Data Structures
class	amg_tag
	A tag for algebraic multigrid (AMG). Used to transport information from the user to the implementation. More...
class	amg_nonzero_scalar
	A class for a scalar that can be written to the sparse matrix or sparse vector datatypes. More...
class	amg_sparsevector_iterator
	Defines an iterator for the sparse vector type. More...
class	amg_sparsevector
	A class for the sparse vector type. More...
class	amg_sparsematrix
	A class for the sparse matrix type. Uses vector of maps as data structure for higher performance and lower memory usage. Uses similar interface as ublas::compressed_matrix. Can deal with transposed of matrix internally: Creation, Storage, Iterators, etc. More...
class	amg_point
	A class for the AMG points. Saves point index and influence measure Holds information whether point is undecided, C or F point. Holds lists of points that are influenced by or influencing this point. More...
struct	classcomp
	Comparison class for the sorted set of points in amg_pointvector. Set is sorted by influence measure from lower to higher with the point-index as tie-breaker. More...
class	amg_pointvector
	A class for the AMG points. Holds pointers of type amg_point in a vector that can be accessed using [point-index]. Additional list of pointers sorted by influence number and index to improve coarsening performance (see amg_coarse_classic_onepass() in amg_coarse.hpp) Constructs indices for C points on the coarse level, needed for interpolation. More...
class	amg_slicing
	A class for the matrix slicing for parallel coarsening schemes (RS0/RS3). More...
Functions
template<typename SparseMatrixType >
void	amg_mat_prod (SparseMatrixType &A, SparseMatrixType &B, SparseMatrixType &RES)
	Sparse matrix product. Calculates RES = A*B.
template<typename SparseMatrixType >
void	amg_galerkin_prod (SparseMatrixType &A, SparseMatrixType &P, SparseMatrixType &RES)
	Sparse Galerkin product: Calculates RES = trans(P)AP.
template<typename SparseMatrixType >
void	test_triplematprod (SparseMatrixType &A, SparseMatrixType &P, SparseMatrixType &A_i1)
	Test triple-matrix product by comparing it to ublas functions. Very slow for large matrices!
template<typename SparseMatrixType , typename PointVectorType >
void	test_interpolation (SparseMatrixType &A, SparseMatrixType &P, PointVectorType &Pointvector)
	Test if interpolation matrix makes sense. Only vanilla test though! Only checks if basic requirements are met!
template<typename InternalType1 , typename InternalType2 , typename InternalType3 >
void	amg_coarse (unsigned int level, InternalType1 &A, InternalType2 &Pointvector, InternalType3 &Slicing, amg_tag &tag)
	Calls the right coarsening procedure.
template<typename InternalType1 , typename InternalType2 >
void	amg_influence (unsigned int level, InternalType1 const &A, InternalType2 &Pointvector, amg_tag &tag)
	Determines strong influences in system matrix, classical approach (RS). Multithreaded!
template<typename InternalType1 , typename InternalType2 >
void	amg_coarse_classic_onepass (unsigned int level, InternalType1 &A, InternalType2 &Pointvector, amg_tag &tag)
	Classical (RS) one-pass coarsening. Single-Threaded! (VIENNACL_AMG_COARSE_CLASSIC_ONEPASS).
template<typename InternalType1 , typename InternalType2 >
void	amg_coarse_classic (unsigned int level, InternalType1 &A, InternalType2 &Pointvector, amg_tag &tag)
	Classical (RS) two-pass coarsening. Single-Threaded! (VIENNACL_AMG_COARSE_CLASSIC).
template<typename InternalType1 , typename InternalType2 , typename InternalType3 >
void	amg_coarse_rs0 (unsigned int level, InternalType1 &A, InternalType2 &Pointvector, InternalType3 &Slicing, amg_tag &tag)
	Parallel classical RS0 coarsening. Multi-Threaded! (VIENNACL_AMG_COARSE_RS0 \|\| VIENNACL_AMG_COARSE_RS3).
template<typename InternalType1 , typename InternalType2 , typename InternalType3 >
void	amg_coarse_rs3 (unsigned int level, InternalType1 &A, InternalType2 &Pointvector, InternalType3 &Slicing, amg_tag &tag)
	RS3 coarsening. Single-Threaded! (VIENNACL_AMG_COARSE_RS3).
template<typename InternalType1 , typename InternalType2 >
void	amg_coarse_ag (unsigned int level, InternalType1 &A, InternalType2 &Pointvector, amg_tag &tag)
	AG (aggregation based) coarsening. Single-Threaded! (VIENNACL_AMG_COARSE_SA).
template<typename MatrixType >
void	printmatrix (MatrixType &mat, int const value=-1)
template<typename VectorType >
void	printvector (VectorType const &vec)
template<typename InternalType1 , typename InternalType2 >
void	amg_interpol (unsigned int level, InternalType1 &A, InternalType1 &P, InternalType2 &Pointvector, amg_tag &tag)
	Calls the right function to build interpolation matrix.
template<typename InternalType1 , typename InternalType2 >
void	amg_interpol_direct (unsigned int level, InternalType1 &A, InternalType1 &P, InternalType2 &Pointvector, amg_tag &tag)
	Direct interpolation. Multi-threaded! (VIENNACL_AMG_INTERPOL_DIRECT).
template<typename InternalType1 , typename InternalType2 >
void	amg_interpol_classic (unsigned int level, InternalType1 &A, InternalType1 &P, InternalType2 &Pointvector, amg_tag &tag)
	Classical interpolation. Don't use with onepass classical coarsening or RS0 (Yang, p.14)! Multi-threaded! (VIENNACL_AMG_INTERPOL_CLASSIC).
template<typename SparseMatrixType >
void	amg_truncate_row (SparseMatrixType &P, unsigned int row, amg_tag &tag)
	Interpolation truncation (for VIENNACL_AMG_INTERPOL_DIRECT and VIENNACL_AMG_INTERPOL_CLASSIC).
template<typename InternalType1 , typename InternalType2 >
void	amg_interpol_ag (unsigned int level, InternalType1 &A, InternalType1 &P, InternalType2 &Pointvector, amg_tag &tag)
	AG (aggregation based) interpolation. Multi-Threaded! (VIENNACL_INTERPOL_SA).
template<typename InternalType1 , typename InternalType2 >
void	amg_interpol_sa (unsigned int level, InternalType1 &A, InternalType1 &P, InternalType2 &Pointvector, amg_tag &tag)
	SA (smoothed aggregate) interpolation. Multi-Threaded! (VIENNACL_INTERPOL_SA).

Function Documentation

void viennacl::linalg::detail::amg::amg_coarse	(	unsigned int	level,
		InternalType1 &	A,
		InternalType2 &	Pointvector,
		InternalType3 &	Slicing,
		amg_tag &	tag
	)

Calls the right coarsening procedure.

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	Pointvector	Vector of points on all levels
	Slicing	Partitioning of the system matrix to different processors (only used in RS0 and RS3)
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_coarse_ag	(	unsigned int	level,
		InternalType1 &	A,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

AG (aggregation based) coarsening. Single-Threaded! (VIENNACL_AMG_COARSE_SA).

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_coarse_classic	(	unsigned int	level,
		InternalType1 &	A,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

Classical (RS) two-pass coarsening. Single-Threaded! (VIENNACL_AMG_COARSE_CLASSIC).

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_coarse_classic_onepass	(	unsigned int	level,
		InternalType1 &	A,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

Classical (RS) one-pass coarsening. Single-Threaded! (VIENNACL_AMG_COARSE_CLASSIC_ONEPASS).

Parameters:

	level	Course level identifier
	A	Operator matrix on all levels
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_coarse_rs0	(	unsigned int	level,
		InternalType1 &	A,
		InternalType2 &	Pointvector,
		InternalType3 &	Slicing,
		amg_tag &	tag
	)

Parallel classical RS0 coarsening. Multi-Threaded! (VIENNACL_AMG_COARSE_RS0 || VIENNACL_AMG_COARSE_RS3).

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all level
	Pointvector	Vector of points on all levels
	Slicing	Partitioning of the system matrix and the other data structures to different processors
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_coarse_rs3	(	unsigned int	level,
		InternalType1 &	A,
		InternalType2 &	Pointvector,
		InternalType3 &	Slicing,
		amg_tag &	tag
	)

RS3 coarsening. Single-Threaded! (VIENNACL_AMG_COARSE_RS3).

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	Pointvector	Vector of points on all levels
	Slicing	Partitioning of the system matrix and the other data structures to different processors
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_galerkin_prod	(	SparseMatrixType &	A,
		SparseMatrixType &	P,
		SparseMatrixType &	RES
	)

Sparse Galerkin product: Calculates RES = trans(P)*A*P.

Parameters:

	A	Operator matrix (quadratic)
	P	Prolongation/Interpolation matrix
	RES	Result Matrix (Galerkin operator)

void viennacl::linalg::detail::amg::amg_influence	(	unsigned int	level,
		InternalType1 const &	A,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

Determines strong influences in system matrix, classical approach (RS). Multithreaded!

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_interpol	(	unsigned int	level,
		InternalType1 &	A,
		InternalType1 &	P,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

Calls the right function to build interpolation matrix.

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	P	Prolongation matrices. P[level] is constructed
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_interpol_ag	(	unsigned int	level,
		InternalType1 &	A,
		InternalType1 &	P,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

AG (aggregation based) interpolation. Multi-Threaded! (VIENNACL_INTERPOL_SA).

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	P	Prolongation matrices. P[level] is constructed
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_interpol_classic	(	unsigned int	level,
		InternalType1 &	A,
		InternalType1 &	P,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

Classical interpolation. Don't use with onepass classical coarsening or RS0 (Yang, p.14)! Multi-threaded! (VIENNACL_AMG_INTERPOL_CLASSIC).

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	P	Prolongation matrices. P[level] is constructed
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_interpol_direct	(	unsigned int	level,
		InternalType1 &	A,
		InternalType1 &	P,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

Direct interpolation. Multi-threaded! (VIENNACL_AMG_INTERPOL_DIRECT).

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	P	Prolongation matrices. P[level] is constructed
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_interpol_sa	(	unsigned int	level,
		InternalType1 &	A,
		InternalType1 &	P,
		InternalType2 &	Pointvector,
		amg_tag &	tag
	)

SA (smoothed aggregate) interpolation. Multi-Threaded! (VIENNACL_INTERPOL_SA).

Parameters:

	level	Coarse level identifier
	A	Operator matrix on all levels
	P	Prolongation matrices. P[level] is constructed
	Pointvector	Vector of points on all levels
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::amg_mat_prod	(	SparseMatrixType &	A,
		SparseMatrixType &	B,
		SparseMatrixType &	RES
	)

Sparse matrix product. Calculates RES = A*B.

Parameters:

	A	Left Matrix
	B	Right Matrix
	RES	Result Matrix

void viennacl::linalg::detail::amg::amg_truncate_row	(	SparseMatrixType &	P,
		unsigned int	row,
		amg_tag &	tag
	)

Interpolation truncation (for VIENNACL_AMG_INTERPOL_DIRECT and VIENNACL_AMG_INTERPOL_CLASSIC).

Parameters:

	P	Interpolation matrix
	row	Row which has to be truncated
	tag	AMG preconditioner tag

void viennacl::linalg::detail::amg::printmatrix	(	MatrixType &	mat,
		int const	value = `-1`
	)

void viennacl::linalg::detail::amg::printvector ( VectorType const & vec )

void viennacl::linalg::detail::amg::test_interpolation	(	SparseMatrixType &	A,
		SparseMatrixType &	P,
		PointVectorType &	Pointvector
	)

Test if interpolation matrix makes sense. Only vanilla test though! Only checks if basic requirements are met!

Parameters:

	A	Operator matrix (quadratic)
	P	Prolongation/Interpolation matrix
	Pointvector	Vector of points

void viennacl::linalg::detail::amg::test_triplematprod	(	SparseMatrixType &	A,
		SparseMatrixType &	P,
		SparseMatrixType &	A_i1
	)

Test triple-matrix product by comparing it to ublas functions. Very slow for large matrices!

Parameters:

	A	Operator matrix (quadratic)
	P	Prolongation/Interpolation matrix
	A_i1	Result Matrix

viennacl::linalg::detail::amg Namespace Reference

Data Structures

Functions

Function Documentation