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TGaussSeidel< T_value > Class Template Reference
implements Gauss-Seidel preconditioner More...
#include <TSOR.hh>
Inheritance diagram for TGaussSeidel< T_value >:
Public Member Functions | |
| TGaussSeidel (const TMatrix< value_t > *A, const gs_type_t gs_type, const real_t damping=real_t(1)) | |
| constructs Gauss-Seidel preconditioner of type gs_type | |
| const TMatrix< value_t > * | matrix () const |
| return internal sparse matrix | |
| gs_type_t | gs_type () const |
| return GaussSeidel type | |
| real_t | 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< value_t > *x, TVector< value_t > *y, const matop_t op=apply_normal) const |
| virtual void | apply_add (const value_t alpha, const TVector< value_t > *x, TVector< value_t > *y, const matop_t op=apply_normal) const |
| virtual void | apply_add (const value_t alpha, const BLAS::Vector< value_t > &x, BLAS::Vector< value_t > &y, const matop_t op=apply_normal) const |
| virtual size_t | domain_dim () const |
| return dimension of domain | |
| virtual size_t | range_dim () const |
| return dimension of range | |
| virtual auto | domain_vector () const -> std::unique_ptr< TVector< value_t > > |
| return vector in domain space | |
| virtual auto | range_vector () const -> std::unique_ptr< TVector< value_t > > |
| return vector in range space | |
 Public Member Functions inherited from TLinearOperator< T_value > | |
| virtual bool | is_real () const |
| return true, if field type is real valued | |
| 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 \f$A = D - E - F\f$, with diagonal D, strictly lower triangular
matrix E and strictly upper triangular matrix F.
For forward GS, the applied operator is \f$ ( D - E )^{-1}\f$,
for backward GS \f$ ( D - F )^{-1}\f$ and the combination of both
for the symmetric GS, i.e., \f$ ( D - F )^{-1} D ( D - E )^{-1}\f$.
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 |
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< T_value >.
◆ apply_add() [1/2]
|
virtual |
same as above but only the dimension of the vector spaces is tested, not the corresponding index sets
Implements TLinearOperator< T_value >.
◆ apply_add() [2/2]
|
virtual |
mapping function with update: \( y := y + \alpha A(x)\). Depending on op, either \(A\), \(A^T\) or \(A^H\) is applied.
Implements TLinearOperator< T_value >.
