Algebra Library. More...

Modules
	CPU Algebra

	CRS Algebra

	lib_algebra Common
	Utilities for libAlgebra.

	Parallel Algebra

	Small Algebra

Classes
class	ug::AlgebraType
	class describing the type of an algebra More...

class	ug::DefaultAlgebra
	Singleton, providing the current default algebra. More...

struct	ug::DenseMatrixFromSparseMatrix< TSparseMatrix >

class	ug::MapSparseMatrix< TValueType >
	sparse matrix for big, variable sparse matrices. More...

class	ug::MapVector< TValueType >

struct	ug::matrix_algebra_type_traits< MapSparseMatrix< T > >

struct	ug::sortStruct< T >

Macros
#define	FORCE_CREATION volatile size_t ___never_happens___ = 0; if(___never_happens___)

#define	UNUSED_VARIABLE(var) ((void) var);
	prevent unused variable-warnings More...

Typedefs
typedef TValueType	ug::MapVector< TValueType >::value_type

typedef MapVector< TValueType >	ug::MapVector< TValueType >::vector_type

Functions
template<typename ABC_type , typename A_type , typename B_type , typename C_type >
void	ug::AddMultiplyOf (ABC_type &M, const A_type &A, const B_type &B, const C_type &C, double epsilonTruncation=0.0)
	Calculates M += ABC. More...

template<typename TSparseMatrix , typename vector_t >
bool	ug::Axpy_transposedCommonSparseMatrix (const TSparseMatrix &A, vector_t &dest, const number &alpha1, const vector_t &v1, const number &beta1, const vector_t &w1)

template<typename TSparseMatrix , typename vector_t >
bool	ug::AxpyCommonSparseMatrix (const TSparseMatrix &A, vector_t &dest, const number &alpha1, const vector_t &v1, const number &beta1, const vector_t &w1)

template<typename TSparseMatrix >
bool	ug::CheckDiagonalInvertible (const ParallelMatrix< TSparseMatrix > &m)

template<typename TSparseMatrix >
bool	ug::CheckDiagonalInvertible (const TSparseMatrix &A)

template<typename TSparseMatrix >
bool	ug::CheckRowIterators (const TSparseMatrix &A)

template<typename TVector >
bool	ug::CheckVectorInvertible (const ParallelVector< TVector > &v)

template<typename TVector >
bool	ug::CheckVectorInvertible (const TVector &v)

template<typename AB_type , typename A_type , typename B_type >
void	ug::CreateAsMultiplyOf (AB_type &M, const A_type &A, const B_type &B)
	Calculates M = A*B. More...

template<typename ABC_type , typename A_type , typename B_type , typename C_type >
void	ug::CreateAsMultiplyOf (ABC_type &M, const A_type &A, const B_type &B, const C_type &C, double epsilonTruncation=0.0)
	Calculates M = ABC. More...

template<typename TSparseMatrix , class TIStream >
void	ug::DeserializeMatrix (TIStream &buf, TSparseMatrix &A)

template<typename Matrix_type , typename Vector_type >
void	ug::diag_step (const Matrix_type &A, Vector_type &c, const Vector_type &d, number damp)
	Performs a jacobi-step. More...

template<typename TDenseType , typename TSparseMatrix >
size_t	ug::GetDenseDoubleFromSparse (TDenseType &A, const TSparseMatrix &S)

template<typename TSparseMatrix >
DenseMatrixFromSparseMatrix< TSparseMatrix >::type &	ug::GetDenseFromSparse (typename DenseMatrixFromSparseMatrix< TSparseMatrix >::type &A, const TSparseMatrix &S)

template<typename TDoubleType , typename TSparseMatrix >
void	ug::GetDoubleFromSparseBlock (TDoubleType &A, const TSparseMatrix &S)

template<typename TSparseMatrix >
size_t	ug::GetDoubleSize (const TSparseMatrix &S)

template<typename TDoubleSparse , typename TSparseMatrix >
size_t	ug::GetDoubleSparseFromBlockSparse (TDoubleSparse &A, const TSparseMatrix &S)

template<typename TSparseMatrix >
size_t	ug::GetMaxConnections (const TSparseMatrix &A)
	returns max number of non-zero connections in rows More...

template<typename TSparseMatrix >
void	ug::GetNeighborhood (const TSparseMatrix &A, size_t node, size_t depth, std::vector< size_t > &indices)

template<typename TSparseMatrix >
void	ug::GetNeighborhood (const TSparseMatrix &A, size_t node, size_t depth, std::vector< size_t > &indices, std::vector< bool > &bVisited, bool bResetVisitedFlags=true)

template<typename TSparseMatrix >
void	ug::GetNeighborhood_worker (const TSparseMatrix &A, size_t node, size_t depth, std::vector< size_t > &indices, std::vector< bool > &bVisited)

template<typename TSparseMatrix >
void	ug::GetNeighborhoodHierachy (const TSparseMatrix &A, size_t node, size_t depth, std::vector< std::vector< size_t > > &indices)

template<typename TSparseMatrix >
void	ug::GetNeighborhoodHierachy (const TSparseMatrix &A, size_t node, size_t depth, std::vector< std::vector< size_t > > &indices, std::vector< bool > &bVisited, bool bResetVisitedFlags=true)

template<typename TSparseMatrix >
void	ug::GetNeighborhoodHierachy_worker (const TSparseMatrix &A, size_t node, size_t depth, size_t maxdepth, std::vector< std::vector< size_t > > &indices, std::vector< bool > &bVisited)

template<typename TSparseMatrix >
size_t	ug::GetNNZs (const TSparseMatrix &A)
	returns the number of non-zeroes (!= number of connections) More...

template<typename Matrix_type , typename Vector_type >
void	ug::gs_step_LL (const Matrix_type &A, Vector_type &c, const Vector_type &d, const number relaxFactor)
	Gauss-Seidel-Iterations. More...

template<typename Matrix_type , typename Vector_type >
bool	ug::gs_step_LL (const Matrix_type &A, Vector_type &x, const Vector_type &b)
	Performs a forward gauss-seidel-step, that is, solve on the lower left of A. More...

template<typename Matrix_type , typename Vector_type >
void	ug::gs_step_UR (const Matrix_type &A, Vector_type &c, const Vector_type &d, const number relaxFactor)
	Performs a backward gauss-seidel-step, that is, solve on the upper right of A. Using gs_step_UR within a preconditioner-scheme leads to the fact that we get the correction by successive inserting the already computed values of c in c = N * d, with c being the correction and d being the defect. N denotes the matrix of the second normal-form of a linear iteration scheme. More...

template<typename Matrix_type , typename Vector_type >
bool	ug::gs_step_UR (const Matrix_type &A, Vector_type &x, const Vector_type &b)
	Performs a backward gauss-seidel-step, that is, solve on the upper right of A. More...

template<typename TSparseMatrix >
bool	ug::IsCloseToBoundary (const TSparseMatrix &A, size_t node, size_t distance)
	gets the neighborhood of a node in the connectivity graph of a SparseMatrix. More...

template<typename TSparseMatrix >
bool	ug::IsDirichletRow (const TSparseMatrix &A, size_t i, size_t alpha)
	Evaluates 'true', iff corresponding row is Dirichlet. More...

	ug::MapVector< TValueType >::MapVector ()
	constructor More...

	ug::MapVector< TValueType >::MapVector (size_t _length)
	constructor with length More...

template<typename TSparseMatrix >
void	ug::MarkNeighbors (const TSparseMatrix &A, size_t node, size_t depth, std::vector< bool > &bVisited)

template<typename matrix_type >
void	ug::MatAdd (matrix_type &M, number alpha1, const matrix_type &A, number alpha2, const matrix_type &B)
	Calculates M = A + B. More...

template<typename matrix_type >
void	ug::MatAddNonDirichlet (matrix_type &M, number alpha1, const matrix_type &A, number alpha2, const matrix_type &B)
	Calculates M = A + B. More...

template<typename vector_t , typename matrix_t >
void	ug::MatMultTransposedAdd (vector_t &dest, const number &alpha1, const vector_t &v1, const number &beta1, const MapSparseMatrix< matrix_t > &A1, const vector_t &w1)
	calculates dest = alpha1v1 + beta1 A1^T *w1; More...

std::ostream &	ug::operator<< (std::ostream &out, const AlgebraType &v)
	writes the Identifier to the output stream More...

template<typename TSparseMatrix >
void	ug::ScaleRow (TSparseMatrix &A, size_t i, number fac)

template<typename TSparseMatrix >
void	ug::ScaleSparseMatrixCommon (TSparseMatrix &A, double d)

template<typename TSparseMatrix , class TOStream >
void	ug::SerializeMatrix (TOStream &buf, const TSparseMatrix &A)

template<typename TSparseMatrix >
void	ug::SetCol (TSparseMatrix &A, size_t i, size_t alpha, number val=0.0)

template<typename TSparseMatrix >
void	ug::SetDirichletRow (TSparseMatrix &A, const std::vector< size_t > vIndex)

template<typename TSparseMatrix >
void	ug::SetDirichletRow (TSparseMatrix &A, size_t i)

template<typename TSparseMatrix >
void	ug::SetDirichletRow (TSparseMatrix &A, size_t i, size_t alpha)

template<typename TSparseMatrix >
void	ug::SetRow (TSparseMatrix &A, size_t i, number val=0.0)

template<typename TSparseMatrix >
void	ug::SetRow (TSparseMatrix &A, size_t i, size_t alpha, number val=0.0)

template<typename Matrix_type , typename Vector_type >
void	ug::sgs_step (const Matrix_type &A, Vector_type &c, const Vector_type &d, const number relaxFactor)
	Performs a symmetric gauss-seidel step. Using sgs_step within a preconditioner-scheme leads to the fact that we get the correction by successive inserting the already computed values of c in c = N * d, with c being the correction and d being the defect. N denotes the matrix of the second normal-form of a linear iteration scheme. More...

template<typename Matrix_type , typename Vector_type >
bool	ug::sgs_step (const Matrix_type &A, Vector_type &x, const Vector_type &b)
	Performs a symmetric gauss-seidel step. More...

Detailed Description

Algebra Library.

Macro Definition Documentation

◆ FORCE_CREATION

#define FORCE_CREATION volatile size_t ___never_happens___ = 0; if(___never_happens___)

use this to force the creation of prsize_t routines or similar for use in gdb.

◆ UNUSED_VARIABLE

#define UNUSED_VARIABLE ( var ) ((void) var);

prevent unused variable-warnings

Typedef Documentation

◆ value_type

template<typename TValueType >

typedef TValueType ug::MapVector< TValueType >::value_type

◆ vector_type

template<typename TValueType >

typedef MapVector<TValueType> ug::MapVector< TValueType >::vector_type

Function Documentation

◆ AddMultiplyOf()

template<typename ABC_type , typename A_type , typename B_type , typename C_type >

void ug::AddMultiplyOf	(	ABC_type &	M,
		const A_type &	A,
		const B_type &	B,
		const C_type &	C,
		double	epsilonTruncation = `0.0`
	)

Calculates M += A*B*C.

Parameters

M	(in/out) Matrix M, M += ABC$
A	(in) Matrix A
B	(in) Matrix B
C	(in) Matrix C

Complete formula for calculating M=A*B*C:

\[ M_{ij} += \sum_{kl} A_{ik} * B_{kl} * C_{lj} \]

References ug::AddMult(), ug::AssignMult(), ug::BlockNorm(), PROFILE_FUNC_GROUP, UG_ASSERT, and UG_THROW.

Referenced by ug::AssembledMultiGridCycle< TDomain, TAlgebra >::init_rap_operator().

◆ Axpy_transposedCommonSparseMatrix()

template<typename TSparseMatrix , typename vector_t >

bool ug::Axpy_transposedCommonSparseMatrix	(	const TSparseMatrix &	A,
		vector_t &	dest,
		const number &	alpha1,
		const vector_t &	v1,
		const number &	beta1,
		const vector_t &	w1
	)

References ug::MatMultTransposedAdd(), and ug::VecScaleAssign().

◆ AxpyCommonSparseMatrix()

template<typename TSparseMatrix , typename vector_t >

bool ug::AxpyCommonSparseMatrix	(	const TSparseMatrix &	A,
		vector_t &	dest,
		const number &	alpha1,
		const vector_t &	v1,
		const number &	beta1,
		const vector_t &	w1
	)

References ug::MatMult(), ug::MatMultAdd(), and ug::VecScaleAssign().

◆ CheckDiagonalInvertible() [1/2]

template<typename TSparseMatrix >

bool ug::CheckDiagonalInvertible ( const ParallelMatrix< TSparseMatrix > & m )

References pcl::AllProcsTrue(), ug::CheckDiagonalInvertible(), and ug::ParallelMatrix< TMatrix >::layouts().

◆ CheckDiagonalInvertible() [2/2]

template<typename TSparseMatrix >

bool ug::CheckDiagonalInvertible ( const TSparseMatrix & A )

References ug::GetInverse(), and UG_LOG.

Referenced by ug::CheckDiagonalInvertible(), and ug::GaussSeidelBase< TAlgebra >::preprocess().

◆ CheckRowIterators()

template<typename TSparseMatrix >

bool ug::CheckRowIterators ( const TSparseMatrix & A )

References UG_LOG.

Referenced by ug::UzawaBase< TDomain, TAlgebra >::extract_schur_update().

◆ CheckVectorInvertible() [1/2]

template<typename TVector >

bool ug::CheckVectorInvertible ( const ParallelVector< TVector > & v )

References pcl::AllProcsTrue(), ug::CheckVectorInvertible(), and ug::ParallelVector< TVector >::layouts().

◆ CheckVectorInvertible() [2/2]

template<typename TVector >

bool ug::CheckVectorInvertible ( const TVector & v )

References ug::GetInverse(), and UG_LOG.

Referenced by ug::CheckVectorInvertible(), and ug::Jacobi< TAlgebra >::preprocess().

◆ CreateAsMultiplyOf() [1/2]

template<typename AB_type , typename A_type , typename B_type >

void ug::CreateAsMultiplyOf	(	AB_type &	M,
		const A_type &	A,
		const B_type &	B
	)

Calculates M = A*B.

Parameters

M	(out) Matrix M, M = A*B$
A	(in) Matrix A
B	(in) Matrix B $ M_{ij} = \sum_k A_{ik} * B_{kj} $ For implementation details, see also CreateAsMultiplyOf(M, A, B, C).

References ug::AddMult(), PROFILE_FUNC_GROUP, and UG_ASSERT.

◆ CreateAsMultiplyOf() [2/2]

template<typename ABC_type , typename A_type , typename B_type , typename C_type >

void ug::CreateAsMultiplyOf	(	ABC_type &	M,
		const A_type &	A,
		const B_type &	B,
		const C_type &	C,
		double	epsilonTruncation = `0.0`
	)

Calculates M = A*B*C.

Parameters

M	(out) Matrix M, M = ABC$
A	(in) Matrix A
B	(in) Matrix B
C	(in) Matrix C

Complete formula for calculating M=A*B*C:

\[ M_{ij} = \sum_{kl} A_{ik} * B_{kl} * C_{lj} \]

Calculation is done on row-basis without a temporary BC or AB matrix. This has shown to be much faster than implementations with temporary matrices due to cache effects. We also added an improved way of storing the results of the calculation: when we go through connections of B and C and want to add the connection (i, j) to M, we need to know if this connection already exists. For this we have an array posInConnections, needs n=A.num_rows() memory. posInConnections[i]: index in the connections for current row (if not in row: -1) tried this also with std::map, but took 1511.53 ms instead of 393.972 ms searching in the connections array is also slower

References ug::AddMult(), ug::AssignMult(), ug::BlockNorm(), PROFILE_FUNC_GROUP, and UG_ASSERT.

◆ DeserializeMatrix()

template<typename TSparseMatrix , class TIStream >

void ug::DeserializeMatrix	(	TIStream &	buf,
		TSparseMatrix &	A
	)

References ug::Deserialize(), and num_connections().

◆ diag_step()

template<typename Matrix_type , typename Vector_type >

void ug::diag_step	(	const Matrix_type &	A,
		Vector_type &	c,
		const Vector_type &	d,
		number	damp
	)

Performs a jacobi-step.

Parameters

A	Matrix $A = D - L - R$
c	will be $c = N * d = D^{-1} d $
d	the vector d.
damp	the damping factor

References ug::InverseMatMult(), and UG_ASSERT.

◆ GetDenseDoubleFromSparse()

template<typename TDenseType , typename TSparseMatrix >

size_t ug::GetDenseDoubleFromSparse	(	TDenseType &	A,
		const TSparseMatrix &	S
	)

References ug::GetDoubleFromSparseBlock(), and ug::GetDoubleSize().

Referenced by ug::LU< TAlgebra >::init_dense().

◆ GetDenseFromSparse()

template<typename TSparseMatrix >

DenseMatrixFromSparseMatrix<TSparseMatrix>::type& ug::GetDenseFromSparse	(	typename DenseMatrixFromSparseMatrix< TSparseMatrix >::type &	A,
		const TSparseMatrix &	S
	)

◆ GetDoubleFromSparseBlock()

template<typename TDoubleType , typename TSparseMatrix >

void ug::GetDoubleFromSparseBlock	(	TDoubleType &	A,
		const TSparseMatrix &	S
	)

References ug::BlockRef().

Referenced by ug::GetDenseDoubleFromSparse(), and ug::GetDoubleSparseFromBlockSparse().

◆ GetDoubleSize()

template<typename TSparseMatrix >

size_t ug::GetDoubleSize ( const TSparseMatrix & S )

References UG_COND_THROW.

Referenced by ug::GetDenseDoubleFromSparse(), and ug::GetDoubleSparseFromBlockSparse().

◆ GetDoubleSparseFromBlockSparse()

template<typename TDoubleSparse , typename TSparseMatrix >

size_t ug::GetDoubleSparseFromBlockSparse	(	TDoubleSparse &	A,
		const TSparseMatrix &	S
	)

References ug::GetDoubleFromSparseBlock(), and ug::GetDoubleSize().

Referenced by ug::IExternalSolver< TAlgebra >::mat_preprocess(), and ug::ILUTScalarPreconditioner< TAlgebra >::preprocess().

◆ GetMaxConnections()

template<typename TSparseMatrix >

size_t ug::GetMaxConnections ( const TSparseMatrix & A )

returns max number of non-zero connections in rows

◆ GetNeighborhood() [1/2]

template<typename TSparseMatrix >

void ug::GetNeighborhood	(	const TSparseMatrix &	A,
		size_t	node,
		size_t	depth,
		std::vector< size_t > &	indices
	)

References ug::GetNeighborhood(), and PROFILE_FUNC_GROUP.

◆ GetNeighborhood() [2/2]

template<typename TSparseMatrix >

void ug::GetNeighborhood	(	const TSparseMatrix &	A,
		size_t	node,
		size_t	depth,
		std::vector< size_t > &	indices,
		std::vector< bool > &	bVisited,
		bool	bResetVisitedFlags = `true`
	)

References ug::GetNeighborhood_worker(), and PROFILE_FUNC_GROUP.

Referenced by ug::BlockGaussSeidel< TAlgebra, backward, forward >::block_preprocess(), ug::BlockGaussSeidelIterative< TAlgebra, backward, forward >::block_preprocess(), ug::SparseBlockGaussSeidel< TAlgebra, backward, forward >::block_preprocess(), and ug::GetNeighborhood().

◆ GetNeighborhood_worker()

template<typename TSparseMatrix >

void ug::GetNeighborhood_worker	(	const TSparseMatrix &	A,
		size_t	node,
		size_t	depth,
		std::vector< size_t > &	indices,
		std::vector< bool > &	bVisited
	)

Referenced by ug::GetNeighborhood().

◆ GetNeighborhoodHierachy() [1/2]

template<typename TSparseMatrix >

void ug::GetNeighborhoodHierachy	(	const TSparseMatrix &	A,
		size_t	node,
		size_t	depth,
		std::vector< std::vector< size_t > > &	indices
	)

References ug::GetNeighborhoodHierachy().

◆ GetNeighborhoodHierachy() [2/2]

template<typename TSparseMatrix >

void ug::GetNeighborhoodHierachy	(	const TSparseMatrix &	A,
		size_t	node,
		size_t	depth,
		std::vector< std::vector< size_t > > &	indices,
		std::vector< bool > &	bVisited,
		bool	bResetVisitedFlags = `true`
	)

References PROFILE_FUNC_GROUP.

Referenced by ug::GetNeighborhoodHierachy().

◆ GetNeighborhoodHierachy_worker()

template<typename TSparseMatrix >

void ug::GetNeighborhoodHierachy_worker	(	const TSparseMatrix &	A,
		size_t	node,
		size_t	depth,
		size_t	maxdepth,
		std::vector< std::vector< size_t > > &	indices,
		std::vector< bool > &	bVisited
	)

◆ GetNNZs()

template<typename TSparseMatrix >

size_t ug::GetNNZs ( const TSparseMatrix & A )

returns the number of non-zeroes (!= number of connections)

◆ gs_step_LL() [1/2]

template<typename Matrix_type , typename Vector_type >

void ug::gs_step_LL	(	const Matrix_type &	A,
		Vector_type &	c,
		const Vector_type &	d,
		const number	relaxFactor
	)

Gauss-Seidel-Iterations.

Here, iteration schemes of gauss-seidel-type are described for solving the linear equation

\f$ A * x = b.      A \in R^{nxn}, x \in R^n, b \in R^n \f$.

Most of the common linear iteration-methods base on the decomposition of A into its diagonal (D) and strict-upper(-U) and strict-lower part (-L),

$ A = D - L - U $.

Among others, W. Hackbusch ('Iterative Loesung grosser Gleichungssysteme'), distinguishes three different forms for describing a linear iteration scheme. The general 'first normal-form' of a linear iteration scheme takes the form

$ x^{m+1} = M * x^m + N * b $,

with some Matrices $ M $ and $ N \in R^{nxn} $. m denotes the iteration index. The general 'second normal-form' of a linear iteration scheme takes the form

$ x^{m+1} = x^m - N * (A * x^m - b) $.

Those linear iteration schemes, which can be represented by the second normal-form are the linear, consistent iteration schemes.

Introducing the correction $ c{m+1} := x^{m+1} - x^m $ and the defect $ d^m := b - A * x^m $ the second normal-form can be rewritten as

$ c = N * d $.

Below, methods for the (forward) Gauss-Seidel step, the backward Gauss-Seidel step and the symmetric Gauss-Seidel step are implemented ('gs_step_LL', 'gs_step_UR' resp. 'sgs_step'). The matrices of the second normal-form are

$ N = (D-L)^{-1}$ for the (forward) Gauss-Seidel step, $ N = (D-U)^{-1}$ for the backward Gauss-Seidel step and $ N = (D-u)^{-1}D(D-U)^{-1} $ for the symmetric Gauss-Seidel step.

References:

W. Hackbusch. Iterative Loesung grosser Gleichungssysteme

See also: gs_step_LL, gs_step_UR, sgs_step

Performs a forward gauss-seidel-step, that is, solve on the lower left of A. Using gs_step_LL within a preconditioner-scheme leads to the fact that we get the correction by successive inserting the already computed values of c in c = N * d, with c being the correction and d being the defect. N denotes the matrix of the second normal-form of a linear iteration scheme.

Parameters

A	Matrix $A = D - L - U$
c	Vector. $ c = N * d = (D-L)^{-1} * d $
d	Vector d.

See also: gs_step_UR, sgs_step

References ug::InverseMatMult(), ug::MatMultAdd(), and s.

Referenced by ug::sgs_step(), and ug::GaussSeidel< TAlgebra >::step().

◆ gs_step_LL() [2/2]

template<typename Matrix_type , typename Vector_type >

bool ug::gs_step_LL	(	const Matrix_type &	A,
		Vector_type &	x,
		const Vector_type &	b
	)

Performs a forward gauss-seidel-step, that is, solve on the lower left of A.

Parameters

A	Matrix $A = D - L - U$
x	will be $x = (D-L)^{-1}b $
b	the vector b.

See also: gs_step_UR, sgs_step

References ug::InverseMatMult(), ug::MatMultAdd(), and s.

◆ gs_step_UR() [1/2]

template<typename Matrix_type , typename Vector_type >

void ug::gs_step_UR	(	const Matrix_type &	A,
		Vector_type &	c,
		const Vector_type &	d,
		const number	relaxFactor
	)

Performs a backward gauss-seidel-step, that is, solve on the upper right of A. Using gs_step_UR within a preconditioner-scheme leads to the fact that we get the correction by successive inserting the already computed values of c in c = N * d, with c being the correction and d being the defect. N denotes the matrix of the second normal-form of a linear iteration scheme.

Parameters

A	Matrix $A = D - L - U$
c	will be $c = N * d = (D-U)^{-1} * d $
d	the vector d.

See also: gs_step_LL, sgs_step

References ug::InverseMatMult(), ug::MatMultAdd(), and s.

Referenced by ug::sgs_step(), and ug::BackwardGaussSeidel< TAlgebra >::step().

◆ gs_step_UR() [2/2]

template<typename Matrix_type , typename Vector_type >

bool ug::gs_step_UR	(	const Matrix_type &	A,
		Vector_type &	x,
		const Vector_type &	b
	)

Performs a backward gauss-seidel-step, that is, solve on the upper right of A.

Parameters

A	Matrix $A = D - L - U$
x	will be $x = (D-U)^{-1}b $
b	the vector b.

See also: gs_step_LL, sgs_step

References ug::InverseMatMult(), ug::MatMultAdd(), and s.

◆ IsCloseToBoundary()

template<typename TSparseMatrix >

bool ug::IsCloseToBoundary	(	const TSparseMatrix &	A,
		size_t	node,
		size_t	distance
	)

gets the neighborhood of a node in the connectivity graph of a SparseMatrix.

Parameters

A	(in) Matrix A
node	(in) the node where to start
depth	(in) the depth of neighborhood. 0 = empty.
indices	(out) the indices of the neighbors
posInConnections	array to speed up computation. Has to be posInConnections[i] = 0 for all i=0..A.num_rows(). Can be NULL.

Note: the node itself is only included if there is a connection from node to node.

determines if a node is close to a unconnected node in the connectivity graph of a SparseMatrix.

Parameters

A	(in) Matrix A
node	(in) the node where to start
distance	(in) up to which distance "close" is.

Returns: if there is a distance long path in graph(A) to an unconnected node, true. otherwise false.

◆ IsDirichletRow()

template<typename TSparseMatrix >

bool ug::IsDirichletRow	(	const TSparseMatrix &	A,
		size_t	i,
		size_t	alpha
	)

Evaluates 'true', iff corresponding row is Dirichlet.

References alpha, ug::BlockRef(), and ug::GetCols().

Referenced by ug::MatAddNonDirichlet().

◆ MapVector() [1/2]

template<typename TValueType >

ug::MapVector< TValueType >::MapVector ( )

inline

constructor

◆ MapVector() [2/2]

template<typename TValueType >

ug::MapVector< TValueType >::MapVector ( size_t _length )

inline

constructor with length

◆ MarkNeighbors()

template<typename TSparseMatrix >

void ug::MarkNeighbors	(	const TSparseMatrix &	A,
		size_t	node,
		size_t	depth,
		std::vector< bool > &	bVisited
	)

◆ MatAdd()

template<typename matrix_type >

void ug::MatAdd	(	matrix_type &	M,
		number	alpha1,
		const matrix_type &	A,
		number	alpha2,
		const matrix_type &	B
	)

Calculates M = A + B.

Parameters

M	(out) Matrix M, M = A + B
A	(in) Matrix A
B	(in) Matrix B note: A and/or B may be equal to M.

References PROFILE_FUNC_GROUP, and UG_ASSERT.

◆ MatAddNonDirichlet()

template<typename matrix_type >

void ug::MatAddNonDirichlet	(	matrix_type &	M,
		number	alpha1,
		const matrix_type &	A,
		number	alpha2,
		const matrix_type &	B
	)

Calculates M = A + B.

Parameters

M	(out) Matrix M, M = A + B
A	(in) Matrix A
B	(in) Matrix B note: A and/or B may be equal to M.

References alpha, ug::BlockRef(), ug::GetRows(), ug::IsDirichletRow(), PROFILE_FUNC_GROUP, and UG_ASSERT.

◆ MatMultTransposedAdd()

template<typename vector_t , typename matrix_t >

void ug::MatMultTransposedAdd	(	vector_t &	dest,
		const number &	alpha1,
		const vector_t &	v1,
		const number &	beta1,
		const MapSparseMatrix< matrix_t > &	A1,
		const vector_t &	w1
	)

inline

calculates dest = alpha1*v1 + beta1 * A1^T *w1;

References ug::MapSparseMatrix< TValueType >::axpy_transposed().

◆ operator<<()

std::ostream & ug::operator<<	(	std::ostream &	out,
		const AlgebraType &	v
	)

inline

writes the Identifier to the output stream

References ug::AlgebraType::blocksize(), ug::AlgebraType::CPU, ug::AlgebraType::GPU, ug::AlgebraType::type(), and ug::AlgebraType::VariableBlockSize.

◆ ScaleRow()

template<typename TSparseMatrix >

void ug::ScaleRow	(	TSparseMatrix &	A,
		size_t	i,
		number	fac
	)

scales (block-)row i.

Parameters

A	(in) Matrix A
i	(in) row to scales
fac	(in) Scaling factor

◆ ScaleSparseMatrixCommon()

template<typename TSparseMatrix >

void ug::ScaleSparseMatrixCommon	(	TSparseMatrix &	A,
		double	d
	)

◆ SerializeMatrix()

template<typename TSparseMatrix , class TOStream >

void ug::SerializeMatrix	(	TOStream &	buf,
		const TSparseMatrix &	A
	)

References num_connections(), and ug::Serialize().

◆ SetCol()

template<typename TSparseMatrix >

void ug::SetCol	(	TSparseMatrix &	A,
		size_t	i,
		size_t	alpha,
		number	val = `0.0`
	)

set value for col for entry (i,alpha).

Parameters

A	(in) Matrix A
i	(in) col to set
alpha	the alpha index
val	the value to be set

References alpha, ug::BlockRef(), and ug::GetRows().

Referenced by ug::IObstacleConstraint< TDomain, TAlgebra >::adjust_restriction().

◆ SetDirichletRow() [1/3]

template<typename TSparseMatrix >

void ug::SetDirichletRow	(	TSparseMatrix &	A,
		const std::vector< size_t >	vIndex
	)

set Dirichlet row for block i.

Parameters

	[in/out]	Matrix A
[in]	vIndex	vector of row indices to set dirichlet, that is A(i,i) = 1.0, A(i,k) = 0.0 for all k != i.

References UG_ASSERT.

◆ SetDirichletRow() [2/3]

template<typename TSparseMatrix >

void ug::SetDirichletRow	(	TSparseMatrix &	A,
		size_t	i
	)

set Dirichlet row for block i.

Parameters

A	(in) Matrix A
i	(in) row to set dirichlet, that is A(i,i) = 1.0, A(i,k) = 0.0 for all k != i.

◆ SetDirichletRow() [3/3]

template<typename TSparseMatrix >

void ug::SetDirichletRow	(	TSparseMatrix &	A,
		size_t	i,
		size_t	alpha
	)

set Dirichlet row for entry (i,alpha).

Parameters

A	(in) Matrix A
i	(in) row to set dirichlet, that is A(i,i)(alpha, alpha) = 1.0, A(i,k)(alpha, beta) = 0.0 for all (k, beta) != (i, alpha)$.
alpha	the alpha index

References alpha, ug::BlockRef(), and ug::GetCols().

◆ SetRow() [1/2]

template<typename TSparseMatrix >

void ug::SetRow	(	TSparseMatrix &	A,
		size_t	i,
		number	val = `0.0`
	)

set value for (block-)row i.

Parameters

A	(in) Matrix A
i	(in) row to scales
val	(in) value to be set

◆ SetRow() [2/2]

template<typename TSparseMatrix >

void ug::SetRow	(	TSparseMatrix &	A,
		size_t	i,
		size_t	alpha,
		number	val = `0.0`
	)

set value for row for entry (i,alpha).

Parameters

A	(in) Matrix A
i	(in) row to set
alpha	the alpha index
val	the value to be set

References alpha, ug::BlockRef(), and ug::GetCols().

Referenced by ug::DirichletBoundary< TDomain, TAlgebra >::adjust_prolongation(), ug::SymP1Constraints< TDomain, TAlgebra >::adjust_prolongation(), ug::OneSideP1Constraints< TDomain, TAlgebra >::adjust_prolongation(), ug::DirichletBoundary< TDomain, TAlgebra >::adjust_restriction(), ug::AssembledMultiGridCycle< TDomain, TAlgebra >::assemble_rim_cpl(), ug::SetInterpolation(), ug::SetRow(), and ug::IProjGaussSeidel< TDomain, TAlgebra >::truncateMat().

◆ sgs_step() [1/2]

template<typename Matrix_type , typename Vector_type >

void ug::sgs_step	(	const Matrix_type &	A,
		Vector_type &	c,
		const Vector_type &	d,
		const number	relaxFactor
	)

Performs a symmetric gauss-seidel step. Using sgs_step within a preconditioner-scheme leads to the fact that we get the correction by successive inserting the already computed values of c in c = N * d, with c being the correction and d being the defect. N denotes the matrix of the second normal-form of a linear iteration scheme.

Parameters

A	Matrix $A = D - L - R$
c	will be $c = N * d = (D-U)^{-1} D (D-L)^{-1} d $
d	the vector d.

See also: gs_step_LL, gs_step_LL

References ug::gs_step_LL(), ug::gs_step_UR(), ug::MatMult(), and s.

Referenced by ug::SymmetricGaussSeidel< TAlgebra >::step().

◆ sgs_step() [2/2]

template<typename Matrix_type , typename Vector_type >

bool ug::sgs_step	(	const Matrix_type &	A,
		Vector_type &	x,
		const Vector_type &	b
	)

Performs a symmetric gauss-seidel step.

Parameters

A	Matrix $A = D - L - R$
x	will be $x = (D-U)^{-1} D (D-L)^{-1} b $
b	the vector b.

See also: gs_step_LL, gs_step_LL

References ug::gs_step_LL(), ug::gs_step_UR(), and ug::MatMult().

M	(out) Matrix M, M = A*B$
A	(in) Matrix A
B	(in) Matrix B \( M_{ij} = \sum_k A_{ik} * B_{kj} \) For implementation details, see also CreateAsMultiplyOf(M, A, B, C).

A	Matrix \(A = D - L - R\)
c	will be \(c = N * d = D^{-1} d \)
d	the vector d.
damp	the damping factor

A	Matrix \(A = D - L - U\)
c	Vector. \( c = N * d = (D-L)^{-1} * d \)
d	Vector d.

A	Matrix \(A = D - L - U\)
x	will be \(x = (D-L)^{-1}b \)
b	the vector b.

A	Matrix \(A = D - L - U\)
c	will be \(c = N * d = (D-U)^{-1} * d \)
d	the vector d.

A	Matrix \(A = D - L - U\)
x	will be \(x = (D-U)^{-1}b \)
b	the vector b.

A	Matrix \(A = D - L - R\)
c	will be \(c = N * d = (D-U)^{-1} D (D-L)^{-1} d \)
d	the vector d.

A	Matrix \(A = D - L - R\)
x	will be \(x = (D-U)^{-1} D (D-L)^{-1} b \)
b	the vector b.

Modules

Classes

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

◆ FORCE_CREATION

◆ UNUSED_VARIABLE

Typedef Documentation

◆ value_type

◆ vector_type

Function Documentation

◆ AddMultiplyOf()

◆ Axpy_transposedCommonSparseMatrix()

◆ AxpyCommonSparseMatrix()

◆ CheckDiagonalInvertible() [1/2]

◆ CheckDiagonalInvertible() [2/2]

◆ CheckRowIterators()

◆ CheckVectorInvertible() [1/2]

◆ CheckVectorInvertible() [2/2]

◆ CreateAsMultiplyOf() [1/2]

◆ CreateAsMultiplyOf() [2/2]

◆ DeserializeMatrix()

◆ diag_step()

◆ GetDenseDoubleFromSparse()

◆ GetDenseFromSparse()

◆ GetDoubleFromSparseBlock()

◆ GetDoubleSize()

◆ GetDoubleSparseFromBlockSparse()

◆ GetMaxConnections()

◆ GetNeighborhood() [1/2]

◆ GetNeighborhood() [2/2]

◆ GetNeighborhood_worker()

◆ GetNeighborhoodHierachy() [1/2]

◆ GetNeighborhoodHierachy() [2/2]

◆ GetNeighborhoodHierachy_worker()

◆ GetNNZs()

◆ gs_step_LL() [1/2]

◆ gs_step_LL() [2/2]

◆ gs_step_UR() [1/2]

◆ gs_step_UR() [2/2]

◆ IsCloseToBoundary()

◆ IsDirichletRow()

◆ MapVector() [1/2]

◆ MapVector() [2/2]

◆ MarkNeighbors()

◆ MatAdd()

◆ MatAddNonDirichlet()

◆ MatMultTransposedAdd()

◆ operator<<()

◆ ScaleRow()

◆ ScaleSparseMatrixCommon()

◆ SerializeMatrix()

◆ SetCol()

◆ SetDirichletRow() [1/3]

◆ SetDirichletRow() [2/3]

◆ SetDirichletRow() [3/3]

◆ SetRow() [1/2]

◆ SetRow() [2/2]

◆ sgs_step() [1/2]

◆ sgs_step() [2/2]