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//*****************************************************************
// Iterative template routine -- CGS
//
// CGS solves the unsymmetric linear system Ax = b
// using the Conjugate Gradient Squared method
//
// CGS follows the algorithm described on p. 26 of the
// SIAM Templates book.
//
// The return value indicates convergence within max_iter (input)
// iterations (0), or no convergence within max_iter iterations (1).
//
// Upon successful return, output arguments have the following values:
//
// x -- approximate solution to Ax = b
// max_iter -- the number of iterations performed before the
// tolerance was reached
// tol -- the residual after the final iteration
//
//*****************************************************************
//
// Slightly modified version of IML++ template. See ReadMe file.
//
// Jesper Andersson
//
#ifndef cgs_h
#define cgs_h
namespace MISCMATHS {
template < class Matrix, class Vector, class Preconditioner, class Real >
int
CGS(const Matrix &A, Vector &x, const Vector &b,
const Preconditioner &M, int &max_iter, Real &tol)
{
Real resid;
Vector rho_1(1), rho_2(1), alpha(1), beta(1);
Vector p, phat, q, qhat, vhat, u, uhat;
Real normb = b.NormFrobenius();
Vector r = b - A*x;
Vector rtilde = r;
if (normb == 0.0)
normb = 1;
if ((resid = r.NormFrobenius() / normb) <= tol) {
tol = resid;
max_iter = 0;
return 0;
}
for (int i = 1; i <= max_iter; i++) {
rho_1(1) = DotProduct(rtilde, r);
if (rho_1(1) == 0) {
tol = r.NormFrobenius() / normb;
return 2;
}
if (i == 1) {
u = r;
p = u;
} else {
beta(1) = rho_1(1) / rho_2(1);
u = r + beta(1) * q;
p = u + beta(1) * (q + beta(1) * p);
}
phat = M.solve(p);
vhat = A*phat;
alpha(1) = rho_1(1) / DotProduct(rtilde, vhat);
q = u - alpha(1) * vhat;
uhat = M.solve(u + q);
x += alpha(1) * uhat;
qhat = A * uhat;
r -= alpha(1) * qhat;
rho_2(1) = rho_1(1);
if ((resid = r.NormFrobenius() / normb) < tol) {
tol = resid;
max_iter = i;
return 0;
}
}
tol = resid;
return 1;
}
} // End namespace MISCMATHS
#endif // End #ifndef cgs_h