Sparse Matrix and Vector classes

Matrix and Vector classes that support a block recursive structure capable of representing the natural structure from Finite Element discretisations. More...

Modules
	Block Recursive Iterative Kernels
	IO for matrices and vectors.
	Provides methods for reading and writing matrices and vectors in various formats.

Files
file	matrixmatrix.hh
	provides functions for sparse matrix matrix multiplication.
file	matrixutils.hh
	Some handy generic functions for ISTL matrices.

Classes
struct	Dune::CompressionStatistics< size_type >
	Statistics about compression achieved in implicit mode. More...
class	Dune::ImplicitMatrixBuilder< M_ >
	A wrapper for uniform access to the BCRSMatrix during and after the build stage in implicit build mode. More...
class	Dune::BCRSMatrix< B, A >
	A sparse block matrix with compressed row storage. More...
class	Dune::BDMatrix< B, A >
	A block-diagonal matrix. More...
class	Dune::BTDMatrix< B, A >
	A block-tridiagonal matrix. More...
class	Dune::BlockVector< B, A >
	A vector of blocks with memory management. More...
class	Dune::Matrix< T, A >
	A generic dynamic dense matrix. More...
struct	Dune::MatMultMatResult< M1, M2 >
	Helper TMP to get the result type of a sparse matrix matrix multiplication ( \(C=A*B\)) More...
struct	Dune::TransposedMatMultMatResult< M1, M2 >
	Helper TMP to get the result type of a sparse matrix matrix multiplication ( \(C=A*B\)) More...
struct	Dune::CheckIfDiagonalPresent< Matrix, blocklevel, l >
	Check whether the a matrix has diagonal values on blocklevel recursion levels. More...
class	Dune::VariableBlockVector< B, A >
	A Vector of blocks with different blocksizes. More...

Functions
template<class T , class A , class A1 , class A2 , int n, int m, int k>
void	Dune::matMultTransposeMat (BCRSMatrix< FieldMatrix< T, n, k >, A > &res, const BCRSMatrix< FieldMatrix< T, n, m >, A1 > &mat, const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &matt, bool tryHard=false)
	Calculate product of a sparse matrix with a transposed sparse matrices ( \(C=A*B^T\)). More...
template<class T , class A , class A1 , class A2 , int n, int m, int k>
void	Dune::matMultMat (BCRSMatrix< FieldMatrix< T, n, m >, A > &res, const BCRSMatrix< FieldMatrix< T, n, k >, A1 > &mat, const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &matt, bool tryHard=false)
	Calculate product of two sparse matrices ( \(C=A*B\)). More...
template<class T , class A , class A1 , class A2 , int n, int m, int k>
void	Dune::transposeMatMultMat (BCRSMatrix< FieldMatrix< T, n, m >, A > &res, const BCRSMatrix< FieldMatrix< T, k, n >, A1 > &mat, const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &matt, bool tryHard=false)
	Calculate product of a transposed sparse matrix with another sparse matrices ( \(C=A^T*B\)). More...
template<class M >
int	Dune::countNonZeros (const M &matrix)
	Get the number of nonzero fields in the matrix. More...

Detailed Description

Matrix and Vector classes that support a block recursive structure capable of representing the natural structure from Finite Element discretisations.

The interface of our matrices is designed according to what they represent from a mathematical point of view. The vector classes are representations of vector spaces:

• FieldVector represents a vector space \(V=K^n\) where the field \(K\) is represented by a numeric type (e.g. double, float, complex). \(n\) is known at compile time.
• BlockVector represents a vector space \(V=W\times W \times W \times\cdots\times W\) where W is itself a vector space.
• VariableBlockVector represents a vector space having a two-level block structure of the form \(V=B^{n_1}\times B^{n_2}\times\ldots \times B^{n_m}\), i.e. it is constructed from \(m\) vector spaces, \(i=1,\ldots,m\).

The matrix classes represent linear maps \(A: V \mapsto W\) from vector space \(V\) to vector space \(W\) the recursive block structure of the matrix rows and columns immediately follows from the recursive block structure of the vectors representing the domain and range of the mapping, respectively:

• FieldMatrix represents a linear map \(M: V_1 \to V_2\) where \(V_1=K^n\) and \(V_2=K^m\) are vector spaces over the same field represented by a numerix type.
• BCRSMatrix represents a linear map \(M: V_1 \to V_2\) where \(V_1=W\times W \times W \times\cdots\times W\) and \(V_2=W\times W \times W \times\cdots\times W\) where W is itself a vector space.
• VariableBCRSMatrix is not yet implemented.

Function Documentation

countNonZeros()

template<class M >

int Dune::countNonZeros ( const M &  matrix )

inline

Get the number of nonzero fields in the matrix.

This is not the number of nonzero blocks, but the number of non zero scalar entries (on blocklevel 1) if the matrix is viewed as a flat matrix.

For FieldMatrix this is simply the number of columns times the number of rows, for a BCRSMatrix<FieldMatrix<K,n,m>> this is the number of nonzero blocks time n*m.

Referenced by Dune::Amg::MatrixHierarchy< M, PI, A >::build().

matMultMat()

template<class T , class A , class A1 , class A2 , int n, int m, int k>

void Dune::matMultMat	(	BCRSMatrix< FieldMatrix< T, n, m >, A > &	res,
		const BCRSMatrix< FieldMatrix< T, n, k >, A1 > &	mat,
		const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &	matt,
		bool	tryHard = false
	)

Calculate product of two sparse matrices ( \(C=A*B\)).

Parameters

res	Matrix for the result of the computation.
mat	Matrix A.
matt	Matrix B.
tryHard	ignored

matMultTransposeMat()

template<class T , class A , class A1 , class A2 , int n, int m, int k>

void Dune::matMultTransposeMat	(	BCRSMatrix< FieldMatrix< T, n, k >, A > &	res,
		const BCRSMatrix< FieldMatrix< T, n, m >, A1 > &	mat,
		const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &	matt,
		bool	tryHard = false
	)

Calculate product of a sparse matrix with a transposed sparse matrices ( \(C=A*B^T\)).

Parameters

res	Matrix for the result of the computation.
mat	Matrix A.
matt	Matrix B, which will be transposed before the multiplication.
tryHard	ignored

transposeMatMultMat()

template<class T , class A , class A1 , class A2 , int n, int m, int k>

void Dune::transposeMatMultMat	(	BCRSMatrix< FieldMatrix< T, n, m >, A > &	res,
		const BCRSMatrix< FieldMatrix< T, k, n >, A1 > &	mat,
		const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &	matt,
		bool	tryHard = false
	)

Calculate product of a transposed sparse matrix with another sparse matrices ( \(C=A^T*B\)).

Parameters

res	Matrix for the result of the computation.
mat	Matrix A, which will be transposed before the multiplication.
matt	Matrix B.
tryHard	ignored