HLIBpro  2.6
TGaussSeidel Class Reference

implements Gauss-Seidel preconditioner More...

#include <TSOR.hh>

Inheritance diagram for TGaussSeidel:
TLinearOperator TTypeInfo

Public Member Functions

 TGaussSeidel (const TMatrix *A, const gs_type_t gs_type, const real damping=1.0)
 constructs Gauss-Seidel preconditioner of type gs_type
 
const TMatrixmatrix () const
 return internal sparse matrix
 
gs_type_t gs_type () const
 return GaussSeidel type
 
real damping_factor () const
 return damping factor
 
bool is_complex () const
 return true, if field type is complex
 
bool is_self_adjoint () const
 return true, of operator is self adjoint
 
virtual void apply (const TVector *x, TVector *y, const matop_t op=apply_normal) const
 
virtual void apply_add (const real alpha, const TVector *x, TVector *y, const matop_t op=apply_normal) const
 
virtual auto domain_vector () const -> std::unique_ptr< TVector >
 return vector in domain space
 
virtual auto range_vector () const -> std::unique_ptr< TVector >
 return vector in range space
 
- Public Member Functions inherited from TTypeInfo
virtual typeid_t type () const =0
 return type ID of object
 
virtual bool is_type (const typeid_t t) const
 return true if local object is of given type ID t
 
virtual std::string typestr () const
 return string representation of type
 

Detailed Description

TGaussSeidel provides application of a Gauss-Seidel type preconditioner for a given matrix \(A = D - E - F\), with diagonal D, strictly lower triangular matrix E and strictly upper triangular matrix F.

For forward GS, the applied operator is \( ( D - E )^{-1}\), for backward GS \( ( D - F )^{-1}\) and the combination of both for the symmetric GS, i.e., \( ( D - F )^{-1} D ( D - E )^{-1}\).

TGaussSeidel implements point-wise and block-wise GS steps. However, point-wise GS is only supported for sparse matrices while block-wise GS is only supported for H-matrices

Member Function Documentation

◆ apply()

virtual void apply ( const TVector x,
TVector y,
const matop_t  op = apply_normal 
) const
virtual

mapping function of linear operator \(A\), e.g. \( y := A(x)\). Depending on op, either \(A\), \(A^T\) or \(A^H\) is applied.

Implements TLinearOperator.

◆ apply_add()

virtual void apply_add ( const real  alpha,
const TVector x,
TVector y,
const matop_t  op = apply_normal 
) const
virtual

mapping function with update: \( y := y + \alpha A(x)\). Depending on op, either \(A\), \(A^T\) or \(A^H\) is applied.

Implements TLinearOperator.