121 lines
3.1 KiB
Mathematica
121 lines
3.1 KiB
Mathematica
|
%%*************************************************************************
|
||
|
|
%% HSDbicgstab
|
||
|
|
%%
|
||
|
|
%% [xx,resnrm,flag] = HSDbicgstab(A,b,M1,tol,maxit)
|
||
|
|
%%
|
||
|
|
%% iterate on bb - (M1)*AA*x
|
||
|
|
%%
|
||
|
|
%% r = b-A*xtrue;
|
||
|
|
%%
|
||
|
|
%%*************************************************************************
|
||
|
|
|
||
|
|
function [xx,resnrm,flag] = mybicgstab(A,b,M1,tol,maxit)
|
||
|
|
|
||
|
|
N = length(b);
|
||
|
|
if (nargin < 5); maxit = min(50,max(5,length(A.mat22))); end;
|
||
|
|
if (nargin < 4); tol = 1e-8; end;
|
||
|
|
tolb = min(1e-4,tol*norm(b));
|
||
|
|
flag = 1;
|
||
|
|
|
||
|
|
x = zeros(N,1);
|
||
|
|
if isstruct(A); r = b-matvec(A,x); else; r = b-mexMatvec(A,x); end;
|
||
|
|
err = norm(r); resnrm(1) = err; minresnrm = err; xx = x;
|
||
|
|
if (err < tolb); return; end
|
||
|
|
|
||
|
|
omega = 1.0;
|
||
|
|
r_tld = r;
|
||
|
|
xold = x;
|
||
|
|
%%
|
||
|
|
%%
|
||
|
|
%%
|
||
|
|
smtol = 1e-40;
|
||
|
|
for iter = 1:maxit,
|
||
|
|
|
||
|
|
rho = (r_tld'*r);
|
||
|
|
if (abs(rho) < smtol)
|
||
|
|
flag = 2; fprintf('*'); break;
|
||
|
|
end
|
||
|
|
if (iter > 1)
|
||
|
|
beta = (rho/rho_1)* (alp/omega);
|
||
|
|
p = r + beta*(p - omega*v);
|
||
|
|
else
|
||
|
|
p = r;
|
||
|
|
end
|
||
|
|
p_hat = precond(A,M1,p);
|
||
|
|
if isstruct(A); v = matvec(A,p_hat); else; v = mexMatvec(A,p_hat); end;
|
||
|
|
alp = rho / (r_tld'*v);
|
||
|
|
s = r - alp*v;
|
||
|
|
|
||
|
|
s_hat = precond(A,M1,s);
|
||
|
|
if isstruct(A); t = matvec(A,s_hat); else; t = mexMatvec(A,s_hat); end;
|
||
|
|
omega = (t'*s) / (t'*t);
|
||
|
|
x = x + alp*p_hat + omega*s_hat;
|
||
|
|
r = s - omega*t;
|
||
|
|
rho_1 = rho;
|
||
|
|
%%
|
||
|
|
%% check convergence
|
||
|
|
%%
|
||
|
|
err = norm(r); resnrm(iter+1) = err;
|
||
|
|
if (err < minresnrm); xold = x; minresnrm = err; end
|
||
|
|
if (err < tolb)
|
||
|
|
break;
|
||
|
|
end
|
||
|
|
if (err > 10*minresnrm)
|
||
|
|
x = xold;
|
||
|
|
fprintf(' err/^ ');
|
||
|
|
break;
|
||
|
|
end
|
||
|
|
if (abs(omega) < smtol)
|
||
|
|
flag = 2; fprintf('*'); break;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
xx = x;
|
||
|
|
%%
|
||
|
|
%%*************************************************************************
|
||
|
|
%%*************************************************************************
|
||
|
|
%% matvec: matrix-vector multiply.
|
||
|
|
%% matrix = [A.mat11, A.mat12; A.mat12', A.mat22]
|
||
|
|
%%*************************************************************************
|
||
|
|
|
||
|
|
function Ax = matvec(A,x);
|
||
|
|
|
||
|
|
m = length(A.mat11); m2 = length(x)-m;
|
||
|
|
if (m2 > 0)
|
||
|
|
x1 = full(x(1:m));
|
||
|
|
else
|
||
|
|
x1 = full(x);
|
||
|
|
end
|
||
|
|
Ax = mexMatvec(A.mat11,x1);
|
||
|
|
if (m2 > 0)
|
||
|
|
x2 = full(x(m+[1:m2]));
|
||
|
|
Ax = Ax + mexMatvec(A.mat12,x2);
|
||
|
|
Ax2 = mexMatvec(A.mat12,x1,1) + mexMatvec(A.mat22,x2);
|
||
|
|
Ax = [Ax; Ax2];
|
||
|
|
end
|
||
|
|
%%*************************************************************************
|
||
|
|
%% precond:
|
||
|
|
%%*************************************************************************
|
||
|
|
|
||
|
|
function Mx = precond(A,L,x)
|
||
|
|
|
||
|
|
m = length(L.perm); m2 = length(x)-m;
|
||
|
|
if (m2 > 0)
|
||
|
|
x1 = full(x(1:m));
|
||
|
|
else
|
||
|
|
x1 = full(x);
|
||
|
|
end
|
||
|
|
if (m2 > 0)
|
||
|
|
x2 = x(m+[1:m2]);
|
||
|
|
w = linsysolvefun(L,x1);
|
||
|
|
z = mexMatvec(A.mat12,w,1) -x2;
|
||
|
|
z = L.Mu \ (L.Ml \ (L.Mp*z));
|
||
|
|
x1 = x1 - mexMatvec(A.mat12,z);
|
||
|
|
end
|
||
|
|
%%
|
||
|
|
Mx = linsysolvefun(L,x1);
|
||
|
|
%%
|
||
|
|
if (m2 > 0)
|
||
|
|
Mx = [Mx; z];
|
||
|
|
end
|
||
|
|
%%*************************************************************************
|