TNL::Matrices Namespace Reference

Namespace for matrix formats. More...

Classes
class	DenseMatrix
	Implementation of dense matrix, i.e. matrix storing explicitly all of its elements including zeros. More...
class	DenseMatrixBase
	Implementation of dense matrix view. More...
class	DenseMatrixElement
	Accessor for dense matrix elements. More...
class	DenseMatrixRowView
	RowView is a simple structure for accessing rows of dense matrix. More...
class	DenseMatrixView
	Implementation of dense matrix view. More...
class	DistributedMatrix
struct	GeneralMatrix
	General non-symmetric matrix type. More...
class	GinkgoOperator
	Wraps a general TNL matrix as a Ginkgo LinOp. More...
class	HypreCSRMatrix
	Wrapper for Hypre's sequential CSR matrix. More...
class	HypreParCSRMatrix
	Wrapper for Hypre's sequential CSR matrix. More...
class	LambdaMatrix
	"Matrix-free matrix" based on lambda functions. More...
class	LambdaMatrixElement
	Accessor for elements of lambda matrix. More...
struct	LambdaMatrixFactory
	Helper class for creating instances of LambdaMatrix. More...
class	LambdaMatrixRowView
	RowView is a simple structure for accessing rows of Lambda matrix. More...
class	LambdaMatrixRowViewIterator
class	MatrixBase
	Base class for the implementation of concrete matrix types. More...
struct	MatrixInfo
class	MatrixOperations
class	MatrixOperations< Devices::Cuda >
class	MatrixReader
	Helper class for importing of matrices from different input formats. More...
class	MatrixRowViewIterator
struct	MatrixType
	Structure for specifying type of sparse matrix. More...
class	MatrixWriter
	Helper class for exporting of matrices to different output formats. More...
class	MultidiagonalMatrix
	Implementation of sparse multidiagonal matrix. More...
class	MultidiagonalMatrixBase
	A common base class for MultidiagonalMatrix and MultidiagonalMatrixView. More...
class	MultidiagonalMatrixElement
	Accessor for multidiagonal matrix elements. More...
class	MultidiagonalMatrixRowView
	RowView is a simple structure for accessing rows of multidiagonal matrix. More...
class	MultidiagonalMatrixView
	Implementation of sparse multidiagonal matrix. More...
class	SparseMatrix
	Implementation of sparse matrix, i.e. matrix storing only non-zero elements. More...
class	SparseMatrixBase
	Implementation of sparse matrix view. More...
class	SparseMatrixElement
	Accessor for sparse matrix elements. More...
class	SparseMatrixRowView
	RowView is a simple structure for accessing rows of sparse matrix. More...
class	SparseMatrixView
	Implementation of sparse matrix view. More...
class	StaticMatrix
struct	SymmetricMatrix
	Symmetric matrix type. More...
class	TridiagonalMatrix
	Implementation of sparse tridiagonal matrix. More...
class	TridiagonalMatrixBase
	A common base class for TridiagonalMatrix and TridiagonalMatrixView. More...
class	TridiagonalMatrixRowView
	RowView is a simple structure for accessing rows of tridiagonal matrix. More...
class	TridiagonalMatrixView
	Implementation of sparse tridiagonal matrix. More...

Typedefs
template<typename T>
using	is_dense_matrix = decltype( isDenseMatrix( std::declval< T >() ) )
template<typename T>
using	is_matrix = decltype( isMatrix( std::declval< T >() ) )
template<typename Matrix>
using	is_sparse_csr_matrix = decltype( isSparseMatrix( std::declval< Matrix >() ) )

Enumerations
enum	ElementsOrganization
enum class	SymmetricMatrixEncoding : std::uint8_t { Complete , LowerPart , UpperPart , SparseMixed }
	Encoding of the matrix elements of the symmetric matrix. More...
enum class	TransposeState : std::uint8_t { None , Transpose }

Functions
template<typename Matrix, typename InVector, typename OutVector>
__global__ void	ColumnMajorDenseMatrixVectorMultiplicationKernel (const Matrix matrix, const InVector inVector, OutVector outVector, int begin, int end, int gridIdx, typename Matrix::RealType matrixMultiplicator, typename Matrix::RealType outVectorMultiplicator)
template<typename Matrix>
void	compressSparseMatrix (Matrix &A)
	Avoids unnecessary zero elements.
template<typename Matrix, typename AdjacencyMatrix>
void	copyAdjacencyStructure (const Matrix &A, AdjacencyMatrix &B, bool has_symmetric_pattern=false, bool ignore_diagonal=true)
template<typename Matrix, typename Index, typename IndexVectorView, typename ValueVectorView, typename RowLengthsVector>
void	copyBuffersToMatrixElements (Matrix &m, const IndexVectorView &thisColumnsBuffer_view, const ValueVectorView &thisValuesBuffer_view, Index baseRow, Index lastRow, Index maxRowLength, RowLengthsVector &thisRowLengths, IndexVectorView rowLocalIndexes_view)
template<typename Matrix1, typename Matrix2>
void	copyDenseToDenseMatrix (Matrix1 &A, const Matrix2 &B)
template<typename Matrix1, typename Matrix2>
void	copyDenseToSparseMatrix (Matrix1 &A, const Matrix2 &B)
template<typename Matrix, typename Index, typename IndexVector, typename ValueVector>
void	copyMatrixElementsToBuffers (const Matrix &m, Index baseRow, Index lastRow, Index maxRowLength, IndexVector &columnsBuffer, ValueVector &valuesBuffer)
template<typename Matrix1, typename Matrix2>
void	copySparseMatrix (Matrix1 &A, const Matrix2 &B)
template<typename Matrix1, typename Matrix2>
std::enable_if_t< std::is_same_v< typename Matrix1::DeviceType, typename Matrix2::DeviceType > >	copySparseMatrix_impl (Matrix1 &A, const Matrix2 &B)
template<typename Matrix1, typename Matrix2>
std::enable_if_t< ! std::is_same_v< typename Matrix1::DeviceType, typename Matrix2::DeviceType > &&std::is_same_v< typename Matrix2::DeviceType, Devices::Host > >	copySparseMatrix_impl (Matrix1 &A, const Matrix2 &B)
template<typename Matrix1, typename Matrix2>
std::enable_if_t< ! std::is_same_v< typename Matrix1::DeviceType, typename Matrix2::DeviceType > &&std::is_same_v< typename Matrix2::DeviceType, Devices::Cuda > >	copySparseMatrix_impl (Matrix1 &A, const Matrix2 &B)
template<typename Matrix1, typename Matrix2>
void	copySparseToDenseMatrix (Matrix1 &A, const Matrix2 &B)
template<typename Matrix1, typename Matrix2>
void	copySparseToSparseMatrix (Matrix1 &A, const Matrix2 &B)
template<int tileDim, typename Matrix, typename Real, typename Index>
__global__ void	DenseInPlaceTranspositionKernel (Matrix matrix, const Real matrixMultiplicator, const typename Matrix::IndexType gridIdx_x, const typename Matrix::IndexType gridIdx_y)
template<int tileDim, typename ResultMatrix, typename Matrix1, typename Matrix2>
__global__ void	DenseMatrixProductKernel (ResultMatrix resultMatrix, const Matrix1 matrixA, const Matrix2 matrixB, const typename ResultMatrix::RealType matrixMultiplicator, TransposeState TransposeA, TransposeState TransposeB, const typename ResultMatrix::IndexType gridIdx_x, const typename ResultMatrix::IndexType gridIdx_y)
template<int tileDim, typename OutputMatrix, typename InputMatrix, typename Real, typename Index>
__global__ void	DenseTranspositionKernel (OutputMatrix resultMatrix, const InputMatrix inputMatrix, const Real matrixMultiplicator, const typename OutputMatrix::IndexType gridIdx_x, const typename OutputMatrix::IndexType gridIdx_y)
template<typename Real>
__cuda_callable__ Real	determinant (const StaticMatrix< Real, 2, 2 > &A)
template<typename Real>
__cuda_callable__ Real	determinant (const StaticMatrix< Real, 3, 3 > &A)
template<typename Real>
__cuda_callable__ Real	determinant (const StaticMatrix< Real, 4, 4 > &A)
template<typename RealType, typename IndexType>
__global__ void	GeamCudaKernel (const IndexType m, const IndexType n, const RealType alpha, const RealType *A, const IndexType lda, const RealType beta, const RealType *B, const IndexType ldb, RealType *C, const IndexType ldc)
template<typename RealType, typename IndexType>
__global__ void	GemvCudaKernel (const IndexType m, const IndexType n, const RealType alpha, const RealType *A, const IndexType lda, const RealType *x, const RealType beta, RealType *y)
template<typename Matrix>
auto	getGinkgoMatrixCsr (std::shared_ptr< const gko::Executor > exec, Matrix &matrix) -> std::unique_ptr< gko::matrix::Csr< typename Matrix::RealType, typename Matrix::IndexType > >
	Converts any TNL sparse matrix to a Ginkgo Csr matrix.
template<typename Matrix>
auto	getGinkgoMatrixCsrView (std::shared_ptr< const gko::Executor > exec, Matrix &matrix) -> std::unique_ptr< gko::matrix::Csr< typename Matrix::RealType, typename Matrix::IndexType > >
	Creates a Ginkgo Csr matrix view from a TNL CSR matrix.
template<typename Matrix, typename Real, int tileDim = 16>
void	getInPlaceTransposition (Matrix &matrix, Real matrixMultiplicator=1.0)
template<typename ResultMatrix, typename Matrix1, typename Matrix2, typename Real, int tileDim = 16>
void	getMatrixProduct (ResultMatrix &resultMatrix, const Matrix1 &matrix1, const Matrix2 &matrix2, Real matrixMultiplicator=1.0, TransposeState transposeA=TransposeState::None, TransposeState transposeB=TransposeState::None)
template<typename OutMatrix, typename InMatrix>
OutMatrix	getSymmetricPart (const InMatrix &inMatrix)
	This function computes \(( A + A^T ) / 2 \), where \( A \) is a square matrix.
template<typename ResultMatrix, typename Matrix, typename Real, int tileDim = 16>
void	getTransposition (ResultMatrix &resultMatrix, const Matrix &matrix, Real matrixMultiplicator=1.0)
template<typename Real>
__cuda_callable__ StaticMatrix< Real, 2, 2 >	inverse (const StaticMatrix< Real, 2, 2 > &A)
template<typename Real>
__cuda_callable__ StaticMatrix< Real, 3, 3 >	inverse (const StaticMatrix< Real, 3, 3 > &A)
template<typename Real>
__cuda_callable__ StaticMatrix< Real, 4, 4 >	inverse (const StaticMatrix< Real, 4, 4 > &A)
constexpr std::false_type	isDenseMatrix (...)
	This checks if the matrix is dense matrix.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
constexpr std::true_type	isDenseMatrix (const DenseMatrixBase< Real, Device, Index, Organization > &)
constexpr std::false_type	isMatrix (...)
	This checks if given type is matrix.
template<typename MatrixElementsLambda, typename CompressedRowLengthsLambda, typename Real, typename Device, typename Index>
constexpr std::true_type	isMatrix (const LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index > &)
template<typename Real, typename Device, typename Index, typename MatrixType, ElementsOrganization Organization>
constexpr std::true_type	isMatrix (const MatrixBase< Real, Device, Index, MatrixType, Organization > &)
constexpr std::false_type	isSparseMatrix (...)
	This checks if the sparse matrix is stored in CSR format.
template<typename Real, typename Device, typename Index, typename MatrixType, typename SegmentsView, typename ComputeReal>
constexpr std::true_type	isSparseMatrix (const SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > &)
template<typename InMatrixView, typename OutMatrixView, typename Real, typename Index>
__global__ void	MultidiagonalMatrixTranspositionCudaKernel (const InMatrixView inMatrix, OutMatrixView outMatrix, const Real matrixMultiplicator, const Index gridIdx)
template<typename Value, std::size_t Rows1, std::size_t SharedDim, std::size_t Columns2, typename Permutation>
StaticMatrix< Value, Rows1, Columns2, Permutation >	operator* (const StaticMatrix< Value, Rows1, SharedDim, Permutation > &matrix1, const StaticMatrix< Value, SharedDim, Columns2, Permutation > &matrix2)
template<typename Value, std::size_t Rows, std::size_t Columns, typename Permutation, typename T>
__cuda_callable__ StaticMatrix< Value, Rows, Columns, Permutation >	operator* (const T &value, StaticMatrix< Value, Rows, Columns, Permutation > a)
template<typename Value, std::size_t Rows, std::size_t Columns, typename Permutation, typename T>
__cuda_callable__ StaticMatrix< Value, Rows, Columns, Permutation >	operator* (StaticMatrix< Value, Rows, Columns, Permutation > a, const T &value)
template<typename Value, std::size_t Rows, std::size_t Columns, typename Permutation>
__cuda_callable__ StaticMatrix< Value, Rows, Columns, Permutation >	operator+ (StaticMatrix< Value, Rows, Columns, Permutation > a, const StaticMatrix< Value, Rows, Columns > &b)
template<typename Value, std::size_t Rows, std::size_t Columns, typename Permutation>
__cuda_callable__ StaticMatrix< Value, Rows, Columns, Permutation >	operator- (StaticMatrix< Value, Rows, Columns, Permutation > a, const StaticMatrix< Value, Rows, Columns > &b)
template<typename Value, std::size_t Rows, std::size_t Columns, typename Permutation, typename T>
__cuda_callable__ StaticMatrix< Value, Rows, Columns, Permutation >	operator/ (StaticMatrix< Value, Rows, Columns, Permutation > a, const T &b)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator<< (File &&file, const DenseMatrixBase< Real, Device, Index, Organization > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator<< (File &&file, const MultidiagonalMatrixBase< Real, Device, Index, Organization > &matrix)
template<typename Real, typename Device, typename Index, typename MatrixType, typename SegmentsView, typename ComputeReal>
File &	operator<< (File &&file, const SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator<< (File &&file, const TridiagonalMatrixBase< Real, Device, Index, Organization > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator<< (File &file, const DenseMatrixBase< Real, Device, Index, Organization > &matrix)
	Serialization of dense matrices into binary files.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator<< (File &file, const MultidiagonalMatrixBase< Real, Device, Index, Organization > &matrix)
	Serialization of multidiagonal matrices into binary files.
template<typename Real, typename Device, typename Index, typename MatrixType, typename SegmentsView, typename ComputeReal>
File &	operator<< (File &file, const SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > &matrix)
	Serialization of sparse matrices into binary files.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator<< (File &file, const TridiagonalMatrixBase< Real, Device, Index, Organization > &matrix)
	Serialization of tridiagonal matrices into binary files.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
std::ostream &	operator<< (std::ostream &str, const DenseMatrixBase< Real, Device, Index, Organization > &matrix)
	Insertion operator for dense matrix and output stream.
template<typename MatrixElementsLambda, typename CompressedRowLengthsLambda, typename Real, typename Device, typename Index>
std::ostream &	operator<< (std::ostream &str, const LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index > &matrix)
	Insertion operator for lambda matrix and output stream.
template<typename MatrixElementsLambda, typename CompressedRowLengthsLambda, typename Real, typename Index>
std::ostream &	operator<< (std::ostream &str, const LambdaMatrixRowView< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Index > &row)
	Insertion operator for a Lambda matrix row.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
std::ostream &	operator<< (std::ostream &str, const MultidiagonalMatrixBase< Real, Device, Index, Organization > &matrix)
	Overloaded insertion operator for printing a matrix to output stream.
template<typename Real, typename Device, typename Index, typename MatrixType, typename SegmentsView, typename ComputeReal>
std::ostream &	operator<< (std::ostream &str, const SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > &matrix)
	Overloaded insertion operator for printing a matrix to output stream.
template<typename SegmentView, typename ValuesView, typename ColumnsIndexesView>
std::ostream &	operator<< (std::ostream &str, const SparseMatrixRowView< SegmentView, ValuesView, ColumnsIndexesView > &row)
	Insertion operator for a sparse matrix row.
template<typename Value, std::size_t Rows, std::size_t Columns, typename Permutation>
std::ostream &	operator<< (std::ostream &str, const StaticMatrix< Value, Rows, Columns, Permutation > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
std::ostream &	operator<< (std::ostream &str, const TridiagonalMatrixBase< Real, Device, Index, Organization > &matrix)
	Overloaded insertion operator for printing a matrix to output stream.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization, typename RealAllocator>
File &	operator>> (File &&file, DenseMatrix< Real, Device, Index, Organization, RealAllocator > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator>> (File &&file, DenseMatrixView< Real, Device, Index, Organization > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization, typename RealAllocator, typename IndexAllocator>
File &	operator>> (File &&file, MultidiagonalMatrix< Real, Device, Index, Organization, RealAllocator, IndexAllocator > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator>> (File &&file, MultidiagonalMatrixView< Real, Device, Index, Organization > &matrix)
template<typename Real, typename Device, typename Index, typename MatrixType, template< typename, typename, typename > class Segments, typename ComputeReal, typename RealAllocator, typename IndexAllocator>
File &	operator>> (File &&file, SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > &matrix)
template<typename Real, typename Device, typename Index, typename MatrixType, template< typename, typename > class SegmentsView, typename ComputeReal>
File &	operator>> (File &&file, SparseMatrixView< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization, typename RealAllocator>
File &	operator>> (File &&file, TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator>> (File &&file, TridiagonalMatrixView< Real, Device, Index, Organization > &matrix)
template<typename Real, typename Device, typename Index, ElementsOrganization Organization, typename RealAllocator>
File &	operator>> (File &file, DenseMatrix< Real, Device, Index, Organization, RealAllocator > &matrix)
	Deserialization of dense matrices from binary files.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator>> (File &file, DenseMatrixView< Real, Device, Index, Organization > &matrix)
	Deserialization of dense matrix views from binary files.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization, typename RealAllocator, typename IndexAllocator>
File &	operator>> (File &file, MultidiagonalMatrix< Real, Device, Index, Organization, RealAllocator, IndexAllocator > &matrix)
	Deserialization of multidiagonal matrices from binary files.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator>> (File &file, MultidiagonalMatrixView< Real, Device, Index, Organization > &matrix)
	Deserialization of multidiagonal matrix views from binary files.
template<typename Real, typename Device, typename Index, typename MatrixType, template< typename, typename, typename > class Segments, typename ComputeReal, typename RealAllocator, typename IndexAllocator>
File &	operator>> (File &file, SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > &matrix)
	Deserialization of sparse matrices from binary files.
template<typename Real, typename Device, typename Index, typename MatrixType, template< typename, typename > class SegmentsView, typename ComputeReal>
File &	operator>> (File &file, SparseMatrixView< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > &matrix)
	Deserialization of sparse matrix views from binary files.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization, typename RealAllocator>
File &	operator>> (File &file, TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator > &matrix)
	Deserialization of tridiagonal matrices from binary files.
template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
File &	operator>> (File &file, TridiagonalMatrixView< Real, Device, Index, Organization > &matrix)
	Deserialization of tridiagonal matrix views from binary files.
template<typename Matrix, typename PermutationArray>
void	permuteMatrixColumns (Matrix &matrix, const PermutationArray &iperm)
template<typename Matrix, typename PermutationArray>
void	permuteMatrixRows (Matrix &matrix, const PermutationArray &perm)
template<typename Array1, typename Array2, typename PermutationArray>
void	reorderArray (const Array1 &src, Array2 &dest, const PermutationArray &perm)
template<typename Matrix1, typename Matrix2, typename PermutationArray>
void	reorderSparseMatrix (const Matrix1 &matrix1, Matrix2 &matrix2, const PermutationArray &perm, const PermutationArray &iperm)
template<typename Real>
__cuda_callable__ Containers::StaticVector< 2, Real >	solve (const StaticMatrix< Real, 2, 2 > &A, const Containers::StaticVector< 2, Real > &b)
template<typename Real>
__cuda_callable__ Containers::StaticVector< 3, Real >	solve (const StaticMatrix< Real, 3, 3 > &A, const Containers::StaticVector< 3, Real > &b)
template<typename Real>
__cuda_callable__ Containers::StaticVector< 4, Real >	solve (const StaticMatrix< Real, 4, 4 > &A, const Containers::StaticVector< 4, Real > &b)
template<typename Matrix1, typename Matrix2>
__global__ void	SparseMatrixCopyKernel (Matrix1 *A, const Matrix2 *B, const typename Matrix2::IndexType *rowLengths, typename Matrix2::IndexType rows)
template<typename Vector, typename Matrix>
__global__ void	SparseMatrixSetRowLengthsVectorKernel (Vector *rowLengths, const Matrix *matrix, typename Matrix::IndexType rows, typename Matrix::IndexType cols)
template<typename Value, std::size_t Rows, std::size_t Columns, typename Permutation>
StaticMatrix< Value, Columns, Rows, Permutation >	transpose (const StaticMatrix< Value, Rows, Columns, Permutation > &A)
template<typename InMatrixView, typename OutMatrixView, typename Real, typename Index>
__global__ void	TridiagonalMatrixTranspositionCudaKernel (const InMatrixView inMatrix, OutMatrixView outMatrix, Real matrixMultiplicator, Index gridIdx)
template<int BlockSize, int ThreadsPerRow, typename Matrix, typename InVector, typename OutVector>
__global__ void	VectorColumnMajorDenseMatrixVectorMultiplicationKernel (const Matrix matrix, const InVector inVector, OutVector outVector, int begin, int end, int gridIdx, typename Matrix::RealType matrixMultiplicator, typename Matrix::RealType outVectorMultiplicator)
template<typename Device, typename Real, typename Index>
SparseMatrixView< Real, Device, Index, GeneralMatrix, Algorithms::Segments::CSRView >	wrapCSRMatrix (const Index &rows, const Index &columns, Index *rowPointers, Real *values, Index *columnIndexes)
	Function for wrapping of arrays defining CSR format into a sparse matrix view.
template<typename Device, typename Real, typename Index, ElementsOrganization Organization = Algorithms::Segments::DefaultElementsOrganization< Device >::getOrganization()>
DenseMatrixView< Real, Device, Index, Organization >	wrapDenseMatrix (const Index &rows, const Index &columns, Real *values)
	Function for wrapping an array of values into a dense matrix view.
template<typename Device, ElementsOrganization Organization, typename Real, typename Index, int Alignment = 1>
auto	wrapEllpackMatrix (const Index rows, const Index columns, const Index nonzerosPerRow, Real *values, Index *columnIndexes) -> decltype(EllpackMatrixWrapper< Device, Organization, Real, Index, Alignment >::wrap(rows, columns, nonzerosPerRow, values, columnIndexes))
	Function for wrapping of arrays defining Ellpack format into a sparse matrix view.

Variables
template<typename T>
constexpr bool	is_dense_matrix_v = is_dense_matrix< T >::value
template<typename T>
constexpr bool	is_matrix_v = is_matrix< T >::value
template<typename Matrix>
constexpr bool	is_sparse_csr_matrix_v = is_sparse_csr_matrix< Matrix >::value
template<typename Index>
constexpr Index	paddingIndex = static_cast< Index >( -1 )
	Padding index value.

Detailed Description

Namespace for matrix formats.

Enumeration Type Documentation

SymmetricMatrixEncoding

enum class TNL::Matrices::SymmetricMatrixEncoding : std::uint8_t

strong

Encoding of the matrix elements of the symmetric matrix.

Enumerator
Complete	All elements of the matrix are stored.
LowerPart	Only lower part of the matrix is stored.
UpperPart	Only upper part of the matrix is stored.
SparseMixed	For each couple of non-zero elements a_ij and a_ji, at least one is encoded. It is handy for example for adjacency matrices of undirected graphs.

Function Documentation

compressSparseMatrix()

template<typename Matrix>

void TNL::Matrices::compressSparseMatrix

(

Matrix &

A

)

Avoids unnecessary zero elements.

This method is especially useful for removing of explicitly coded zero elements but it also removes unnecessary padding elements.

Template Parameters

Matrix

is the matrix type.

Parameters

A	is the matrix to be compressed.

getSymmetricPart()

template<typename OutMatrix, typename InMatrix>

OutMatrix TNL::Matrices::getSymmetricPart

(

const InMatrix &

inMatrix

)

This function computes \(( A + A^T ) / 2 \), where \( A \) is a square matrix.

Template Parameters

InMatrix	is the type of the input matrix.
OutMatrix	is the type of the output matrix.

Parameters

inMatrix

is the input matrix.

Returns

the output matrix.

operator<<() [1/7]

template<typename Real, typename Device, typename Index, ElementsOrganization Organization>

std::ostream & TNL::Matrices::operator<<	(	std::ostream &	str,
		const DenseMatrixBase< Real, Device, Index, Organization > &	matrix )

Insertion operator for dense matrix and output stream.

Parameters

str	is the output stream.
matrix	is the dense matrix.

Returns

reference to the stream.

operator<<() [2/7]

template<typename MatrixElementsLambda, typename CompressedRowLengthsLambda, typename Real, typename Device, typename Index>

std::ostream & TNL::Matrices::operator<<	(	std::ostream &	str,
		const LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index > &	matrix )

Insertion operator for lambda matrix and output stream.

Parameters

str	is the output stream.
matrix	is the lambda matrix.

Returns

reference to the stream.

operator<<() [3/7]

template<typename MatrixElementsLambda, typename CompressedRowLengthsLambda, typename Real, typename Index>

std::ostream & TNL::Matrices::operator<<	(	std::ostream &	str,
		const LambdaMatrixRowView< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Index > &	row )

Insertion operator for a Lambda matrix row.

Parameters

str	is an output stream.
row	is an input Lambda matrix row.

Returns

reference to the output stream.

operator<<() [4/7]

template<typename Real, typename Device, typename Index, ElementsOrganization Organization>

std::ostream & TNL::Matrices::operator<<	(	std::ostream &	str,
		const MultidiagonalMatrixBase< Real, Device, Index, Organization > &	matrix )

Overloaded insertion operator for printing a matrix to output stream.

Template Parameters

Real	is a type of the matrix elements.
Device	is a device where the matrix is allocated.
Index	is a type used for the indexing of the matrix elements.

Parameters

str	is a output stream.
matrix	is the matrix to be printed.

Returns

a reference to the output stream std::ostream.

operator<<() [5/7]

template<typename Real, typename Device, typename Index, typename MatrixType, typename SegmentsView, typename ComputeReal>

std::ostream & TNL::Matrices::operator<<	(	std::ostream &	str,
		const SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > &	matrix )

Overloaded insertion operator for printing a matrix to output stream.

Template Parameters

Real	is a type of the matrix elements.
Device	is a device where the matrix is allocated.
Index	is a type used for the indexing of the matrix elements.

Parameters

str	is a output stream.
matrix	is the matrix to be printed.

Returns

a reference to the output stream std::ostream.

operator<<() [6/7]

template<typename SegmentView, typename ValuesView, typename ColumnsIndexesView>

std::ostream & TNL::Matrices::operator<<	(	std::ostream &	str,
		const SparseMatrixRowView< SegmentView, ValuesView, ColumnsIndexesView > &	row )

Insertion operator for a sparse matrix row.

Parameters

str	is an output stream.
row	is an input sparse matrix row.

Returns

reference to the output stream.

operator<<() [7/7]

template<typename Real, typename Device, typename Index, ElementsOrganization Organization>

std::ostream & TNL::Matrices::operator<<	(	std::ostream &	str,
		const TridiagonalMatrixBase< Real, Device, Index, Organization > &	matrix )

Overloaded insertion operator for printing a matrix to output stream.

Template Parameters

Real	is a type of the matrix elements.
Device	is a device where the matrix is allocated.
Index	is a type used for the indexing of the matrix elements.

Parameters

str	is a output stream.
matrix	is the matrix to be printed.

Returns

a reference to the output stream std::ostream.

wrapCSRMatrix()

template<typename Device, typename Real, typename Index>

SparseMatrixView< Real, Device, Index, GeneralMatrix, Algorithms::Segments::CSRView > TNL::Matrices::wrapCSRMatrix ( const Index & rows, const Index & columns, Index * rowPointers, Real * values, Index * columnIndexes )

nodiscard

Function for wrapping of arrays defining CSR format into a sparse matrix view.

Template Parameters

Device	is a device on which the arrays are allocated.
Real	is a type of matrix elements values.
Index	is a type for matrix elements indexing.

Parameters

rows	is a number of matrix rows.
columns	is a number of matrix columns.
rowPointers	is an array holding row pointers of the CSR format ( ROW_INDEX here)
values	is an array with values of matrix elements ( V here)
columnIndexes	is an array with column indexes of matrix elements ( COL_INDEX here)

Returns

instance of SparseMatrixView with CSR format.

The size of array rowPointers must be equal to number of rows + 1. The last element of the array equals to the number of all nonzero matrix elements. The sizes of arrays values and columnIndexes must be equal to this number.

Example

#include <iostream>
#include <TNL/Matrices/DenseMatrix.h>
#include <TNL/Matrices/MatrixWrapping.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
wrapMatrixView()
{
   /***
    * Encode the following matrix to CSR format...
    *
    * /  1  2  0  0 \.
    * |  0  6  0  0 |
    * |  9  0  0  0 |
    * \  0  0 15 16 /
    */
   const int rows( 4 ), columns( 4 );
   TNL::Containers::Vector< double, Device > valuesVector{ 1, 2, 6, 9, 15, 16 };
   TNL::Containers::Vector< int, Device > columnIndexesVector{ 0, 1, 1, 0, 2, 3 };
   TNL::Containers::Vector< int, Device > rowPointersVector{ 0, 2, 3, 4, 6 };
 
   double* values = valuesVector.getData();
   int* columnIndexes = columnIndexesVector.getData();
   int* rowPointers = rowPointersVector.getData();
 
   /***
    * Wrap the arrays `rowPointers, `values` and `columnIndexes` to sparse matrix view
    */
   auto matrix = TNL::Matrices::wrapCSRMatrix< Device >( rows, columns, rowPointers, values, columnIndexes );
 
   std::cout << "Matrix reads as: " << std::endl << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Wrapping matrix view on host: " << std::endl;
   wrapMatrixView< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Wrapping matrix view on CUDA device: " << std::endl;
   wrapMatrixView< TNL::Devices::Cuda >();
#endif
}

Output

Wrapping matrix view on host: 
Matrix reads as: 
Row: 0 ->     0:1       1:2   
Row: 1 ->     1:6   
Row: 2 ->     0:9   
Row: 3 ->     2:15      3:16  
 
Wrapping matrix view on CUDA device: 
Matrix reads as: 
Row: 0 ->     0:1       1:2   
Row: 1 ->     1:6   
Row: 2 ->     0:9   
Row: 3 ->     2:15      3:16  
 

wrapDenseMatrix()

template<typename Device, typename Real, typename Index, ElementsOrganization Organization = Algorithms::Segments::DefaultElementsOrganization< Device >::getOrganization()>

DenseMatrixView< Real, Device, Index, Organization > TNL::Matrices::wrapDenseMatrix ( const Index & rows, const Index & columns, Real * values )

nodiscard

Function for wrapping an array of values into a dense matrix view.

Template Parameters

Device	is a device on which the array is allocated.
Real	is a type of array elements.
Index	is a type for indexing of matrix elements.
Organization	is matrix elements organization - see TNL::Algorithms::Segments::ElementsOrganization.

Parameters

rows	is a number of matrix rows.
columns	is a number of matrix columns.
values	is the array with matrix elements values.

Returns

instance of DenseMatrixView wrapping the array.

The array size must be equal to product of rows and columns. The dense matrix view does not deallocate the input array at the end of its lifespan.

Example

#include <iostream>
#include <TNL/Matrices/DenseMatrix.h>
#include <TNL/Matrices/MatrixWrapping.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
wrapMatrixView()
{
   const int rows( 3 ), columns( 4 );
   TNL::Containers::Vector< double, Device > valuesVector{
      // clang-format off
      1,  2,  3,  4,
      5,  6,  7,  8,
      9, 10, 11, 12
      // clang-format on
   };
   double* values = valuesVector.getData();
 
   /***
    * Wrap the array `values` to dense matrix view
    */
   auto matrix = TNL::Matrices::wrapDenseMatrix< Device >( rows, columns, values );
   std::cout << "Matrix reads as: " << std::endl << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Wrapping matrix view on host: " << std::endl;
   wrapMatrixView< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Wrapping matrix view on CUDA device: " << std::endl;
   wrapMatrixView< TNL::Devices::Cuda >();
#endif
}

Output

Wrapping matrix view on host: 
Matrix reads as: 
Row: 0 ->     0:1       1:2       2:3       3:4   
Row: 1 ->     0:5       1:6       2:7       3:8   
Row: 2 ->     0:9       1:10      2:11      3:12  
Wrapping matrix view on CUDA device: 
Matrix reads as: 
Row: 0 ->     0:1       1:4       2:7       3:10  
Row: 1 ->     0:2       1:5       2:8       3:11  
Row: 2 ->     0:3       1:6       2:9       3:12  

wrapEllpackMatrix()

template<typename Device, ElementsOrganization Organization, typename Real, typename Index, int Alignment = 1>

auto TNL::Matrices::wrapEllpackMatrix ( const Index rows, const Index columns, const Index nonzerosPerRow, Real * values, Index * columnIndexes ) -> decltype( EllpackMatrixWrapper< Device, Organization, Real, Index, Alignment >::wrap( rows, columns, nonzerosPerRow, values, columnIndexes ) )

nodiscard

Function for wrapping of arrays defining Ellpack format into a sparse matrix view.

This is to prevent from appearing in Doxygen documentation.

Template Parameters

Device	is a device on which the arrays are allocated.
Real	is a type of matrix elements values.
Index	is a type for matrix elements indexing.
Alignment	defines alignment of data. The number of matrix rows is rounded to a multiple of this number. It it useful mainly for GPUs.

Parameters

rows	is a number of matrix rows.
columns	is a number of matrix columns.
nonzerosPerRow	is number of nonzero matrix elements in each row.
values	is an array with values of matrix elements.
columnIndexes	is an array with column indexes of matrix elements.

Returns

instance of SparseMatrixView with CSR format.

The sizes of arrays values and columnIndexes must be equal to rows * nonzerosPerRow. Use -1 as a column index for padding zeros.

Example

#include <iostream>
#include <TNL/Matrices/DenseMatrix.h>
#include <TNL/Matrices/MatrixWrapping.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
wrapMatrixView()
{
   /***
    * Encode the following matrix to Ellpack format...
    *
    * /  1  2  0  0 \.
    * |  0  6  0  0 |
    * |  9  0  0  0 |
    * \  0  0 15 16 /
    */
   const int rows( 4 ), columns( 4 );
   TNL::Containers::Vector< double, Device > valuesVector{ 1, 2, 6, 0, 9, 0, 15, 16 };
   TNL::Containers::Vector< int, Device > columnIndexesVector{ 0, 1, 1, -1, 0, -1, 2, 3 };
 
   double* values = valuesVector.getData();
   int* columnIndexes = columnIndexesVector.getData();
 
   /***
    * Wrap the arrays `values` and `columnIndexes` to sparse matrix view
    */
   auto matrix = TNL::Matrices::wrapEllpackMatrix< Device, TNL::Algorithms::Segments::RowMajorOrder >(
      rows, columns, 2, values, columnIndexes );
 
   std::cout << "Matrix reads as: " << std::endl << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Wrapping matrix view on host: " << std::endl;
   wrapMatrixView< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Wrapping matrix view on CUDA device: " << std::endl;
   wrapMatrixView< TNL::Devices::Cuda >();
#endif
}

Output

Wrapping matrix view on host: 
Matrix reads as: 
Row: 0 ->     0:1       1:2   
Row: 1 ->     1:6   
Row: 2 ->     0:9   
Row: 3 ->     2:15      3:16  
 
Wrapping matrix view on CUDA device: 
Matrix reads as: 
Row: 0 ->     0:1       1:2   
Row: 1 ->     1:6   
Row: 2 ->     0:9   
Row: 3 ->     2:15      3:16  
 

Variable Documentation

paddingIndex

template<typename Index>

Index TNL::Matrices::paddingIndex = static_cast< Index >( -1 )

constexpr

Padding index value.

Padding index is used for column indexes of padding zeros. Padding zeros are used in some sparse matrix formats for better data alignment in memory.