11 #ifndef EIGEN_BICGSTAB_H 12 #define EIGEN_BICGSTAB_H 28 template<
typename MatrixType,
typename Rhs,
typename Dest,
typename Preconditioner>
29 bool bicgstab(
const MatrixType& mat,
const Rhs& rhs, Dest& x,
30 const Preconditioner& precond,
Index& iters,
31 typename Dest::RealScalar& tol_error)
35 typedef typename Dest::RealScalar RealScalar;
36 typedef typename Dest::Scalar Scalar;
37 typedef Matrix<Scalar,Dynamic,1> VectorType;
38 RealScalar tol = tol_error;
39 Index maxIters = iters;
42 VectorType r = rhs - mat * x;
45 RealScalar r0_sqnorm = r0.squaredNorm();
46 RealScalar rhs_sqnorm = rhs.squaredNorm();
56 VectorType v = VectorType::Zero(n), p = VectorType::Zero(n);
57 VectorType y(n), z(n);
58 VectorType kt(n), ks(n);
60 VectorType s(n), t(n);
62 RealScalar tol2 = tol*tol*rhs_sqnorm;
63 RealScalar eps2 = NumTraits<Scalar>::epsilon()*NumTraits<Scalar>::epsilon();
67 while ( r.squaredNorm() > tol2 && i<maxIters )
72 if (
abs(rho) < eps2*r0_sqnorm)
78 rho = r0_sqnorm = r.squaredNorm();
82 Scalar beta = (rho/rho_old) * (alpha / w);
83 p = r + beta * (p - w * v);
87 v.noalias() = mat * y;
89 alpha = rho / r0.dot(v);
93 t.noalias() = mat * z;
95 RealScalar tmp = t.squaredNorm();
100 x += alpha * y + w * z;
104 tol_error =
sqrt(r.squaredNorm()/rhs_sqnorm);
111 template<
typename _MatrixType,
112 typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
117 template<
typename _MatrixType,
typename _Preconditioner>
118 struct traits<
BiCGSTAB<_MatrixType,_Preconditioner> >
120 typedef _MatrixType MatrixType;
121 typedef _Preconditioner Preconditioner;
157 template<
typename _MatrixType,
typename _Preconditioner>
163 using Base::m_iterations;
165 using Base::m_isInitialized;
167 typedef _MatrixType MatrixType;
168 typedef typename MatrixType::Scalar Scalar;
169 typedef typename MatrixType::RealScalar RealScalar;
170 typedef _Preconditioner Preconditioner;
187 template<
typename MatrixDerived>
193 template<
typename Rhs,
typename Dest>
194 void _solve_with_guess_impl(
const Rhs& b, Dest& x)
const 197 for(
Index j=0; j<b.cols(); ++j)
199 m_iterations = Base::maxIterations();
200 m_error = Base::m_tolerance;
202 typename Dest::ColXpr xj(x,j);
203 if(!internal::bicgstab(matrix(), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error))
207 : m_error <= Base::m_tolerance ?
Success 209 m_isInitialized =
true;
213 using Base::_solve_impl;
214 template<
typename Rhs,
typename Dest>
217 x.resize(this->rows(),b.
cols());
219 _solve_with_guess_impl(b,x);
228 #endif // EIGEN_BICGSTAB_H const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Namespace containing all symbols from the Eigen library.
Definition: Core:287
Definition: EigenBase.h:29
BiCGSTAB(const EigenBase< MatrixDerived > &A)
Definition: BiCGSTAB.h:188
Definition: Constants.h:434
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Definition: Constants.h:432
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
Definition: Eigen_Colamd.h:50
BiCGSTAB()
Definition: BiCGSTAB.h:175
A bi conjugate gradient stabilized solver for sparse square problems.
Definition: BiCGSTAB.h:113
Index cols() const
Definition: EigenBase.h:62
Base class for linear iterative solvers.
Definition: IterativeSolverBase.h:143
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
Definition: Constants.h:436