A NUMA-aware compressed row storage matrix adhering mostly to the Dune ISTL interface (to complete...) More...

#include <threadedMatrix.hh>

Detailed Description

template<class Entry, class Index = size_t>
class Kaskade::NumaBCRSMatrix< Entry, Index >

A NUMA-aware compressed row storage matrix adhering mostly to the Dune ISTL interface (to complete...)

This class distributes the matrix rows block-wise across available NUMA nodes to exploit the higher memory bandwidth in parallelized matrix-vector products and similar operations.

As the distribution of matrix entries to the NUMA nodes is optimized for equidistribution of storage size and computational effort in matrix vector products, transpose times vector multiplications are much slower than plain matrix-vector multiplications (roughly factor 6).

If the matrix is a priori specified as being symmetric, only the lower triangular elements are stored and can be accessed. Nevertheless, all linear algebra operations (i.e., matrix vector products) act on the complete symmetric matrix. Note that symmetric storage incurs a significant performance penalty for matrix-vector products (roughly factor 3), and should only be used if those operations are rare. In contrast, transpose times vector multiplications do not suffer.

For creating a NumaBCRSMatrix, a sparsity pattern (NumaCRSPattern) has to be provided. This in turn is created using a creator object (NumaCRSPatternCreator). This multi-stage creation allows efficient creation while avoiding stateful interfaces (incompletely created objects). The matrix creation can be done as follows:

// define the pattern creator for a 9x9 matrix
NumaCRSPatternCreator<> creator(9,9);
// add a diagonal entry
creator.addElement(2,2);
// create the matrix
NumaBCRSMatrix<Dune::FieldMatrix<double,1,1>> matrix(creator);
// fill the entry
matrix[2][2] = 1.0;

Concurrent calls to one NumaBCRSMatrix object are not safe.

Template Parameters

Entry	the type of matrix elements (in general Dune::FieldMatrix<double,n,m>)
Index	integral type for row/column indices (usually int, long, or size_t), defaults to size_t

Definition at line 2114 of file threadedMatrix.hh.

Public Types
typedef ScalarType< Entry >	Scalar

typedef Scalar	field_type

typedef Entry	block_type

using	value_type = Entry

using	size_type = Index

typedef ThreadedMatrixDetail::NumaBCRSMatrixIterator< Entry, Index >	iterator
	iterator type stepping through the rows More...

typedef ThreadedMatrixDetail::NumaBCRSMatrixConstIterator< Entry, Index >	const_iterator

typedef iterator	row_type

typedef const_iterator	const_row_type

typedef iterator	ConstRowIterator

using	ColIterator = typename iterator::Iterator
	column iterator stepping through the entries of a row More...

using	ConstColIterator = typename iterator::ConstIterator
	column iterator stepping through the const entries of a row More...

Public Member Functions
Assignment and simple in-place modifications
Self &	operator= (Self const &mat)=default
	Copy assignment. More...

Self &	operator= (Self &&mat)=default
	Move assignment. More...

Self &	operator= (Entry const &a)
	Assigns the given value to each entry. More...

Self &	operator= (typename Entry::field_type const &a)
	Assigns the given scalar value to each entry. More...

template<class Arguments , class Operation >
Self &	operator= (ThreadedMatrixDetail::NumaBCRSMatrixExpression< Arguments, Operation > const &e)
	NOT YET IMPLEMENTED Assigns the given Numa matrix expression. More...

template<class EntryB , class IndexB >
Self &	operator+= (NumaBCRSMatrix< EntryB, IndexB > const &B)
	Adds a sparse matrix to this one. More...

template<class EntryB , class IndexB >
Self &	operator-= (NumaBCRSMatrix< EntryB, IndexB > const &B)
	Subtracts a sparse matrix from this one. More...

template<class Factor >
Self &	operator*= (Factor a)
	Multiplication with a "scalar". More...

Element access
Matrix entries can be accessed via iterators or by direct access. Iterators allow row-major scanning of existing matrix entries, with an iterator iterating over the rows and for each row an iterator iterating over the entries in that row. Direct access is provided by the subscript operator [], which returns a row (reference), which in turn provides a subscript operator for selecting the column, e.g., A[i][j] = 42; Note that the second (column) subscript has logarithmic complexity in the number of entries in the row.
iterator	begin ()
	returns an iterator to the first row More...

const_iterator	begin () const

iterator	end ()
	returns an iterator to the first row More...

const_iterator	end () const

row_type	operator[] (Index r)
	Subscript operator allowing random access to rows. More...

const_row_type	operator[] (Index r) const

Submatrix extraction
template<class RowIndices , class ColIndices >
Self	operator() (RowIndices const &ri, ColIndices const &ci) const

General matrix information.
Index	N () const
	The number of rows. More...

Index	M () const
	The number of columns. More...

size_t	nonzeroes () const
	Returns the number of structurally nonzero elements. More...

std::shared_ptr< NumaCRSPattern< Index > >	getPattern () const
	Returns a pointer to the sparsity pattern. More...

Chunk &	chunk (int i)
	Obtains a reference to the given chunk. More...

bool	exists (Index r, Index c) const
	returns true if (r,c) is structurally nonzero More...

field_type	frobenius_norm () const
	Computes the Frobenius norm \( \\|A\\|_F = \sqrt{\mathrm{tr}(A^TA)} \). More...

field_type	frobenius_norm2 () const
	Computes the square of the Frobenius norm \( \\|A\\|_F^2 = \mathrm{tr}(A^TA) \). More...

Matrix-vector operations
template<class X , class Y >
field_type	mv (X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow Ax \) with computation of \( y^T x \) if A is square. More...

template<class X , class Y >
void	mtv (X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow A^Tx \). More...

template<class X , class Y >
void	mmv (X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow -Ax \). More...

template<class X , class Y >
field_type	smv (field_type const &a, X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow aAx \). More...

template<class X , class Y >
void	smtv (field_type const &a, X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow aA^Tx \). More...

template<class X , class Y >
field_type	umv (X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow y + Ax \) and subsequent computation of \( y^T x \) if A is square. More...

template<class X , class Y >
void	umtv (X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow y + A^Tx \). More...

template<class X , class Y >
field_type	usmv (field_type const &a, X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow y + aAx \) and subsequent computation of \( y^T x \) if A is square. More...

template<class X , class Y >
void	usmtv (field_type const &a, X const &x, Y &y) const
	Matrix-vector multiplication \( y \leftarrow y + aA^Tx \). More...

Related Functions
(Note that these are not member functions.)
template<class IndexP , class EntryP , class IndexA , class EntryA >
auto	conjugation (NumaBCRSMatrix< EntryP, IndexP > const &P, NumaBCRSMatrix< EntryA, IndexA > const &A, bool onlyLowerTriangle=false, bool createDiagonal=false)
	Creates the conjugation product \( P^T A P\). More...

template<class Target , class Source , class RowIndices , class ColIndices >
Target	submatrix (Source const &A, RowIndices const &ri, ColIndices const &ci)
	extracts a sparse or dense submatrix of \( A \) More...

template<class EntryA , class EntryB , class IndexA , class IndexB >
auto	operator* (NumaBCRSMatrix< EntryA, IndexA > const &A, NumaBCRSMatrix< EntryB, IndexB > const &B)
	Computes the matrix-matrix product \( (A,B) \mapsto AB \). More...

template<class Entry , class Index >
std::ostream &	operator<< (std::ostream &out, NumaBCRSMatrix< Entry, Index > const &A)
	Writes a NumaBCRSMatrix to an output stream. More...

template<class SparseMatrix >
DynamicMatrix< typename SparseMatrix::block_type >	full (SparseMatrix const &A)
	Converts a sparse NumaBCRSMatrix to a dense matrix. More...

template<class SparseMatrix , class RowRange , class ColRange >
DynamicMatrix< typename SparseMatrix::block_type >	full (SparseMatrix const &A, RowRange const &rows, ColRange const &cols)
	Converts a subrange of a sparse matrix to a dense matrix. More...

template<class Entry , class Index , class Index2 >
NumaBCRSMatrix< Entry, Index >	operator+ (NumaBCRSMatrix< Entry, Index > const &A, NumaBCRSMatrix< Entry, Index2 > const &B)
	Matrix addition \( (A,B) \mapsto A+B \). The sparsity patterns of both matrices can be different. The size of the matrices have to be the same. Both must not have symmetric storage. More...

template<class Entry , class Index >
auto	transpose (NumaBCRSMatrix< Entry, Index > const &A)
	Creates the transposed sparse matrix \( A^T \). More...

template<class Target , class Source , class RowIndices , class ColIndices >
Target	eraseRowsNCols (Source const &A, RowIndices const &ri, ColIndices const &ci)
	"deletes" rows/columns by extracting a copy of the matrix keeping the non-deleted rows/columns. More...

template<class Target , class Source , class RowIndices >
Target	eraseRows (Source const &A, RowIndices const &ri)
	"deletes" rows by extracting a copy of the matrix keeping only the non-deleted rows. More...

template<class Target , class Source , class ColIndices >
Target	eraseCols (Source const &A, ColIndices const &ci)
	"deletes" columns by extracting a copy of the matrix keeping only the non-deleted columns. More...

template<class Source >
std::vector< size_t >	nonZeroColumns (Source const &A)
	returns all indices of nonzero columns. More...

template<int row2, int col2, int row1, int col1, class Scalar , class Index >
NumaBCRSMatrix< Dune::FieldMatrix< Scalar, row2, col2 >, Index >	reshapeBlocks (NumaBCRSMatrix< Dune::FieldMatrix< Scalar, row1, col1 >, Index > const &A)
	reshapes NumaBRCSMAtrix entry block structure More...

template<int blockrows, int blockcols, class Scalar , class Index >
NumaBCRSMatrix< Dune::FieldMatrix< Scalar, blockrows, blockcols >, Index >	horzcat (NumaBCRSMatrix< Dune::FieldMatrix< Scalar, blockrows, blockcols >, Index > const &A, NumaBCRSMatrix< Dune::FieldMatrix< Scalar, blockrows, blockcols >, Index > const &B)
	concatenate two matrices horizontally More...

template<int blockrows, int blockcols, class Scalar , class Index >
NumaBCRSMatrix< Dune::FieldMatrix< Scalar, blockrows, blockcols >, Index >	vertcat (NumaBCRSMatrix< Dune::FieldMatrix< Scalar, blockrows, blockcols >, Index > const &A, NumaBCRSMatrix< Dune::FieldMatrix< Scalar, blockrows, blockcols >, Index > const &B)
	concatenate two matrices vertically More...

template<int blockrows, int blockcols, class Index = size_t>
NumaBCRSMatrix< Dune::FieldMatrix< double, blockrows, blockcols >, Index >	diagcat (NumaBCRSMatrix< Dune::FieldMatrix< double, blockrows, blockcols >, Index > const &A, NumaBCRSMatrix< Dune::FieldMatrix< double, blockrows, blockcols >, Index > const &B)
	concatenate two matrices diagonally, resulting matrix is zero on the off block-diagonal More...

Constructors
	NumaBCRSMatrix ()
	Constructs an empty 0x0 matrix. More...

	NumaBCRSMatrix (Self const &A)=default
	Copy constructor. More...

	NumaBCRSMatrix (Self &&A)=default
	Move constructor. More...

	NumaBCRSMatrix (NumaCRSPatternCreator< Index > const &creator, Entry const &init=Entry(0))
	Constructor creating a matrix from a given sparsity pattern creator. More...

	NumaBCRSMatrix (std::shared_ptr< NumaCRSPattern< Index > > const &pattern_, Entry const &init=Entry(0))
	Constructor creating a matrix from a given sparsity pattern. More...

template<class Expanded , class Condensed , class Matrix >
	NumaBCRSMatrix (Expanded const &eIndices, Condensed const &cIndices, Matrix const &mat)
	Deprecated. Use simpler version without cIndices instead. More...

template<class Expanded , class Matrix >
	NumaBCRSMatrix (Expanded const &eIndices, Matrix const &mat)
	Indexed submatrix constructor. More...

template<class Matrix >
	NumaBCRSMatrix (std::shared_ptr< NumaCRSPattern< Index > > const &pattern_, Matrix const &matrix, bool isSymmetric, bool isTransposed)
	Constructor copying a given matrix. More...

template<class OtherEntry >
	NumaBCRSMatrix (NumaBCRSMatrix< OtherEntry, Index > const &matrix)
	Constructor copying a given matrix. More...

template<class Matrix >
	NumaBCRSMatrix (Matrix const &matrix, bool isSymmetric, bool isTransposed=false, bool symmetric=false)
	Constructor. More...

	NumaBCRSMatrix (NumaBCRSMatrix< Entry, Index > const &matrix, bool isSymmetric, bool isTransposed=false, bool symmetric=false)
	Constructor. More...

Entering data
template<class LMIterator >
void	scatter (LMIterator first, LMIterator last)
	Scatters given sub-matrices into the matrix by adding up their entries. More...

template<class RowIndices , class ColIndices , class BinaryOp = std::plus<Entry>>
void	scatter (DynamicMatrix< Entry > const &B, RowIndices const &rows, ColIndices const &cols, BinaryOp const &op=BinaryOp())
	Scatters given submarix into the matrix. More...

Member Typedef Documentation

◆ block_type

template<class Entry , class Index = size_t>

typedef Entry Kaskade::NumaBCRSMatrix< Entry, Index >::block_type

Definition at line 2122 of file threadedMatrix.hh.

◆ ColIterator

template<class Entry , class Index = size_t>

using Kaskade::NumaBCRSMatrix< Entry, Index >::ColIterator = typename iterator::Iterator

column iterator stepping through the entries of a row

Definition at line 2137 of file threadedMatrix.hh.

◆ const_iterator

template<class Entry , class Index = size_t>

typedef ThreadedMatrixDetail::NumaBCRSMatrixConstIterator<Entry,Index> Kaskade::NumaBCRSMatrix< Entry, Index >::const_iterator

Definition at line 2130 of file threadedMatrix.hh.

◆ const_row_type

template<class Entry , class Index = size_t>

typedef const_iterator Kaskade::NumaBCRSMatrix< Entry, Index >::const_row_type

Definition at line 2132 of file threadedMatrix.hh.

◆ ConstColIterator

template<class Entry , class Index = size_t>

using Kaskade::NumaBCRSMatrix< Entry, Index >::ConstColIterator = typename iterator::ConstIterator

column iterator stepping through the const entries of a row

Definition at line 2140 of file threadedMatrix.hh.

◆ ConstRowIterator

template<class Entry , class Index = size_t>

typedef iterator Kaskade::NumaBCRSMatrix< Entry, Index >::ConstRowIterator

Definition at line 2134 of file threadedMatrix.hh.

◆ field_type

template<class Entry , class Index = size_t>

typedef Scalar Kaskade::NumaBCRSMatrix< Entry, Index >::field_type

Definition at line 2121 of file threadedMatrix.hh.

◆ iterator

template<class Entry , class Index = size_t>

typedef ThreadedMatrixDetail::NumaBCRSMatrixIterator<Entry,Index> Kaskade::NumaBCRSMatrix< Entry, Index >::iterator

iterator type stepping through the rows

Definition at line 2129 of file threadedMatrix.hh.

◆ row_type

template<class Entry , class Index = size_t>

typedef iterator Kaskade::NumaBCRSMatrix< Entry, Index >::row_type

Definition at line 2131 of file threadedMatrix.hh.

◆ Scalar

template<class Entry , class Index = size_t>

typedef ScalarType<Entry> Kaskade::NumaBCRSMatrix< Entry, Index >::Scalar

Definition at line 2120 of file threadedMatrix.hh.

◆ size_type

template<class Entry , class Index = size_t>

using Kaskade::NumaBCRSMatrix< Entry, Index >::size_type = Index

Definition at line 2124 of file threadedMatrix.hh.

◆ value_type

template<class Entry , class Index = size_t>

using Kaskade::NumaBCRSMatrix< Entry, Index >::value_type = Entry

Definition at line 2123 of file threadedMatrix.hh.

Constructor & Destructor Documentation

◆ NumaBCRSMatrix() [1/11]

template<class Entry , class Index = size_t>

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix ( )

inline

Constructs an empty 0x0 matrix.

Definition at line 2151 of file threadedMatrix.hh.

◆ NumaBCRSMatrix() [2/11]

template<class Entry , class Index = size_t>

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix ( Self const & A )

default

Copy constructor.

◆ NumaBCRSMatrix() [3/11]

template<class Entry , class Index = size_t>

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix ( Self && A )

default

Move constructor.

◆ NumaBCRSMatrix() [4/11]

template<class Entry , class Index = size_t>

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix	(	NumaCRSPatternCreator< Index > const &	creator,
		Entry const &	init = `Entry(0)`
	)

inline

Constructor creating a matrix from a given sparsity pattern creator.

This is a convenience constructor that creates a new pattern under the hood.

Parameters

creator	the sparsity pattern creatorof the matrix to be constructed
init	initialization value for the entries

Definition at line 2173 of file threadedMatrix.hh.

◆ NumaBCRSMatrix() [5/11]

template<class Entry , class Index = size_t>

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix	(	std::shared_ptr< NumaCRSPattern< Index > > const &	pattern_,
		Entry const &	init = `Entry(0)`
	)

inline

Constructor creating a matrix from a given sparsity pattern.

Parameters

pattern	the sparsity pattern of the matrix to be constructed
init	initialization value for the entries

Definition at line 2183 of file threadedMatrix.hh.

◆ NumaBCRSMatrix() [6/11]

template<class Entry , class Index = size_t>

template<class Expanded , class Condensed , class Matrix >

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix	(	Expanded const &	eIndices,
		Condensed const &	cIndices,
		Matrix const &	mat
	)

inline

Deprecated. Use simpler version without cIndices instead.

This constructor will be made private after 2022-12.

Definition at line 2203 of file threadedMatrix.hh.

◆ NumaBCRSMatrix() [7/11]

template<class Entry , class Index = size_t>

template<class Expanded , class Matrix >

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix	(	Expanded const &	eIndices,
		Matrix const &	mat
	)

inline

Indexed submatrix constructor.

This works like Matlab A(idx,idx), where idx is given by eIndices. It creates a \( n \times n \) matrix \( a \) from the \( N \times \) N matrix \( A \), where \( a_{ij} = A_{e_ie_j} \). Of course, \( n \le N \) has to hold.

Template Parameters

Expanded an array type with value type convertible to Index

Parameters

eIndices	sorted global array of size \( n \) of expanded indices
mat	a square matrix with BCRSMatrix interface

Definition at line 2242 of file threadedMatrix.hh.

◆ NumaBCRSMatrix() [8/11]

template<class Entry , class Index = size_t>

template<class Matrix >

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix	(	std::shared_ptr< NumaCRSPattern< Index > > const &	pattern_,
		Matrix const &	matrix,
		bool	isSymmetric,
		bool	isTransposed
	)

inline

Constructor copying a given matrix.

Template Parameters

Matrix the type of the supplied matrix to copy (usually a Dune::BCRSMatrix or a NumaBCRSMatrix with different scalar type).

Parameters

pattern	the sparsity pattern to use
matrix	the matrix to be copied (shall have the given sparsity pattern)
isSymmetric	whether the supplied matrix is symmetric (then only its lower triangular part is accessed)
isTransposed	whether the supplied matrix is transposed

Definition at line 2258 of file threadedMatrix.hh.

◆ NumaBCRSMatrix() [9/11]

template<class Entry , class Index = size_t>

template<class OtherEntry >

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix ( NumaBCRSMatrix< OtherEntry, Index > const & matrix )

inline

Constructor copying a given matrix.

Template Parameters

OtherEntry The entry type of the matrix to be copied. The entries shall have the same dimension (but possibly different scalar type).

Parameters

matrix the matrix to be copied (shall conform to the Dune::BCRSMatrix interface)

Use this for switching between different entry types (e.g. float vs double). The sparsity pattern is shared between both matrices.

The number of chunks created is the number of NUMA nodes as reported by NumaThreadPool.

Definition at line 2281 of file threadedMatrix.hh.

◆ NumaBCRSMatrix() [10/11]

template<class Entry , class Index = size_t>

template<class Matrix >

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix	(	Matrix const &	matrix,
		bool	isSymmetric,
		bool	isTransposed = `false`,
		bool	symmetric = `false`
	)

inline

Constructor.

Template Parameters

Matrix the type of the supplied matrix to copy (shall conform to the Dune::BCRSMatrix interface)

Parameters

matrix	the matrix to be copied
isSymmetric	whether the supplied matrix is symmetric (then only its lower triangular part is accessed, requires square matrix and entries)
isTransposed	whether the supplied matrix is transposed
symmetric	whether only the lower triangular part should be stored (requires a square matrix and entries)

This is a convenience constructor that creates a new sparsity pattern from scratch. The number of chunks created is the number of NUMA nodes as reported by NumaThreadPool.

Note that !isSymmetric && symmetric is highly questionable and hence not allowed.

Definition at line 2302 of file threadedMatrix.hh.

◆ NumaBCRSMatrix() [11/11]

template<class Entry , class Index = size_t>

Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix	(	NumaBCRSMatrix< Entry, Index > const &	matrix,
		bool	isSymmetric,
		bool	isTransposed = `false`,
		bool	symmetric = `false`
	)

inline

Constructor.

Parameters

matrix	the matrix to be copied (shall conform to the Dune::BCRSMatrix interface)
isSymmetric	whether the supplied matrix is symmetric (then only its lower triangular part is accessed, requires square matrix and entries)
isTransposed	whether the supplied matrix is transposed
symmetric	whether only the lower triangular part should be stored (requires a square matrix and entries)

This is a convenience constructor that creates a new sparsity pattern from scratch. Use it for switching between symmetric/normal storage patterns and for creating transposed matrices.

The number of chunks created is the number of NUMA nodes as reported by NumaThreadPool.

Note that !isSymmetric && symmetric is highly questionable and hence not allowed.

Definition at line 2333 of file threadedMatrix.hh.

Member Function Documentation

◆ begin() [1/2]

template<class Entry , class Index = size_t>

iterator Kaskade::NumaBCRSMatrix< Entry, Index >::begin ( )

inline

returns an iterator to the first row

In symmetric storage, the iterators iterate only through the lower triangular part that is actually stored.

Definition at line 2468 of file threadedMatrix.hh.

Referenced by Kaskade::Matrix_to_Triplet< NumaBCRSMatrix< Dune::FieldMatrix< K, N, M >, Index > >::call(), Kaskade::ThreadedMatrixDetail::CRSChunk< Entry, Index >::entrywiseOp(), Kaskade::NumaBCRSMatrix< Entry, Index >::frobenius_norm2(), Kaskade::ThreadedMatrixDetail::getRowCount(), Kaskade::Matrix_to_Triplet< NumaBCRSMatrix< Dune::FieldMatrix< K, N, M >, Index > >::nnz(), Kaskade::NumaBCRSMatrix< Entry, Index >::operator<<(), Kaskade::writeToMatlab(), and Kaskade::writeToMatlabBinary().

◆ begin() [2/2]

template<class Entry , class Index = size_t>

const_iterator Kaskade::NumaBCRSMatrix< Entry, Index >::begin ( ) const

inline

Definition at line 2469 of file threadedMatrix.hh.

◆ chunk()

template<class Entry , class Index = size_t>

Chunk & Kaskade::NumaBCRSMatrix< Entry, Index >::chunk ( int i )

inline

Obtains a reference to the given chunk.

Definition at line 2532 of file threadedMatrix.hh.

Referenced by Kaskade::ThreadedMatrixDetail::NumaBCRSRow< Entry, Index >::update().

◆ end() [1/2]

template<class Entry , class Index = size_t>

iterator Kaskade::NumaBCRSMatrix< Entry, Index >::end ( )

inline

returns an iterator to the first row

Definition at line 2474 of file threadedMatrix.hh.

Referenced by Kaskade::Matrix_to_Triplet< NumaBCRSMatrix< Dune::FieldMatrix< K, N, M >, Index > >::call(), Kaskade::NumaBCRSMatrix< Entry, Index >::frobenius_norm2(), Kaskade::ThreadedMatrixDetail::getRowCount(), Kaskade::Matrix_to_Triplet< NumaBCRSMatrix< Dune::FieldMatrix< K, N, M >, Index > >::nnz(), Kaskade::NumaBCRSMatrix< Entry, Index >::operator+(), Kaskade::NumaBCRSMatrix< Entry, Index >::operator<<(), Kaskade::NumaBCRSMatrix< Entry, Index >::scatter(), Kaskade::writeToMatlab(), and Kaskade::writeToMatlabBinary().

◆ end() [2/2]

template<class Entry , class Index = size_t>

const_iterator Kaskade::NumaBCRSMatrix< Entry, Index >::end ( ) const

inline

Definition at line 2475 of file threadedMatrix.hh.

◆ exists()

template<class Entry , class Index = size_t>

bool Kaskade::NumaBCRSMatrix< Entry, Index >::exists	(	Index	r,
		Index	c
	)		const

inline

returns true if (r,c) is structurally nonzero

Definition at line 2537 of file threadedMatrix.hh.

◆ frobenius_norm()

template<class Entry , class Index = size_t>

field_type Kaskade::NumaBCRSMatrix< Entry, Index >::frobenius_norm ( ) const

inline

Computes the Frobenius norm \( \|A\|_F = \sqrt{\mathrm{tr}(A^TA)} \).

Todo:: parallelize

Definition at line 2546 of file threadedMatrix.hh.

◆ frobenius_norm2()

template<class Entry , class Index = size_t>

field_type Kaskade::NumaBCRSMatrix< Entry, Index >::frobenius_norm2 ( ) const

inline

Computes the square of the Frobenius norm \( \|A\|_F^2 = \mathrm{tr}(A^TA) \).

Todo:: parallelize

Definition at line 2555 of file threadedMatrix.hh.

Referenced by Kaskade::NumaBCRSMatrix< Entry, Index >::frobenius_norm().

◆ getPattern()

template<class Entry , class Index = size_t>

std::shared_ptr< NumaCRSPattern< Index > > Kaskade::NumaBCRSMatrix< Entry, Index >::getPattern ( ) const

inline

Returns a pointer to the sparsity pattern.

Definition at line 2527 of file threadedMatrix.hh.

Referenced by Kaskade::insertMatrixBlockIndices(), Kaskade::NumaBCRSMatrix< Entry, Index >::operator+(), Kaskade::ThreadedMatrixDetail::NumaBCRSMatrixConstIterator< Entry, Index >::operator++(), and Kaskade::ThreadedMatrixDetail::NumaBCRSMatrixConstIterator< Entry, Index >::operator--().

◆ M()

template<class Entry , class Index = size_t>

Index Kaskade::NumaBCRSMatrix< Entry, Index >::M ( ) const

inline

The number of columns.

Definition at line 2514 of file threadedMatrix.hh.

Referenced by Kaskade::NumaBCRSMatrix< Entry, Index >::conjugation(), Kaskade::MGProlongation::galerkinProjection(), Kaskade::insertMatrixBlockIndices(), Kaskade::MatrixTraits< NumaBCRSMatrix< Entry, Index > >::isSquare(), Kaskade::nonNestedProlognationStack(), Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix(), Kaskade::NumaBCRSMatrix< Entry, Index >::operator*(), and Kaskade::writeToMatlab().

◆ mmv()

template<class Entry , class Index = size_t>

template<class X , class Y >

void Kaskade::NumaBCRSMatrix< Entry, Index >::mmv	(	X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow -Ax \).

Definition at line 2594 of file threadedMatrix.hh.

◆ mtv()

template<class Entry , class Index = size_t>

template<class X , class Y >

void Kaskade::NumaBCRSMatrix< Entry, Index >::mtv	(	X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow A^Tx \).

Parameters

x	a vector of size M()
y	a vector of size N()

Note that transpose times vector operations are quite expensive (a factor of 6 slower than matrix-vector operations) and should be avoided. If you need transpose times vector products, consider storing a transposed matrix directly.

Definition at line 2588 of file threadedMatrix.hh.

◆ mv()

template<class Entry , class Index = size_t>

template<class X , class Y >

field_type Kaskade::NumaBCRSMatrix< Entry, Index >::mv	(	X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow Ax \) with computation of \( y^T x \) if A is square.

Parameters

x	a vector of size M()
y	a vector of size N()

Definition at line 2577 of file threadedMatrix.hh.

◆ N()

template<class Entry , class Index = size_t>

Index Kaskade::NumaBCRSMatrix< Entry, Index >::N ( ) const

inline

The number of rows.

Definition at line 2509 of file threadedMatrix.hh.

Referenced by Kaskade::NumaBCRSMatrix< Entry, Index >::conjugation(), Kaskade::NumaBCRSMatrix< Entry, Index >::end(), Kaskade::MGProlongation::galerkinProjection(), Kaskade::insertMatrixBlockIndices(), Kaskade::MatrixTraits< NumaBCRSMatrix< Entry, Index > >::isSquare(), Kaskade::makeAuxiliarySpaceMultigridStack(), Kaskade::nonNestedProlognationStack(), Kaskade::NumaBCRSMatrix< Entry, Index >::NumaBCRSMatrix(), Kaskade::NumaBCRSMatrix< Entry, Index >::operator*(), Kaskade::ThreadedMatrixDetail::NumaBCRSMatrixConstIterator< Entry, Index >::operator++(), Kaskade::ThreadedMatrixDetail::NumaBCRSMatrixConstIterator< Entry, Index >::operator+=(), Kaskade::ThreadedMatrixDetail::NumaBCRSRow< Entry, Index >::update(), and Kaskade::writeToMatlab().

◆ nonzeroes()

template<class Entry , class Index = size_t>

size_t Kaskade::NumaBCRSMatrix< Entry, Index >::nonzeroes ( ) const

inline

Returns the number of structurally nonzero elements.

In symmetric storage, the number of actually stored entries is smaller, usually by a factor of almost two.

Definition at line 2522 of file threadedMatrix.hh.

◆ operator()()

template<class Entry , class Index = size_t>

template<class RowIndices , class ColIndices >

Self Kaskade::NumaBCRSMatrix< Entry, Index >::operator()	(	RowIndices const &	ri,
		ColIndices const &	ci
	)		const

inline

Definition at line 2492 of file threadedMatrix.hh.

◆ operator*=()

template<class Entry , class Index = size_t>

template<class Factor >

Self & Kaskade::NumaBCRSMatrix< Entry, Index >::operator*= ( Factor a )

inline

Multiplication with a "scalar".

The factor a can be a scalar or a quadratic matrix of compatible static size.

Definition at line 2435 of file threadedMatrix.hh.

◆ operator+=()

template<class Entry , class Index = size_t>

template<class EntryB , class IndexB >

Self & Kaskade::NumaBCRSMatrix< Entry, Index >::operator+= ( NumaBCRSMatrix< EntryB, IndexB > const & B )

inline

Adds a sparse matrix to this one.

The sparsity pattern of B must be a subset of our sparsity pattern.

Definition at line 2411 of file threadedMatrix.hh.

◆ operator-=()

template<class Entry , class Index = size_t>

template<class EntryB , class IndexB >

Self & Kaskade::NumaBCRSMatrix< Entry, Index >::operator-= ( NumaBCRSMatrix< EntryB, IndexB > const & B )

inline

Subtracts a sparse matrix from this one.

The sparsity pattern of B must be a subset of our sparsity pattern.

Definition at line 2423 of file threadedMatrix.hh.

◆ operator=() [1/5]

template<class Entry , class Index = size_t>

Self & Kaskade::NumaBCRSMatrix< Entry, Index >::operator= ( Entry const & a )

inline

Assigns the given value to each entry.

Definition at line 2371 of file threadedMatrix.hh.

◆ operator=() [2/5]

template<class Entry , class Index = size_t>

Self & Kaskade::NumaBCRSMatrix< Entry, Index >::operator= ( Self && mat )

default

Move assignment.

The matrices need not be of same size or sparsity pattern.

◆ operator=() [3/5]

template<class Entry , class Index = size_t>

Self & Kaskade::NumaBCRSMatrix< Entry, Index >::operator= ( Self const & mat )

default

Copy assignment.

The matrix becomes a copy of the given one, no matter what its previous structure or size was. The sparsity pattern is shared between both matrices.

◆ operator=() [4/5]

template<class Entry , class Index = size_t>

template<class Arguments , class Operation >

Self & Kaskade::NumaBCRSMatrix< Entry, Index >::operator= ( ThreadedMatrixDetail::NumaBCRSMatrixExpression< Arguments, Operation > const & e )

inline

NOT YET IMPLEMENTED Assigns the given Numa matrix expression.

Definition at line 2394 of file threadedMatrix.hh.

◆ operator=() [5/5]

template<class Entry , class Index = size_t>

Self & Kaskade::NumaBCRSMatrix< Entry, Index >::operator= ( typename Entry::field_type const & a )

inline

Assigns the given scalar value to each entry.

Definition at line 2385 of file threadedMatrix.hh.

◆ operator[]() [1/2]

template<class Entry , class Index = size_t>

row_type Kaskade::NumaBCRSMatrix< Entry, Index >::operator[] ( Index r )

inline

Subscript operator allowing random access to rows.

This has constant complexity.

Definition at line 2482 of file threadedMatrix.hh.

◆ operator[]() [2/2]

template<class Entry , class Index = size_t>

const_row_type Kaskade::NumaBCRSMatrix< Entry, Index >::operator[] ( Index r ) const

inline

Definition at line 2483 of file threadedMatrix.hh.

◆ scatter()

template<class Entry , class Index = size_t>

template<class LMIterator >

void Kaskade::NumaBCRSMatrix< Entry, Index >::scatter	(	LMIterator	first,
		LMIterator	last
	)

inline

Scatters given sub-matrices into the matrix by adding up their entries.

Template Parameters

LMIterator a forward iterator with value type of LocalMatrix (requirements see below).

Local matrices \( a \) in the range [first,last[ are scattered into the global matrix as follows:

\[ A_{I_k,J_l} \leftarrow A_{I_k,J_l} + a_{i_k,j_l} \quad 0\le k < r, 0\le l < c \]

The possibly different ordering of entries in the local and global matrices is taken into account by the indirect indexing via \( (I_k,J_k) \) for the global indices and \( (i_k,j_l) \) for the local indices.

Objects a of LocalMatrix type have to provide the following access:

a(ik,jl) is the value of the local matrix entry \( a_{i_k,j_l} \)
ridx() returns a range of \( (I_k,i_k) \) pairs (of type std::pair), sorted ascendingly according to \( I_k \)
cidx() returns a range of \( (J_l,j_l) \) pairs (of type std::pair), sorted ascendingly according to \( J_l \)

In case LocalMatrix::lumped is true, then ridx()==cidx() shall hold and only the diagonal of \( a \) is to be scattered.

In contrast to the other methods, this method can (and should) be called concurrently from different threads.

Definition at line 2673 of file threadedMatrix.hh.

◆ smtv()

template<class Entry , class Index = size_t>

template<class X , class Y >

void Kaskade::NumaBCRSMatrix< Entry, Index >::smtv	(	field_type const &	a,
		X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow aA^Tx \).

Note that transpose times vector operations are quite expensive (a factor of 6 slower than matrix-vector operations) and should be avoided. If you need transpose times vector products, consider storing a transposed matrix directly.

Definition at line 2609 of file threadedMatrix.hh.

◆ smv()

template<class Entry , class Index = size_t>

template<class X , class Y >

field_type Kaskade::NumaBCRSMatrix< Entry, Index >::smv	(	field_type const &	a,
		X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow aAx \).

Definition at line 2600 of file threadedMatrix.hh.

◆ umtv()

template<class Entry , class Index = size_t>

template<class X , class Y >

void Kaskade::NumaBCRSMatrix< Entry, Index >::umtv	(	X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow y + A^Tx \).

Note that transpose times vector operations are quite expensive (a factor of 6 slower than matrix-vector operations) and should be avoided. If you need transpose times vector products, consider storing a transposed matrix directly.

Definition at line 2624 of file threadedMatrix.hh.

◆ umv()

template<class Entry , class Index = size_t>

template<class X , class Y >

field_type Kaskade::NumaBCRSMatrix< Entry, Index >::umv	(	X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow y + Ax \) and subsequent computation of \( y^T x \) if A is square.

Definition at line 2615 of file threadedMatrix.hh.

◆ usmtv()

template<class Entry , class Index = size_t>

template<class X , class Y >

void Kaskade::NumaBCRSMatrix< Entry, Index >::usmtv	(	field_type const &	a,
		X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow y + aA^Tx \).

Note that transpose times vector operations are quite expensive (a factor of 6 slower than matrix-vector operations) and should be avoided. If you need transpose times vector products, consider storing a transposed matrix directly.

Definition at line 2639 of file threadedMatrix.hh.

◆ usmv()

template<class Entry , class Index = size_t>

template<class X , class Y >

field_type Kaskade::NumaBCRSMatrix< Entry, Index >::usmv	(	field_type const &	a,
		X const &	x,
		Y &	y
	)		const

inline

Matrix-vector multiplication \( y \leftarrow y + aAx \) and subsequent computation of \( y^T x \) if A is square.

Definition at line 2630 of file threadedMatrix.hh.

Friends And Related Function Documentation

◆ scatter()

template<class Entry , class Index = size_t>

template<class RowIndices , class ColIndices , class BinaryOp = std::plus<Entry>>

void scatter	(	DynamicMatrix< Entry > const &	B,
		RowIndices const &	rows,
		ColIndices const &	cols,
		BinaryOp const &	op = `BinaryOp()`
	)

This performs \( A_{r_i c_j} = A_{r_i c_j} \circ B_{ij} \) for \( i,j \) indexing the provided matrix \( B \). Here, \( \circ \) denotes the given binary operation, which defaults to addition (the classical scatter operation).

Template Parameters

RowIndices	an STL sequence type with value_type convertible to Index
ColIndices	an STL sequence type with value_type convertible to Index
BinaryOp	a binary callable type with `op(Entry const, Entry const)` convertible to Entry.

Parameters

B	the given matrix data
rows	the target row indices \( r_i \) for ourselves
cols	the target col indices \( c_i \) for ourselves
op	an arbitrary binary operation on Entry, defaults to plus

Note that all entries \( A_{r_ic_i} \) must exist in this matrix.

As long as the row or column indices do not overlap, this method can safely be called concurrently.

Definition at line 2704 of file threadedMatrix.hh.

The documentation for this class was generated from the following files:

Detailed Description

Public Types

Public Member Functions

Related Functions

Constructors

Entering data

Member Typedef Documentation

◆ block_type

◆ ColIterator

◆ const_iterator

◆ const_row_type

◆ ConstColIterator

◆ ConstRowIterator

◆ field_type

◆ iterator

◆ row_type

◆ Scalar

◆ size_type

◆ value_type

Constructor & Destructor Documentation

◆ NumaBCRSMatrix() [1/11]

◆ NumaBCRSMatrix() [2/11]

◆ NumaBCRSMatrix() [3/11]

◆ NumaBCRSMatrix() [4/11]

◆ NumaBCRSMatrix() [5/11]

◆ NumaBCRSMatrix() [6/11]

◆ NumaBCRSMatrix() [7/11]

◆ NumaBCRSMatrix() [8/11]

◆ NumaBCRSMatrix() [9/11]

◆ NumaBCRSMatrix() [10/11]

◆ NumaBCRSMatrix() [11/11]

Member Function Documentation

◆ begin() [1/2]

◆ begin() [2/2]

◆ chunk()

◆ end() [1/2]

◆ end() [2/2]

◆ exists()

◆ frobenius_norm()

◆ frobenius_norm2()

◆ getPattern()

◆ M()

◆ mmv()

◆ mtv()

◆ mv()

◆ N()

◆ nonzeroes()

◆ operator()()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator=() [1/5]

◆ operator=() [2/5]

◆ operator=() [3/5]

◆ operator=() [4/5]

◆ operator=() [5/5]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ scatter()

◆ smtv()

◆ smv()

◆ umtv()

◆ umv()

◆ usmtv()

◆ usmv()

Friends And Related Function Documentation

◆ scatter()