [x,iter,flg,inner]=my_fgmres(A,b,tol,restart,maxit,M1,M2,p_type,x0)
% FGMRES 
% [x,iter,flg,inner]=my_fgmres(A,b,tol,restart,maxit,M1,M2,p_type,x0)
% this is the implementation of preconditioned GMRES method
% m is the number of restart, 
% p is the preconditioning type, p=0: implicit preconditioner; p=1 explicit
% preconditioner
% flg=0 success; flg=1 fail;

% Developed by: Plum_Liliang UESTC China
% Date        : 2006-06-30

% checking input arguments and assign default value
[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

if m~=m_b
    error('The right-hand vecotor must have the same length of A!')
end

if nargin<2
    error('Not enough input arguments!');
end
if nargin<3 | tol==[]
    tol=1e-6;
end
if nargin<4 | restart==[]
    restart=min(10); % the maximum outer iteration is assigned to 10 defaultly
end
if nargin<5 | maxit==[]
    maxit=min(20,n);
end

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

% Check the preconditioners
if nargin>=6 & ~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>=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

if nargin<8 | p_type==[]
    p_type=0;
end

% check the initial guess
if nargin<9 | x0==[]
    x0=zeros(n,1); % the initial guess is defaultly 0-vector;
else
    [m_x,n_x]=size(x0);
    if m_x~=n | n_x~=1
        error ('The initial guess should be has the same size with the right-hand vector!');
    end
end